115
anode (Q^) becomes forwardbiased and begins to inject
holes into the base region, subsequently modulating
and increasing the conductance of the device. Experimental
decomposition of the total current into its constituent
anode end drain components has revealed that this abrupt
increase in conductance, after the LIGBT is activated,
results primarily from the modulation of R and not from
epi
an increase in the anode (BJT) current. The modulation of
this resistance tends to increase the DMOST current, but
also tends to limit the excitation of which is driven
by the internal voltage drop. We note that physical
insight predicts and experimental results confirm that this
drop activates predominantly and not Q2, which is one
reason why our assumed partitioning is representative.
In Figure 55 we show the experimental decomposition
of anode and drain current for the HIGBT mode of operation.
Also shown, for comparison, is the LIGBT currentvoltage
characteristic. Figure 55 clearly illustrates that the
anode current in the HIGBT mode is only a small fraction of
the total current, and furthermore, only a fraction of the
IGBT current. This decompostion and comparison of internal
currents verifies our partioning scheme and also explains
why the latchup onset for the HIGBT mode is much greater
than that for the LIGBT mode. In both modes of operation
the emitter current of I is approximately the same
at the onset of latchup. Obviously however, the primary
(
104
EB
= V
JEB
q("n+V
W
M
rJ i
dx
p( x)
(b1)
T5TT)
kT
q
ln(
Â£(01
N
)
epi
(53)
where WM
equals Nep' the baseregion doping density JE is the
emitter (anode) current density, and b /^//Wp is the
electron/hole mobility ratio. (We generically refer to the
n base region as also the epi region, even though it may
not have been produced by epitaxial growth as in the case
for our devices modeled in Section 5.3.)
Using the quasiequilibrium assumption, we express
p(0), and hence V in terms of VTC,D:
Sp 1 J IjD
p( o)
n. 2
i
N
exp(
qV
JEB .
epi
kT
(54)
(If in a simulation p(0) is calculated to be less than or
equal to Nepi' the model is defaulted to the offstate
since the highinjection analysis is inapplicable.) For
negligible recombination in the emitterbase junction
spacecharge region, JE can be related to p(0) following
conventional PlNdiode theory [Be79]:
Jn =
b+1
~b~
* JNO*
pm
n.
]
qA IS
x = 0
(55)
74
neglect any mobile carrier charge that might exist in the
spacecharge region for very high current densities [Gh77].
To relate p(0) in (42) to VAB, it is necessary to
characterize V since
epi
V = v + V
AB epi JEB
(44)
where
VJEB vijln t
P( 0)N
Â£Â£i]
n.
(45)
is the emitterbase junction voltage (not equal to the
quasiFermi potential separation) [Wa83]. In (45), Nep
is the doping density in the n~ epitaxial base of the pnp
BJT and VT=kT/q is the thermal voltage. Accounting for the
conductivity modulation, we give V ^ by the integral of
the electric field across the quasineutral base, where the
field is related to p(x) through a combination of the hole
and electron current expressions [Gh77]:
dx
epi q ( v+fJ ) J p(x)
11 V n
WM
M
rJ
(bl) kT
(b+1) q
In (
P(0)
N
epi
(46)
155
[Je87]
[Ku85]
[La85]
[ L i 6 7 ]
[Mc87]
[Mc85]
[Mu87]
[Mu77]
[Na75]
[Pi8 4 ]
H. Jeong and J.G. Fossum, "Physical Modeling
of HighCurrent Transients for Bipolar
Transistor Circuit Simulation," IEEE Trans.
Electron Devices, vol. ED34, pp. 848905,
April 1987.
D.S. Kuo, J.Y. Choi, D. Giadomenico, C. Hu,
S.P. Sapp, K.A. Sassaman, and R. Bregar,
"Modeling the Turnoff Characteristics of the
BipolarMOS Transistor," IEEE Electron Device
Lett., vol. EDL6, pp. 211214, May 1985.
J.E. Lary and R.L. Anderson, "Effective Base
Resistances of Bipolar Transistors," IEEE
Trans. Electron Devices, vol. ED32, pp.
25032505, Nov. 1985.
J. Lindmayer and W. Schneider, "Theory of
Lateral Transistors," SolidState Electron.,
vol. 10, pp. 225234, 1967.
R.J. McDonald, J.G. Fossum, "Physical Modeling
of LIGT Structures for SPICE Simulation of Power
Integrated Circuits," ECS Symposium, Philadelphia,
PA, May 1015, 1987.
R.J. McDonald, J.G. Fossum, and M.A. Shibib,
"A Physical Model for the Conductance of
Gated PIN Switches," IEEE Trans. Electron
Devices, vol. ED32, pp. 13141320, July 1985.
S. Mukherjee, M. Amato, and V. Rumennik,
"Influence of Device Structures on the
Transient and Steady State Characteristics
of LIGT," ECS Symposium, Philadelphia, PA,
May 1015, 1987.
R.S. Muller and T.I. Kamins, Device
Electronics for Integrated Circuits.
New York: Wiley, 1977.
L.W. Nagel, "SPXCE2: A Computer Program to
Simulate Semiconductor Circuits," Electronics
Research Lab., University of California,
Berkeley, Memo. ERLM250, May 1975.
M.R. Pinto, C.S. Rafferty, and R.W. Dutton,
PISCESII User's Manual. Stanford,
CA: Stanford University, 1984.
ACKNOWLEDGEMENTS
The support of the IEC at the University of Florida,
the NSF, and the SRC is acknowledged.
The technical guidance of Dr. M. A. Shibib of AT&T
Bell Laboratories in designing and fabricating the special
test structures used in this dissertation is appreciated.
His participation on the qualifying exam and on the final
defense also merits a note of gratitude.
iii
130
during phase two, then the solution to (512) implies a
fast linearly decaying current, inversly proportional to
RnB" 0ur mdel simulations for the HIGBT turnoff
transient (Figure 511) clearly show the predicted linear
nature of the second phase. Experimental corroboration of
this analysis can be inferred from [Go86], where the decay
during phase two is found to be approximately linear in
time. Thus, to effect a fast turnoff, R should be made
ni5
as small as possible, but consistent with the constraint
for a low onset voltage (R _<
nb m3
The circuit topology as depicted in Figure 54, and
used in our simulations, is not capable of maintaining a
latched state (steadystate solution) during transient
operations in SPICE. As a consequence, it is not possible
to observe dynamic latchup directly, i.e., to see the
anode current remain constant with time when the gate
voltage is removed. However, the onset of dynamic latchup
may be indirectly observed by monitoring the current *CNPNf
which represents the injection of electrons by the
parasitic n+pn~ BJT.
We demonstrate the ability of the modeling methodology
to predict the onset of dynamic latchup in Figure 512,
where we have plotted the current, ICNPN/ as a function of
time for a resistively loaded LIGBT turnoff transient.
The sharp increase in IcNPN during the fast turnoff
transient (TFa^=2ns) indicates the onset of dynamic
latchup and is consistent with
21
[He68]:
(220)
From (29), (210), (212), and (214), we see that JNA and
C 2 2
Jp are proportional to [n(0)] and [n(W)] respectively.
In contrast, using (211) we see that
(221)
where
(222)
is an average carrier density in the ji region. Thus as J
increases, a larger portion of the current is supported by
recombination in the anode and cathode regions; becomes
negligible. Furthermore, since dn/dx H, as can be seen
by differentiating (211), the diffusion current in the n
region becomes negligible as J increases [He68]; the holes
and electrons predominantly drift across the n region.
102
gain in the BJT modules, which invalidates the commonly
used SPICE GummelPoon model [Ge78], necessitate new (more
physical) models.
We first focus our attention on the onedimensional
lowgain pnp BJT constituent module (see Figure 51), and
overview the development given in Chapter 4. The low
doping density in the wide n~ base region implies that,
under normal forwardmode operation, high injection will
prevail throughout the base. Consequently, the base
transport problem is described by the ambipolar transport
equation with p=n, the solution of which gives
n ( x ) = p ( x ) =
P(0)sinh(^^)
LA
sinh(^)
la
(51)
where p(0) is the hole density at the edge of the
emitterbase (p+n~) junction spacecharge region, L is the
~ n
ambipolar diffusion length, and W is the voltagedependent
width of the quasineutral base region. We describe W
through the depletion approximation at the reversebiased
collectorbase (pn~) junction:
" WB Xd
W
(52)
Figure 41. Basic IGBT structure.
48
The IGBT is turned off by removing the gate voltage, and
hence the MOS channel through which electrons flow for
recombination in the p+ anode and n epi regions. The
removal of the channel occurs quickly, on the order of the
electron transit time which is typically a few tenths of a
nanosecond [Ba81]. In order to characterize the IGBT
turnoff transient, the external circuit, represented in
Figure 33, must be considered. When the channel is
removed (virtually instantaneously), but 1 cannot
drop instantaneously because the reverse bias on the pn
junction (J2 in Figure 33) does not increase abruptly; the
depletion capacitance of J2 is (partially) charged in short
but finite time, as controlled by the external circuit.
This initial phase is completed when I, defined by the
external circuit and developed reverse bias on J2 (V^)
equals the timedependent BJT collector current, defined by
the (timedependent) depletionregion width of J2. Little
carrier recombination occurs during this fast transient.
The second phase of the turnoff, however, is controlled by
carrier recombination in the epi region (and perhaps in the
anode region), and hence the completion of the development
of Vj2 is slower than the first phase. The carrier
lifetimes are typically longer than the time constant that
characterizes the initial transient.
Since the first phase is usually much faster than the
second, we will characterize the composite turnoff by
54
^MOS' wrongly implied in Baliga [Ba85] and Kuo et
al. [Ku85].
To demonstrate the virtual independence of the
transient result (311) from the steadystate analysis,
and
which defines I
obtain
0
IMOs' we combine (39)(3ll) to
r2eSVB,AI,1
xdm f qN i I
M epi 0
1/2
(312)
Thus measurement of the first phase of the turnoff
transient, i.e., of IQ and Al, enables evaluation of x^m,
which from (311) describes the constitution (an<^
I c ( b jt ) ^ f t^ie steacJyonstate current Ig.
The slower decay of I [from IgAI) to zero] in the
second phase of the turnoff is similar to the transient
response of a BJT in the active mode following the abrupt
removal of the base current [Mu77]. Whereas the
firstphase transient is controlled predominantly by the
charging of the J2 depletion capacitance, we assume that
the secondphase transient is controlled by carrier
recombination. Thus the J2 displacement current [dQ^/dt
in (34)] is neglected, and we write, based on (35),
Qp(t)
'tp
Kt)
(313)
51
where Qp
(t) is
the
hole charge
n base
region
and
Ttp is
base
transit
time
in
(35)
is
depletion regi
on
(width
xd>
moving boundary, which is not
previous work [Ba85,Ku85], is
phase of the as we demonstr
highinjection conditions, we a
stored in the quasineutral
transit time for holes. The
imedependent because the
of J2 is expanding. This
accounted for properly in
most important in the first
ate below. For prevalent
ssume [Gh77]
TtP(t)
[WBXd(t))
(36)
where Wg is the metallurgical base width of the vertical
p+np BJT and KA is a constant less than unity discussed
below. Rigorously (36) (with KA=1) applies to a
onedimensional device in which there is no recombination
in the base nor back injection into the emitter. However,
we assume that it (with KA<1) is representative of the
actual IGBT structure illustrated in Figure 31.
Independent of the finite base current, KA accounts for the
multidimensional carrier flow in the epi, in which case to
first order it could be given as the ratio of the BJT
collector and emitter areas. We note also that KA*1 can
effectively account for the influence of the base current
(recombination in both the n epi and the p+ anode) on the
transit time [Ku85].
CHAPTER 6
SUMMARY AND CONCLUSIONS WITH RECOMMENDATIONS
6.1 Summary and Conclusions
The culmination of this dissertation manifests itself
in Chapter 5 where we brought together the physical
insights and techniques presented in earlier chapters to
develop a methodology for constructing, and implementing in
SPICE, physical network representations for a general class
of HV/P IC devices exemplified by the LIGBT. We verified
our network models by comparison with PISCES simulations
and by comparison with experimental results obtained from
specially designed test structures. Included in the novel
network representations were several highinjection and
unique effects inherent in HV/P IC devices, heretofore not
represented in more empirical (less accurate) equivalent
circuit models. The effects characterized included
conductivity modulation, enhanced back injection,
multidimensional current flow, and the onset of static and
dynamic latchup.
134
121
the onset of latchup is properly accounted for in the
dQjCi
models as the charging current, gt' contributes to the
voltage drop across and hence helps to induce latchup.
5.4 Simulations/Verification
In Figure 57 we show modelsimulated and measured
currentvoltage curves for the LIGBT mode of operation for
three different values of the gate voltage. For
illustrative clarity, the measured curves were cut off just
prior to latchup. The agreement between experiment and
theory is good (~10% error), thus lending support to our
particular partitioning and modeling methodology.
Discrepancies between the model predictions and
experimental results may be attributed to the firstorder
DMOST model (SPICE/Level 2) that we used.
In Figure 58 we compare measured and modelsimulated
transient turnoff characteristics of the LIGBT. At time
t=0 the gate voltage is removed and a typical twophase
turnoff transient, as discussed in Chapter 3, is observed.
Our model simulations are in good agreement with
experiment. Discrepancies between the model and experiment
may be attributed to parasitics associated with the probe
station, since our transient measurements were performed on
a wafer and not on mounted devices. The turnoff time may
seem faster than expected for a lifetime of 2.6//S, but
this is due to the large proportion of base current, a
113
experimental results. To first order, they may be
estimated from PISCES results. This particular partition
is indeed representative of the device as implied by (a)
PISCES simulations, (b) experimental decomposition of
current voltage characteristics, and (c) relative
excitations of Q^ and Q2 in the hybrid HIGBT mode of
operation discussed later.
The SPICE model for the LIGBT mode is shown in Figure
54. It consists of a simple MOSFET and 11 UDCSs. The
UDCSs labeled with the subscript one represent and those
with the subscript two represent Q2. The current source
ICNPN moc^e*s the third constituent BJT at the cathode as
it, when activated by the voltage drop in the pbase
reflected by RpB> effects the onset of latchup, which is
discussed later.
In the hybrid HIGBT mode of operation, the anode and
drain are tied together and raised to a positive voltage
relative to the source. The gate voltage, as in the the
LIGBT mode, is above the threshold voltage. For low drain
voltages, the device behaves as a DMOST, in series with a
large resistance, R .. The anode does not inject because
epi J
it is at the same potential as the drain. As the drain
current through R ^ is increased, an internal voltage drop
develops (vertically in this particular device) across a
portion of the epi region. When this voltage drop becomes
approximately 0.6V (viz., a diode drop) a portion of the
105
where DA is the ambipolar diffusivity, and Jnq is the
saturation current density that defines the back injection
of electrons into the quasineutral eitter region. The
base current density, JB, is the sum of the back injection
current plus the integrated recombination current in the
base region:
JB =
JN0[
ElSi^
n.
i
w
q J
0
p( x)
TH
dx
(56)
where xH is the highinjection carrier lifetime [Note that
1/2
La=(Dath) 7 ]. The collector current density, Jc, is
expressed as JJ. The crosssectional area A relates the
terminal currents l_ and l_ (and In) to the respective
current densities.
The transient modeling of the transistor is done using
a chargebased method employing the quasistatic
approximation. This approximation, which is used
extensively for IC modeling [Ge78], is generally adequate
except for circuits much faster than typical power ICs
[Fo86b].
The predominant charges in the widebase BJT module
(in the forwardactive mode) are the quasineutral
14
To account for the effect of the shield, i.e., to
define AEfn, we neglect recombination in the shield, which
is typically much less than the carrier fluxes through the
shield. Then AE^ can be related to the electron current
Fn
c
density JN flowing in the shield, which constitues part of
the total current density J described by basic PINdiode
theory.
For simplicity, we assume an (effective) uniformly
doped shield. Since the shieldcathode junction is in low
g
injection, the uniformdoping assumption implies that JN is
diffusion current, which is nearly constant:
N
_ An
q nws
qD n?
M n i
naws
AE
exp(
FC w ,
Â£y~)[exp(
AE
Fn
kT
) 1]
(23)
where Dr is the (average) electron diffusion coefficient in
the shield, NA is the (~ peak) doping density, and Wg is
the (effective) width of the shield. From (23),
AE
FC
AE
Fn
4
kT In 1 +
JN FsexP( kf>
kTn?
i
(24)
where
A kAWS
S qDn
(25)
BIOGRAPHICAL SKETCH
Robert James McDonald was born in Queens, New York, in
1954. He received the BSEE degree (Magna Cum Laude,
3.75/4.0) from Virginia Tech in 1982 and the ME degree in
electrical engineering from the University of Florida in
1984. His doctoral research involves modeling of HV/P IC
devices.
He received a General Moters Scholarship in 1980, a
Graduate Council Fellowship from the University of Florida
in 1982, and an SRC Fellowship in 1986.
He is a member of Phi Kappa Phi, Eta Kappa Nu, and
IEEE.
158
79
CP
A (IA IB)
hi
(414
In (414), and in (48), (49), and (411), we have crudely
accounted for the twodimensionality of the pnp BJT by
including the (constant) collectoremitter area ratio,
which is less than unity. Although this accounting is
semiempirical it does reflect the reduced base transport
factor in a typical IGBT due to hole injection into a
portion of the base that is laterally removed from the
collector, as shown in Chapter 3 [Fo86a]. Model
predictions made without the area ratio do not compare
favorably with experimental results, whereas those made
with it do. We note that for lateral devices,discussed in
Chapter 5, however, a more physical accounting for the
multidimensional effects is essential.
Because of the implicit nature of the model equations
(42)(414), it is not possible to express p(0), and hence
the terminal currents, as explicit functions of V.D and
At)
BK'
Thus, for a given VAB and VRK. supplied by the SPICE2
BK
nodal analysis, (44) is solved iteratively (Newton's
method) for p(0) in a FORTRAN (UDCS) subroutine, and the
model equations are then used to determine IM, IOT,, I..,
^ MOS CP CN
Vepi' PB' an<^ JC The moc*e* clearly quasistatic; at
each point in time, the steadystate model equations are
solved in a UDCS subroutine and the solution (a terminal
67
not necessarily in explicit form, for the quasistatic
device terminal currents and charges (the models are
chargebased) in terms of the terminal voltages. This
system of equations, i.e. a physical device model, is part
of a subroutine that is referenced by userdefined
controlled sources (UDCSs) in SLICE [Ha84], one of the many
enhanced versions of SPICE2 that have been written. The
UDCSs generally available in enhanced versions of SPICE2,
are simple FORTRAN subroutines [Ve86] that constitute the
"equivalentcircuit" model, which simulates both
steadystate and (quasistatic) transient device
characteristics. With judicious programming and data
storage, UDCSs can be used effectively for simulation of
circuits in which the number of HV/P devices is not
excessive.
4.2 Modeling Methodology
The utility of the novel methodoly is demonstrated by
its application to the IGBT [Ba84b], as illustrated in
Figure 41. The IGBT is representative of emerging HV/P
devices that merge MOS and bipolar structures to exploit
the advantages of both. The (nchannel) IGBT shown is
effectively a vertical pnp BJT, the base of which is driven
by a DMOST, with a parasitic npn BJT at the cathode that
can cause latchup and loss of gate control of the IGBT
switch. In contrast to the conventional DMOST, the
a representative HV/P IC device, the LIGBT, and the derived
model is implemented in SPICE via userdefined controlled
sources (UDCSs).
The methodology is supported by rigorous theoretical
analyses of several HV/P IC devices, twodimensional
numerical device simulations with PISCES, and experimental
results obtained from specially fabricated test structures.
The resulting physical network representations, in addition
to the CAD ability they afford, will facilitate optimal
device (process) design under an actual circuit (transient)
environment, a capability that most device simulators do
not have.
vi 1
109
simulation process. This implementation of an implicitly
formulated model allows for flexibilty in the modeling
methodolgy, and enables truly physical device models to be
incorporated into the device simulator.
We now exemplify the modeling methodogy by applying it
to the LIGBT test structure, and partitioning the structure
into onedimensional modules for each mode of operation.
5.3 Application/Demonstration
Test structure of LIGBTs were fabricated using the
dielectricisolation (DI) BCMOS technology [Go87] developed
at ATT Bell Laboratories. The LIGBT is dielectrical
isolated from the substrate and from other components to
minimize parasitic effects, thus allowing access to the
drain of the DMOST separately from the anode of the LIGBT
and making it easier to measure electrical parameters of
the structure. This facilities the demonstration of our
modeling methology, including the parameter extraction and
comparisons between model predictions and device
measurements.
The LIGBT structure shown in Figure 51 can operate in
several modes (PIN, DMOST, LIGBT, HIGBT) depending on the
terminal configuration. We must therefore develop a
systematic and consistent approach to modeling the various
modes of operation. The physical nature of our constituent
modules facilitates parameter extraction by minimizing the
63
effects of a buffer region on device performance, as
presented in Chapter 2, may be applied to IGBT structures
to study the tradeoff between decreased turnoff time and
increased onresistance arising from the bufferinduced
reduction in baseregion mobile carrier concentration.
The utility of the physical insight afforded by our
model for the transient turnoff should be stressed.
Whereas previous work has shown that TQ is reduced by
decreasing th and increasing AI, it has not demonstrated
how the reduction obtains and it has not clearly revealed
how AI can be increased most effectively. Furthermore the
previous work, which is based strictly on onedimensional
analysis, did not reveal the subtle but critical influence
of the IGBT geometry on its transient turnoff
characteristic. The constant KA<1 in our model, although
somewhat empirical, reflects this influence. Our analysis
can further facilitate model parameter evaluation for IGBT
circuit simulation. For example, it is possible to
interpret a measured turnoff transient using our analysis
and extract, for a given onstate current Iq, values for
IMOS (an<^ hence 3)/ th/ and jno* This utility
interest in the general area of CAD of HVICs.
should be of
37
Table 21. GDS parameter values inferred from
theoreticalexperimental currentvoltage
correlation.
JN0
=
4X10~12
A/cm2
JP0

lxlO12
A/cm2
T0
=
1X105
sec
Fs
_
1.5x1011
2
Vsec/cm
"n
920
cm /Vsec
"p
=
330
2
cm /Vsec
A
5X105
2
cm
137
(subcircuit) for a particular HV/P structure, without
recourse to UDCSs. We now outline several research areas
essential for the construction of a CAD library for HV/P IC
design.
First, we recommend the extension of our empirical
DMOST model. Since the DMOST is an integral part of many
HV/P devices, it is essential that a simple and accurate
model for this common HV/P device be developed. The device
physics underlying the DMOST when the drain region becomes
conductivity modulated needs clarification. The simple Sun
and Plummer [Su78] model is not applicable to DMOSTs in
which the drain undergoes significant
conductivitymodulation, as in the LIGBT.
Second, we recommend extending our widebase BJT model
(Appendix A) for all regions of operation, thus making it a
viable circuitsimulation tool. In addition, since nearly
all LIGBTs employ punchthrough shields, a more
representative widebase BJT would be a p+n+np structure.
The insights gained from modeling the GDS in Chapter 2
would be helpful in characterizing such a transistor
structure.
Third, we recommend the creation of a standard
PINdiode model for circuit simulation. Many HV/P
structures contain this basic device, and such a model
would be useful for parameterextraction methods involving
optimization techniques, as was done in Chapter 5.
38
Table 22. Calculated dependences of R and R
on Jtgo' Jpo' and To for w=35' /um. The
remaining parameter values are given
in Table 21. The values of R and
Ron in parentheses were calculated
accounting explicitly for carrier
carrier scattering [Ch70].
JN0 (A/cm2)
Jp0 (A/cm2)
tQ (/vs)
V (2)
eon (a)
4XlO~12
12
1X10
10
81.7
(77.7)
21.5
(27.5)
4X1012
5X10_13
10
69.4
(71.3)
16.1
(25.1)
5X1013
12
1X10
10
62.3
(67.2)
12.5
(22.5)
12
4X10
12
1X10 1Z
50
68.5
(69.2)
16.5
(23.0)
4X10~12
5X1013
50
59.6
(64.0)
12.4
(21.0)
5X1013
12
1X10
50
54.2
(60.7)
9.6
(18.6)
5X1013
5X1013
50
50.2
(57.7)
7.7
(16.9)
77
The composite base current IB of the pnp BJT, in the
steadystate, is the sum of recombination current from the
n base region and that from the p+ emitter region. It is
expressed as
XB "
PB
TH
aejno[
p(0) i2
n. J
(411)
where xH is the highinjection carrier lifetime [Gh77] in
the base. The second term in (411) obtains for
quasiequilibrium because low injection prevails in the
emitter. The electrons that support the recombination
current IB are supplied by the DMOST (iMqs^ under normal
operation, but in part also by the npn BJT (1CN) near
latchup:
IM0S 1B ICN '
(412)
Analytical decomposition of ID, as well as characterization
O
of the n base transport current ICp/ must be done
implicitly and hence demonstrates poignantly the essence
(flexibility) of the modeling methodolgy, in contrast to
the lessflexible equivalentcircuit modeling built into
SPICE2.
45
IMOS IB(BJT)
(31)
where I
is the base current in the p+n p BJT, which
comprises recombination in both the base (n epi) and
+
emitter (p
anode) regions. The IGBT (anodecathode)
current I is
(32)
I = I
+ I
B(BJT)
C(BJT)
the base transport (hole) current. Note that the actual
current gain of the BJT, 3 = Ic ( b JT)/JB ( B JT ) dePends
critically on the geometry of the IGBT structure.
Consequently, analysis of the device for the transient as
well as steadystate conditions must somehow account for
the multidimensional carrier flow.
The IGBT voltage VA can be written as the sum of four
voltage drops
+
(33)
112
Figure 53
PISCES simulation for the
shown in Figure 51. The
the negative hole current
current vectors around the
LIGBT structure
arrows indicate
vectors. The
junctions (high
grid density) have been removed for
illustrative clarity.
55
where rfcp is an average transit time, which can be crudely
approximated based on (36), as
(WBXdm
4K D
A p
(314)
with x^m given by (312). The use of (314) greatly
simplifies the analysis of the second transient, and hence
facilitates physical insight and identification of critical
device parameters that define the turnoff. The
simplication is representative because typically the
increase in x^ beyond x^m is less than x^ ; the relative
change in during the transient during the transient is
smaller than that of Qp. The decay of I(t) in our model is
thus defined predominantly by the timedependence of Qp(t)
[Ku77]; and errors resulting from the use of (314) are
minor and do not derogate the utility of the model.
In BJT terminology, I(t) is the emitter current, which
is equated in (313) to the collector current because the
base current is constrained to zero [Mu77]:
p(t) + dP(t) +
th dt
n(t)
n
+ dQn(t:
dt
0.
(315)
4
IGBT structure. The effects of the expanding depletion
region at the cathode and of minoritycarrier injection
into the anode are properly accounted for. Consequently
the physics underlying the turnoff time is clarified, and
device design criteria for shortening it, without
considerably degrading the onstate current conduction
capability, are suggested.
In Chapter 4, a novel methodology for flexible SPICE
implementation of physical models for HV/P devices,
accounting for their unique characteristics, is presented
and demonstrated. The implementation is achieved, without
having to modify the simulator code, by utilizing UDCSs
that reference a subroutine which defines, not necessarily
in explicit form, the system of model equations. The
simultaneous solution of the equations, which describes the
integrated charges in the device and the quasistatic
terminal currents in terms of the terminal voltages, is
effected by the SPICE2 nodel analysis. The methodolgy is
exemplified by modeling a particular highvoltage device,
the IGBT, in which conductivity modulation and latchup are
accounted for. SPICE simulations of dc and transient
characteritics of IGBT switching circuits are discussed and
shown to be representative of measurements. The
flexibility of the modeling methodolgy for HV/P IC CAD is
demonstrated by simulating effects of both static and
dymanic latchup in the merged bipolar/MOS structure of the
IGBT.
2
those ICs employing MOScontrolled bipolar devices, has
been at a near standstill. Common highinjection effects,
such as conductivity modulation and enhanced back
injection, are not properly accounted for in existing,
empirical circuit models for HV/P devices [Pa86].
Furthermore, these models vitually ignore multidimensional
carrier flow, which is typical in integrated HV/P devices.
Thus, there exists a need for developing new physically
based models for HV/P devices and implementing these models
in a circuit simulator, e.g., SPICE [Na75],
This dissertation is concerned with the development
and implementation of network representations for a general
class of merged MOScontrolled bipolar structures, e.g.,
the lateral insulatedgate bipolar transistor (LIGBT)
[Da84, Si85], The major contributions made in this work
are as follows:
(1) the general formulation and solution of the
steadystate transport problem for the
basic p+pnpn+ structure, in terms
of quasiFermi level potentials, explicitly
showing the effect of the p punchthrough
shield on the transport problem;
(2) the physical (chargecontrol) characterization of
the IGBT turnoff transient, clearly identifying
the device parameters controlling the important
charging mechanisms;
80
current or charge density) is then referenced by the main
SPICE2 nodal analysis program [Ve86]. We note that in
addition to the transcapacitances in (410), the
transconductances 9I^/3Vj for each current UDCS must be
evaluated in the nodal analysis. These evaluations are
done numerically using firstorder finitedifference
approximations.
The merged structure of the IGBT makes model parameter
evaluation difficult because of twodimensional current
flow and inaccessibility of internal model nodes for
measurement. Model parameters for the DMOST and BJT
components of the IGBT can be estimated from a knowledge of
processing variables, doping density profiles, and
geometry. The threshold voltage for the DMOST can be
estimated from measurements of Ia^VGK^' although the
channel conductance cannot be inferred experimentally
without a special test structure. The two most important
As will be
shown in Section 4.3, these two parameters greatly
influence the steadystate onresitance and turnoff time
of the IGBT. From a knowledge of the pnp BJT emitter
doping density, Jnq can be estimated analytically [Fo81];
and th can be obtained from a fitting of a measured
turnoff transient once Jnq is known, as described in
Chapter 3.
from a knowledge of the pbase doping density, or Gummel
parameters for the pnp BJT are xH and jnq
NO
For the npn BJT, I_.T and Rn,, can be estimated
c SN BN
153
[ B e 8 5 ]
[Be79]
[Ch70]
[Da84]
t De86 ]
[ F15 7 ]
t Fo77 ]
[Fo86a]
[Fo87 ]
[Fo81 ]
H.W. Becke, "Approaches to Isolation in High
Voltage Integrated Circuits," IEDM Tech. Dig.,
pp. 724727, 1985.
F. Berz, R.W. Copper, and S. Fagg,
"Recombination in the End Regions of PIN
Diodes," SolidState Electron., vol. 22,
pp. 293301, 1979.
S.C. Choo, Effect of Carrier Lifetime on the
Forward Characteristics of HighPower Devices,"
IEE trans. Electron Devices, vol. ED17,
pp. 647652, Sept. 1970.
M. Darwish and K. Board, "Lateral Resurfed
Comfet," Electron. Lett., vol. 20, pp. 519 520,
June 1984.
M.J. Declereq and J.D. Plummer, "Avalanche
Breakdown in High Voltage DMOS Devices,"
IEEE Trans. Electron Devices, vol. ED23,
pp. 16, Jan. 1976.
N.H. Fletcher, "The High Current Limit for
Semiconductor Junction Devices," Proc. IRE,
vol. 22, pp. 862872, June 1957.
J.G. Fossum and F.A. Lindholm, "The Dependence
of OpenCircuit Voltage on Illumination Level
in PN Junction Solar Cells," IEEE Trans.
Electron Devices, vol. ED24, pp. 325329,
April, 1977.
J.G. Fossum and R.J. McDonald, "ChargeControl
Analysis of the COMFET Turnoff Transient,"
IEEE Trans. Electron Devices, vol. Ed33,
pp. 13771382, Sept. 1986.
J.G. Fossum and R.J. McDonald, "Analysis of
the Unique Characteristics of the Hybrid
LIGT/DMOST (HIGT)," IEEE Device Research Conf.
Santa Barbara, CA, June 2224, 1987.
J.G. Fossum and M.A. Shibib, "An Analytic Model
for MinorityCarrier Transport in Heavily
Doped Regions of Silicon Devices," IEEE Trans.
Electron Devices, vol. Ed28, pp. 10181023,
Sept. 1981.
APPENDIX A
HIGHCURRENT TRANSPORT IN WIDEBASE BJTs
In this appendix we briefly overview carrier transport
in widebase (p+n~p and n+p~n) BJT structures. The
approach is based on an ambipolar transport analysis and
has its historical roots set in PINdiode theory [He68].
Consider a p+n p transistor structure operating in the
forwardactive mode for which high injection (p=n>>ND)
obtains in the n~ base region. A straightforward ambipolar
analysis [He68] can be used to equate the electron
recombination current density in the p+ emitter, JN, to the
electron current density in the n base at the edge (x=0)
of the emitterbase junction spacecharge region
(neglecting any spacecharge region recombination), thereby
yielding the following relation between JN and the total
emitter current density, JE:
N
b
F+T
qDAnf
x=0
(A1 )
139
5
In Chapter 5, to enable CAD of power integrated
circuits, new physical models for lateral HV/P devices, in
particular LIGBT [Da84, Si85, Mu87] structures, are
developed and implemented in SPICE. The models are
chargebased, and, via regional partitioning, account for
the unique features of HV/P devices unaccounted for in
conventional equivalentcircuit models. The implementation
of the models in the circuit simulator is flexible and
allows these features (e.g., multidimensional carrier flow,
conductivity modulation, latchup, transcapacitance) to be
simulated without having to sacrifice much physics through
excessive empiricism. Device measurements of specially
designed test structures, supplemented with twodimensional
numerical device simulations, support the modeling
methodology and the model parameter extraction.
We summarize, in Chapter 6, the main conclusions and
accomplishments of this dissertation. We also suggest
ideas and avenues for future research.
In Appendix A, we briefly describe highcurrent
carrier transport in widebase transistor structures. The
resulting simplified model predicts a fundamental
difference for the highcurrent 8s of pnp and npn
transistors. The physical insight afforded by the
simplified analysis will be useful for device engineers
designing complementary iGBTs.
132
experimental results. Note that for a slower turnoff
transient (TFal^=200ns), ICNPN remains unchanged during the
time period shown in Figure 512. Eventually, for such a
slow transient, ^cnpn decrease to zero and the onset
of dynamic latchup will not manifest itself. Our
simulations indicate that the primary current responsible
for initiating the onset of dynamic latchup for the above
dQjCi
circuit conditions is the displacement current, Jt'
However, for other circuit conditions the increase in the
transient collector current could be made significant. We
note that the utility of the model to predict the onset of
dynamic latchup will make it useful for optimizing device
design under an actual circuit (transient) environment.
5.5 Summary
We have developed a device modeling methodology needed
for the CAD of HV/P ICs that is also useful for optimal
device (process) design. The methodology is based on a
regional partitioning of LIGBT structures through physical
insight gained from numerical simulations (PISCES) and
experimental results (special test devices). The regional
partitioning of a lateral structure defines an array of new
onedimensional device modules, which properly (physically)
model the unique features of HV/P devices. We have
demonstrated this flexible quasi2D methodology on an
LIGBT test structure for all possible active modes of
70
Gate
Figure 42. UDCS representation of the IGBT
implemented in SLICE/SPICE2. This is
not an equivalent circuit; the node B
is labeled merely to signify the internal
connection between the base region of the
pnp BJT and the drain of the DMOST. The
anode of the IGBT is referred to as the
emitter of the pnp BJT, and the cathode
as the collector.
65
shown to be
representative of
measurements taken
from
the
literature.
Both static and
dynamic
latchup for
the
IGBT
are simulated, thus demonstrating the
flexibility
of
the
modeling methodolgy for HV/P IC CAD.
Recent advances in silicon IC processing technologies
have intensified development of "smart" high voltage/power
(HV/P) circuits, in which lowpower logic and highvoltage
devices are integrated on the same chip. Computeraided
design (CAD) of such circuits is critically dependent on
reliable device simulation, for example with SPICE2 [Na75].
HV/P devices have unique characteristics that are not
amenable to lumpedelement, equivalentcircuit
representation, and hence the builtin device models in
SPICE2 are generally inadequate. Such characteristics
include effects of merging bipolar and MOS structures,
latchup, conductivity modulation, and movingboundary
(during transient) conditions. The inadequacy of the
SPICE2 MOSFET models for HV/P IC simulations is clearly
inferable from [Su80]. The SPICE2 BJT (GummelPoon (Ge7 8])
model is clearly deficient; for example, its basic
(integralchargecontrol [Ge78]) assumption is invalid for
HV/P BJTs having significant back injection or relatively
low currents gains.
Therefore to enable reliable CAD of HV/P ICs, new
device models must be implemented in SPICE2, or in
comparable circuit simulators. Because of the unique
125
t (ns)
Figure 59. Measured HIGBT anode/drain current versus
anode/drain voltage for three values of
gate voltage (VQ = 6V, 8V and 10V from right
to left respectively). The measured curves
are terminated just prior to the onset of
latchup.
88
[Ba85,Ku85], our SLICE/SPICE2 simulations show that the
abrupt drop in IA(t) is not equal to the steadystate DMOST
current = (even when I.T is zero), and that the slow
decay of the second phase is not a simple exponential
function of the highinjection lifetime tH.
These
differences result, respectively, from the unique effects
of the expanding depletion region at the basecollector
junction and the back injection of electrons into the
emitter characterized by Jnq, poignantly demonstrated in
Chapter 3.
In Figure 47 we show simulated IGBT resistive
turnoff transients for various values of x and To
H NO
stress the influence of these parameters, we used a small
value for RGR that ensured the insignificance of transients
associated with the gatetocathode capacitance. The
magnitude of the fast initial drop in anode current and
subsequent slower decay are both dependent on th and JNg
These simulations and others have shown that changes in Jnq
should be considered as a means of optimizing the tradeoff
between turnoff time and onresistance. We stress that
these results could not be obtained using standard SPICE2
BJT models because of the limitations inherent in the
GummelPoon model [Ge78] and its implementation in SPICE2.
We stress that the results in Figure 47 are ideal in
that, in addition to negligible gate delay, there is also
no inductance in the load. For contrast, we show in
15
is a shield factor that can be used to relate AE_ to the
Fn
actual properties of the (diffused or implanted) p shield.
To relate Fg to an actual p shield in which NA varies,
note that generally
dx
(26)
S
N J D
n
(shield)
and that n(x)1/NA(x). Since the greatest contribution to
the integral in (26) comes from the region of the shield
where N (x) is a maximum (and D (x) a minimum), F in (25)
n q
can be evaluated for this region, the width W of which can
O
be estimated from the actual NA(x).
We now incorporate (24) into basic PINdiode theory
to characterize the conduction properties of the GDS. This
involves generating a system of equations, the simultaneous
solution of which for a specified J yields AEFn, AE ,
AEfc, V VA* The resulting J(VA) characteristic, with the
crosssectional area A (I=JA), then defines RDC and RQN
We note, based on results of calculations discussed in
Section 2.4, that typically AEFn~kT, which means that the
shield reduces considerably the carrier injection level in
the ji region
R
'ON*
near the cathode and hence increases R
and
133
operation. Both dc and transient measurements, including
static and dynamic latchup, support the modeling
methodolgy. In addition, this study points out the need
for further work in extending previous DMOST models [Su80]
for cases when the enhancementmode device has its bulk
region conductivitymodulated, as is the case for the
LIGBT. Also, the physics underlying the onset of latchup
needs clarification, especially in regards to the
conductivity modulation of prior to latchup.
The constituent chargebased modules, which are easily
implemented into SPICE via UDCSs, allow for a network
representation of the structure that can be used to
simulate the device under actual circuit (transient)
conditions, a feature most device simulators do not have.
Consequently, the methodology may be useful in optimizing
device design under an actual transient environment, in
addition to the CAD capability it affords.
CHAPTER 5
HIGHVOLTAGE/POWER INTGRATED CIRCUIT DEVICE MODELING
5.1 Introduction
This chapter combines and extends much of the work and
insight gained in previous chapters. In this chapter, new
physical models, and a general modeling methodology, for
lateral HV/P devices, in particular LIGBT structures, are
developed, and the models are implemented in SPICE via
UDCSs. The
models are chargebased, and via regional
partitioning,
account for the unique features of lateral
HV/P devices
(multidimensional carrier flow, conductivity
modulation, latchup, transcapacitance) unaccounted for in
conventional
equivalentcircuit models. Device
measurements
of specially designed test structures,
supplemented
with twodimensional numerical device
simulations, support the modeling methodolgy and the model
parameter extraction.
The implementation of the models in the circuit
simulator is flexible, and differs from the implementation
in Chapter 4 in that the model is implicitly formulated
97
C SET Y VALUE OF DIE1/DVBE
C
IF(FLGY.LT.l.0)THEN
Y Q*AÂ£1*DA/WB*P0/VT
GOTO 876
END IF
Z1 2*(B+1)/B*AE1*JN0*P0**2/NI**2/VT
Z2 (B+l)/B*Q*DA*AEl*PO/LA/VT/TANH(W/LA)
Y Z1 + Z2
876 CONTINUE
GOTO 39910
300 CONTINUE
C
C SET Y VALUE OF DIE1/DVBC BY FINITE DIFFERENCE
C
IFCFLGY.LT.1.0)THEN
Y0 .0
GOTO 765
END IF
W WB <2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
Y1
VBC VBC + H
W WB C2*ES*(PHI+ABS(VBC))/CND*Q))**.3
Y2 IHCW/LA) )
Y (Y2YD/H
VBCVBCH
GOTO 99910
765 CONTINUE
99910 CONTINUE
RETURN
END
C
C THE FOLLOWING LISTING IS A SUBROUTINE WHICH CALCULATES
C THE COLLECTOR CURRENT, IC, GIVEN THE NODE VOLTAGES VBE
C AND VBC THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR
C THE SPECIAL FORMAT USED IN UDCS IMPLEMENTATION
C
SUBROUTINE U1CLT1(Y,IFLAG,LP,NP,LC,NC,JERR0R)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND,NI, JNO,I Cl, LA
SPECIAL COmON BLANK
COPWCN/BLANK/XC 64)
60TOC50,100,200,300),IFLAG+2
50 CONTINUE
IFCNC.NE.2) JERROR 99010
GOTO 99910
100 CONTINUE
PHI.6
ES1.035E12
NI1.3E10
UN1350.0
UP4B0.0
BUN/UP
01.6E19
VT.02586
DA2*VT*UN*UP/( UN+UP )
C
C SET Y VALUE OF I Cl
C
WB
XCLP+l)
T0
XCLP42)
JNO
XCLP+3)
ND
XCLP+4)
AE1*
XCLP+5)
H
XCLP+6)
32
and that for W<0.3La, the first term in (230) is linear in
W, independent of LA. We note, based on the discussion in
Section 2.3, that the second term in (231), as well as
n(0) and n(W), is virtually independent of W. Thus (231)
correlates well with the plots in Figure 25.
Discrepancies between the two slopes, i.e., in the slopes
and in the extrapolated intercepts, can thus be attributed
to the uncertainties in A, p and p
n p
C A
(carriercarrier scattering), and to the neglect of (R^+R^)
respectively.
Measured and predicted values of the incremental
(quasistatic) resistance, RQN=AVA/AI centered at I=30mA,
2
are plotted versus W in Figure 26. Referring to (2), we
can write
R
ON
AV
AI
(232)
since the quasiFermi level terms vary little relative to
AV^ at high currents. Differentiating (27) then, in which
_2
we note based on Section 2.3 that J=I/An and that for
W>3La, =(La/W)[n(0)+n(W)], we obtain
R ~
ON qA(//n+// )LA[n(0)+n(W) ] '
(233)
71
The UDCS [Ve86] "circuit" model for the IGBT is shown
in Figure 42. In fact, the model is not an equivalent
circuit, but is a physical representation comprising six
UDCSs, each of which is defined implicitly by the system of
model equations in terms of the emitterbase and
basecollector voltages (VAB and VBR) of the pnp BJT. The
choice of node voltages used to define the UDCSs is not
unique. Alternative choices, as demonstrated in Chapter 5,
can be considered for a particular device to effect a
tradeoff among model flexibilty, complexity, and
computational efficiency. The steadystate characteristics
of the IGBT are simulated by the UDCSs IM0S (the component
of the pnp BJT base current supplied by the DMOST), Icp
(the pnp BJT collector current), and Vepi (the voltage drop
across the n~ base region). The transient characteristics
are simulated by the chargebased UDCSs [Ve86] dQpB/dt (the
charging current defined by the carriers in the
quasineutral base region of the pnp BJT) and dQT/dt (the
charging current defined by the depletion charge at the
basecollector junction of the pnp BJT). Charging currents
associated with free carriers in other regions of the
device are typically negligible. For example, the charging
current defined by the minority electrons in the
quasineutral p+ emitter (anode) region is negligible, even
though the total pnp BJT base current (lM0S + ICN) must
include a component due to recombination in the emitter, as
shown in Chapter 3 [Fo86a]. The resistance RpN simulates
56
We are assuming that high injection (p=n) prevails in the
base region throughout the main turnoff transient, and
hence we use the highinjection carrier lifetime th as
defined by SRH theory [Gh77]. This is a reasonable
assumption for a device in which conductivity modulation is
essential in the onstate. In (315), Qn is the minority
electron charge in the quasineutral p+ anode (emitter)
reqion and Tn is an average (effective) electron lifetime
(chargecontrol time). The dynamics of Qn, which is not
accounted for properly in previous work [Ba85,Ku85], can
influence the secondphase transient as we show below.
For quasi equilibrium and negligible recombination in
the p+n~ junction spacecharge region, Qn can be related to
Qp using the quasistatic approximation. In the
quasisteady state, the solution [Gh77] to the ambipolar
transport equation in the quasineutral base region (with
p=n) yields, for less than the ambipolar diffusion
length, Qp^qAfWgx^) p( 0 )/2 where p(0) is the hole density
at the edge of the spacecharge region and A is the device
_ 2
area. Using Qn/Tn=AJNQ[p(0)/ni] [Gh77], where Jnq is the
saturation current density associated with the electron
injection (recombination) into the p+ anode, we have
118
Figure 56. Network representation for the HIGBT mode
of operation.
Anode
Figure 31.
IGBT unit cell and current components.
The solid arrows depict hole flow and
the dashed arrows depict electron flow.
96
orderofmagnitude longer than those for the builtin
models. For largerscale HVICs, new HV/P device models,
once they are developed and standardized based on the
methodolgy presented in this paper, could be written into
the SPICE2 code to reduce CPU times to acceptable values.
53
in (38),
the "final
the hole
negligable
xdm the
" reverse
density
"final"
bias vj2m
in the
value of
, which for
depletion
, is [Gh77]
corresponding to
low enough that
region is indeed
xdm
2gSVJ2m
qN
^ epi
1/2
(39)
The external circuit (Figure 33) in which is chosen so
that I = Iq in the steady on state defines Vj2m (>0):
V
J2m
(310)
From (37) and (38) then,
AI *
T T
IMOS ^1
1
1]} (311)
I0 I1
'^dn/V'
where
V
IMOS' and ^ (I0
~IMOS//IMOS ^
are described
by
the
steadystate
analysis.
Note that
ai
the
fast
drop
in the
current is,
in general
, less than
the
(steadystate) MOSFET current. Only for xcjm<
36
To demonstrate in more detail the influences of JTri,
NO
Jp0, and Tq on he GDS resistance, we give in Table 22
calculated (using the model in Section 2.2) values of R
DC
(I=25mA) and RQN (l=30mA) for various values of these
parameters. We chose an intermediate value for
W=357//m, and we used the remaining parameter values in
Table 21. The cathode and the anode series resistances
were not included. We see from Table 22 that the
resistances are most sensitive to Jpg, even though the
"intrinsic" currentvoltage characteristic, J(VTF ), can
J
be independent of Jon [see (228)]. Both RDC and
pn
R,
can
p0 t__ v DC ** *'0N
be reduced considerably by increasing Tq and/or deceasing
JN0 as well as Jp.
The resistance values in parentheses in Table 2.2 were
calculated by accounting for the carriercarrier scattering
using an iterative technique [Ch70]. That is, the carrier
mobility values used in the final model calculation were
chosen to be compatible with the calculated average carrier
density in the it region as defined by empirical
characterizations of the mobilitydensity dependences for
holes and electrons. The calculations show that
carriercarrier scattering tends to diminish the reductions
in resistance discussed above, especially with regard to
Rq^. Nonetheless we can conclude, based on these
calculations and others, that RQN (intrinsic) for a typical
93
electrons supporting the recombination current in the pnp
BJT, and I
MOS
is reduced to zero. In this condition, the
device is latched, and removal of the gate voltage will
have no effect on the IA The transition from a stable
operating point to the latched condition requires only a
small increase in applied current because of the
exponential dependence of ICN on Icp.
The IGBT can also latch during turnoff transients if
the lateral hole current in the base of the npn BJT, which,
at the start of the transient, consists of Icp plus the
displacement current dQJC/dt, is sufficiently high to
effectively forwardbias the npn BJT emitterbase junction.
The magnitude of dQJC/dt depends on the rate of change of
the gatetocathode voltage as defined by the IGBT model
and the external circuitry. In the ideal case, if is
VJI\
removed instantaneously, then the initial magnitude of
dQJC/dt is equal to the steadystate current supplied
by the DMOST, as discussed Chapter 3 [Fo86a]. If is
removed slowly, then the initial magnitude of dQJ(_,/dt will
be negligible, and the IGBT will not latch. In Figure 410
we show a simulation of dynamic latchup in the IGBT, which
occurs because VGR(t) drops abruptly (due to a small RGK as
discussed previously). The turnon of the BJT, which
triggers the latchup, is indicated by the rapid increase
in its collector current ICN(t) shown in Figure 410.
Beyond this point in time, I^(t) remains finite even though
VGR(t) has dropped to zero.
52
Because the carrier lifetime (in the base) is long
relative to the duration of the initial fast transient, we
assume that Q is invariant in the first phase, even though
XT
the holes (and electrons) are redistributed in time in the
epi region. Thus as holes are swept out of the collector
to increase Qj2' electrons are forced toward the emitter,
thereby increasing the hole injection from the emitter to
maintain neutrality. This increase in Q which
approximately equals the increase in is much smaller
than Q and hence does not threaten the validity of (35).
Jr
From (31), (32), (35), and (36) then, we can write
I0 = IMOS +
pO
WV4K. D
B/ A p
(37)
since x^O for t<0. Equation (37) defines Q^q, the
steadystate value of Q which remains virtually intact
ir
during the initial first transient.
The fast transient subsides when dQ^/dt^O, or from
( 3 4 ) ( 3 7 ) when II^ where
Q
*0 "
/4KADt
I0 IMOS
(1wv2
(38)
27
In the
lowercurrent
regions
I and II in Figure
23,

the I(vPn )
J
and l(VA)
curves
are coincident and
are
independent
of W. In
region
I, Iaexp(qVA/2kT)
is
predominantly recombination in the shieldcathode junction
spacecharge region. Low injection prevails everywhere,
+
and hence VA=vPn For higher currents, but still low
injection, in region II, J becomes important. However
+
because V 0, still V and J.aexp(qV./2kT) The onset
of high injection in the it region occurs near the
transition point between regions II and III, where still
Vn< Above this point our model applies.
2.4 Experimental Corroboration and Discussion
In this section we present experimental data, taken
from a variety of GDS structures fabricated at Bell
Laboratories (Reading), that support the model described in
Section 2.2. We also use the simpler analytic model
developed in Section 2.3 to qualitatively explain the data.
Finally we discuss model calculations that reveal the
dependences of the currentvoltage characteristic on
critical device and material parameters.
+
Measured I(V^n ) and I(VA) in the highinjection
regime are plotted in Figure 24. The data are taken from
a GDS test structure having four anodes placed at different
lengths from the cathode, two (W=228/vm, 615/ym) of which
correspond to the data plotted. Also plotted in Figure 24
REFERENCES
[Ap79] J.A. Appels and H.M.J. Vaes, "High Voltage
Thin Layer Devices (RESURF devices)," IEDM
Tech. Dig., pp. 238241, 1979.
[Ba81] B.J. Baliga, "Silicon Power Field Controlled
devices and Integrated Circuits," in Silicon
Integrated Circuits, D. Kahng, Ed., Applied
Solid State Science Series, Supplement 2B.
New York: Academic Press, 1981.
[Ba84a] B.J. Baliga, "Switching Speed Enhancement
in Insulated Gate Transistors by Electron
Irradiation," IEEE Electron Devices, vol.
ED31, pp. 17901795, 1984.
[Ba85] B.J. Baliga, "Analysis of Insulated Gate
Transistor Turnoff Characteristics," IEEE
Electron Device Lett.,vol. EDL6, pp. 7477,
Feb. 1985.
[Ba84b] B.J. Baliga, M.S. Adler, R.P. Love, P.V. Gray,
and N.D. Zommer, "The Insulated Gate
Transistor: A New ThreeTerminal MOSControlled
Bipolar Power Device," IEEE Trans. Electron
Devices, vol. ED31, pp. 821828, 1984.
[Ba84c] B.J. Baliga and D.Y. Chen (eds.), Power
Transistors: Device Design and Applications.
New York: IEEE Press, 1984.
[Ba70] R. Baron and J.W. Mayer, Double Injection in
Semiconductors," in Semiconductors and
Semimetals, vol. 6, pp. 202313. New York:
Academic Press, 1970.
152
35
n ( O ) = n t
r bI i1/2
i A(b+i)JNoJ
(235)
and from (210), (214), and (224)
I
1/2
(236)
n(W)
A( b+1) JpQexp (
where AEpn is constant as given by (225). Thus, reduction
in both Jnq and Jpg would reduce RDC and RqN> but because a
reduction in will also decrease AE this will produce
PO Fn c
larger reductions in the resistances than a reduction in
Jnq. We note from (225) also that designing the p shield
such that Fg>0 would reduce the resistances, but would also
tend to negate its shielding effect.
An increase in Tq will also decrease the resistances.
For W>3La, (231) and (233 )(236 ) show that RQN and RDC
1/2
vary as 1/Tq However, for long Tq, or short W
(W<0.3La), Rqn and RDC are independent of ; further
decreases in W produce no additional reduction in the
resistances. Because of the effects of carriercarrier
scattering, changes in parameters that increase n(0) and
n(W), which tend to decrease the resistances, will also
cause a reduction in carrier mobility, and hence the
decreases in RQN and RDC predicted by (231) and (233) can
be overestimated.
89
t (ns)
IGBT anode current versus time from
simulation of resistive turnoff transient
for various values of th and JN0 (RGK = 5
52) .
Figure 47.
31
200
160
120
a
o
o
ce
80
40
//
/ /
/ /
/ /
/ ^Theoretical
Experimental^ / /
> /
Â¡f
/ /
/ /
/ /
* /
/?
//
L .//
}/
20
40
W2(10*Vm2)
Measured and calculated de resistance
versus the square of the itregion length.
The dashed lines emphasize the linear
dependences.
Figure 25.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
ssum, Cnairman
(e^try G. /Possum, Chairman
Professor of Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Fred A. Lindholm
Professor of Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Arnost Neugro
Professor of
Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Edward K. Walsh
Professor of Engineering Sciences
19
Combining (24) with (212)(215), we obtain the
following system of three equations in the three unknowns,
AE
FA'
AE
FC'
AE
Fn'
JN0exp(n^)=BTrJ+e[exP(2T^Â£)exP(2i^)cosh(r) ]'
A
(216)
^FC+^Fn 5 ^^FC ^^FA W
Jp0exp( ^ )=BbTj + p[eXp(21~)exp(7j^)cosh(i)],
A
(217)
where
AE AE F
AEpn=kTln{l+[Jexp( ^(^oexpljS)] Sj) (218)
k Tn
i
3=2kTn./7 u /L. (Â¡j +/j )sinh(W/L.). To solve the system,
i n p a n p A
we must specify Jpg JNg, W' T0' ant^ FS" Then for a given
J, a suitable numerical method must be used to derive AEpA,
AE_, AE^ We have used an IMSL subroutine to solve the
system with a high degree of accuracy. From the solution
A C
n(x), JK and JN are determined.
91
Figure 48 a simulated turnoff transient for an IGBT in
Figure 44 with an inductive load, including a gate delay.
A distinctive characteristic of this turnoff transient is
the sharp rise of the anodetocathode voltage vAK(t),
which even shows overshoot and ringing as do corresponding
measurements [Ba84c]. This unique vAR(t) transient results
from a damped resonance defined by the load inductance in
combination with the junction capacitance repesented by the
charging current dQJ(_,/dt in our model.
To further demonstrate the utility of the modeling
methodology, we simulate the static latchup of a
representative IGBT, but with a larger npn BJT base
resistance
latch, causing loss of gate control, if driven too hard.
For the static case, depicted in Figure 49 by the
simulated IA(VAK)/ latchup is approached by increasing IA>
As characterized in Section 4.2, Icp also increases, and
subsequently, because of the increased forward bias I_RD.T
on the emitterbase junction of the npn BJT, so does lCN
At the onset of latchup, ICN increases abruptly, thereby
reducing IM0S accordance with the recombination in the
RBN. As mentioned previously, the IGBT may
pnp BJT. The reduction of IMQS decreases the voltage
dropped across the DMOST and results in the
negativeresistance region shown in Figure 49. The
process is regenerative, and as the applied current is
increased further, ultimately ICN supplies all the
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A METHODOLOGY FOR PHYSICAL MODELING OF
HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICES
FOR CIRCUIT SIMULATION
By
ROBERT JAMES MCDONALD
December 1987
Chairman: Dr. J.G. Fossum
Major Department: Electrical Engineering
This dissertation presents a modeling methodology for
the construction of physical network representations for
highvoltage/power integratedcircuit (HV/P IC) devices.
The effects of multidimensional carrier flow, baseregion
conductivity modulation, significant emitter recombination,
nonreciprocal transcapacitance, and the onset of latchup
(static and dynamic), heretofore unaccounted for in
empirical circuit models, are physically accounted for in
our chargebased formalism. The methodology is applied to
vi
20
To generate the
determine V which
across the it region.
[Ha52,He68], we have
J(VA) characteristic, we must now
is the integral of the electric field
Again using basic PINdiode theory
V_ =
9
w
I
0
dx
n (x)
, b1, kT
5+T ~q
, r n(0 ) 1
1 'lwT1
(219)
The integration in (219) can be done analytically. Thus
the combination of (219) with (29) and (210) defines,
for a given J, V Our characterization of J(V ) is then
It
given by (21), (216)(218 ) and (19), the solution of
which must be obtained numerically. Representative results
will be presented in Section 2.4.
2.3 Physical Insight (Simplified Model)
A numerical solution to the system of equations
described in Section 2.2 is not necessary to gain useful
physical insight into the GDS operation. In this section
we describe this insight, and in doing so define a simpler
analytic model for J(VA) that is valid for high values of J
2
(1001000 A/cm ) of practical concern.
The total current J is the sum of the recombination
currents in the p+p anode, it, and n+ cathode regions
92
vAk (V)
Figure 49.
V''i
Simulation of static latchup in the IGBT:
driving anode current versus the resulting
anodecathode voltage with gatecathode
voltage equal to 10 V (ISN = 2 x 1012 A
and Rbn = 0.175 ) .
154
[Fo86b]
t Ge78]
[Gh77]
[Go8 3]
[Go87]
[G086]
[Ha85]
[Ha52 ]
t Ha84]
[Ha81]
J.G. Fossum and S. Veeraraghavan, "Partitioned
Charge Based Modeling of Bipolar Transistors
for NonQuasiStatic Circuit Simulation,"
IEEE Electron Device Lett., vol. EDL7,
pp. 652654, Dec. 1986.
I.E. Getreu, Modeling the Bipolar Transistor.
New York: Elsevier, 1978.
S.K. Ghandi, Semiconductor Power Devices.
New York: Wiley, 1977.
A.M. Goodman, J.P. Russel, L.A. Goodman,
C.J. Neuse, and J.M. Neilson, "Improved
COMFET's with Fast Switching Speed and
High Current Capability," IEDM Tech. Dig.
pp. 7982, 1983.
C.A. Goodwin, M.A. Shibib, R.A. Furnanage,
C.Y. Lu, P.C. Riffe, N.S. Tsai, and J.L.
Schmoyer, "A Dielectrically Isolated Bipolar
CMOSDMOS (BCDMOS) Technology for High Voltage
Applications," ECS Symposium, Philadelphia, PA,
May 1015, 1987.
P.A. Gough, M.R. Simpson, and V. Rumennik,
"Fast Switching Lateral Insulated Gate
Transistors," IEDM Tech. Dig., pp. 218221,
1986.
S. Hachad, C. Cros, D. Darees, J. M. Dorkel,
and P. Leturcq, "Latchup Critria in Insulated
Gate pnpn Structures," IEEE Trans. Electron
Devices, vol. ED32, pp. 594598, March 1985.
R.N. Hall, "Power Rectifiers and Transistors,"
Proc. IRE, vol. 40, pp. 15121518, Nov. 1952.
Harris Semiconductor Corp., SLICE Manual Rev.
4.08. Melbourne, FL: Harris Semiconductor
Corp., Jan. 1984.
A.R. Hartman, J.E. Berthold, T.J. Riley,
J.E. Kohl, Y.H. Wong, H.T. Weston, and
R.S. Scott, "530V Integrated Diode Switch
for Telecommunications," IEDM Tech. Dig.
pp. 250257, 1981.
A. Herlet, "Forward Characteristics of
Silicon Power Rectifiers at High Current
Densities," SolidState Electron., vol. 11,
pp. 717742, 1968.
[He68]
128
In Figure 511 we show a modelsimulated transient
turnoff characteristic for the HIGBT. Because the HIGBT
current for our test structure consists mainly of DMOST
drain current, the magnitude of the first phase is quite
large, but the conventional twophase IGBT turnoff
transient is clearly manifested. However, the influence of
RnB' Provides a path for carrier removal during the
transient, needs to be physically characterized so that
design criteria for an optimal HIGBT structure may be
suggested [Fo87], A cursory analysis of how RnB affects
the HIGBT transient turnoff is presented below.
To develop physical insight into how Rnfi affects
transient response, we extend the analysis in Chapter 2 by
adding a term ^vjgB//RnB^ to equation (215), thus
accounting for carrier removal through the drain during
phase two. If we neglect all components of recombination
current, assuming the dominant component of current is
carrier removal through R
differential equation for the charge residing in the base
region during phase two results:
nB, then the following simple
dQ
B
V
dt
JEB
lnB
( 513
If one assumes that VJEB remains relatively constant ()
61
The dependence of Tq on carrier lifetime illustrated
by the carrier lifetimes plotted in Figure 34 is
consistent with other measurements [Ba84a,Ba85] that show
Tq decreasing strongly with increasing electron irradiation
~ 1
dose. Calculations and measurements imply Tqth which
implies that the time dependence in the denominator of
(319) is unimportant for these devices (that have low t ) .
We note further that measured dependences [Ba84a,Ba85] of
Tq on VB and on Iq are explained well by our firstorder
model. For a given th, calculations show Tq increasing
weakly with increasing VB for constant Iq, and decreasing
with increasing IQ for constant Vfi. The Tq(Vb) dependence
is weak because x^m in (312) and implicitly in (313),
which defines Tq, does not change appreciably when Iq is
held constant, as can be seen from (310) and (311). The
Tq(Iq) dependence is more pronounced (Tq can be halved by
increasing Iq) because AI in (311) increases more rapidly
than Iq; viz., IMOS' which includes the p+ anode
recombination component, increases faster than Iq. We
infer from the model however that Tq will saturate for
sufficiently high Iq becauses ultimately iMqs' which
comprises predominantly the anode recombination current,
becomes proportional to IQ.
From our analysis, we can suggest a way to quicken the
turnoff, independent of shortening th which increases RQN
149
C INITIALIZE THE VOLTAGES WD MAKE CURRENT 0.0 IN OC CASE
C
VBE XCLC+l)
VBC XCLC+2)
1F(TIME.EQ.0.0)THEN
1RVBE.LT.0.56)THEN
P0 NI**2/ND*EXP(VBE/VT)
Y 0.0
FLGY0.0
GOTO 987
END IF
FLGY 2.0
IF< VBE.GT.0.78)P03E16
IF((VBE.GT.0.36).AND.(VBE.LT.O.7B))
P0NI**2/ND*EXP(VBE/VT)
END IF
WNB(2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
QBlQ*A*LA*P0*(COSH(W/LA)1.0)/SINH(W/LA)
XCLP+8) QB1
Y0.0
X(LP+9)Y
X
XCLP+ll) QB1
X(LP+i2)Y
RETURN
ELSE
C
C UPDATE CHARGE AND CURRENT IF LOCAL TRUNCATION ERROR CRITERIA ARE MET
C
!F( ( INITF.EQ.6) .AND. (DELTA.GE.XCLP+10) ) )THEN
X(LP+8)XCLP+ll)
X(LP+9)*X(LP+12)
END IF
QB1Q*A*LA*P0*(COSH(W/LA)1.0)/SINH(W/LA)
X(LP+11)QB1
X(LP+10)DELTA
IF(DELTA.EQ.O.O)THEN
Y0.0
ELSE
Y((QB1X(LP+8))*2.O/DELTA)X(LP+9)
ENDIF
X(LP+12)Y
ENDIF
C NO ERROR CHECKING
YNOER 0
987 CONTINUE
RETURN
200 CONTINUE
C
C SET Y VALUE OF DQB/DVBE
C
IFCFLGY.LT.1.0)THEN
Y 0.0
GOTO 876
END IF
IFCDELTA.EQ.O.O)THEN
Y0.0
ELSE
y Q*A*LA*PO*(COSH(W/LA)1.0)/SINH(W/LA)/VT
Y 2.0+Y/DELTA
ENDIF
876 CONTINUE
RETURN
300 CONTINUE
C
108
B
Figure 52.
Chargebased network representation for a
widebase, lowf3 pnp BJT.
34
which corresponds well to the plots in Figure 26.
W<0.3L>a, =[ n( 0 )+n(W) ]/2 and
R
ON
W
qA(//n+/Vp) [ n( 0 )+n(W) ]
(234)
As additional support
(231) and (233) imply a
the slopes of the RDC
characteristics, which is
We note further, since (23
that the extrapolation
characteristic yields direc
find (Rg+Rg)=6S2, which i
inferred from the measured
we expect RsRS' this re
for our model. The signif
experimental and theoreti
Figure 26 is due to, as we
explicit accounting of the
carriercarrier scattering.
GDS design criteria
for our theory, we note that
factor of two difference between
2 2
vs. W and R., vs. W
ON
reflected by the measured data.
C A
3) does not account for (Rg+Rg),
of the
measured R_.T vs.
ON
W 2
tly this
series resistance.
We
s about
+
twice the value
of Rg
>
characteristic.
Since
suit provides additional support
icant discrepancy between the
cal values of RQN plotted in
show later, our omission of an
reduction in mobility caused by
to minimize RQC and RQN are
and (234).
suggested by (231), (233)
(212), and (223),
From (29)
73
Nepi>'
the base transport equation simplifies to
d2p(x)~ p(x) n
,2 2 U
d x L.
A
1 /2
where LA t=(DATH) 1 is the ambipolar diffusion length
[Gh77]. The solution to (41), precluding a forward bias
on the basecollector junction, is
p(x)
p(0)sinh(^)
la
sinh(^)
(42)
where p(0) is the hole (or electron) density at the edge
(x=0) of the emitterbase junction spacecharge region and
W is the effective base width. From Figure 4.1,
W = Wb xd (43)
where WB is the metallurgical n base width and x^, which
is a function of VBR, is the width of the depletion region
at the onesided basecollector junction of the pnp BJT.
We define X[(VBK) based on the depletion approximation, and
6
In Appendix B, we briefly overview a representative
UDCS SLICE/SPICE implementation of a chargebased network
representation for a widebase, low3 pnp bipolar
transistor, a key model in the methodology for modeling
HV/P devices as dicussed in Chapter 5.
120
Experimental results and computer simulations have
indicated that the latchup point is only a weak function
of the gate voltage and that the base resistance, R^g, is
the most important parameter in determining the onset of
latchup because of the exponential voltage dependence of
the injected electrons. We note that the gain of the n+pn~
BJT also has an influence on the latchup point, albeit not
a strong one. In the dynamic case, both the charging
dQ
cu
JC
rrent, ^ Â£ and the transient collector current
contribute to the voltage drop across R^g and hence aid in
inducing latchup.
The onset of latchup in both the LIGBT and HIGBT
modes is simulated by the network models in Figure 54 and
Figure 56 via a voltagecontrolled current source I
CNPN
(Igsexp (VriR/VT) ) in which the controlling voltage, V^R, is
pB' T
pB'
developed across the assumed constant n+pn base
resistance, RpB* T^e Preexponential factor, Igs, is
related to the gain of the n+pn~ BJT through the Gummel
number. However, PISCES simulations have shown that R _
pb
undergoes significant conductivity modulation just prior to
latchup, and hence R D and Icc should be considered as
p D O
semiempirical modeling parameters. Because of the
SS
physical nature of our models, the values used for I
(2X10 ^A) and R (888) are close to those predicted from
pb
PISCES simulations. Note in Figure 54 and Figure 56 that
78
The lateral flow of the collected holes Icp in the
base of the npn BJT forwardbiases the emitterbase
junction and causes electrons to be injected into the base
of the pnp BJT (see Figure 41). This pbase transport
current can be approximated by [Ha85]
JCN = 1SN exp(^M) (413)
where IgN is the collector saturation current of the npn
BJT and Rbn is an average, or lumped, base resistance
[La85], both of which vary inversely with the pbase Gummel
number [Ge78]. However note that because of the
exponential dependence of ICN on Icp, only for conditions
near latchup is the contribution of to the anode
current I.=A_J. significant. When I.T=0, IMrkÂ£.=ID and the
A E A J CN MOS B
DMOST supplies all the electrons necessary for
recombination in the pnp BJT. However when the IGBT is
latched, the electrons necessary for recombination are
supplied by the npn BJT (ICN), and IMOS=0
The implicit description of the current UDCSs is
completed by equating the pnp BJT collector current (Icp)
to the difference between the emitter current (1^) and the
base current (ID):
Jd
59
Curve
^ H 0s)
t Ois)
Calculated IGBT turnoff transient for
three values of th and of J Device
parameter values used are an= 0.1 cm2,
6 0 /m,
0.5; I,
1014 cm3
and
&
157
[Wa83] R.M. Warner and B.L. Grung, Transistors:
Fundamentals for the IntegratedCircuit
Engineer. New York: Wiley, 1983.
[We82] H.T. Weston, H.W. Becke, J.E. Berthold, J.C.
Gammel, A.R. Hartman, J.E. Kohl, M. A. Shibib,
R.K. Smith, and Y.H. Wong, "Monolithic High
Voltage Gated Diode Crosspoint Array IC," IEDM
Tech. Dig., pp. 14, 1982.
[Yi85] H. Yilmaz, W. Ron Van Dell, K. Owyang, and
M.F. Chang, "Insulated Gate Transistor Physics:
Modeling and Optimization of the OnState
Characteristics," IEEE Trans. Electron Devices,
vol. Ed33, pp. 13771382, Sept. 1986.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Dorothea E. Burk
Associate Professor of Electrical
Engineering
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate
School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December 1987
Dean, Graduate School
119
R
nS
L
avct
L
MVNepi + P>
(511)
where L is the
crosssectional
depends on p.
substitution for
resistor
area, and
A simple
p yields:
length, Av is the vertical
a is the conductivity, which
algebraic manipulation and
nS
1 +
B1
qAWN
epi
(512)
where Rq is the value of Rfig when p=0.
Both the LIGBT mode and the HIGBT mode can undergo
static or dynamic latchup. Static latchup occurs when
the collector current of Ic^, produces approximately a
diode voltage drop across the lateral resistance RpB in the
base of the parasitic n+pn transistor. When this voltage
drop develops, electrons are injected by the n+pn_ BJT into
the base of Q1, increasing its conduction, and hence
triggering the regenerative process associated with the SCR
[Gh77] defined by and the n+pn~ BJT. Removal of the
gate voltage at this point will not turn off the LIGBT or
HIGBT since the DMOST supplies only a small fraction of the
base current for and the main path for current flow is
now through the SCR, which can only be turned off by
reducing the total current below the holding point.
101
I
Figure 51. Special LIGBT test structure (symmetric
about the axis shown). The spacing between
the 10 fjm deep p+ anode and the cathode is
78 /jm. The thickness of the n~ ( 5 x 1014
cm3) layer is 35 //m and the depth is 300
/jm.
C SET Y VALUE OF DQB/DVBC
c
IF(FLGY.LT.1.0)THEN
Y 0.0
SOTO 765
END IF
IF(DELTA.EQ.0.0)THEN
Y0.0
ELSE
YQ*A*P0*ES^)D/O^ (2*ES* ( PH I+ABS (VBC))/ND*Q) *. 5
Y 2.0*Y/DELTA
ENDIF
763 CONTINUE
RETURN
END
CA****** ********* A ******* A** ********** *********************
C THIS SUBROUTINE CALCULATES THE CHARGE ASSOCIATED
C WITH THE REVERSEBIASED COLLECTORBASE JUNCTION AS A
C FUNCTION OF THE NODE VOLTAGES VBE AND V8C FOR
C CHARACTERIZATION OF THE TRANSIENT CHARGING CURRENTS
C BY A UDCS IVE86]
C
C*************A *********************************** *********
SUBROUTINE UQJC1(Y,I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND
SPECIAL COMMON BLANK
COMMON/BLANK/X( 64)
COMMON/STATUS/OMEGA,TIME,DELTA,DEL0LDC7) ,AG(7) ,VT,XNI ,
Â£ EGFET .MODE .MODEDC, I CALC, INITF .METHOD IORD ,MAXORD,NONCON,
Â£ ITERNO,ITEMNO,NOSOLV
COMMON/KNSTNT/TWOPI ,XL0G2.XLOGIO,R00T2,RAD,BOLTZ,CHARGE,
Â£ CTOK,GMIN,RELTOL,ABSTOL,VNTOL,TRTOL,CHGTOL,EPSO,EPSSIL,EPSOX
IF(TIME.EQ.O.O) THEN
AC X(LP+1)
ND X(LP+2)
XI X(LP+3)
X2 X(LP+4)
X3XCLP+5)
ENDIF
GOTO!50,100,200).IFLAG+2
30 CONTINUE
RETURN
100 CONTINUE
C
C INITIALIZE THE VOLTAGES AND MAKE CURRENT 0.0 IN DC CASE
C
VBC XCLC+l)
IF(TIME.EQ.O.O)THEN
QJCAC*(2.07E12A1.6E19*ND*ABS(.6+VBC))**.3
QJCY
X(LP+8) QJC
Y0.0
X(LP+9)Y
X
X(LP+11) QJC
X(LP+12)Y
RETURN
ELSE
C
C UPDATE CHARGE AND CURRENT IF LOCAL TRUNCATION ERROR CRITERIA ARE MET
C
IF((INITF.EQ.6).AND.(DELTA.GE.X(LP+10)))THEN
110
empirical optimization needed. In addition, the modular
approach allows for a straightforward network
representation of the LIGBT structure as will be shown in
this section. We note that in all cases, the simulation of
the actual symmetrical device involves area doubling of the
model derived from the halfstructure shown in Figure 51.
With the cathode floating, the drain tied to ground
and the anode biased to a positive voltage, the LIGBT
structure operates as a forwardbiased PINdiode. The
PINdiode currentvoltage characteristic can be used to
obtain information regarding recombination properties of
the n epi region (xH) and of the p+ anode region (JNg).
An optimization program was written to extract from
measured IV characteristics the three adjustable
parameters (th, Jnq, and JpQ, the cathode counterpart of
Jnq) of a onedimensional PINdiode model [Mc85]. The
13 2
optimization yielded th=2.6/us and JnQ = 6x10 A/cm at
room temperature. These parameter values were found to be
commensurate with measured turnoff transients of the
LIGBT, discussed below.
In the DMOST mode, the anode is left floating and the
drain is set at a positive voltage relative to the source
(cathode). The DMOST is empirically modeled as a simple
MOSFET (SPICE/level 2 [Ha84]) with a resistor, R ., tied
' epi
to the drain which accounts for the large n~ epi
resistance. Although this model is inadequate in general,
106
baseregion charge QB and the collectorbase junction
depletionregion charge Qj^. For quasistatic conditions,
Qb is given by the integral of (51) from x=0 to x=W:
W
Qb = qA J p(x)dx ; (57)
0
and
Q= qAN .x ,
JC M epi d
(58)
The charging currents are derived from (57) and (58):
dQ. r 9Q. dV.
= 2 1
^Tt j 9Vj dt
(59)
9Qi
where i=B,JC and j=JEB,BC. The transcapacitances, in
j
(59) can be nonreciprocal, and hence the chargebased
model is more representative of the actual charge dynamics
than a conventional capacitancebased model.
Our low3 BJT (with wide, lightly doped base) module
differs significantly from the conventional GummelPoon
A METHODOLOGY FOR PHYSICAL MODELING OF
HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICES
FOR CIRCUIT SIMULATION
By
ROBERT JAMES MCDONALD
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987
18
is supported by electron injection from the it region:
 vo)
5TT J +
2kT"n"p
"n+"p
dn
Hi
x=0
(213)
where bAThe expression for JN(0) in (213)
which is evaluated using (211), derives [F157]
J=JN+Jp with p=n. In the n+ cathode, the
recombination current can be expressed as [Fo81]
from
hole
JP JP0
exp(AEFC+AEFn)
if
(214)
and is supported by hole injection from the n region
[Fl57 ] :
Jp Vw) ETT
J 
2kTVp
"n^p
dn
Hi
x=W
(215)
In (212) and (214), Jnq and JpQ are constant
parameters (saturation current densities) that are defined
by the properties of the heavily doped anode and cathode
[Fo81].
90
t ((IS)
Figure 48. IGBT anode current, (normalized)
anodecathode voltage, and gatecathode
voltage versus time from simulation of
turnoff transient with inductive load.
In Figure 44, Z is a series combination
of 8 /t/H and 35 S31; RQK = 100 S3.
/ 30 (V)
(mA)
116
Measured LIGBT current versus the anode
voltage and measured HIGBT current and
anode component of HIGBT current versus
the anode/drain (shorted) voltage.
Figure 55.
124
substantial fraction (1/2) of which is p+emitter
recombination (first term in (54)). The expeditious
effects of anode recombination on the LIGT turnoff
transient have been demonstrated in Chapter 3. We stress
that such transient simulations are not possible with
conventional SPICE transistor models. We also note that if
the gate voltage is removed fast enough, then the sum of
the transient collector current and collectorbase junction
displacement current may be sufficient to forward bias the
n+pn transistor and subsequently cause dynamic latchup.
For the circuit conditions shown in Figure 58, dynamic
latchup will occur if the gate voltage is removed in less
than five nanoseconds.
In Figure 59 we show measured currentvoltage curves,
terminating at latchup, for the HIGBT mode of operation
for three different values of gate voltage. It can be seen
that the trigger current for the LIGBT (Q^) excitation is
approximately 13mA, independent of VG, implying that an
internal voltage drop is responsible for the triggering.
The onset voltage may be estimated by using our network
model for the HIGBT shown in Figure 56 and noting that the
applied voltage splits between RnB' RnS' an<^ tlie DM0ST
channel resistance. The total voltage across the HIGBT,
just prior to triggering, consists of three terms: a
channel drop, VCH> which depends on the DMOST gate voltage,
a drop across Rng, and a drop across RnB, which is
156
[Pa86]
D.N. Pattanayak, A.L. Robinson, T.P. Chow,
M.S. Adler, B.J. Baliga, and E.J. Wildi,
"NChannel Lateral Insulated Gate Transistors:
Part I SteadyState Characteristics," IEEE
Trans. Electron Devices, vol. ED33, pp. 1956
1963, Dec. 1986.
[R086]
A.L. Robinson, D.N. Pattanayak, M.S. Adler,
B.J. Baliga, and E.J. Wildi, "Lateral
Insulated Gate Transistors with Improved
Latching Characteristics," IEEE Electron
Device Lett., vol. EDL7, pp. 6163, Feb. 1986.
[Ru8 3]
J.P. Russel, A.M. Goodman, L.A. Goodman, and
J.M.Neilson, "The COMFET: A New High
Conductance MOSGated Device," IEEE Electron
Device Lett., vol. EDL4, pp. 6365, 1983.
[Sh80]
P.W. Shackle, A.R. Hartman, T.J. Riley,
J.C. North, and J.E. Berthold, "A 500 V
Monolithic Bidirectional 2x2 Crosspoint
Array," ISSCC Tech. Dig. pp. 170171, 1980.
[Si 8 5]
M.R. Simpson, P.A. Gough, F. Hshich, and
V. Rumennik, "Analysis of the Lateral Insulated
Gate Transistor," IEDM Tech. Dig., pp. 740743,
1985.
[Sm82]
R.K. Smith, H.W. Becke, J.C. Gammel, M.A.
Shibib, and Y.H. Wong, "An Analytic Model
for the Forward Characteristics of Gated
PIN Switches Applied to Lateral Structures,"
IEDM Tech. Dig., pp. 1114, 1982.
[Su80]
S.C. Sun and J.D. Plummer, "Modeling of the
OnResistance of LDMOS, VDMOS and VMOS Power
transistors," IEEE Trans. Electron Devices,
vol. ED27, pp. 356367, Feb. 1980.
[Va76]
A. Van der Ziel, Solid State Physical
Electronics. Englewood Cliffs, New Jersey:
PrenticeHall, 1976.
[Ve86]
S. Veeraraghavan, J.G. Fossum, and W.R.
Eisenstadt, "SPICE Simulation of SOI MOSFET
Integrated Circuits," IEEE Trans. Computer
Aided Design of ICAS, vol. CAD5, pp. 653658,
Oct. 1986.
CHAPTER 2
A PHYSICAL MODEL FOR THE CONDUCTANCE
OF LATERAL p pixpn STRUCTURES FOR HVICs
2.1 Introduction
This chapter concerns the forward, steadystate
currentvoltage characteristics I(VA) f a P+P^Pn+
structure, the GDS [We82,Ha81], used in HVICs. We develop
an analytic model for I(VA) based on a onedimensional
regional representation of the device. The model yields
physical descriptions of RQN(=AVA/AI) and the dc resistance
Rdc(=Va/I) at high operating currents where these
resistances must be minimized to ensure efficient GDS
operation [Sm82]. Such minimization is aided by the model,
which clearly identifies the underlying physical mechanisms
and the associated parameters.
The resulting model also has applications to other
HV/P IC devices employing punchthrough shields (aka buffer
regions) for which the development of effective and
efficient network models for circuit simulation is of
primary interest. In addition, the proper modeling of the
7
CN Sa(A)
94
Figure 410. Simulation of dynamic latchup in the
IGBT: anode current, npn BJT collector
current, and driving gatecathode voltage
versus time with R = 15 S! (I = 2 x
1012 A and R = 0.175 Q).
n N
95
4.4 Summary
A methodology for SPICE implementation of
highvoltage/power integrated circuit device models has
been presented and demonstrated. The methodology is
flexible and enables an accounting for the unique
characteristics associated with HV/P IC devices, such as
merging bipolar and MOS structures, latchup, conductivity
modulation, and moving boundary conditions. A
representative HV/P device, the IGBT, was modeled using a
system of implicit equations relating the quasistatic
device terminal currents and charges to the terminal
voltages. The physical IGBT model was implemented in
SLICE/SPICE2 by using UDCSs, simple FORTRAN subroutines
referenced in the SPICE2 nodal analysis. Simulations of
IGBT circuits, reflecting dc and transient characteristics
of the HV switch were described. These simulations, which
included static and dynamic latchup, are not possible with
builtin SPICE2 lumpedelement models, and thus poignantly
demonstrate the need for and utility of the new flexible
and physical modeling methdology. CPU times required to do
the simulations with the UDCS model are substantially
longer than times for (invalid) simulations with builtin
models in SPICE2. However they are not prohibitive for
smallscale circuits; typically the new models necessitated
CPU times, for both dc and transient simulatons, about an
107
model in several ways that make it physically
representative of highvoltage devices. The chargebased
formalism (59) properly accounts for transcapacitances,
which cannot be represented faithfully by reciprocal
capacitors [Fo86b], The baseregion voltage drop vep in
(53) is modeled directly and generally (even for (3<1,
viz., very high Jg). The relationship (55) from PINdiode
theory ensures the proper simulation of the emitter
efficiency for highinjection conditions in the base
region. For example in the limit of very high injection,
the model with (55) correctly predicts 3l/b
(baseregion mobilities). Thus, highvoltage p+n~p and
n+p n BJTs have different limiting current gains (Appendix
A) .
The network representation of the chargebased low(3
pnp BJT module is shown in Figure 52. The module is
implemented in SPICE via userdefined controlled sources
(UDCSs) [Ve86] in a novel manner which allows the circuit
simulator to solve the nonlinear equations implied by
(51)(58). UDCSs are FORTRAN subroutines in SLICE
[Ha84], an enhanced version of SPICE2. Each element of the
module is a UDCS that describes the current (and associated
transconductance or transcapacitance calculated numerically
using finitedifference approximations) via the system of
equations described above (Appendix B). The SPICE nodal
analysis accesses the subroutines iteratively in the
41
anode. The resulting analysis identifies important
charging mechanisms and suggests device design criteria for
decreasing the turnoff time. The analysis subsequently
aids in developing accurate and simple equivalent network
representations for LIGBT structures, as shown in Chapters
4 and 5.
Until recently, highvoltage powerswitching devices
were either bipolar (e.g. gated PINdiode [Sm82]) or MOS
(e.g., power MOSFET [Ba81]). A particular application
dictated the technology to be used based on a tradeoff
between its advantages and disadvantages. Bipolar power
devices generally yield low onresistance RQN
(highcurrentdensity operation) because of conductivity
modulation, but slow switching because of the
minoritycarrier storage. MOS power devices are fast
switching because of short minoritycarrier (channel)
transit time, but generally have high RQN because of the
lightly doped drift region.
Recently a new family of power semiconductor devices
based on integrating bipolar and fieldeffect technologies
was introduced. The IGBT [Ru83,Ba84b] is basically a
MOSFET (VDMOS) having a pn junction connected to the drain
that, in the onstate, injects minority carriers into, and
modulates the conductivity of, the drain (drift) region.
The basic IGBT structure is shown in Figure 31. With it,
virtually any desired tradeoff between switching speed and
Figure 5
114
r
Network representation for the LIGBT mode
of operation.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
ABSTRACT vi
CHAPTERS
1 INTRODUCTION ..1
2 A PHYSICAL MODEL FOR THE CONDUCTANCE
OF LATERAL p pnpn STRUCTURES FOR HVICs ...7
2.1 Introduction 7
2.2 Model Development 9
2.3 Physical Insight (Simplified Model) 20
2.4 Experimental Corroboration and Discussion 27
2.5 Summary 39
3 CHARGECONTROL ANALYSIS OF THE IGBT
TURNOFF TRANSIENT 4 0
3.1 Introduction 40
3.2 Model 44
3.3 Discussion. 58
4 HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICE
MODELINGA FIRST APPROACH 64
4.1 Introduction 64
4.2 Modeling Methodology 67
4.3 SPICE Simulations and Discussion 81
4.4 Summa ry 9 5
5 HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICE
MODELING 97
5.1 Introduction 97
5.2 Modeling Methodology 100
5.3 Application/Demonstration .109
5.4 Simulation/Verification 121
5.5 Summary
6 SUMMARY AND CONCLUSIONS WITH RECOMMENDATIONS ..134
iv
13
junction
nea
r the
anode;
V is
n
the
drop
region;
vnp
J
is
the dr<
op across
the
np j
cathode;
and
vpn
J
i s the
drop acri
oss the p
junction,
Ref ei
rring
to Figure
22
highinj
?cti
on (p:
=n>>N
An
) where NAji is
the
density)
in
the it
region
, we have
then
from
across the n
unction near the
shieldcathode
and assuming
acceptor doping
(21)
qVA
+ AEFn + ^Vn
(22)
where AEpA and AEFC are the EFnEFp separations at the pn
and np junctions respectively, and AEfn is the change in
EFn across the p shield at the cathode. We assume that the
majorityhole quasiFermi level is virtually flat across
the p shield, in which the injection level is low; thus
qVpn =AEFn+AEFC. In deriving (22) we used the
quasiequilibrium relations qVpn; = AEFA/2( kT ) In( NAjl/n^ ) and
qvJP=AEFC/2+(kT)ln(NAn/n.).
Hence for a given GDS current density J, AEFA, ^efc'
AEFn, and must be determined before (22) can be used to
give the desired J(VA) characteristic. These
determinations are made by incorporating into basic
PINdiode theory a model for carrier transport in the p
shield, which reduces the injection of electrons into the n
region.
75
where WM(
equals N ^; JA is the anode (emitter) current density and
b=/un//Up is the electron/hole mobility ratio.
For negligible recombination in the emitter junction
spacecharge region, is related to p(0) as follows
[Be79]:
(47)
x=0
where is the ambipolar diffusivity [Gh77] and Jnq is the
saturation current density defined by the back injection of
electrons into the quasineutral emitter region [Fo81].
Equations ( 4 4 ) ( 4 7 ) relate p(0) to VAB and V^, the
independent nodevoltage differences in the model. Now
(42) and (43) can be used with these relations, and the
quasistatic approximation, to characterize the UDCSs in
terms of these voltages. We note that although these
characterizations are implicit, the model is implemented in
SPICE2 directly via access of the UDCSs by the nodal
analysis [Ve86].
The UDCS is given by (46). The quasistatic
depletion charge density at the basecollector junction is
CJC ^ep^d
(48)
o o o
X(LP+8)X(LP+11)
X(LP+9)X(LP+12)
ENDIF
QJCAC*(2.07E12*1. 6E19*ND*ABS( .6WBC) )**.3
QJCY
X(LP+11)QJC
X(LP+10)DELTA
IF(DELTA.EQ.0.O)THEN
Y0.0
ELSE
YCCQJCX(LP+8))*2.0/DELTA)X
END IF
X(LP+12)Y
ENDIF
C NO ERROR CHECKING
YNOER O
RETURN
200 CONTINUE
SET Y VALUE OF DQJC/DUBC
IF
Y0.0
ELSE
Y AC*.5*(2.07E12*1.GE19*ND)*(ABS<.64VBC)**.3)
Y 2*Y/DELTA
Y0.0
ENDIF
RETURN
END
CHAPTER 1
INTRODUCTION
The field of highvoltage and power integrated
circuits is a rapidly emerging and expanding technology.
Three basic processing efforts have made highvoltage/power
(HV/P) devices practical for circuit integration: one, the
advent of a lateral, doublediffused MOS (DMOS) process
[De86], which produced integrated highspeed, highvoltage
display drivers; two, improved isolation techniques, such
as dielectric isolation [Be85, Sh80] and field reduction
techniques such as RESURF [Ap79], which reduced parasitic
interactions and provided higher breakdown voltages; three,
the functional integration of bipolar and MOS devices
[Ru83], which dramatically lowered device onresistance and
consequently increased the power handling capability of
HV/P integrated circuits (ICs), while maintaining the
advantages of the MOS gate. However, although great
strides in the process technology of HV/P ICs have taken
place, the area of circuit modeling for
computeraideddesign (CAD) of HV/P ICs, especially for
1
72
the lateral voltage drop in the base region of the npn BJT,
which is important only near latchup as we discuss later.
The six UDCSs reference the same userdefined
subroutine that defines the system of model equations.
This set of equations is quasistatic; that is, and
r d
QJC, as well as IMQS, Icpr ICN/ and Vepi, are described in
the steady state in terms of V.n and VDI,, and then the
transient currents are characterized through the
quasistatic approximation [Va76] which equates the
timedependences to the steadystate dependences in terms
of VAB(t) and VBK(t). Virtually all device models used
today for circuit simulation are quasistatic. Although we
use the quasistatic approximation here, with some support
for its validity, we recognize the need to consider the
possible occurence of nonquasistatic (NQS) effects in
each particular model development. Proper accounting for
the NQS effects in SPICE models is a formidable task, but
can be facilitated [Fo86b] by the new methodology presented
in this chapter.
We now describe the physical model equations in
detail. The sytem of equations is based on the solution to
the onedimensional ambipolar transport equation [Gh77]
describing the carrier densities in the quasineutral n~
base region. Twodimensional effects are considered later.
Since the IGBT operates under highinjection (conductivity
modulated) conditions in the n~ base region (p = n >>
8
anode and cathode recombination, when highinjection
obtains in the low dopedbase region, provides the impetus
for developing a new BJT model as derived in Chapters 4 and
5 and highlighted in Appendix A.
The gated diode switch (GDS), illustrated in Figure
21, is a dielectrically isolated highvoltage integrated
circuit silicon device used in monolithic crosspoint arrays
applicable to telephone switching networks. The device is
basically a PlNdiode with an n+ gate in the i(n) region
and p shields surrounding the p+ anode and the n+ cathode.
The n gate facilitates the turnoff of the switch, but
does not affect the forward bias (ON) characteristics,
which closely resemble those of a PINdiode at highcurrent
levels. The cathode shield prevents punchthrough between
the gate and the cathode in the offstate, and has been
shown to limit the injection of electrons into the n region
and hence increases the incremental onresistence of the
device [Sm82]. The "anode shield" facilitates a reliable
contact to the anode, but does not provide any electrical
benefit.
Our onedimensional analytic model, which can be
applied generally to gated bipolar switches, and hence has
application to HV/P ICs, is based on a system of equations
derived from previously developed PINdiode theory
[Ha52,He68,Fl57,Be79] for highinjection conditions. The
equations are solved numerically to yield the desired I(VA)
it is a tale told by an idiot,
full of sound and fury,
signifying nothing.
Shakespeare
Gatedrive circuitry for IGBT transient
simulations. The pulse voltage, V wai
defined to fall from 10.7 to zero
ns. The voltage Vcc was set at 350 V.
igure 44.
crH
58
Thus I(t) can decay faster than exponentially if currents
associated Qn(t), reflected by the second term in the
denominator of (319), are significant. If J
NO
is
negligibly small, then (319) reduces to a simple
exponential decay defined by the numerator. However for
typical values of the model parameters, the second term in
the denominator of (319) can be significant.
3.3 Discussion
Our analysis of the IGBT turnoff transient is first
order, and describes, in terms of the steadyonstate
current components, an initial fast drop AI of the current,
followed by a slower decay of I(t), which can be, depending
on somewhat sharper than an exponential falloff
having a time constant equal to tH. In Figure 34 we plot
the composite turnoff characteristic for a typical IGBT
predicted by our analysis for three assumed values of th
and of JN0, the two most significant material parameters
that must be controlled for optimal device design. As
noted previously, a steadystate analysis is needed to
evaluate parameters in our transient model. In the
derivation of the I(t) characteristics plotted in Figure
34, we first used a numerical solution of the steadystate
ambipolar transport in a quasitwodimensional
representation of the widebase p+n p BJT to estimate the
constitution of Iq in (31) and (32). Then, with IM0S and
IEl( B+l )/B*( AE1*JNO*PO**2/NI**2+Q*DA*AE1*PO/LA/TANH(W/LA) )
VDEMVT*(Bl)/(B+l)*LOG(PO/ND)
VEPIVDEMSINH(W/LA)*IE1*LA/AE1/Q/(UN+UP)/P0*
SLOG(TANH( (WXS)/LA)/TANH(W/LA) )
Z2VEPI
IF(IFLG.EQ.1)THEN
ZlVEPI
VBCVBC+H
IFLG2
GOTO 789
END IF
VBCVBCH
YCZ2ZD/H
765 CONTINUE
GOTO 99910
99910 CONTINUE
RETURN
END
C************ A******* A**** ********* A A A ****** ******
C THIS SUBROUTINE CALCULATES THE CHARGE IN THE BASE
C REGION AS A FUCTION OF THE NODE VOLTAGES VBE &D VBC
C FOR THE CHARACTERIZATION OF THE TRANSIENT CHARGING
C CURRENTS BY A UDCS [VE86]
C* ** ***************** ******** *"* ********** *** A A** *
c
SUBROUTINE UQB1( Y, I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND, JNO.NI.JNOl
SPECIAL COMMON BLANK
COMMON/BLANK/X ( 64 )
COMMON/STATUS/OMEGA ,T1ME, DELTA DELOLDC 7) ,AG(7) ,VT,XNI ,
6 EGFET .MODE .MODEDC I CALC, INITF .METHOD, IORD .MAXORD .NONCON,
6 1TERNO.ITEJMO.NOSOLV
COMMON/KNSTNT/TWOPI.XL0G2.XL0G10.R00T2,RAD,BOLTZ,CHARGE,
& CTOK,GMIN,RELTOL,ABSTOL.UNTOL.TRTOL,CHGTOL,EPSO,EPSSIL,EPSOX
IF(TIME.EQ.O.O) THEN
WBlXILP+l)
TO XCLP+2)
JN01XCLP+3)
NDXCLP+4)
AElX(LP+5)
HXC LP+6)
WBWB1
jnojnoi
A AE1
ENDIF
VT.02586
NI1.3E10
UN1350
UP480
BUN/UP
PHI.6
ES1035E12
Q1.6E19
DA2*VT*UN*UP/( UN+UP)
TH2*T0
LASQRT(DA*TH)
GOTO(50,100,200,300),!FLAG+2
50 CONTINUE
RETURN
100 CONTINUE
Ill
it suffices here for assessing the validity of the modeling
methodology applied predominantly to the bipolar aspects of
the LIGBT. Fitting this model to the measured
linearregion transconductance, we extract values for R
eP1
(325 9), the threshold voltage (2.6 V), and the
transconductance factor (1.9X10^ A/V).
In the LIGBT mode, the drain is left floating and a
positive voltage is applied to the anode. With the gate
biased above the threshold voltage, the nchannel supplies
base current for the lateral p+n~p BJT. Our
quasitwodimensional modeling of this transistor is done
by partitioning it into two onedimensional transistors,
and Q2, each represented by BJT modules described in
Section 5.2. The partitioning is defined based upon
results we obtained from PISCES simulations, which show
that the ratio of lateraltovertical injection from the p+
anode (emitter) is nearly excitationindependent. Figure
53 shows a typical PISCES result for the hole current
distribution in our test structure for the LIGBT mode of
operation. The onedimensional current flow in the center
section of the structure is clearly seen and demonstrates
that the quasitwodimensional modeling via partitioning is
a viable approach. The active area and base width for
are defined by the anode diffusion depth and the geometry,
as illustrated in Figure 51. The base width and area for
Q2 are defined to make the simulated current agree with
CHAPTER 4
HIGHVOLTAGE/POWER INTEGRATED CIRCUIT DEVICE
MODELINGA FIRST APPROACH
4.1 Introduction
This chapter introduces a novel methodology for
flexible SPICE2 implementation of physical models for HV/P
IC devices developed in chapters 2 and 3. The model
implementation is applied to the IGBT of Chapter 3 and is
achieved without modification of the SPICE2 source code by
utilizing UDCSs that access FORTRAN subroutines which
define, implicitly, the current and charge as functions of
the controlling node voltages. The implicit problem is
numerically solved in a FORTRAN subroutine and its solution
(a current or charge) is referenced by the SPICE2 main
program. This highly flexible means (first approach) of
model implementation differs from that presented in Chapter
5, where the implicit model equations are solved by the
SPICE2 main program, thus trading model flexibility for
computational efficiency. SPICE2 simulations of dc and
transient characteristics of IGBT switching circuits are
64
49
External biasing and turnoff_circuitry
for the IGBT transient analysis.
Figure 33.
140
where
increasing
is
the ambipolar di
ffusivity,
dp/dx
i s the
of
the hole
(elect
ron) conce
nt
ration. For
current densi
ties,
the second
term
on the
s j
Lde of Al
will
always bee
ome ne
gligible
i s
proportional
to p( 0
) (p(x): x
= 0
) wh
ereas JN
tional to p(0)
2 [ Gh7
7]. Thus,
at
high
current
the
base current
consis
ts primari
iy
of
emitter
ion
current, as
shown
in Chapter
2,
and
equation
used to to find
a limi
ting value
for
the BJT
current gain:
e
pnp
JE JN
JN
1
B
(A2 )
A similar analysis for an n+p n structure yields a
different high current limit for the gain:
8 b .
Hnpn
(A3 )
Physically, the difference between the highcurrent 8s
for pnp and npn transistors results from the unequal
electron and hole mobilities. Thus typical npn and pnp
BJTs used in HV/P ICs have very different limiting 8s. If
6.1 Summary and Conclusions 134
6.2 Recommendations 136
APPENDICES
A HIGH CURRENT CARRIER TRANSPORT IN WIDEBASE BJTs 139
B UDCS/S LICE/S PICE MODEL IMPLEMENTATION 142
REFERENCES 152
BIOGRAPHICAL SKETCH 158
v
129
t (ns)
Figure 511. Modelsimulated HIGBT anode/drain current
versus time for a resistive load of 100 G
and offstate voltage of 6 V. The gate
voltage of 10 V falls to zero in 25 ns.
23
Hence for sufficiently high J, AEpn is a constant,
independent of J as well as W and parameters associated
with the anode.
The approximations (223)(225) are insightful. They
imply that for a given high J, the injection level in the n
region near the anode, i.e., n(0), is defined primarily by
Jnq, and that the injection level near the cathode, i.e.,
n(W), is defined primarily by Jp^ and Fg. This means that
V^n is independent of W and the anode parameters, even
A
though JN is a significant component of J.
Consistent with the simplifications in (223)(225)
is the neglect of the second term in the expression (219)
for V^, which is typically ~kT/q. Thus for high J,
W
VE ~ q{fJn+fJ )
r dx
J n( x)
(226)
in which the integral is evaluated using (211). A further
crude approximation can be made by writing (226) as
Vn =
JW
q(VVn
(227
66
device characteristics and model complexities, such
implementation will require either modifying existing
simulator codes to accommodate new specific models, or
developing new methodologies for general model
incorporation. This paper describes a simple, flexible and
physical approach to the latter implementation. The
methodoly is exemplified through an application to a
representative device, the insulated gate transistor (IGBT)
[Ba84b], an HV/P switch comprising merged bipolar and MOS
structures. Although the (vertical) IGBT is not a common
integrated device, we use it to demonstrate the modeling
methodology, which is intended primarily for CAD of HV/P
ICs, because (i) it is well documented, and (ii) its basic
operation is not unlike that of other merged bipolar/MOS
devices which are integrated, e.g., the lateral IGBT
(LIGBT) [R086].
We stress that this chapter introduces and
demonstrates a novel device modeling concept for HV/P
circuit simulation, but does not include the simulation of
any actual device nor a complete corroboration of model
assumptions. The viability of the methodology is implied
by the physical nature of the models and is shown through
qualitative comparisons between model predictions and
published measured characteristics.
The new SPICE modeling approach, presented in Section
4.2 and demonstrated in Section 4.3, utilizes expressions,
50
first describing only the fast drop AI in the current that
occurs in the first phase, and then modeling the subsequent
decay of X(t) in the second phase, which defines the
turnoff time. If VG is removed at t=0, and I = Iq in the
steadystate for t<0 as described by (32), then for t>0
I(t) ~ 1C(BJT)(+
dQj2(t)
~St
(34)
where is the charge associated with the depletion
capacitance of J2. For t=0+, I is Iq, and and
dQj2/dt, which equals IM0S in (31), are defined by the
steadystate characterization of the IGBT, KV^). Hence
our transient analysis is dependent on the steadystate
model. We stress, however, the utility of the transient
model, independent of the steadystate analysis. As we
will show, the dc current components in (31) and (32)
become parameters of the transient model and can evaluated
by comparing theoretical and experimental characterizations
of the turnoff transient.
Using a chargecontrol representation, we express the
transient BJT collector current in (34) as
Qp(t)
IC(BJT) = Tt (t)
(35)
IGBT
CHAPTER 3
CHARGECONTROL ANALYSIS OF THE
TURNOFF TRANSIENT
3.1 Introduction
This chapter concerns the modeling of another common
HV/P IC device, the IGBT [Ba85]. In Chapter 2, an
analytical model for the steadystate IV characteristics
of a GDS was developed and experimentally verified. In
this chapter we utilize the physical insight gained in
modeling the GDS to develop a quasistatic charge control
model for the IGBT turnoff transient [Ba85]. The model,
with minor modifications, is also applicable to the hybrid
IGBT (HIGBT) [Fo87,Si85] turnoff transient, as
demonstrated in Chapter 5.
The analysis presented in this chapter describes the
transient behavior of the IGBT in terms of its steadystate
current components. The effects of minoritycarrier
injection into the anode are properly accounted for, within
the limits of the quasistatic approximation, by using the
physically correct PXNdiode boundary condition at the
40
76
where Ac is the (effective)
The quasistatic carrier
region is the integral of (
basecollector
charge in the qua
41) from x=0 to
junction
sineutral
x=W:
area.
base
W
Qb = qA J p(x)dx
0
(49)
where A^ is the emitter, or
chargingcurrent UDCSs in the model
and (49):
anode, area. The
are derived from (48)
dQ. 8Q. dV.
i = x i 1
dt L 9V. dt
j 3
where i=JC, PB
and j =AB,
BK.
Therefore
the
" transcapacitance"
3Qi/8Vj must
also be
described
in the
UDCS, either analyti
cally or numerically.
We note
from
(49) and (410) that the transcapacitances associated with
QpB cannot be described in closed form, and hence
finitedifference approximations are used in the UDCS
dQpB/dt to characterize them numerically.
60
3 evaluated for a specified IQ, ( 39 ) ( 311) give AI and
(319) describes the transient decay I(t). The value of KA
(=0.5) used in the transient analysis is consistent with
the quasitwodimensional treatment of the steadystate
carrier transport: K . /A.
a collector
Comparisons of the predicted characteristics in Figure
34 with published data [Ru83,Ba84b,Ba84a,Ba85,Ku85,Go83]
indicate that our model is representative of typical IGBTs.
The dependence on xH of both AI and I(t) is consistent with
corresponding measurements. The dependence on JNg has not
been studied experimentally, but is, we believe, depicted
faithfully. The predicted AI increases with increasing
Jnq, for Iq held constant, because 8 decreases. For the
same reason, AI increases with increasing xH, but the
dependence is not unrelated to the value of JnQ, and the
change is not simply equal to IM0S (=Iq/3) as implied in
previous work [Ba85,Ku85].
The I(t) dependence also may be more complex than
previously indicated [Ba84a,Ba85,Ku85]. Whereas the time
13 2
dependence predicted for Jnq=2X10 A/cm is nearly
exponential [ exp(t/xH)], indicating that the second term
in the denominator of (319) is unimportant, the predicted
transients become supraexponential as Jnq increases. This
dependence of course is related to xH, becoming significant
as xH decreases. For xR sufficiently short, and/or for Jnq
sufficiently small, I(t) is exponential and Tq is defined
directly by xH.
60
26
observations are consistent with (214) and (224), which
imply
+
qvPn (228)
J = (b+l)JpQexp(j^i)
for high J.
+
The difference between the I(vPn ) and I(VA) curves in
region III is
(229)
The approximation (229) follows from (22) since
AEpA=AEFÂ£, i.e., n(0)~n(W), for high J as discussed
previously. The two I(VA) characteristics in Figure 23
are thus described in essence by (227), except for very
high J where is influenced by carriercarrier scattering
[Gh77] and bandband Auger recombination [Gh77].
Carriercarrier scattering reduces the hole and electron
mobilities, which tends to increase as indicated in
(227). Auger recombination reduces the carrier lifetime,
which tends to decrease in (222) and hence also increase
11
device. We
are interested in
the steady
state
cur rentvoItage
characteristic of
the GDS with
the
gate
floating; the
gate can therefore
be ignored
in
the
onedimensional
model.
In our development of the physical model, we use the
quasiFermi levels to link the anodecathode terminal
conditions to the internal device physics. This approach
facilitates physical insight into the operation of the
device, especially with regard to how changes in excitation
(carrier injection) at the cathode affect the excitation
and recombination current at the anode. The energyband
diagram for a forwardbiased GDS is shown in Figure 22.
It implies how the applied anodecathode voltage defines
the hole and electron quasiFermi levels, EFp and EFn, and
hence the carrier density and electric field in the device.
The applied voltage (V^>0) equals the sum of the
internal voltage drops:
V. = VP P + v?11 + V + v!JP + Vpn (21)
A J J It J J
+
where Vp p is the drop across the highlow junction in the
anode, which is virtually zero because the p shield is
doped high enough to prevent highinjection for all normal
operating conditions; Vpn; is the drop across the pn
39
4 2
GDS (W~2Q0/vm, A~10 cm ) can be reduced to <1052 by
12 2
decreasing Jnq and Jpg to <10 A/cm and increasing Tq to
~50 /usec.
2.5 Summary
A onedimensional, regional model for the forward
currentvoltage characteristic of the GDS, as described in
Section 2.1, has been presented and supported
experimentally. It requires generally numerical evaluation
of the analytic expressions, although for high currents it
can be simplified to avoid the numerical characterization.
The model yields expressions for the dc and incremental
resistance of the GDS at high currents, which show for the
GDS test structures used (W>3LA) that the RDC and RQN have
2 2
W dependence, that the slope of the R^ vs. W curve
2
should be onehalf of the slope of the RDC vs. W curve,
2
and that the extrapolated intercept of the RQN vs. W
C A
curve should yield the series contact resistance (Rg+Rg).
In addition to the familiar parametric dependences, the
resistances were shown to decrease with increasing carrier
lifetime in the ji region and with decreasing saturation
current desities for both the cathode and the anode.
83
is low to provide high voltage blocking. A forward bias of
approximately 0.6 V is required to produce high injection
and conductivity modulation, which lowers the resistance of
the epi region. Our model equations are valid only in this
region of operation; for lowinjection conditions, I is in
the milliamprange and is well below any current of
practical concern. No attempt has been made to model the
reverseblocking mode of operation, where VAK<0. The
methodology is flexible and this region of operation could
be modeled by including UDCSs, or modifying existing ones
to account for the leakage (generation) current associated
with the reversebiased emitter junctions of the npn and
pnp BJTs. In this extension, the effects of an n+ buffer
layer at the anode, modeled for the GDS in Chapter 2, would
have to be included.
To exemplify transient IGBT simulations, we use the
representative gatedrive circuit [Ba84c] shown in Figure
44. The diode isolates the pulse generator during
turnoff transients. The impedance Z repesents a load on
the IGBT, which typically is resistive, inductive, or a
combination of both. The resistor R_ provides a path to
discharge the gatetocathode capacitance; it influences
the turnoff characteristic by limiting the rate of change
of VGK, and hence limits the rate of change of the anode
current,
A'
If R_ is sufficiently small (109), then
depending on the steadystate value of 1^,
the IGBT may
87
Figure 46. IGBT anode current, DMOST drain current,
and gatecathode voltage versus time from
simulation of turnoff transient defined
in Figure 44 with resistive load Z = 35
SJ and Rqk = 5 ffi (th = 0.8 //s, JN0 = I0"12
A/cm2) .
47
t
Figure 32. Typical IGBT turnoff transient showing
two distinct phases.
16
The carrier transport (drift, diffusion, and
recombination) in the 11 region is defined by the ambipolar
transport equation [Ha52,He68]
(27)
where
(28)
In writing (27), we have assumed, in addition to high
injection (p=n), that the electron and hole mobilities,
u and u are constant, and that the electron and hole
n n
(SHR) recombination times are equal (to Tq) and constant.
Effects of carriercarrier scattering [Gh77] and bandband
Auger recombination [Gh77], which tend to invalidate these
assumptions, will be discussed later.
The highinjection assumption, which requires that Tq
be long enough to avoid spacechargelimited flow [Ba70],
is not restrictive with regard to modeling RDC and r0n
defined for the GDS at relatively
for typical values of Tq ensure
The boundary conditions for (27)
These resistances are
high values of J, which
highinjection levels.
98
such that the circuit simulator derives the solution to the
implicit nonlinear system of equations. In Chapter 4, the
implementation required the implicit system of model
equations to be solved by a FORTRAN algorithm accessed by
the SPICE nodal analysis, and consequently the implemented
SPICE model was computationly inefficient. The new
implementation presented in this chapter, although not as
flexible as that of Chapter 4, is nearly twenty times
faster.
We describe in this chapter the development of new
models for HV/P devices, in particular for lateral IGBT
[Da84,Pa86,Mc87,Si85] structures which are representative
of the HV/P devices in power ICs. The models are physical,
yet are implemented in SPICE, as we describe, through
flexible techniques which do not require sacrificing
physics through excessive empiricism. Thus the models can
be used to aid optimal device (process) design as well as
for CAD of HV/P ICs.
In the application of the modeling methodolgy to the
LIGBT, the device is regionally partitioned into three
onedimensional bipolar transistors (BJTs) coupled to the
DMOS transistor, yielding a quasitwodimensional model for
the LIGBT. The consistuent device structures are
reresented by physical chargebased models in which
currents and charges are related to junction voltages
implicitly by sets of equations derived by solving the
C THIS SUBROUTINE CALCULATES THE VOLTAGE DROP DUE
C TO CONDUCTIVITY MODULATION IN THE BASE REGION
C AS A FUNCTION OF THE NODE VOLTAGES VBE AND VBC
C THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR
C DETAILS IN USING THIS SUBROUTINE IN A UDCS CIRCUIT
C FILE
SUBROUTINE IVEPTKY IFLAG,LP,NP,LC,NC, JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND,NI,JNO,I El,LA
SPECIAL COMMON BLANK
COHMON/BLANK/X (S4 )
GOTOC 50,100*200,300),IFLAG+2
50 CONTINUE
IF(NC.NE.2) JERROR 99010
GOTO 99910
100 CONTINUE
PHI.S
ES1.035E12
NI1.3E10
UN1330.0
UPA80.0
BUN/UP
VT.02586
Q1.6E19
DA 2*VT*UN*UP/(UN+UP)
C
WBXCLP+1)
TO XC LP+2)
JNO XCLP+3)
NDXCLP+4)
AE1 X(LP+5)
H XCLP+G)
XX1XCLP+7)
XX2X(LP+B)
XX3X(LP+9)
VBE X(LC+1)
VBC X(LC+2)
TH2*T0
LA SQRT(DA*TH)
C
C CONVERGENCE ENHANCEMENT
lF(VBE.GT.O.eO)THEN
VBEVT*LOG (VBE/VT )
END IF
IF(VBE.LT.0.53)THEN
FLGY 0.0
P0NI**2*EXP(VBE/VT)/ND
Y 0.0
GOTO 987
END IF
IF((VBE.8T.0.55).AND.(VBE.LT.0.80))
P0NI**2/ND*EXP(VBE/VT)
END IF
FLGY 2.0
CALCULATE W THE ACTIVE BASE WIDTH AND
CALCULATE XS, THE POINT AT WHICH P(X)ND
W WB (2*ES*(PHI+ABS(VBC))/(ND*Q))** .5
ZZ ND/PO*SINH(W/LA)
XSWLA*LOG(ZZ + SORT(ZZ**2+1))
SET Y VALUE OF VEPI
IE1(B+1)/B*(AE1*JNO*PO**2/NI**2+0*DA*AE1*PO/LA/TANH(W/LA))
VDEMVT*(B1)/(B+1)*LOG(PO/ND)
VEPI VDEMSINH(W/LA)*I El*LA/AEl/Q/( UN+UP)/PO*
8L0G(TANH( (WXS)/LA)/TANH(W/LA) )
Y VEPI
987 CONTINUE
GOTO 99910
200 CONTINUE
C
C SET Y VALUE OF DVEP/DVBE
c
IFCFLGY.LT. l.OUHEN
Y 0.0
GOTO 876
END IF
IFLG1
567 CONTINUE
C
C CALCULATE W THE ACTIVE BASE WIDTH AND
C CALCULATE XS, THE POINT AT WHICH PCXJND
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
ZZ ND/P0*SINH(W/LA)
XSWLA*LOG(ZZ + SQRT(ZZ**2+1))
C
C SET Z VALUE OF VEPI .
C
IE1(B+1)/B*(AE1*JNO*PO**2/NI**2+0*DA*AE1*PO/LA/TANH(W/LA) )
VDEMVT*CB1)/< B+l)*LOGC PO/ND)
VEPI VDEMSINH ( W/LA) I E1*LA/AE1/Q/ ( UN+UP ) /PO*
SLOGCTANHC (WXS)/LA)/TANH(W/LA) )
Z2VEPI
IFCIFLG.EO.DTHEN
ZlVEPI
VBEVBE+H
IFLG2
GOTO 567
END IF
VBEVBEH
YCZ2ZD/H
876 CONTINUE
GOTO 99910
300 CONTINUE
C
C SET Y VALUE OF DVEP/DVBC
C
IFCFLGY.LT.1.0)THEN
Y 0.0
GOTO 765
END IF
IFLG1
789 CONTINUE
C
C CALCULATE W THE ACTIVE BASE WIDTH AND
C CALCULATE XS, THE POINT AT WHICH PCXIND
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
ZZ ND/PO*SINHCW/LA)
XSHJLA*LOGCZZ + SQRTCZZ**2+1) )
C
C SET Z VALUE OF VEPI
44
optimal device design. In this chapter we develop a
quasistatic chargecontrol (analytic) description of the
transient turnoff characteristic, which is physically
insightful and which suggests device design criteria for
shortening the turnoff time, without increasing RQN
considerably.
The chargecontrol model we develop is similar to one
previously developed Kuo et al. [Ku85], but does not
involve the assumptions and approximations implicit in Kuo
et al. [Ku85] that limit the validity of the model and in
fact result in misconceptions concerning the physics
underlying the turnoff transient. In particular, the
effects of the expanding depletion region at the cathode
and of minoritycarrier injection into the anode, which are
not currently accounted for in [Ku85], nor in earlier work
[Ba84a], are represented in our model.
3.2 Model
The basic (unitcell) structure of the (nchannel)
IGBT, shown in Figure 31, comprises a DMOS FET merged with
a BJT. The components of current, which is
multidimensional, are indicated in the Figure 31 for the
steady onstate (gate voltage VG sufficiently positive to
induce an nchannel between the the n+ cathode an the n~
epi region, and the anodecathode voltage V>0). The
MOSFET channel (electron) current IMOs suPPorts carrier
recombination in the BJT
99
pertinent ambipolar transport problems. Charging currents
in the transient model are represented by timederivatives
of the quasistatic charges, which implicitly (without
capacitors) account for charge conservation and
nonreciprocal transcapacitance.
The models are implemented in SPICE via userdefined
controlled sources (UDCSs), which are FORTRAN subroutines
accessed by the SPICE nodal analysis. The UDCSs define the
systems of model equations, which are analytic but must be
solved simultaineously and hence numerically. The solution
of the equations is derived by the nodal analysis.
The LIGBT model and the methodology are supported by
measurements of specially designed test structures, which
also support the model parameter extraction. This
verification is facilitated by twodimensional numerical
device simulations with PISCES [Pi84] that provide needed
physical insight regarding, for example, currentcrowding
effects, and imply how the partitioning of the LIGBT should
be done to effectively account for coupling among the
constituent devices. The test devices are lateral
structures designed to allow experimental access to
different regions of the LIGBT, for different modes of
operation, i.e., as a DMOS transistor, as an IGBT, or as a
"hybrid LIGT/DMOST" (HIGBT) [Si85,Fo87] with the anode
terminal shorted to the DMOST drain. This latter mode of
operation depends on an internal voltage drop to
APPENDIX B
UDCS/SLICE/SPICE MODEL IMPLEMENTATION
In this appendix we briefly overview a representative
UDCS SLICE/SPICE implementation of a chargebased network
representation for a widebase, low3 pnp BJT, as depicted
in Figure 52.
The general theory and mechanical details behind the
implementation of steadystate UDCS network models into
SLICE/SPICE can be found in the SLICE Manual Rev. 4.08
[Ha84]. The general theory behind the implementation of
transient UDCS network models in SLICE is discussed in
Veeraraghavan et al. [Ve86].
The implicit nature of the network model and the novel
use of numerical derivatives (finite differences) for the
transconductances and transcapacitances are delineated via
comment statements in the following FORTRAN code listing,
which details each UDCS subroutine for the BJT model shown
in Figure 52.
142
43
Rqn can be effected by controlling the carrier
(recombination) lifetime in the n drift (epitaxial) region
[Ba84a]. The device retains the highinputimpedance gate
of the MOSFET, and has the added advantage of
reverseblocking capability.
The IGBT structure does, however, contain a parasitic
pnpn thyristor that can latchup at high currents and
thereby negate the gate control. Below the latchup
current, the steadystate currentvoltage characteristic
(in the onstate) is defined by the DMOS, in series with
the underlying (fowardbiased) pn junction and in parallel
with the parasitic vertical pnp bipolarjunction transistor
(BJT). That is, the anodecathode current comprises the
DMOS channel current, which supplies electrons that
recombine in accord with with the properties of the forward
biased pn junction, and the BJT collector current, which
results from holes injected from the underlying
(emitterbase) junction.
The electrical coupling between the constituent MOSFET
and BJT in the basic IGBT structure results in a unique
transient turnoff characteristic [Ru83,Ba84b,
Ba84a,Ba85,Ku85] comprising an initial rapid drop in
forward current, followed by a slower decay. Previous
analyses [Ru83,Ba84b,Ba84a,Ba85,Ku85] of this
characteristic are either qualitative or incomplete, and do
not adequately reflect the underlying physics to facilitate
123
Figure 58. Modelsimulated and measured LIGBT anode
current versus time for a resistive load
of 300 52 and offstate voltage of 4.5 V.
The gate voltage of 10 V falls to zero in
200 ns.
A METHODOLOGY FOR PHYSICAL MODELING OF
HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICES
FOR CIRCUIT SIMULATION
By
ROBERT JAMES MCDONALD
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1987
it is a tale told by an idiot,
full of sound and fury,
signifying nothing.
Shakespeare
ACKNOWLEDGEMENTS
The support of the IEC at the University of Florida,
the NSF, and the SRC is acknowledged.
The technical guidance of Dr. M. A. Shibib of AT&T
Bell Laboratories in designing and fabricating the special
test structures used in this dissertation is appreciated.
His participation on the qualifying exam and on the final
defense also merits a note of gratitude.
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
ABSTRACT vi
CHAPTERS
1 INTRODUCTION ..1
2 A PHYSICAL MODEL FOR THE CONDUCTANCE
OF LATERAL p pnpn STRUCTURES FOR HVICs ...7
2.1 Introduction 7
2.2 Model Development 9
2.3 Physical Insight (Simplified Model) 20
2.4 Experimental Corroboration and Discussion 27
2.5 Summary 39
3 CHARGECONTROL ANALYSIS OF THE IGBT
TURNOFF TRANSIENT 4 0
3.1 Introduction 40
3.2 Model 44
3.3 Discussion. 58
4 HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICE
MODELINGA FIRST APPROACH 64
4.1 Introduction 64
4.2 Modeling Methodology 67
4.3 SPICE Simulations and Discussion 81
4.4 Summa ry 9 5
5 HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICE
MODELING 97
5.1 Introduction 97
5.2 Modeling Methodology 100
5.3 Application/Demonstration .109
5.4 Simulation/Verification 121
5.5 Summary
6 SUMMARY AND CONCLUSIONS WITH RECOMMENDATIONS ..134
iv
6.1 Summary and Conclusions 134
6.2 Recommendations 136
APPENDICES
A HIGH CURRENT CARRIER TRANSPORT IN WIDEBASE BJTs 139
B UDCS/S LICE/S PICE MODEL IMPLEMENTATION 142
REFERENCES 152
BIOGRAPHICAL SKETCH 158
v
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A METHODOLOGY FOR PHYSICAL MODELING OF
HIGHVOLTAGE/POWER INTEGRATEDCIRCUIT DEVICES
FOR CIRCUIT SIMULATION
By
ROBERT JAMES MCDONALD
December 1987
Chairman: Dr. J.G. Fossum
Major Department: Electrical Engineering
This dissertation presents a modeling methodology for
the construction of physical network representations for
highvoltage/power integratedcircuit (HV/P IC) devices.
The effects of multidimensional carrier flow, baseregion
conductivity modulation, significant emitter recombination,
nonreciprocal transcapacitance, and the onset of latchup
(static and dynamic), heretofore unaccounted for in
empirical circuit models, are physically accounted for in
our chargebased formalism. The methodology is applied to
vi
a representative HV/P IC device, the LIGBT, and the derived
model is implemented in SPICE via userdefined controlled
sources (UDCSs).
The methodology is supported by rigorous theoretical
analyses of several HV/P IC devices, twodimensional
numerical device simulations with PISCES, and experimental
results obtained from specially fabricated test structures.
The resulting physical network representations, in addition
to the CAD ability they afford, will facilitate optimal
device (process) design under an actual circuit (transient)
environment, a capability that most device simulators do
not have.
vi 1
CHAPTER 1
INTRODUCTION
The field of highvoltage and power integrated
circuits is a rapidly emerging and expanding technology.
Three basic processing efforts have made highvoltage/power
(HV/P) devices practical for circuit integration: one, the
advent of a lateral, doublediffused MOS (DMOS) process
[De86], which produced integrated highspeed, highvoltage
display drivers; two, improved isolation techniques, such
as dielectric isolation [Be85, Sh80] and field reduction
techniques such as RESURF [Ap79], which reduced parasitic
interactions and provided higher breakdown voltages; three,
the functional integration of bipolar and MOS devices
[Ru83], which dramatically lowered device onresistance and
consequently increased the power handling capability of
HV/P integrated circuits (ICs), while maintaining the
advantages of the MOS gate. However, although great
strides in the process technology of HV/P ICs have taken
place, the area of circuit modeling for
computeraideddesign (CAD) of HV/P ICs, especially for
1
2
those ICs employing MOScontrolled bipolar devices, has
been at a near standstill. Common highinjection effects,
such as conductivity modulation and enhanced back
injection, are not properly accounted for in existing,
empirical circuit models for HV/P devices [Pa86].
Furthermore, these models vitually ignore multidimensional
carrier flow, which is typical in integrated HV/P devices.
Thus, there exists a need for developing new physically
based models for HV/P devices and implementing these models
in a circuit simulator, e.g., SPICE [Na75],
This dissertation is concerned with the development
and implementation of network representations for a general
class of merged MOScontrolled bipolar structures, e.g.,
the lateral insulatedgate bipolar transistor (LIGBT)
[Da84, Si85], The major contributions made in this work
are as follows:
(1) the general formulation and solution of the
steadystate transport problem for the
basic p+pnpn+ structure, in terms
of quasiFermi level potentials, explicitly
showing the effect of the p punchthrough
shield on the transport problem;
(2) the physical (chargecontrol) characterization of
the IGBT turnoff transient, clearly identifying
the device parameters controlling the important
charging mechanisms;
3
(3) the development and experimental verification
of a physical (chargebased) methodology for
modeling HV/P IC structures including the
effects of multidimensional carrier flow,
baseregion conductivity modulation, and
enhanced back injection;
(4) the implementation of the LIGBT model into SPICE
through userdefined controlled sources (UDCSs)
with implicit characterizations and numerical
representations for transconductances and
transcapacitanees.
In Chapter 2, we develop analytic models for the
steadystate forward currentvoltage characteristic of a
(p+pnpn+) gateddiode switch (GDS) [We82]. The models,
which apply generally to gated bipolar switches, are based
on a system of equations derived from basic pindiode
theory. They provide physical insight into GDS operation
and suggest optimal design criteria to minimize the dc and
incremental resistances at high currents. Measured data
taken from a variety of GDS test structures are discussed
in support of the models.
In Chapter 3, a quasistatic chargecontrol analysis
of the unique transient turnoff characteristic of the IGBT
[Be85] is developed. The analysis describes the transient
behavior in terms of steadyonstate current components
that flow in the constituent MOSFET and BJT in the basic
4
IGBT structure. The effects of the expanding depletion
region at the cathode and of minoritycarrier injection
into the anode are properly accounted for. Consequently
the physics underlying the turnoff time is clarified, and
device design criteria for shortening it, without
considerably degrading the onstate current conduction
capability, are suggested.
In Chapter 4, a novel methodology for flexible SPICE
implementation of physical models for HV/P devices,
accounting for their unique characteristics, is presented
and demonstrated. The implementation is achieved, without
having to modify the simulator code, by utilizing UDCSs
that reference a subroutine which defines, not necessarily
in explicit form, the system of model equations. The
simultaneous solution of the equations, which describes the
integrated charges in the device and the quasistatic
terminal currents in terms of the terminal voltages, is
effected by the SPICE2 nodel analysis. The methodolgy is
exemplified by modeling a particular highvoltage device,
the IGBT, in which conductivity modulation and latchup are
accounted for. SPICE simulations of dc and transient
characteritics of IGBT switching circuits are discussed and
shown to be representative of measurements. The
flexibility of the modeling methodolgy for HV/P IC CAD is
demonstrated by simulating effects of both static and
dymanic latchup in the merged bipolar/MOS structure of the
IGBT.
5
In Chapter 5, to enable CAD of power integrated
circuits, new physical models for lateral HV/P devices, in
particular LIGBT [Da84, Si85, Mu87] structures, are
developed and implemented in SPICE. The models are
chargebased, and, via regional partitioning, account for
the unique features of HV/P devices unaccounted for in
conventional equivalentcircuit models. The implementation
of the models in the circuit simulator is flexible and
allows these features (e.g., multidimensional carrier flow,
conductivity modulation, latchup, transcapacitance) to be
simulated without having to sacrifice much physics through
excessive empiricism. Device measurements of specially
designed test structures, supplemented with twodimensional
numerical device simulations, support the modeling
methodology and the model parameter extraction.
We summarize, in Chapter 6, the main conclusions and
accomplishments of this dissertation. We also suggest
ideas and avenues for future research.
In Appendix A, we briefly describe highcurrent
carrier transport in widebase transistor structures. The
resulting simplified model predicts a fundamental
difference for the highcurrent 8s of pnp and npn
transistors. The physical insight afforded by the
simplified analysis will be useful for device engineers
designing complementary iGBTs.
6
In Appendix B, we briefly overview a representative
UDCS SLICE/SPICE implementation of a chargebased network
representation for a widebase, low3 pnp bipolar
transistor, a key model in the methodology for modeling
HV/P devices as dicussed in Chapter 5.
CHAPTER 2
A PHYSICAL MODEL FOR THE CONDUCTANCE
OF LATERAL p pixpn STRUCTURES FOR HVICs
2.1 Introduction
This chapter concerns the forward, steadystate
currentvoltage characteristics I(VA) f a P+P^Pn+
structure, the GDS [We82,Ha81], used in HVICs. We develop
an analytic model for I(VA) based on a onedimensional
regional representation of the device. The model yields
physical descriptions of RQN(=AVA/AI) and the dc resistance
Rdc(=Va/I) at high operating currents where these
resistances must be minimized to ensure efficient GDS
operation [Sm82]. Such minimization is aided by the model,
which clearly identifies the underlying physical mechanisms
and the associated parameters.
The resulting model also has applications to other
HV/P IC devices employing punchthrough shields (aka buffer
regions) for which the development of effective and
efficient network models for circuit simulation is of
primary interest. In addition, the proper modeling of the
7
8
anode and cathode recombination, when highinjection
obtains in the low dopedbase region, provides the impetus
for developing a new BJT model as derived in Chapters 4 and
5 and highlighted in Appendix A.
The gated diode switch (GDS), illustrated in Figure
21, is a dielectrically isolated highvoltage integrated
circuit silicon device used in monolithic crosspoint arrays
applicable to telephone switching networks. The device is
basically a PlNdiode with an n+ gate in the i(n) region
and p shields surrounding the p+ anode and the n+ cathode.
The n gate facilitates the turnoff of the switch, but
does not affect the forward bias (ON) characteristics,
which closely resemble those of a PINdiode at highcurrent
levels. The cathode shield prevents punchthrough between
the gate and the cathode in the offstate, and has been
shown to limit the injection of electrons into the n region
and hence increases the incremental onresistence of the
device [Sm82]. The "anode shield" facilitates a reliable
contact to the anode, but does not provide any electrical
benefit.
Our onedimensional analytic model, which can be
applied generally to gated bipolar switches, and hence has
application to HV/P ICs, is based on a system of equations
derived from previously developed PINdiode theory
[Ha52,He68,Fl57,Be79] for highinjection conditions. The
equations are solved numerically to yield the desired I(VA)
9
characteristic. The model is more useful as an
engineeringdesign aid than is a direct numerical solution
of the fundamental carrier transport equations [Sm82]
because it is simpler and because it affords physical
insight. The role of the cathode pshield, as well as
those of the n+ cathode, the p+ anode, and the ji region, in
defining I(V^) is clearly described by the model, thereby
aiding optimal GDS design.
The physical insight provided is utilized to develop
an even simpler model, valid for high currents at which RQN
and RDc are of interest, that requires no recourse to
numerical techniques. This model, although not as accurate
as the other, is useful because it enables quick
assessments of possible device design modifications not
only for the GDS, but also, as shown in Appendix A, for the
BJT portion of the LIGBT. The models are supported by
measured data taken from a variety of GDS structures
fabricated at Bell Laboratories (Reading).
2.2 Model Development
The structure of the GDS, fabricated in a "tub" of
dielectrically isolated (DI) silicon, is illustrated in
Figure 21. Because the (anodecathode) length is
typically much longer than the tub thickness, the
onedimensional p+pnpn+ model, also shown in Figure 21,
for the GDS is representative of the basic operation of the
10
Anode Gate Cathode
Figure 21. Gateddiode switch (GDS) cross section and
corresponding onedimensional model.
11
device. We
are interested in
the steady
state
cur rentvoItage
characteristic of
the GDS with
the
gate
floating; the
gate can therefore
be ignored
in
the
onedimensional
model.
In our development of the physical model, we use the
quasiFermi levels to link the anodecathode terminal
conditions to the internal device physics. This approach
facilitates physical insight into the operation of the
device, especially with regard to how changes in excitation
(carrier injection) at the cathode affect the excitation
and recombination current at the anode. The energyband
diagram for a forwardbiased GDS is shown in Figure 22.
It implies how the applied anodecathode voltage defines
the hole and electron quasiFermi levels, EFp and EFn, and
hence the carrier density and electric field in the device.
The applied voltage (V^>0) equals the sum of the
internal voltage drops:
V. = VP P + v?11 + V + v!JP + Vpn (21)
A J J It J J
+
where Vp p is the drop across the highlow junction in the
anode, which is virtually zero because the p shield is
doped high enough to prevent highinjection for all normal
operating conditions; Vpn; is the drop across the pn
pasexqpjBAVJOj
' sao
e jog uieaBeip pueqA6jaua
'Z~Z
M 0
Zl
13
junction
nea
r the
anode;
V is
n
the
drop
region;
vnp
J
is
the dr<
op across
the
np j
cathode;
and
vpn
J
i s the
drop acri
oss the p
junction,
Ref ei
rring
to Figure
22
highinj
?cti
on (p:
=n>>N
An
) where NAji is
the
density)
in
the it
region
, we have
then
from
across the n
unction near the
shieldcathode
and assuming
acceptor doping
(21)
qVA
+ AEFn + ^Vn
(22)
where AEpA and AEFC are the EFnEFp separations at the pn
and np junctions respectively, and AEfn is the change in
EFn across the p shield at the cathode. We assume that the
majorityhole quasiFermi level is virtually flat across
the p shield, in which the injection level is low; thus
qVpn =AEFn+AEFC. In deriving (22) we used the
quasiequilibrium relations qVpn; = AEFA/2( kT ) In( NAjl/n^ ) and
qvJP=AEFC/2+(kT)ln(NAn/n.).
Hence for a given GDS current density J, AEFA, ^efc'
AEFn, and must be determined before (22) can be used to
give the desired J(VA) characteristic. These
determinations are made by incorporating into basic
PINdiode theory a model for carrier transport in the p
shield, which reduces the injection of electrons into the n
region.
14
To account for the effect of the shield, i.e., to
define AEfn, we neglect recombination in the shield, which
is typically much less than the carrier fluxes through the
shield. Then AE^ can be related to the electron current
Fn
c
density JN flowing in the shield, which constitues part of
the total current density J described by basic PINdiode
theory.
For simplicity, we assume an (effective) uniformly
doped shield. Since the shieldcathode junction is in low
g
injection, the uniformdoping assumption implies that JN is
diffusion current, which is nearly constant:
N
_ An
q nws
qD n?
M n i
naws
AE
exp(
FC w ,
Â£y~)[exp(
AE
Fn
kT
) 1]
(23)
where Dr is the (average) electron diffusion coefficient in
the shield, NA is the (~ peak) doping density, and Wg is
the (effective) width of the shield. From (23),
AE
FC
AE
Fn
4
kT In 1 +
JN FsexP( kf>
kTn?
i
(24)
where
A kAWS
S qDn
(25)
15
is a shield factor that can be used to relate AE_ to the
Fn
actual properties of the (diffused or implanted) p shield.
To relate Fg to an actual p shield in which NA varies,
note that generally
dx
(26)
S
N J D
n
(shield)
and that n(x)1/NA(x). Since the greatest contribution to
the integral in (26) comes from the region of the shield
where N (x) is a maximum (and D (x) a minimum), F in (25)
n q
can be evaluated for this region, the width W of which can
O
be estimated from the actual NA(x).
We now incorporate (24) into basic PINdiode theory
to characterize the conduction properties of the GDS. This
involves generating a system of equations, the simultaneous
solution of which for a specified J yields AEFn, AE ,
AEfc, V VA* The resulting J(VA) characteristic, with the
crosssectional area A (I=JA), then defines RDC and RQN
We note, based on results of calculations discussed in
Section 2.4, that typically AEFn~kT, which means that the
shield reduces considerably the carrier injection level in
the ji region
R
'ON*
near the cathode and hence increases R
and
16
The carrier transport (drift, diffusion, and
recombination) in the 11 region is defined by the ambipolar
transport equation [Ha52,He68]
(27)
where
(28)
In writing (27), we have assumed, in addition to high
injection (p=n), that the electron and hole mobilities,
u and u are constant, and that the electron and hole
n n
(SHR) recombination times are equal (to Tq) and constant.
Effects of carriercarrier scattering [Gh77] and bandband
Auger recombination [Gh77], which tend to invalidate these
assumptions, will be discussed later.
The highinjection assumption, which requires that Tq
be long enough to avoid spacechargelimited flow [Ba70],
is not restrictive with regard to modeling RDC and r0n
defined for the GDS at relatively
for typical values of Tq ensure
The boundary conditions for (27)
These resistances are
high values of J, which
highinjection levels.
17
are thus simplified to
P(0)
aefa
n(0) = niexp(2k^) (29)
and
P(W)
aefc
n(W) niexp(y^) (210)
where x=0 and x=W denote the anode and cathode ends of the
ti region, the length of which is W (see Figure 21). The
solution to (27) is then
p(x)
n(0)sinh(WLx) + n(W)sinh(Lx)
= n(x) Aw A (2 11)
sinh(ip)
la
This
solution is coupled to the carrier transport in
the anode and cathode by defining the minoritycarrier
recombination currents in those regions. In the p+p anode,
this current, which can be expressed as [Fo81]
ii
< a
a
AE (212)
JN0eXP( kT >
(212)
18
is supported by electron injection from the it region:
 vo)
5TT J +
2kT"n"p
"n+"p
dn
Hi
x=0
(213)
where bAThe expression for JN(0) in (213)
which is evaluated using (211), derives [F157]
J=JN+Jp with p=n. In the n+ cathode, the
recombination current can be expressed as [Fo81]
from
hole
JP JP0
exp(AEFC+AEFn)
if
(214)
and is supported by hole injection from the n region
[Fl57 ] :
Jp Vw) ETT
J 
2kTVp
"n^p
dn
Hi
x=W
(215)
In (212) and (214), Jnq and JpQ are constant
parameters (saturation current densities) that are defined
by the properties of the heavily doped anode and cathode
[Fo81].
19
Combining (24) with (212)(215), we obtain the
following system of three equations in the three unknowns,
AE
FA'
AE
FC'
AE
Fn'
JN0exp(n^)=BTrJ+e[exP(2T^Â£)exP(2i^)cosh(r) ]'
A
(216)
^FC+^Fn 5 ^^FC ^^FA W
Jp0exp( ^ )=BbTj + p[eXp(21~)exp(7j^)cosh(i)],
A
(217)
where
AE AE F
AEpn=kTln{l+[Jexp( ^(^oexpljS)] Sj) (218)
k Tn
i
3=2kTn./7 u /L. (Â¡j +/j )sinh(W/L.). To solve the system,
i n p a n p A
we must specify Jpg JNg, W' T0' ant^ FS" Then for a given
J, a suitable numerical method must be used to derive AEpA,
AE_, AE^ We have used an IMSL subroutine to solve the
system with a high degree of accuracy. From the solution
A C
n(x), JK and JN are determined.
20
To generate the
determine V which
across the it region.
[Ha52,He68], we have
J(VA) characteristic, we must now
is the integral of the electric field
Again using basic PINdiode theory
V_ =
9
w
I
0
dx
n (x)
, b1, kT
5+T ~q
, r n(0 ) 1
1 'lwT1
(219)
The integration in (219) can be done analytically. Thus
the combination of (219) with (29) and (210) defines,
for a given J, V Our characterization of J(V ) is then
It
given by (21), (216)(218 ) and (19), the solution of
which must be obtained numerically. Representative results
will be presented in Section 2.4.
2.3 Physical Insight (Simplified Model)
A numerical solution to the system of equations
described in Section 2.2 is not necessary to gain useful
physical insight into the GDS operation. In this section
we describe this insight, and in doing so define a simpler
analytic model for J(VA) that is valid for high values of J
2
(1001000 A/cm ) of practical concern.
The total current J is the sum of the recombination
currents in the p+p anode, it, and n+ cathode regions
21
[He68]:
(220)
From (29), (210), (212), and (214), we see that JNA and
C 2 2
Jp are proportional to [n(0)] and [n(W)] respectively.
In contrast, using (211) we see that
(221)
where
(222)
is an average carrier density in the ji region. Thus as J
increases, a larger portion of the current is supported by
recombination in the anode and cathode regions; becomes
negligible. Furthermore, since dn/dx H, as can be seen
by differentiating (211), the diffusion current in the n
region becomes negligible as J increases [He68]; the holes
and electrons predominantly drift across the n region.
22
Therefore for sufficiently high J, (213) and (215)
can be simplified [He68] to
(223)
and
(224)
These simplifications can be easily checked for
selfconsistency with presumed high values of J using the
model in Section 2.2. In fact it can be shown that for a
given J, (223) and (224), with (212) and (214), yield
valid approximations for AE. and ( AE+AE_.T) even when the
diffusion current in the n region, reflected by the second
terms in (13) and (15), is comparable to the drift current.
The approximation (224) enables an additional
simplification regarding AEFn across the p shield.
Combining (14), (18), and (24) yields
(225)
i
23
Hence for sufficiently high J, AEpn is a constant,
independent of J as well as W and parameters associated
with the anode.
The approximations (223)(225) are insightful. They
imply that for a given high J, the injection level in the n
region near the anode, i.e., n(0), is defined primarily by
Jnq, and that the injection level near the cathode, i.e.,
n(W), is defined primarily by Jp^ and Fg. This means that
V^n is independent of W and the anode parameters, even
A
though JN is a significant component of J.
Consistent with the simplifications in (223)(225)
is the neglect of the second term in the expression (219)
for V^, which is typically ~kT/q. Thus for high J,
W
VE ~ q{fJn+fJ )
r dx
J n( x)
(226)
in which the integral is evaluated using (211). A further
crude approximation can be made by writing (226) as
Vn =
JW
q(VVn
(227
24
where is given by (222). Although not as accurate as
(226), (227) is insightful as we demonstrate later.
We have now defined a simpler analytic model for the
highcurrent J(VA) charactersitic of the GDS. For a given
J, V. is given by (22), in which V is approximated by
(226) or (227), AEpn is approximated by (225), AE^ is
FC
approximated by (214) and (224), and AE?A is approximated
by (212) and (223). We discuss the accuracy of this
model in Section 2.4.
Using the insight accompanying the development of this
model, we now offer a qualitative explanation of the
complete currentvoltage characteristic of the GDS.
Typical measured characteristics are shown in Figure 23.
The data were taken from a GDS test structure having two
anodes placed at different lengths from the cathode.
+
Figure 23 includes plots of I(yPn ) as well as I(V ) for
J +
both anodes. Note that the I(V^n ) characeristics are
virtually coincident.
To explain the characeristics, we consider three
distinct regions of the curves as indicated in Figure 23.
Our models are applicable in region III where
highinjection obtains in the ti region. We note in this
4
region that Iexp(qV^n /kT) except for very high I where
series resistance in the cathode (=352) causes the
+
characteristic to bend.
Further, the I(V^n )
characteristics appears to be independent of W. These
I (A)
25
Figure 23. Measured GDS current versus applied voltage
(VA) and shieldcathod voltage drop (V^" )
for two different nregion lengths
and W2). Three distinct regions
(I,II,III) of operation are indicated.
26
observations are consistent with (214) and (224), which
imply
+
qvPn (228)
J = (b+l)JpQexp(j^i)
for high J.
+
The difference between the I(vPn ) and I(VA) curves in
region III is
(229)
The approximation (229) follows from (22) since
AEpA=AEFÂ£, i.e., n(0)~n(W), for high J as discussed
previously. The two I(VA) characteristics in Figure 23
are thus described in essence by (227), except for very
high J where is influenced by carriercarrier scattering
[Gh77] and bandband Auger recombination [Gh77].
Carriercarrier scattering reduces the hole and electron
mobilities, which tends to increase as indicated in
(227). Auger recombination reduces the carrier lifetime,
which tends to decrease in (222) and hence also increase
27
In the
lowercurrent
regions
I and II in Figure
23,

the I(vPn )
J
and l(VA)
curves
are coincident and
are
independent
of W. In
region
I, Iaexp(qVA/2kT)
is
predominantly recombination in the shieldcathode junction
spacecharge region. Low injection prevails everywhere,
+
and hence VA=vPn For higher currents, but still low
injection, in region II, J becomes important. However
+
because V 0, still V and J.aexp(qV./2kT) The onset
of high injection in the it region occurs near the
transition point between regions II and III, where still
Vn< Above this point our model applies.
2.4 Experimental Corroboration and Discussion
In this section we present experimental data, taken
from a variety of GDS structures fabricated at Bell
Laboratories (Reading), that support the model described in
Section 2.2. We also use the simpler analytic model
developed in Section 2.3 to qualitatively explain the data.
Finally we discuss model calculations that reveal the
dependences of the currentvoltage characteristic on
critical device and material parameters.
+
Measured I(V^n ) and I(VA) in the highinjection
regime are plotted in Figure 24. The data are taken from
a GDS test structure having four anodes placed at different
lengths from the cathode, two (W=228/vm, 615/ym) of which
correspond to the data plotted. Also plotted in Figure 24
I (A)
28
Figure 24. GDS current versus applied voltage +
(VA) and shieldcathode voltage drop (Vpn )
for two different nregion lengths (W2 J
and ). The solid curves represent
experimental measurements and the points
represent calculations using the
model derived in Section 2.2.
29
are the corresponding predictions yielded by the model in
Section 2.2 through computeraided numerical solution of
the model equations.
The model parameter values used are listed in Table
21. They were initially estimated from knowledge of the
device structure and of typical ranges of their values,
using the insight afforded by the simpler model in Section
2.3, and then altered such that excellent correlation with
the measured data was obtained. Hence the
experimentaltheoretical agreement not only supports the
model, but also provides estimations of the important
device and material parameters. We stress that these
estimations are not a unique set; relatively small
perturbations about these values do not significantly
change the experimentaltheoretical correlation.
The inferred value Tq=10 psec is not significantly
influenced by bandband Auger recombination [Gh77] because
 17 3
n<10 cm as implied by the calculations. However, the
2 2
values p =920cm /Vsec and p =330cm /Vsec are m
n p
effect average values that reflect significant
carriercarrier scattering [Gh77] at the higher currents,
an effect that we have not explicitly accounted for. This
effect could be incorporated into the model if more exact
parameter determinations were desired, but no additional
insight into the operation of the GDS would be gained
[Ch70] .
30
5 2
The area A=5xl0 cm of the onedimensional is merely
an effective representation of the actual threedimensional
geometry. It is reasonable because it is comparable to the
actual cathode and anode areas. The anode area is actually
larger than the cathode area, which implies that Jnq and
JpQ are perhaps more comparable in value than shown in
Table 21.
We now discuss measured and predicted resistances of
the GDS. The dc resistance, RDC=VA/I at I=25mA, is plotted
2
versus W in Figure 25. The fact that both the
experimental and theoretical plots become linear for long W
supports in essence our model. This dependence is
explained as follows. From (22) and (227),
R
W
DC
qA(/n+//p)n
1 ,aefa
ql [ 2
AE
FC
AEW
(230)
where I=25mA. We note the actual RDC differs from (230)
C A
by a constant series resistance, (Rg+Rg), associated with
the anode and cathode.
W>3La,
Using (222), we see that for
DC
W2 1 ,6EFA aEFC
qA(//n+i< )LA[n(0)+n(w) ] ql' 2 2
+AEFn>
(231)
31
200
160
120
a
o
o
ce
80
40
//
/ /
/ /
/ /
/ ^Theoretical
Experimental^ / /
> /
Â¡f
/ /
/ /
/ /
* /
/?
//
L .//
}/
20
40
W2(10*Vm2)
Measured and calculated de resistance
versus the square of the itregion length.
The dashed lines emphasize the linear
dependences.
Figure 25.
32
and that for W<0.3La, the first term in (230) is linear in
W, independent of LA. We note, based on the discussion in
Section 2.3, that the second term in (231), as well as
n(0) and n(W), is virtually independent of W. Thus (231)
correlates well with the plots in Figure 25.
Discrepancies between the two slopes, i.e., in the slopes
and in the extrapolated intercepts, can thus be attributed
to the uncertainties in A, p and p
n p
C A
(carriercarrier scattering), and to the neglect of (R^+R^)
respectively.
Measured and predicted values of the incremental
(quasistatic) resistance, RQN=AVA/AI centered at I=30mA,
2
are plotted versus W in Figure 26. Referring to (2), we
can write
R
ON
AV
AI
(232)
since the quasiFermi level terms vary little relative to
AV^ at high currents. Differentiating (27) then, in which
_2
we note based on Section 2.3 that J=I/An and that for
W>3La, =(La/W)[n(0)+n(W)], we obtain
R ~
ON qA(//n+// )LA[n(0)+n(W) ] '
(233)
33
100
80
60
z
o
ce
40
20
0*
Experimental^/
r
/
/
/
/ /
/
/
/
J jf ^Theoretical
/ /
/ v*
7 /
//
1/
i /
f
Rg+R=60
1 L
20 40
W2 (108j.m2)
J L
Figure 26. Measured and calculated incremental
ONresistance versus the square of the
nregion length. The dashed lines
emphasize the linear dependences. The
determination of the extrinsic series
resistance from the extrapolation of the
experimental data is illustrated.
34
which corresponds well to the plots in Figure 26.
W<0.3L>a, =[ n( 0 )+n(W) ]/2 and
R
ON
W
qA(//n+/Vp) [ n( 0 )+n(W) ]
(234)
As additional support
(231) and (233) imply a
the slopes of the RDC
characteristics, which is
We note further, since (23
that the extrapolation
characteristic yields direc
find (Rg+Rg)=6S2, which i
inferred from the measured
we expect RsRS' this re
for our model. The signif
experimental and theoreti
Figure 26 is due to, as we
explicit accounting of the
carriercarrier scattering.
GDS design criteria
for our theory, we note that
factor of two difference between
2 2
vs. W and R., vs. W
ON
reflected by the measured data.
C A
3) does not account for (Rg+Rg),
of the
measured R_.T vs.
ON
W 2
tly this
series resistance.
We
s about
+
twice the value
of Rg
>
characteristic.
Since
suit provides additional support
icant discrepancy between the
cal values of RQN plotted in
show later, our omission of an
reduction in mobility caused by
to minimize RQC and RQN are
and (234).
suggested by (231), (233)
(212), and (223),
From (29)
35
n ( O ) = n t
r bI i1/2
i A(b+i)JNoJ
(235)
and from (210), (214), and (224)
I
1/2
(236)
n(W)
A( b+1) JpQexp (
where AEpn is constant as given by (225). Thus, reduction
in both Jnq and Jpg would reduce RDC and RqN> but because a
reduction in will also decrease AE this will produce
PO Fn c
larger reductions in the resistances than a reduction in
Jnq. We note from (225) also that designing the p shield
such that Fg>0 would reduce the resistances, but would also
tend to negate its shielding effect.
An increase in Tq will also decrease the resistances.
For W>3La, (231) and (233 )(236 ) show that RQN and RDC
1/2
vary as 1/Tq However, for long Tq, or short W
(W<0.3La), Rqn and RDC are independent of ; further
decreases in W produce no additional reduction in the
resistances. Because of the effects of carriercarrier
scattering, changes in parameters that increase n(0) and
n(W), which tend to decrease the resistances, will also
cause a reduction in carrier mobility, and hence the
decreases in RQN and RDC predicted by (231) and (233) can
be overestimated.
36
To demonstrate in more detail the influences of JTri,
NO
Jp0, and Tq on he GDS resistance, we give in Table 22
calculated (using the model in Section 2.2) values of R
DC
(I=25mA) and RQN (l=30mA) for various values of these
parameters. We chose an intermediate value for
W=357//m, and we used the remaining parameter values in
Table 21. The cathode and the anode series resistances
were not included. We see from Table 22 that the
resistances are most sensitive to Jpg, even though the
"intrinsic" currentvoltage characteristic, J(VTF ), can
J
be independent of Jon [see (228)]. Both RDC and
pn
R,
can
p0 t__ v DC ** *'0N
be reduced considerably by increasing Tq and/or deceasing
JN0 as well as Jp.
The resistance values in parentheses in Table 2.2 were
calculated by accounting for the carriercarrier scattering
using an iterative technique [Ch70]. That is, the carrier
mobility values used in the final model calculation were
chosen to be compatible with the calculated average carrier
density in the it region as defined by empirical
characterizations of the mobilitydensity dependences for
holes and electrons. The calculations show that
carriercarrier scattering tends to diminish the reductions
in resistance discussed above, especially with regard to
Rq^. Nonetheless we can conclude, based on these
calculations and others, that RQN (intrinsic) for a typical
37
Table 21. GDS parameter values inferred from
theoreticalexperimental currentvoltage
correlation.
JN0
=
4X10~12
A/cm2
JP0

lxlO12
A/cm2
T0
=
1X105
sec
Fs
_
1.5x1011
2
Vsec/cm
"n
920
cm /Vsec
"p
=
330
2
cm /Vsec
A
5X105
2
cm
38
Table 22. Calculated dependences of R and R
on Jtgo' Jpo' and To for w=35' /um. The
remaining parameter values are given
in Table 21. The values of R and
Ron in parentheses were calculated
accounting explicitly for carrier
carrier scattering [Ch70].
JN0 (A/cm2)
Jp0 (A/cm2)
tQ (/vs)
V (2)
eon (a)
4XlO~12
12
1X10
10
81.7
(77.7)
21.5
(27.5)
4X1012
5X10_13
10
69.4
(71.3)
16.1
(25.1)
5X1013
12
1X10
10
62.3
(67.2)
12.5
(22.5)
12
4X10
12
1X10 1Z
50
68.5
(69.2)
16.5
(23.0)
4X10~12
5X1013
50
59.6
(64.0)
12.4
(21.0)
5X1013
12
1X10
50
54.2
(60.7)
9.6
(18.6)
5X1013
5X1013
50
50.2
(57.7)
7.7
(16.9)
39
4 2
GDS (W~2Q0/vm, A~10 cm ) can be reduced to <1052 by
12 2
decreasing Jnq and Jpg to <10 A/cm and increasing Tq to
~50 /usec.
2.5 Summary
A onedimensional, regional model for the forward
currentvoltage characteristic of the GDS, as described in
Section 2.1, has been presented and supported
experimentally. It requires generally numerical evaluation
of the analytic expressions, although for high currents it
can be simplified to avoid the numerical characterization.
The model yields expressions for the dc and incremental
resistance of the GDS at high currents, which show for the
GDS test structures used (W>3LA) that the RDC and RQN have
2 2
W dependence, that the slope of the R^ vs. W curve
2
should be onehalf of the slope of the RDC vs. W curve,
2
and that the extrapolated intercept of the RQN vs. W
C A
curve should yield the series contact resistance (Rg+Rg).
In addition to the familiar parametric dependences, the
resistances were shown to decrease with increasing carrier
lifetime in the ji region and with decreasing saturation
current desities for both the cathode and the anode.
IGBT
CHAPTER 3
CHARGECONTROL ANALYSIS OF THE
TURNOFF TRANSIENT
3.1 Introduction
This chapter concerns the modeling of another common
HV/P IC device, the IGBT [Ba85]. In Chapter 2, an
analytical model for the steadystate IV characteristics
of a GDS was developed and experimentally verified. In
this chapter we utilize the physical insight gained in
modeling the GDS to develop a quasistatic charge control
model for the IGBT turnoff transient [Ba85]. The model,
with minor modifications, is also applicable to the hybrid
IGBT (HIGBT) [Fo87,Si85] turnoff transient, as
demonstrated in Chapter 5.
The analysis presented in this chapter describes the
transient behavior of the IGBT in terms of its steadystate
current components. The effects of minoritycarrier
injection into the anode are properly accounted for, within
the limits of the quasistatic approximation, by using the
physically correct PXNdiode boundary condition at the
40
41
anode. The resulting analysis identifies important
charging mechanisms and suggests device design criteria for
decreasing the turnoff time. The analysis subsequently
aids in developing accurate and simple equivalent network
representations for LIGBT structures, as shown in Chapters
4 and 5.
Until recently, highvoltage powerswitching devices
were either bipolar (e.g. gated PINdiode [Sm82]) or MOS
(e.g., power MOSFET [Ba81]). A particular application
dictated the technology to be used based on a tradeoff
between its advantages and disadvantages. Bipolar power
devices generally yield low onresistance RQN
(highcurrentdensity operation) because of conductivity
modulation, but slow switching because of the
minoritycarrier storage. MOS power devices are fast
switching because of short minoritycarrier (channel)
transit time, but generally have high RQN because of the
lightly doped drift region.
Recently a new family of power semiconductor devices
based on integrating bipolar and fieldeffect technologies
was introduced. The IGBT [Ru83,Ba84b] is basically a
MOSFET (VDMOS) having a pn junction connected to the drain
that, in the onstate, injects minority carriers into, and
modulates the conductivity of, the drain (drift) region.
The basic IGBT structure is shown in Figure 31. With it,
virtually any desired tradeoff between switching speed and
Anode
Figure 31.
IGBT unit cell and current components.
The solid arrows depict hole flow and
the dashed arrows depict electron flow.
43
Rqn can be effected by controlling the carrier
(recombination) lifetime in the n drift (epitaxial) region
[Ba84a]. The device retains the highinputimpedance gate
of the MOSFET, and has the added advantage of
reverseblocking capability.
The IGBT structure does, however, contain a parasitic
pnpn thyristor that can latchup at high currents and
thereby negate the gate control. Below the latchup
current, the steadystate currentvoltage characteristic
(in the onstate) is defined by the DMOS, in series with
the underlying (fowardbiased) pn junction and in parallel
with the parasitic vertical pnp bipolarjunction transistor
(BJT). That is, the anodecathode current comprises the
DMOS channel current, which supplies electrons that
recombine in accord with with the properties of the forward
biased pn junction, and the BJT collector current, which
results from holes injected from the underlying
(emitterbase) junction.
The electrical coupling between the constituent MOSFET
and BJT in the basic IGBT structure results in a unique
transient turnoff characteristic [Ru83,Ba84b,
Ba84a,Ba85,Ku85] comprising an initial rapid drop in
forward current, followed by a slower decay. Previous
analyses [Ru83,Ba84b,Ba84a,Ba85,Ku85] of this
characteristic are either qualitative or incomplete, and do
not adequately reflect the underlying physics to facilitate
44
optimal device design. In this chapter we develop a
quasistatic chargecontrol (analytic) description of the
transient turnoff characteristic, which is physically
insightful and which suggests device design criteria for
shortening the turnoff time, without increasing RQN
considerably.
The chargecontrol model we develop is similar to one
previously developed Kuo et al. [Ku85], but does not
involve the assumptions and approximations implicit in Kuo
et al. [Ku85] that limit the validity of the model and in
fact result in misconceptions concerning the physics
underlying the turnoff transient. In particular, the
effects of the expanding depletion region at the cathode
and of minoritycarrier injection into the anode, which are
not currently accounted for in [Ku85], nor in earlier work
[Ba84a], are represented in our model.
3.2 Model
The basic (unitcell) structure of the (nchannel)
IGBT, shown in Figure 31, comprises a DMOS FET merged with
a BJT. The components of current, which is
multidimensional, are indicated in the Figure 31 for the
steady onstate (gate voltage VG sufficiently positive to
induce an nchannel between the the n+ cathode an the n~
epi region, and the anodecathode voltage V>0). The
MOSFET channel (electron) current IMOs suPPorts carrier
recombination in the BJT
45
IMOS IB(BJT)
(31)
where I
is the base current in the p+n p BJT, which
comprises recombination in both the base (n epi) and
+
emitter (p
anode) regions. The IGBT (anodecathode)
current I is
(32)
I = I
+ I
B(BJT)
C(BJT)
the base transport (hole) current. Note that the actual
current gain of the BJT, 3 = Ic ( b JT)/JB ( B JT ) dePends
critically on the geometry of the IGBT structure.
Consequently, analysis of the device for the transient as
well as steadystate conditions must somehow account for
the multidimensional carrier flow.
The IGBT voltage VA can be written as the sum of four
voltage drops
+
(33)
46
+ 
where n is
the
drop
across the
underlying p+n
junction; V
J epi
i s
the
vertical
drop across the
(conductivitymodulated) epi
region; IRg
is the drop across
the extrinsic series resistance Rg; and the last term is
the (lateral) drop across the channel of the MOSFET, where,
following [Su80], R and R^ represent effective
lumpedchannel resistances of the "seriesconnected"
enhancement and depletionmode devices. The implicit
formulation in terms of the junction voltages for the
steadystate IGBT transport problem, and its corresponding
numerical solution, are given in chapters 4 and 5.
The conductivity modulation that produces the
excellent steadystate forward currentvoltage
characteristic, viz., low of the IGBT can
ON
unfortunately cause the turnoff time to be much longer
than that of a conventional power MOSFET. A typical IGBT
turnoff transient [Ru83,Ba84b,Ba84a,Ba85,Ku85] is unique
as illustrated in Figure 32. It shows an initial rapid
drop in the forward current, followed by a slower decay,
which reflects the lifetime of the carriers stored in the
epi region. The turnoff time can be shortened by reducing
the carrier lifetime, for example, via electron irradiation
[Ba84a] or intentional metallic impurity doping [Go83].
Such techniques have resulted in turnoff times of less
than 200ns, but with accompanying increases in RQN because
of the reduced carrier injection levels in the epi region.
47
t
Figure 32. Typical IGBT turnoff transient showing
two distinct phases.
48
The IGBT is turned off by removing the gate voltage, and
hence the MOS channel through which electrons flow for
recombination in the p+ anode and n epi regions. The
removal of the channel occurs quickly, on the order of the
electron transit time which is typically a few tenths of a
nanosecond [Ba81]. In order to characterize the IGBT
turnoff transient, the external circuit, represented in
Figure 33, must be considered. When the channel is
removed (virtually instantaneously), but 1 cannot
drop instantaneously because the reverse bias on the pn
junction (J2 in Figure 33) does not increase abruptly; the
depletion capacitance of J2 is (partially) charged in short
but finite time, as controlled by the external circuit.
This initial phase is completed when I, defined by the
external circuit and developed reverse bias on J2 (V^)
equals the timedependent BJT collector current, defined by
the (timedependent) depletionregion width of J2. Little
carrier recombination occurs during this fast transient.
The second phase of the turnoff, however, is controlled by
carrier recombination in the epi region (and perhaps in the
anode region), and hence the completion of the development
of Vj2 is slower than the first phase. The carrier
lifetimes are typically longer than the time constant that
characterizes the initial transient.
Since the first phase is usually much faster than the
second, we will characterize the composite turnoff by
49
External biasing and turnoff_circuitry
for the IGBT transient analysis.
Figure 33.
50
first describing only the fast drop AI in the current that
occurs in the first phase, and then modeling the subsequent
decay of X(t) in the second phase, which defines the
turnoff time. If VG is removed at t=0, and I = Iq in the
steadystate for t<0 as described by (32), then for t>0
I(t) ~ 1C(BJT)(+
dQj2(t)
~St
(34)
where is the charge associated with the depletion
capacitance of J2. For t=0+, I is Iq, and and
dQj2/dt, which equals IM0S in (31), are defined by the
steadystate characterization of the IGBT, KV^). Hence
our transient analysis is dependent on the steadystate
model. We stress, however, the utility of the transient
model, independent of the steadystate analysis. As we
will show, the dc current components in (31) and (32)
become parameters of the transient model and can evaluated
by comparing theoretical and experimental characterizations
of the turnoff transient.
Using a chargecontrol representation, we express the
transient BJT collector current in (34) as
Qp(t)
IC(BJT) = Tt (t)
(35)
51
where Qp
(t) is
the
hole charge
n base
region
and
Ttp is
base
transit
time
in
(35)
is
depletion regi
on
(width
xd>
moving boundary, which is not
previous work [Ba85,Ku85], is
phase of the as we demonstr
highinjection conditions, we a
stored in the quasineutral
transit time for holes. The
imedependent because the
of J2 is expanding. This
accounted for properly in
most important in the first
ate below. For prevalent
ssume [Gh77]
TtP(t)
[WBXd(t))
(36)
where Wg is the metallurgical base width of the vertical
p+np BJT and KA is a constant less than unity discussed
below. Rigorously (36) (with KA=1) applies to a
onedimensional device in which there is no recombination
in the base nor back injection into the emitter. However,
we assume that it (with KA<1) is representative of the
actual IGBT structure illustrated in Figure 31.
Independent of the finite base current, KA accounts for the
multidimensional carrier flow in the epi, in which case to
first order it could be given as the ratio of the BJT
collector and emitter areas. We note also that KA*1 can
effectively account for the influence of the base current
(recombination in both the n epi and the p+ anode) on the
transit time [Ku85].
52
Because the carrier lifetime (in the base) is long
relative to the duration of the initial fast transient, we
assume that Q is invariant in the first phase, even though
XT
the holes (and electrons) are redistributed in time in the
epi region. Thus as holes are swept out of the collector
to increase Qj2' electrons are forced toward the emitter,
thereby increasing the hole injection from the emitter to
maintain neutrality. This increase in Q which
approximately equals the increase in is much smaller
than Q and hence does not threaten the validity of (35).
Jr
From (31), (32), (35), and (36) then, we can write
I0 = IMOS +
pO
WV4K. D
B/ A p
(37)
since x^O for t<0. Equation (37) defines Q^q, the
steadystate value of Q which remains virtually intact
ir
during the initial first transient.
The fast transient subsides when dQ^/dt^O, or from
( 3 4 ) ( 3 7 ) when II^ where
Q
*0 "
/4KADt
I0 IMOS
(1wv2
(38)
53
in (38),
the "final
the hole
negligable
xdm the
" reverse
density
"final"
bias vj2m
in the
value of
, which for
depletion
, is [Gh77]
corresponding to
low enough that
region is indeed
xdm
2gSVJ2m
qN
^ epi
1/2
(39)
The external circuit (Figure 33) in which is chosen so
that I = Iq in the steady on state defines Vj2m (>0):
V
J2m
(310)
From (37) and (38) then,
AI *
T T
IMOS ^1
1
1]} (311)
I0 I1
'^dn/V'
where
V
IMOS' and ^ (I0
~IMOS//IMOS ^
are described
by
the
steadystate
analysis.
Note that
ai
the
fast
drop
in the
current is,
in general
, less than
the
(steadystate) MOSFET current. Only for xcjm<
54
^MOS' wrongly implied in Baliga [Ba85] and Kuo et
al. [Ku85].
To demonstrate the virtual independence of the
transient result (311) from the steadystate analysis,
and
which defines I
obtain
0
IMOs' we combine (39)(3ll) to
r2eSVB,AI,1
xdm f qN i I
M epi 0
1/2
(312)
Thus measurement of the first phase of the turnoff
transient, i.e., of IQ and Al, enables evaluation of x^m,
which from (311) describes the constitution (an<^
I c ( b jt ) ^ f t^ie steacJyonstate current Ig.
The slower decay of I [from IgAI) to zero] in the
second phase of the turnoff is similar to the transient
response of a BJT in the active mode following the abrupt
removal of the base current [Mu77]. Whereas the
firstphase transient is controlled predominantly by the
charging of the J2 depletion capacitance, we assume that
the secondphase transient is controlled by carrier
recombination. Thus the J2 displacement current [dQ^/dt
in (34)] is neglected, and we write, based on (35),
Qp(t)
'tp
Kt)
(313)
55
where rfcp is an average transit time, which can be crudely
approximated based on (36), as
(WBXdm
4K D
A p
(314)
with x^m given by (312). The use of (314) greatly
simplifies the analysis of the second transient, and hence
facilitates physical insight and identification of critical
device parameters that define the turnoff. The
simplication is representative because typically the
increase in x^ beyond x^m is less than x^ ; the relative
change in during the transient during the transient is
smaller than that of Qp. The decay of I(t) in our model is
thus defined predominantly by the timedependence of Qp(t)
[Ku77]; and errors resulting from the use of (314) are
minor and do not derogate the utility of the model.
In BJT terminology, I(t) is the emitter current, which
is equated in (313) to the collector current because the
base current is constrained to zero [Mu77]:
p(t) + dP(t) +
th dt
n(t)
n
+ dQn(t:
dt
0.
(315)
56
We are assuming that high injection (p=n) prevails in the
base region throughout the main turnoff transient, and
hence we use the highinjection carrier lifetime th as
defined by SRH theory [Gh77]. This is a reasonable
assumption for a device in which conductivity modulation is
essential in the onstate. In (315), Qn is the minority
electron charge in the quasineutral p+ anode (emitter)
reqion and Tn is an average (effective) electron lifetime
(chargecontrol time). The dynamics of Qn, which is not
accounted for properly in previous work [Ba85,Ku85], can
influence the secondphase transient as we show below.
For quasi equilibrium and negligible recombination in
the p+n~ junction spacecharge region, Qn can be related to
Qp using the quasistatic approximation. In the
quasisteady state, the solution [Gh77] to the ambipolar
transport equation in the quasineutral base region (with
p=n) yields, for less than the ambipolar diffusion
length, Qp^qAfWgx^) p( 0 )/2 where p(0) is the hole density
at the edge of the spacecharge region and A is the device
_ 2
area. Using Qn/Tn=AJNQ[p(0)/ni] [Gh77], where Jnq is the
saturation current density associated with the electron
injection (recombination) into the p+ anode, we have
57
Q2
Q IE
n Q0
(316)
where Qq is a constant charge given approximately by
Q0 =
a 2 2 TT ,2
Aq n.(WBxdm)
4inJN0
(317)
With (316), (315) is
firstorder, nonlinear
differential equation for the quasistatic Q (t), which can
P
be solved analytically. If we assume t <
n ri
likely for the asymmetrically doped p+n~ junction, we get
Qp(t)
QpOeXp(
~pOTH [lexp( ^)]
(318)
1 +
Q0Tn
H
where t=0 is now taken as the start of this secondphase
transient. Now I(t) is defined by (313), (314), and
(318), which with (38) yield
Kt)
It exp()
lh
(319)
I1JN0TH
2 2
AK.q nTD
1 p
[1exp()]
H
1 +
58
Thus I(t) can decay faster than exponentially if currents
associated Qn(t), reflected by the second term in the
denominator of (319), are significant. If J
NO
is
negligibly small, then (319) reduces to a simple
exponential decay defined by the numerator. However for
typical values of the model parameters, the second term in
the denominator of (319) can be significant.
3.3 Discussion
Our analysis of the IGBT turnoff transient is first
order, and describes, in terms of the steadyonstate
current components, an initial fast drop AI of the current,
followed by a slower decay of I(t), which can be, depending
on somewhat sharper than an exponential falloff
having a time constant equal to tH. In Figure 34 we plot
the composite turnoff characteristic for a typical IGBT
predicted by our analysis for three assumed values of th
and of JN0, the two most significant material parameters
that must be controlled for optimal device design. As
noted previously, a steadystate analysis is needed to
evaluate parameters in our transient model. In the
derivation of the I(t) characteristics plotted in Figure
34, we first used a numerical solution of the steadystate
ambipolar transport in a quasitwodimensional
representation of the widebase p+n p BJT to estimate the
constitution of Iq in (31) and (32). Then, with IM0S and
59
Curve
^ H 0s)
t Ois)
Calculated IGBT turnoff transient for
three values of th and of J Device
parameter values used are an= 0.1 cm2,
6 0 /m,
0.5; I,
1014 cm3
and
&
60
3 evaluated for a specified IQ, ( 39 ) ( 311) give AI and
(319) describes the transient decay I(t). The value of KA
(=0.5) used in the transient analysis is consistent with
the quasitwodimensional treatment of the steadystate
carrier transport: K . /A.
a collector
Comparisons of the predicted characteristics in Figure
34 with published data [Ru83,Ba84b,Ba84a,Ba85,Ku85,Go83]
indicate that our model is representative of typical IGBTs.
The dependence on xH of both AI and I(t) is consistent with
corresponding measurements. The dependence on JNg has not
been studied experimentally, but is, we believe, depicted
faithfully. The predicted AI increases with increasing
Jnq, for Iq held constant, because 8 decreases. For the
same reason, AI increases with increasing xH, but the
dependence is not unrelated to the value of JnQ, and the
change is not simply equal to IM0S (=Iq/3) as implied in
previous work [Ba85,Ku85].
The I(t) dependence also may be more complex than
previously indicated [Ba84a,Ba85,Ku85]. Whereas the time
13 2
dependence predicted for Jnq=2X10 A/cm is nearly
exponential [ exp(t/xH)], indicating that the second term
in the denominator of (319) is unimportant, the predicted
transients become supraexponential as Jnq increases. This
dependence of course is related to xH, becoming significant
as xH decreases. For xR sufficiently short, and/or for Jnq
sufficiently small, I(t) is exponential and Tq is defined
directly by xH.
60
61
The dependence of Tq on carrier lifetime illustrated
by the carrier lifetimes plotted in Figure 34 is
consistent with other measurements [Ba84a,Ba85] that show
Tq decreasing strongly with increasing electron irradiation
~ 1
dose. Calculations and measurements imply Tqth which
implies that the time dependence in the denominator of
(319) is unimportant for these devices (that have low t ) .
We note further that measured dependences [Ba84a,Ba85] of
Tq on VB and on Iq are explained well by our firstorder
model. For a given th, calculations show Tq increasing
weakly with increasing VB for constant Iq, and decreasing
with increasing IQ for constant Vfi. The Tq(Vb) dependence
is weak because x^m in (312) and implicitly in (313),
which defines Tq, does not change appreciably when Iq is
held constant, as can be seen from (310) and (311). The
Tq(Iq) dependence is more pronounced (Tq can be halved by
increasing Iq) because AI in (311) increases more rapidly
than Iq; viz., IMOS' which includes the p+ anode
recombination component, increases faster than Iq. We
infer from the model however that Tq will saturate for
sufficiently high Iq becauses ultimately iMqs' which
comprises predominantly the anode recombination current,
becomes proportional to IQ.
From our analysis, we can suggest a way to quicken the
turnoff, independent of shortening th which increases RQN
62
because V ^ in (33) increases.
For a given t, the
H
turnoff time can be reduced by increasing AI, which
decreases the secondphase decay in I(t) needed to turn off
the device, and by enhancing the significance of the
denominator in (319), which exploits the supraexponential
decay. Physically, these changes lower 0 and make IM0Sr
which is controlled directly and without delay by the gate,
a larger component of the steadyonstate current, and they
make carrier removal through the p+ anode more significant
in the transient. They can be effected by increasing Jnq,
which could be done perhaps by reducing the doping density
and the electron lifetime and/or transit time in the
heavily doped p+anode region [Fo81], The benefit of such
an increase is illustrated in Figure 34. Reducing in
(319), for example by decreasing the BJT collectoremitter
area ratio, would produce similar benefit. We note however
from (33) that if the MOSFET resistances R and R are
ih JD
substantial, then increasing J
NO
and/or decreasing K,
(i.e., reducing 0) could significantly increase RQN.
An n+ punchthrough shield (buffer region), as
described in Chapter 2, may also be used in IGBT
structures. The n+ buffer region reduces the emitter
efficiency of the constituent widebase BJT and, for a
given current level, makes IMqS a larger component of the
steadyonstate current, thus subsequently decreasing the
turnoff time. The methodology for characterizing the
63
effects of a buffer region on device performance, as
presented in Chapter 2, may be applied to IGBT structures
to study the tradeoff between decreased turnoff time and
increased onresistance arising from the bufferinduced
reduction in baseregion mobile carrier concentration.
The utility of the physical insight afforded by our
model for the transient turnoff should be stressed.
Whereas previous work has shown that TQ is reduced by
decreasing th and increasing AI, it has not demonstrated
how the reduction obtains and it has not clearly revealed
how AI can be increased most effectively. Furthermore the
previous work, which is based strictly on onedimensional
analysis, did not reveal the subtle but critical influence
of the IGBT geometry on its transient turnoff
characteristic. The constant KA<1 in our model, although
somewhat empirical, reflects this influence. Our analysis
can further facilitate model parameter evaluation for IGBT
circuit simulation. For example, it is possible to
interpret a measured turnoff transient using our analysis
and extract, for a given onstate current Iq, values for
IMOS (an<^ hence 3)/ th/ and jno* This utility
interest in the general area of CAD of HVICs.
should be of
CHAPTER 4
HIGHVOLTAGE/POWER INTEGRATED CIRCUIT DEVICE
MODELINGA FIRST APPROACH
4.1 Introduction
This chapter introduces a novel methodology for
flexible SPICE2 implementation of physical models for HV/P
IC devices developed in chapters 2 and 3. The model
implementation is applied to the IGBT of Chapter 3 and is
achieved without modification of the SPICE2 source code by
utilizing UDCSs that access FORTRAN subroutines which
define, implicitly, the current and charge as functions of
the controlling node voltages. The implicit problem is
numerically solved in a FORTRAN subroutine and its solution
(a current or charge) is referenced by the SPICE2 main
program. This highly flexible means (first approach) of
model implementation differs from that presented in Chapter
5, where the implicit model equations are solved by the
SPICE2 main program, thus trading model flexibility for
computational efficiency. SPICE2 simulations of dc and
transient characteristics of IGBT switching circuits are
64
65
shown to be
representative of
measurements taken
from
the
literature.
Both static and
dynamic
latchup for
the
IGBT
are simulated, thus demonstrating the
flexibility
of
the
modeling methodolgy for HV/P IC CAD.
Recent advances in silicon IC processing technologies
have intensified development of "smart" high voltage/power
(HV/P) circuits, in which lowpower logic and highvoltage
devices are integrated on the same chip. Computeraided
design (CAD) of such circuits is critically dependent on
reliable device simulation, for example with SPICE2 [Na75].
HV/P devices have unique characteristics that are not
amenable to lumpedelement, equivalentcircuit
representation, and hence the builtin device models in
SPICE2 are generally inadequate. Such characteristics
include effects of merging bipolar and MOS structures,
latchup, conductivity modulation, and movingboundary
(during transient) conditions. The inadequacy of the
SPICE2 MOSFET models for HV/P IC simulations is clearly
inferable from [Su80]. The SPICE2 BJT (GummelPoon (Ge7 8])
model is clearly deficient; for example, its basic
(integralchargecontrol [Ge78]) assumption is invalid for
HV/P BJTs having significant back injection or relatively
low currents gains.
Therefore to enable reliable CAD of HV/P ICs, new
device models must be implemented in SPICE2, or in
comparable circuit simulators. Because of the unique
66
device characteristics and model complexities, such
implementation will require either modifying existing
simulator codes to accommodate new specific models, or
developing new methodologies for general model
incorporation. This paper describes a simple, flexible and
physical approach to the latter implementation. The
methodoly is exemplified through an application to a
representative device, the insulated gate transistor (IGBT)
[Ba84b], an HV/P switch comprising merged bipolar and MOS
structures. Although the (vertical) IGBT is not a common
integrated device, we use it to demonstrate the modeling
methodology, which is intended primarily for CAD of HV/P
ICs, because (i) it is well documented, and (ii) its basic
operation is not unlike that of other merged bipolar/MOS
devices which are integrated, e.g., the lateral IGBT
(LIGBT) [R086].
We stress that this chapter introduces and
demonstrates a novel device modeling concept for HV/P
circuit simulation, but does not include the simulation of
any actual device nor a complete corroboration of model
assumptions. The viability of the methodology is implied
by the physical nature of the models and is shown through
qualitative comparisons between model predictions and
published measured characteristics.
The new SPICE modeling approach, presented in Section
4.2 and demonstrated in Section 4.3, utilizes expressions,
67
not necessarily in explicit form, for the quasistatic
device terminal currents and charges (the models are
chargebased) in terms of the terminal voltages. This
system of equations, i.e. a physical device model, is part
of a subroutine that is referenced by userdefined
controlled sources (UDCSs) in SLICE [Ha84], one of the many
enhanced versions of SPICE2 that have been written. The
UDCSs generally available in enhanced versions of SPICE2,
are simple FORTRAN subroutines [Ve86] that constitute the
"equivalentcircuit" model, which simulates both
steadystate and (quasistatic) transient device
characteristics. With judicious programming and data
storage, UDCSs can be used effectively for simulation of
circuits in which the number of HV/P devices is not
excessive.
4.2 Modeling Methodology
The utility of the novel methodoly is demonstrated by
its application to the IGBT [Ba84b], as illustrated in
Figure 41. The IGBT is representative of emerging HV/P
devices that merge MOS and bipolar structures to exploit
the advantages of both. The (nchannel) IGBT shown is
effectively a vertical pnp BJT, the base of which is driven
by a DMOST, with a parasitic npn BJT at the cathode that
can cause latchup and loss of gate control of the IGBT
switch. In contrast to the conventional DMOST, the
Figure 41. Basic IGBT structure.
69
conductivity of the n~ epitaxial region (base) of the IGBT
is modulated by carrier injection from the p+ anode
(emitter), thereby lowering the onresistance but also
increasing the turnoff time because of the excess carrier
storage. The device has been previously modeled [Yi85] by
connecting numerical models for the DMOST and pnp BJT
through a modulated base resitance. Such modeling aids
optimal device design, but is impractical for circuit
simulation and provides little insight into how device
parameters affect the dynamic response of the IGBT in a
circuit, or an HVIC.
We emphasize in this paper the SPICE simulation of the
constituent widebase (lowcurrentgain) pnp BJT and
parasitic npn BJT. We thereby stress the inclusion in the
model of unique characteristics like low BJT gain,
baseregion conductivity modulation, and latchup, which
are not properly accounted for in the builtin SPICE2
models. The DMOST is modeled using a standard level2
SPICE2 MOSFET model [Ha84]. Because of the high level of
conductivity modulation in the n base region, effects of
the parasitic JFET [Yi85] at the drain of the DMOST can, to
first order, be ignored when calculating the onresistance.
The methodolgy presented, however, is flexible enough to
model the JFET effects if desired, but at the cost of
increased model complexity.
70
Gate
Figure 42. UDCS representation of the IGBT
implemented in SLICE/SPICE2. This is
not an equivalent circuit; the node B
is labeled merely to signify the internal
connection between the base region of the
pnp BJT and the drain of the DMOST. The
anode of the IGBT is referred to as the
emitter of the pnp BJT, and the cathode
as the collector.
71
The UDCS [Ve86] "circuit" model for the IGBT is shown
in Figure 42. In fact, the model is not an equivalent
circuit, but is a physical representation comprising six
UDCSs, each of which is defined implicitly by the system of
model equations in terms of the emitterbase and
basecollector voltages (VAB and VBR) of the pnp BJT. The
choice of node voltages used to define the UDCSs is not
unique. Alternative choices, as demonstrated in Chapter 5,
can be considered for a particular device to effect a
tradeoff among model flexibilty, complexity, and
computational efficiency. The steadystate characteristics
of the IGBT are simulated by the UDCSs IM0S (the component
of the pnp BJT base current supplied by the DMOST), Icp
(the pnp BJT collector current), and Vepi (the voltage drop
across the n~ base region). The transient characteristics
are simulated by the chargebased UDCSs [Ve86] dQpB/dt (the
charging current defined by the carriers in the
quasineutral base region of the pnp BJT) and dQT/dt (the
charging current defined by the depletion charge at the
basecollector junction of the pnp BJT). Charging currents
associated with free carriers in other regions of the
device are typically negligible. For example, the charging
current defined by the minority electrons in the
quasineutral p+ emitter (anode) region is negligible, even
though the total pnp BJT base current (lM0S + ICN) must
include a component due to recombination in the emitter, as
shown in Chapter 3 [Fo86a]. The resistance RpN simulates
72
the lateral voltage drop in the base region of the npn BJT,
which is important only near latchup as we discuss later.
The six UDCSs reference the same userdefined
subroutine that defines the system of model equations.
This set of equations is quasistatic; that is, and
r d
QJC, as well as IMQS, Icpr ICN/ and Vepi, are described in
the steady state in terms of V.n and VDI,, and then the
transient currents are characterized through the
quasistatic approximation [Va76] which equates the
timedependences to the steadystate dependences in terms
of VAB(t) and VBK(t). Virtually all device models used
today for circuit simulation are quasistatic. Although we
use the quasistatic approximation here, with some support
for its validity, we recognize the need to consider the
possible occurence of nonquasistatic (NQS) effects in
each particular model development. Proper accounting for
the NQS effects in SPICE models is a formidable task, but
can be facilitated [Fo86b] by the new methodology presented
in this chapter.
We now describe the physical model equations in
detail. The sytem of equations is based on the solution to
the onedimensional ambipolar transport equation [Gh77]
describing the carrier densities in the quasineutral n~
base region. Twodimensional effects are considered later.
Since the IGBT operates under highinjection (conductivity
modulated) conditions in the n~ base region (p = n >>
73
Nepi>'
the base transport equation simplifies to
d2p(x)~ p(x) n
,2 2 U
d x L.
A
1 /2
where LA t=(DATH) 1 is the ambipolar diffusion length
[Gh77]. The solution to (41), precluding a forward bias
on the basecollector junction, is
p(x)
p(0)sinh(^)
la
sinh(^)
(42)
where p(0) is the hole (or electron) density at the edge
(x=0) of the emitterbase junction spacecharge region and
W is the effective base width. From Figure 4.1,
W = Wb xd (43)
where WB is the metallurgical n base width and x^, which
is a function of VBR, is the width of the depletion region
at the onesided basecollector junction of the pnp BJT.
We define X[(VBK) based on the depletion approximation, and
74
neglect any mobile carrier charge that might exist in the
spacecharge region for very high current densities [Gh77].
To relate p(0) in (42) to VAB, it is necessary to
characterize V since
epi
V = v + V
AB epi JEB
(44)
where
VJEB vijln t
P( 0)N
Â£Â£i]
n.
(45)
is the emitterbase junction voltage (not equal to the
quasiFermi potential separation) [Wa83]. In (45), Nep
is the doping density in the n~ epitaxial base of the pnp
BJT and VT=kT/q is the thermal voltage. Accounting for the
conductivity modulation, we give V ^ by the integral of
the electric field across the quasineutral base, where the
field is related to p(x) through a combination of the hole
and electron current expressions [Gh77]:
dx
epi q ( v+fJ ) J p(x)
11 V n
WM
M
rJ
(bl) kT
(b+1) q
In (
P(0)
N
epi
(46)
75
where WM(
equals N ^; JA is the anode (emitter) current density and
b=/un//Up is the electron/hole mobility ratio.
For negligible recombination in the emitter junction
spacecharge region, is related to p(0) as follows
[Be79]:
(47)
x=0
where is the ambipolar diffusivity [Gh77] and Jnq is the
saturation current density defined by the back injection of
electrons into the quasineutral emitter region [Fo81].
Equations ( 4 4 ) ( 4 7 ) relate p(0) to VAB and V^, the
independent nodevoltage differences in the model. Now
(42) and (43) can be used with these relations, and the
quasistatic approximation, to characterize the UDCSs in
terms of these voltages. We note that although these
characterizations are implicit, the model is implemented in
SPICE2 directly via access of the UDCSs by the nodal
analysis [Ve86].
The UDCS is given by (46). The quasistatic
depletion charge density at the basecollector junction is
CJC ^ep^d
(48)
76
where Ac is the (effective)
The quasistatic carrier
region is the integral of (
basecollector
charge in the qua
41) from x=0 to
junction
sineutral
x=W:
area.
base
W
Qb = qA J p(x)dx
0
(49)
where A^ is the emitter, or
chargingcurrent UDCSs in the model
and (49):
anode, area. The
are derived from (48)
dQ. 8Q. dV.
i = x i 1
dt L 9V. dt
j 3
where i=JC, PB
and j =AB,
BK.
Therefore
the
" transcapacitance"
3Qi/8Vj must
also be
described
in the
UDCS, either analyti
cally or numerically.
We note
from
(49) and (410) that the transcapacitances associated with
QpB cannot be described in closed form, and hence
finitedifference approximations are used in the UDCS
dQpB/dt to characterize them numerically.
77
The composite base current IB of the pnp BJT, in the
steadystate, is the sum of recombination current from the
n base region and that from the p+ emitter region. It is
expressed as
XB "
PB
TH
aejno[
p(0) i2
n. J
(411)
where xH is the highinjection carrier lifetime [Gh77] in
the base. The second term in (411) obtains for
quasiequilibrium because low injection prevails in the
emitter. The electrons that support the recombination
current IB are supplied by the DMOST (iMqs^ under normal
operation, but in part also by the npn BJT (1CN) near
latchup:
IM0S 1B ICN '
(412)
Analytical decomposition of ID, as well as characterization
O
of the n base transport current ICp/ must be done
implicitly and hence demonstrates poignantly the essence
(flexibility) of the modeling methodolgy, in contrast to
the lessflexible equivalentcircuit modeling built into
SPICE2.
78
The lateral flow of the collected holes Icp in the
base of the npn BJT forwardbiases the emitterbase
junction and causes electrons to be injected into the base
of the pnp BJT (see Figure 41). This pbase transport
current can be approximated by [Ha85]
JCN = 1SN exp(^M) (413)
where IgN is the collector saturation current of the npn
BJT and Rbn is an average, or lumped, base resistance
[La85], both of which vary inversely with the pbase Gummel
number [Ge78]. However note that because of the
exponential dependence of ICN on Icp, only for conditions
near latchup is the contribution of to the anode
current I.=A_J. significant. When I.T=0, IMrkÂ£.=ID and the
A E A J CN MOS B
DMOST supplies all the electrons necessary for
recombination in the pnp BJT. However when the IGBT is
latched, the electrons necessary for recombination are
supplied by the npn BJT (ICN), and IMOS=0
The implicit description of the current UDCSs is
completed by equating the pnp BJT collector current (Icp)
to the difference between the emitter current (1^) and the
base current (ID):
Jd
79
CP
A (IA IB)
hi
(414
In (414), and in (48), (49), and (411), we have crudely
accounted for the twodimensionality of the pnp BJT by
including the (constant) collectoremitter area ratio,
which is less than unity. Although this accounting is
semiempirical it does reflect the reduced base transport
factor in a typical IGBT due to hole injection into a
portion of the base that is laterally removed from the
collector, as shown in Chapter 3 [Fo86a]. Model
predictions made without the area ratio do not compare
favorably with experimental results, whereas those made
with it do. We note that for lateral devices,discussed in
Chapter 5, however, a more physical accounting for the
multidimensional effects is essential.
Because of the implicit nature of the model equations
(42)(414), it is not possible to express p(0), and hence
the terminal currents, as explicit functions of V.D and
At)
BK'
Thus, for a given VAB and VRK. supplied by the SPICE2
BK
nodal analysis, (44) is solved iteratively (Newton's
method) for p(0) in a FORTRAN (UDCS) subroutine, and the
model equations are then used to determine IM, IOT,, I..,
^ MOS CP CN
Vepi' PB' an<^ JC The moc*e* clearly quasistatic; at
each point in time, the steadystate model equations are
solved in a UDCS subroutine and the solution (a terminal
80
current or charge density) is then referenced by the main
SPICE2 nodal analysis program [Ve86]. We note that in
addition to the transcapacitances in (410), the
transconductances 9I^/3Vj for each current UDCS must be
evaluated in the nodal analysis. These evaluations are
done numerically using firstorder finitedifference
approximations.
The merged structure of the IGBT makes model parameter
evaluation difficult because of twodimensional current
flow and inaccessibility of internal model nodes for
measurement. Model parameters for the DMOST and BJT
components of the IGBT can be estimated from a knowledge of
processing variables, doping density profiles, and
geometry. The threshold voltage for the DMOST can be
estimated from measurements of Ia^VGK^' although the
channel conductance cannot be inferred experimentally
without a special test structure. The two most important
As will be
shown in Section 4.3, these two parameters greatly
influence the steadystate onresitance and turnoff time
of the IGBT. From a knowledge of the pnp BJT emitter
doping density, Jnq can be estimated analytically [Fo81];
and th can be obtained from a fitting of a measured
turnoff transient once Jnq is known, as described in
Chapter 3.
from a knowledge of the pbase doping density, or Gummel
parameters for the pnp BJT are xH and jnq
NO
For the npn BJT, I_.T and Rn,, can be estimated
c SN BN
81
number [Ge78]. Parameter exractions from latchup
measurements could be done, but would not be straight
forward because of the difficulty in isolating important
current components, e.g., Icp.
4.3 SPICE Simulations and Discussion
In this section we demonstrate the utility of the
modeling methodology used to develop the SPICE IGBT model
in Section 4.2. Results of representative IGBT circuit
simulations on SPICE are presented and discussed. Figure
43 shows simulated dc IGBT currentvoltage characteristics
for various values of gatetocathode voltage, V_v.
Typical parameter values were used for these simulations,
and the results shown are representative of typical
vertical IGBTs. For VGR sufficiently high, the DMOST
operates in the linear region, and the IAVAK relationship,
where VAK is the anodecathode voltage, is linear. This
linearity indicates that the onresistance of the IGBT in
this case is not affected by the nonlinear V ., but is
epi
controlled by the DMOST channel conductance and by contact
resistance. For lower V.,,, I. tends to saturate with
increasing VAK This saturation occurs because the DMOST
is driven to the saturation region, and therefore I^_
(=IB), and hence Icp are limited. For VA less than about
0.6 V, the IGBT does not conduct any appreciable current
because the unmodulated n epi resistance is so large; N
17 epi
82
vAk (V)
Simulated IGBT anode current versus
anodecathode voltage for various
gatecathode voltages. The DMOST
threshold voltage is 3 V.
Figure 43.
83
is low to provide high voltage blocking. A forward bias of
approximately 0.6 V is required to produce high injection
and conductivity modulation, which lowers the resistance of
the epi region. Our model equations are valid only in this
region of operation; for lowinjection conditions, I is in
the milliamprange and is well below any current of
practical concern. No attempt has been made to model the
reverseblocking mode of operation, where VAK<0. The
methodology is flexible and this region of operation could
be modeled by including UDCSs, or modifying existing ones
to account for the leakage (generation) current associated
with the reversebiased emitter junctions of the npn and
pnp BJTs. In this extension, the effects of an n+ buffer
layer at the anode, modeled for the GDS in Chapter 2, would
have to be included.
To exemplify transient IGBT simulations, we use the
representative gatedrive circuit [Ba84c] shown in Figure
44. The diode isolates the pulse generator during
turnoff transients. The impedance Z repesents a load on
the IGBT, which typically is resistive, inductive, or a
combination of both. The resistor R_ provides a path to
discharge the gatetocathode capacitance; it influences
the turnoff characteristic by limiting the rate of change
of VGK, and hence limits the rate of change of the anode
current,
A'
If R_ is sufficiently small (109), then
depending on the steadystate value of 1^,
the IGBT may
Gatedrive circuitry for IGBT transient
simulations. The pulse voltage, V wai
defined to fall from 10.7 to zero
ns. The voltage Vcc was set at 350 V.
igure 44.
crH
85
t(XS)
Figure 45. IGBT anode current, DMOST drain current,
and gatecathode voltage versus time from
simulation of turnoff transient defined
in Figure 44 with resistive load ZL = 35
52 and R = 200 52 (xH = 0.8 /js, Jn0 =
1012 A/cm2) .
86
latch during turnoff. Mechanisms that produce latchup in
the IGBT will be simulated and discussed later.
In Figure 45 we show a simulated turnoff transient
for a typical IGBT in Figure 44 with a resistive load.
The turnoff delay reflected by IA(t) results because of
the finite time needed to discharge the gatetocathode
capacitance of the DMOST, and is a function of
GK'
This
discharging time is evident in the VGK(t) decay shown,
which is much slower than the fall of the VG(t) pulse.
Note that VGR(t) influences IA(t) by controlling the
conductance of the DMOST. As shown in Figure 45, the
DMOST transient drain current, ID(t), which, from Figure
42, equals I
+ dQ /dt dQT_/dt, does not begin to
fall until VGR(t) has decreased to a value that causes the
DMOST to saturate (see Figure 43). Further reduction of
V_(t) decreases the DMOST (saturation) current I^(t), and
UI\ D
hence IA(t) as well. Eventually (t) becomes less than
GK'
the DMOST threshold voltage, and ID(t) drops to zero.
IA(t), which includes ID(t), follows the decrease in ID(t)
until it becomes a negligible component, after which lA(t)
decays in accordance with the recombination in the pnp BJT
[Fo86a]. If VGK is reduced very rapidly, for example by
decreasing RGR, then ID falls to zero very quickly,
resulting in the more idealized twophase turnoff
transient [Fo86a,Ba85,Ku85] shown by simulation in Figure
44. In contrast to previous analytical
results
87
Figure 46. IGBT anode current, DMOST drain current,
and gatecathode voltage versus time from
simulation of turnoff transient defined
in Figure 44 with resistive load Z = 35
SJ and Rqk = 5 ffi (th = 0.8 //s, JN0 = I0"12
A/cm2) .
88
[Ba85,Ku85], our SLICE/SPICE2 simulations show that the
abrupt drop in IA(t) is not equal to the steadystate DMOST
current = (even when I.T is zero), and that the slow
decay of the second phase is not a simple exponential
function of the highinjection lifetime tH.
These
differences result, respectively, from the unique effects
of the expanding depletion region at the basecollector
junction and the back injection of electrons into the
emitter characterized by Jnq, poignantly demonstrated in
Chapter 3.
In Figure 47 we show simulated IGBT resistive
turnoff transients for various values of x and To
H NO
stress the influence of these parameters, we used a small
value for RGR that ensured the insignificance of transients
associated with the gatetocathode capacitance. The
magnitude of the fast initial drop in anode current and
subsequent slower decay are both dependent on th and JNg
These simulations and others have shown that changes in Jnq
should be considered as a means of optimizing the tradeoff
between turnoff time and onresistance. We stress that
these results could not be obtained using standard SPICE2
BJT models because of the limitations inherent in the
GummelPoon model [Ge78] and its implementation in SPICE2.
We stress that the results in Figure 47 are ideal in
that, in addition to negligible gate delay, there is also
no inductance in the load. For contrast, we show in
89
t (ns)
IGBT anode current versus time from
simulation of resistive turnoff transient
for various values of th and JN0 (RGK = 5
52) .
Figure 47.
90
t ((IS)
Figure 48. IGBT anode current, (normalized)
anodecathode voltage, and gatecathode
voltage versus time from simulation of
turnoff transient with inductive load.
In Figure 44, Z is a series combination
of 8 /t/H and 35 S31; RQK = 100 S3.
/ 30 (V)
91
Figure 48 a simulated turnoff transient for an IGBT in
Figure 44 with an inductive load, including a gate delay.
A distinctive characteristic of this turnoff transient is
the sharp rise of the anodetocathode voltage vAK(t),
which even shows overshoot and ringing as do corresponding
measurements [Ba84c]. This unique vAR(t) transient results
from a damped resonance defined by the load inductance in
combination with the junction capacitance repesented by the
charging current dQJ(_,/dt in our model.
To further demonstrate the utility of the modeling
methodology, we simulate the static latchup of a
representative IGBT, but with a larger npn BJT base
resistance
latch, causing loss of gate control, if driven too hard.
For the static case, depicted in Figure 49 by the
simulated IA(VAK)/ latchup is approached by increasing IA>
As characterized in Section 4.2, Icp also increases, and
subsequently, because of the increased forward bias I_RD.T
on the emitterbase junction of the npn BJT, so does lCN
At the onset of latchup, ICN increases abruptly, thereby
reducing IM0S accordance with the recombination in the
RBN. As mentioned previously, the IGBT may
pnp BJT. The reduction of IMQS decreases the voltage
dropped across the DMOST and results in the
negativeresistance region shown in Figure 49. The
process is regenerative, and as the applied current is
increased further, ultimately ICN supplies all the
92
vAk (V)
Figure 49.
V''i
Simulation of static latchup in the IGBT:
driving anode current versus the resulting
anodecathode voltage with gatecathode
voltage equal to 10 V (ISN = 2 x 1012 A
and Rbn = 0.175 ) .
93
electrons supporting the recombination current in the pnp
BJT, and I
MOS
is reduced to zero. In this condition, the
device is latched, and removal of the gate voltage will
have no effect on the IA The transition from a stable
operating point to the latched condition requires only a
small increase in applied current because of the
exponential dependence of ICN on Icp.
The IGBT can also latch during turnoff transients if
the lateral hole current in the base of the npn BJT, which,
at the start of the transient, consists of Icp plus the
displacement current dQJC/dt, is sufficiently high to
effectively forwardbias the npn BJT emitterbase junction.
The magnitude of dQJC/dt depends on the rate of change of
the gatetocathode voltage as defined by the IGBT model
and the external circuitry. In the ideal case, if is
VJI\
removed instantaneously, then the initial magnitude of
dQJC/dt is equal to the steadystate current supplied
by the DMOST, as discussed Chapter 3 [Fo86a]. If is
removed slowly, then the initial magnitude of dQJ(_,/dt will
be negligible, and the IGBT will not latch. In Figure 410
we show a simulation of dynamic latchup in the IGBT, which
occurs because VGR(t) drops abruptly (due to a small RGK as
discussed previously). The turnon of the BJT, which
triggers the latchup, is indicated by the rapid increase
in its collector current ICN(t) shown in Figure 410.
Beyond this point in time, I^(t) remains finite even though
VGR(t) has dropped to zero.
CN Sa(A)
94
Figure 410. Simulation of dynamic latchup in the
IGBT: anode current, npn BJT collector
current, and driving gatecathode voltage
versus time with R = 15 S! (I = 2 x
1012 A and R = 0.175 Q).
n N
95
4.4 Summary
A methodology for SPICE implementation of
highvoltage/power integrated circuit device models has
been presented and demonstrated. The methodology is
flexible and enables an accounting for the unique
characteristics associated with HV/P IC devices, such as
merging bipolar and MOS structures, latchup, conductivity
modulation, and moving boundary conditions. A
representative HV/P device, the IGBT, was modeled using a
system of implicit equations relating the quasistatic
device terminal currents and charges to the terminal
voltages. The physical IGBT model was implemented in
SLICE/SPICE2 by using UDCSs, simple FORTRAN subroutines
referenced in the SPICE2 nodal analysis. Simulations of
IGBT circuits, reflecting dc and transient characteristics
of the HV switch were described. These simulations, which
included static and dynamic latchup, are not possible with
builtin SPICE2 lumpedelement models, and thus poignantly
demonstrate the need for and utility of the new flexible
and physical modeling methdology. CPU times required to do
the simulations with the UDCS model are substantially
longer than times for (invalid) simulations with builtin
models in SPICE2. However they are not prohibitive for
smallscale circuits; typically the new models necessitated
CPU times, for both dc and transient simulatons, about an
96
orderofmagnitude longer than those for the builtin
models. For largerscale HVICs, new HV/P device models,
once they are developed and standardized based on the
methodolgy presented in this paper, could be written into
the SPICE2 code to reduce CPU times to acceptable values.
CHAPTER 5
HIGHVOLTAGE/POWER INTGRATED CIRCUIT DEVICE MODELING
5.1 Introduction
This chapter combines and extends much of the work and
insight gained in previous chapters. In this chapter, new
physical models, and a general modeling methodology, for
lateral HV/P devices, in particular LIGBT structures, are
developed, and the models are implemented in SPICE via
UDCSs. The
models are chargebased, and via regional
partitioning,
account for the unique features of lateral
HV/P devices
(multidimensional carrier flow, conductivity
modulation, latchup, transcapacitance) unaccounted for in
conventional
equivalentcircuit models. Device
measurements
of specially designed test structures,
supplemented
with twodimensional numerical device
simulations, support the modeling methodolgy and the model
parameter extraction.
The implementation of the models in the circuit
simulator is flexible, and differs from the implementation
in Chapter 4 in that the model is implicitly formulated
97
98
such that the circuit simulator derives the solution to the
implicit nonlinear system of equations. In Chapter 4, the
implementation required the implicit system of model
equations to be solved by a FORTRAN algorithm accessed by
the SPICE nodal analysis, and consequently the implemented
SPICE model was computationly inefficient. The new
implementation presented in this chapter, although not as
flexible as that of Chapter 4, is nearly twenty times
faster.
We describe in this chapter the development of new
models for HV/P devices, in particular for lateral IGBT
[Da84,Pa86,Mc87,Si85] structures which are representative
of the HV/P devices in power ICs. The models are physical,
yet are implemented in SPICE, as we describe, through
flexible techniques which do not require sacrificing
physics through excessive empiricism. Thus the models can
be used to aid optimal device (process) design as well as
for CAD of HV/P ICs.
In the application of the modeling methodolgy to the
LIGBT, the device is regionally partitioned into three
onedimensional bipolar transistors (BJTs) coupled to the
DMOS transistor, yielding a quasitwodimensional model for
the LIGBT. The consistuent device structures are
reresented by physical chargebased models in which
currents and charges are related to junction voltages
implicitly by sets of equations derived by solving the
99
pertinent ambipolar transport problems. Charging currents
in the transient model are represented by timederivatives
of the quasistatic charges, which implicitly (without
capacitors) account for charge conservation and
nonreciprocal transcapacitance.
The models are implemented in SPICE via userdefined
controlled sources (UDCSs), which are FORTRAN subroutines
accessed by the SPICE nodal analysis. The UDCSs define the
systems of model equations, which are analytic but must be
solved simultaineously and hence numerically. The solution
of the equations is derived by the nodal analysis.
The LIGBT model and the methodology are supported by
measurements of specially designed test structures, which
also support the model parameter extraction. This
verification is facilitated by twodimensional numerical
device simulations with PISCES [Pi84] that provide needed
physical insight regarding, for example, currentcrowding
effects, and imply how the partitioning of the LIGBT should
be done to effectively account for coupling among the
constituent devices. The test devices are lateral
structures designed to allow experimental access to
different regions of the LIGBT, for different modes of
operation, i.e., as a DMOS transistor, as an IGBT, or as a
"hybrid LIGT/DMOST" (HIGBT) [Si85,Fo87] with the anode
terminal shorted to the DMOST drain. This latter mode of
operation depends on an internal voltage drop to
100
forwardbias the anode junction and activate the IGBT. The
test structures were fabricated using a
dielectricisolation process [Go78] which eliminates
parasitic substrate effects. The utility of the flexible
and physical modeling is emphasized by SPICE simulations of
the LIGBT which reflects the three possible active modes of
operation. Furthermore, the onset of both static and
dynamic latchup can be be simulated straightforwardly with
the physical SPICE model.
5.2 Modeling Methodolgy
We demonstrate the modeling methology through an
application to the LIGBT structure illustrated in Figure
51. The fabrication of this specially designed device is
described in Section 5.3. To develop a
quasitwodimensional model, we partition the structure
into onedimensional constituent componenets as indicated
in Figure 51. The basis for this partitioning rests upon
physicl insight gained from device measurements in the
various modes of operation (PIN, DMOST, LIGBT, HIGBT) and
from device simulations using PISCES. Subdividing a
multidimensional structure into coupled onedimensional
devices is not uncommon [Li67], but in this case of HV/P
devices the empiricism implied must be minimized through
proper accounting for the underlying physics. The unique
effects of significant back injection, baseregion
conductivity modulation, and the associated low current
101
I
Figure 51. Special LIGBT test structure (symmetric
about the axis shown). The spacing between
the 10 fjm deep p+ anode and the cathode is
78 /jm. The thickness of the n~ ( 5 x 1014
cm3) layer is 35 //m and the depth is 300
/jm.
102
gain in the BJT modules, which invalidates the commonly
used SPICE GummelPoon model [Ge78], necessitate new (more
physical) models.
We first focus our attention on the onedimensional
lowgain pnp BJT constituent module (see Figure 51), and
overview the development given in Chapter 4. The low
doping density in the wide n~ base region implies that,
under normal forwardmode operation, high injection will
prevail throughout the base. Consequently, the base
transport problem is described by the ambipolar transport
equation with p=n, the solution of which gives
n ( x ) = p ( x ) =
P(0)sinh(^^)
LA
sinh(^)
la
(51)
where p(0) is the hole density at the edge of the
emitterbase (p+n~) junction spacecharge region, L is the
~ n
ambipolar diffusion length, and W is the voltagedependent
width of the quasineutral base region. We describe W
through the depletion approximation at the reversebiased
collectorbase (pn~) junction:
" WB Xd
W
(52)
103
where Wfi is the metallurgical base width and
x^= [ (()+VBC )/qNgpi ] 7 is the (onesided) collectorbase
(step) junction depletionregion width. In writing (51),
we have assumed that the simplified ambipolar transport
equation (p=n) is valid over the entire quasineutral base
region and thus, as done in [Fo77], we have implicitly
neglected the effects of the relatively narrow
lowinjection region near the collector. In addition,
consistent with PISCES simulations for typical operating
conditions, the effects of mobile carriers in the
collectorbase junction spacecharge region, viz.,
quasisaturation [Je87], have been neglected. Indeed in
the widebase transistor, the base widening associated with
quasisaturation is negligible.
In contrast to the GummelPoon model, our (lowp)
module properly accounts for, via (51), possibly
substantial recombination in the base region. Furthermore,
the module must account for possibly substantial
recombination in the p+ emitter region as well as a
currentinduced electric field in the
conductivitymodulated base region which arises to support
the quasineurality. The integral of this electric field
across the base region defines a voltage drop, V i, which
causes the emitterbase junction voltage, VTr,D, to be less
than the applied terminal voltage, V,,D:
Ej JD
104
EB
= V
JEB
q("n+V
W
M
rJ i
dx
p( x)
(b1)
T5TT)
kT
q
ln(
Â£(01
N
)
epi
(53)
where WM
equals Nep' the baseregion doping density JE is the
emitter (anode) current density, and b /^//Wp is the
electron/hole mobility ratio. (We generically refer to the
n base region as also the epi region, even though it may
not have been produced by epitaxial growth as in the case
for our devices modeled in Section 5.3.)
Using the quasiequilibrium assumption, we express
p(0), and hence V in terms of VTC,D:
Sp 1 J IjD
p( o)
n. 2
i
N
exp(
qV
JEB .
epi
kT
(54)
(If in a simulation p(0) is calculated to be less than or
equal to Nepi' the model is defaulted to the offstate
since the highinjection analysis is inapplicable.) For
negligible recombination in the emitterbase junction
spacecharge region, JE can be related to p(0) following
conventional PlNdiode theory [Be79]:
Jn =
b+1
~b~
* JNO*
pm
n.
]
qA IS
x = 0
(55)
105
where DA is the ambipolar diffusivity, and Jnq is the
saturation current density that defines the back injection
of electrons into the quasineutral eitter region. The
base current density, JB, is the sum of the back injection
current plus the integrated recombination current in the
base region:
JB =
JN0[
ElSi^
n.
i
w
q J
0
p( x)
TH
dx
(56)
where xH is the highinjection carrier lifetime [Note that
1/2
La=(Dath) 7 ]. The collector current density, Jc, is
expressed as JJ. The crosssectional area A relates the
terminal currents l_ and l_ (and In) to the respective
current densities.
The transient modeling of the transistor is done using
a chargebased method employing the quasistatic
approximation. This approximation, which is used
extensively for IC modeling [Ge78], is generally adequate
except for circuits much faster than typical power ICs
[Fo86b].
The predominant charges in the widebase BJT module
(in the forwardactive mode) are the quasineutral
106
baseregion charge QB and the collectorbase junction
depletionregion charge Qj^. For quasistatic conditions,
Qb is given by the integral of (51) from x=0 to x=W:
W
Qb = qA J p(x)dx ; (57)
0
and
Q= qAN .x ,
JC M epi d
(58)
The charging currents are derived from (57) and (58):
dQ. r 9Q. dV.
= 2 1
^Tt j 9Vj dt
(59)
9Qi
where i=B,JC and j=JEB,BC. The transcapacitances, in
j
(59) can be nonreciprocal, and hence the chargebased
model is more representative of the actual charge dynamics
than a conventional capacitancebased model.
Our low3 BJT (with wide, lightly doped base) module
differs significantly from the conventional GummelPoon
107
model in several ways that make it physically
representative of highvoltage devices. The chargebased
formalism (59) properly accounts for transcapacitances,
which cannot be represented faithfully by reciprocal
capacitors [Fo86b], The baseregion voltage drop vep in
(53) is modeled directly and generally (even for (3<1,
viz., very high Jg). The relationship (55) from PINdiode
theory ensures the proper simulation of the emitter
efficiency for highinjection conditions in the base
region. For example in the limit of very high injection,
the model with (55) correctly predicts 3l/b
(baseregion mobilities). Thus, highvoltage p+n~p and
n+p n BJTs have different limiting current gains (Appendix
A) .
The network representation of the chargebased low(3
pnp BJT module is shown in Figure 52. The module is
implemented in SPICE via userdefined controlled sources
(UDCSs) [Ve86] in a novel manner which allows the circuit
simulator to solve the nonlinear equations implied by
(51)(58). UDCSs are FORTRAN subroutines in SLICE
[Ha84], an enhanced version of SPICE2. Each element of the
module is a UDCS that describes the current (and associated
transconductance or transcapacitance calculated numerically
using finitedifference approximations) via the system of
equations described above (Appendix B). The SPICE nodal
analysis accesses the subroutines iteratively in the
108
B
Figure 52.
Chargebased network representation for a
widebase, lowf3 pnp BJT.
109
simulation process. This implementation of an implicitly
formulated model allows for flexibilty in the modeling
methodolgy, and enables truly physical device models to be
incorporated into the device simulator.
We now exemplify the modeling methodogy by applying it
to the LIGBT test structure, and partitioning the structure
into onedimensional modules for each mode of operation.
5.3 Application/Demonstration
Test structure of LIGBTs were fabricated using the
dielectricisolation (DI) BCMOS technology [Go87] developed
at ATT Bell Laboratories. The LIGBT is dielectrical
isolated from the substrate and from other components to
minimize parasitic effects, thus allowing access to the
drain of the DMOST separately from the anode of the LIGBT
and making it easier to measure electrical parameters of
the structure. This facilities the demonstration of our
modeling methology, including the parameter extraction and
comparisons between model predictions and device
measurements.
The LIGBT structure shown in Figure 51 can operate in
several modes (PIN, DMOST, LIGBT, HIGBT) depending on the
terminal configuration. We must therefore develop a
systematic and consistent approach to modeling the various
modes of operation. The physical nature of our constituent
modules facilitates parameter extraction by minimizing the
110
empirical optimization needed. In addition, the modular
approach allows for a straightforward network
representation of the LIGBT structure as will be shown in
this section. We note that in all cases, the simulation of
the actual symmetrical device involves area doubling of the
model derived from the halfstructure shown in Figure 51.
With the cathode floating, the drain tied to ground
and the anode biased to a positive voltage, the LIGBT
structure operates as a forwardbiased PINdiode. The
PINdiode currentvoltage characteristic can be used to
obtain information regarding recombination properties of
the n epi region (xH) and of the p+ anode region (JNg).
An optimization program was written to extract from
measured IV characteristics the three adjustable
parameters (th, Jnq, and JpQ, the cathode counterpart of
Jnq) of a onedimensional PINdiode model [Mc85]. The
13 2
optimization yielded th=2.6/us and JnQ = 6x10 A/cm at
room temperature. These parameter values were found to be
commensurate with measured turnoff transients of the
LIGBT, discussed below.
In the DMOST mode, the anode is left floating and the
drain is set at a positive voltage relative to the source
(cathode). The DMOST is empirically modeled as a simple
MOSFET (SPICE/level 2 [Ha84]) with a resistor, R ., tied
' epi
to the drain which accounts for the large n~ epi
resistance. Although this model is inadequate in general,
Ill
it suffices here for assessing the validity of the modeling
methodology applied predominantly to the bipolar aspects of
the LIGBT. Fitting this model to the measured
linearregion transconductance, we extract values for R
eP1
(325 9), the threshold voltage (2.6 V), and the
transconductance factor (1.9X10^ A/V).
In the LIGBT mode, the drain is left floating and a
positive voltage is applied to the anode. With the gate
biased above the threshold voltage, the nchannel supplies
base current for the lateral p+n~p BJT. Our
quasitwodimensional modeling of this transistor is done
by partitioning it into two onedimensional transistors,
and Q2, each represented by BJT modules described in
Section 5.2. The partitioning is defined based upon
results we obtained from PISCES simulations, which show
that the ratio of lateraltovertical injection from the p+
anode (emitter) is nearly excitationindependent. Figure
53 shows a typical PISCES result for the hole current
distribution in our test structure for the LIGBT mode of
operation. The onedimensional current flow in the center
section of the structure is clearly seen and demonstrates
that the quasitwodimensional modeling via partitioning is
a viable approach. The active area and base width for
are defined by the anode diffusion depth and the geometry,
as illustrated in Figure 51. The base width and area for
Q2 are defined to make the simulated current agree with
112
Figure 53
PISCES simulation for the
shown in Figure 51. The
the negative hole current
current vectors around the
LIGBT structure
arrows indicate
vectors. The
junctions (high
grid density) have been removed for
illustrative clarity.
113
experimental results. To first order, they may be
estimated from PISCES results. This particular partition
is indeed representative of the device as implied by (a)
PISCES simulations, (b) experimental decomposition of
current voltage characteristics, and (c) relative
excitations of Q^ and Q2 in the hybrid HIGBT mode of
operation discussed later.
The SPICE model for the LIGBT mode is shown in Figure
54. It consists of a simple MOSFET and 11 UDCSs. The
UDCSs labeled with the subscript one represent and those
with the subscript two represent Q2. The current source
ICNPN moc^e*s the third constituent BJT at the cathode as
it, when activated by the voltage drop in the pbase
reflected by RpB> effects the onset of latchup, which is
discussed later.
In the hybrid HIGBT mode of operation, the anode and
drain are tied together and raised to a positive voltage
relative to the source. The gate voltage, as in the the
LIGBT mode, is above the threshold voltage. For low drain
voltages, the device behaves as a DMOST, in series with a
large resistance, R .. The anode does not inject because
epi J
it is at the same potential as the drain. As the drain
current through R ^ is increased, an internal voltage drop
develops (vertically in this particular device) across a
portion of the epi region. When this voltage drop becomes
approximately 0.6V (viz., a diode drop) a portion of the
Figure 5
114
r
Network representation for the LIGBT mode
of operation.
115
anode (Q^) becomes forwardbiased and begins to inject
holes into the base region, subsequently modulating
and increasing the conductance of the device. Experimental
decomposition of the total current into its constituent
anode end drain components has revealed that this abrupt
increase in conductance, after the LIGBT is activated,
results primarily from the modulation of R and not from
epi
an increase in the anode (BJT) current. The modulation of
this resistance tends to increase the DMOST current, but
also tends to limit the excitation of which is driven
by the internal voltage drop. We note that physical
insight predicts and experimental results confirm that this
drop activates predominantly and not Q2, which is one
reason why our assumed partitioning is representative.
In Figure 55 we show the experimental decomposition
of anode and drain current for the HIGBT mode of operation.
Also shown, for comparison, is the LIGBT currentvoltage
characteristic. Figure 55 clearly illustrates that the
anode current in the HIGBT mode is only a small fraction of
the total current, and furthermore, only a fraction of the
IGBT current. This decompostion and comparison of internal
currents verifies our partioning scheme and also explains
why the latchup onset for the HIGBT mode is much greater
than that for the LIGBT mode. In both modes of operation
the emitter current of I is approximately the same
at the onset of latchup. Obviously however, the primary
(
(mA)
116
Measured LIGBT current versus the anode
voltage and measured HIGBT current and
anode component of HIGBT current versus
the anode/drain (shorted) voltage.
Figure 55.
117
conduction mechanisms and the appropriate partitioning of a
particular HIGT depend critically on the device geometry,
as shown in [Mu87], and demonstrated in Section 5.4.
The SPICE model for the hybrid device is shown in
Figure 56. It contains modules for the MOSFET, two
resistors R and R the sum of which is R and a
nS nB epi
single lateral pnp transistor, The value for RnB
(458), which we assume to be constant, is estimated by
noting that it takes about 0.6V (a diode drop) of internal
voltage drop at the trigger current to turn on The
modulation of R .is semiempirically accounted for in R .
epi c 2 nS
which is simulated by a UDCS, as discussed below.
The portion of the DMOST drain resistance associated
with RnS is a function of the total majority carrier
concentration, and thus is a function of the carrier
injection by The variation of RnS with injection level
is modeled by using an average excess hole (electron, p=n)
density, p:
W
5 W J p(x,dx *
VB1
qWA
(510
where p(x) is given by (51), and Qg is given by (57)
We
can use (510) to express Rng:
118
Figure 56. Network representation for the HIGBT mode
of operation.
119
R
nS
L
avct
L
MVNepi + P>
(511)
where L is the
crosssectional
depends on p.
substitution for
resistor
area, and
A simple
p yields:
length, Av is the vertical
a is the conductivity, which
algebraic manipulation and
nS
1 +
B1
qAWN
epi
(512)
where Rq is the value of Rfig when p=0.
Both the LIGBT mode and the HIGBT mode can undergo
static or dynamic latchup. Static latchup occurs when
the collector current of Ic^, produces approximately a
diode voltage drop across the lateral resistance RpB in the
base of the parasitic n+pn transistor. When this voltage
drop develops, electrons are injected by the n+pn_ BJT into
the base of Q1, increasing its conduction, and hence
triggering the regenerative process associated with the SCR
[Gh77] defined by and the n+pn~ BJT. Removal of the
gate voltage at this point will not turn off the LIGBT or
HIGBT since the DMOST supplies only a small fraction of the
base current for and the main path for current flow is
now through the SCR, which can only be turned off by
reducing the total current below the holding point.
120
Experimental results and computer simulations have
indicated that the latchup point is only a weak function
of the gate voltage and that the base resistance, R^g, is
the most important parameter in determining the onset of
latchup because of the exponential voltage dependence of
the injected electrons. We note that the gain of the n+pn~
BJT also has an influence on the latchup point, albeit not
a strong one. In the dynamic case, both the charging
dQ
cu
JC
rrent, ^ Â£ and the transient collector current
contribute to the voltage drop across R^g and hence aid in
inducing latchup.
The onset of latchup in both the LIGBT and HIGBT
modes is simulated by the network models in Figure 54 and
Figure 56 via a voltagecontrolled current source I
CNPN
(Igsexp (VriR/VT) ) in which the controlling voltage, V^R, is
pB' T
pB'
developed across the assumed constant n+pn base
resistance, RpB* T^e Preexponential factor, Igs, is
related to the gain of the n+pn~ BJT through the Gummel
number. However, PISCES simulations have shown that R _
pb
undergoes significant conductivity modulation just prior to
latchup, and hence R D and Icc should be considered as
p D O
semiempirical modeling parameters. Because of the
SS
physical nature of our models, the values used for I
(2X10 ^A) and R (888) are close to those predicted from
pb
PISCES simulations. Note in Figure 54 and Figure 56 that
121
the onset of latchup is properly accounted for in the
dQjCi
models as the charging current, gt' contributes to the
voltage drop across and hence helps to induce latchup.
5.4 Simulations/Verification
In Figure 57 we show modelsimulated and measured
currentvoltage curves for the LIGBT mode of operation for
three different values of the gate voltage. For
illustrative clarity, the measured curves were cut off just
prior to latchup. The agreement between experiment and
theory is good (~10% error), thus lending support to our
particular partitioning and modeling methodology.
Discrepancies between the model predictions and
experimental results may be attributed to the firstorder
DMOST model (SPICE/Level 2) that we used.
In Figure 58 we compare measured and modelsimulated
transient turnoff characteristics of the LIGBT. At time
t=0 the gate voltage is removed and a typical twophase
turnoff transient, as discussed in Chapter 3, is observed.
Our model simulations are in good agreement with
experiment. Discrepancies between the model and experiment
may be attributed to parasitics associated with the probe
station, since our transient measurements were performed on
a wafer and not on mounted devices. The turnoff time may
seem faster than expected for a lifetime of 2.6//S, but
this is due to the large proportion of base current, a
(mA)
122
Figure 57. Modelsimulated (solid) and measured
(dashed) LIGBT anode current versus
anode voltage for three values of gate
voltage (VG = 12V, 10V and 8V from left to
right). The measured curves are terminated
just prior to the onset of latchup; the
modelsimulated curves are terminated just
prior to the predicted latchup onset.
123
Figure 58. Modelsimulated and measured LIGBT anode
current versus time for a resistive load
of 300 52 and offstate voltage of 4.5 V.
The gate voltage of 10 V falls to zero in
200 ns.
124
substantial fraction (1/2) of which is p+emitter
recombination (first term in (54)). The expeditious
effects of anode recombination on the LIGT turnoff
transient have been demonstrated in Chapter 3. We stress
that such transient simulations are not possible with
conventional SPICE transistor models. We also note that if
the gate voltage is removed fast enough, then the sum of
the transient collector current and collectorbase junction
displacement current may be sufficient to forward bias the
n+pn transistor and subsequently cause dynamic latchup.
For the circuit conditions shown in Figure 58, dynamic
latchup will occur if the gate voltage is removed in less
than five nanoseconds.
In Figure 59 we show measured currentvoltage curves,
terminating at latchup, for the HIGBT mode of operation
for three different values of gate voltage. It can be seen
that the trigger current for the LIGBT (Q^) excitation is
approximately 13mA, independent of VG, implying that an
internal voltage drop is responsible for the triggering.
The onset voltage may be estimated by using our network
model for the HIGBT shown in Figure 56 and noting that the
applied voltage splits between RnB' RnS' an<^ tlie DM0ST
channel resistance. The total voltage across the HIGBT,
just prior to triggering, consists of three terms: a
channel drop, VCH> which depends on the DMOST gate voltage,
a drop across Rng, and a drop across RnB, which is
125
t (ns)
Figure 59. Measured HIGBT anode/drain current versus
anode/drain voltage for three values of
gate voltage (VQ = 6V, 8V and 10V from right
to left respectively). The measured curves
are terminated just prior to the onset of
latchup.
126
approximately a diode drop, V^. The voltage drop across
R then is simply the current through R times R _
nb J nB ns
(VcjRnS/RnB) The total voltage across the HIGBT, just
prior to triggering, may then be expressed as,
V^H+V^(1+Rng/Rn0). Thus the relative magnitudes of RnS and
RnB greatly influence the onset voltage. To effect optimal
HIGBT design (low onset voltage), RnS should be made much
less than RnB* Later we will show that RnB plays an
important role in determining the transient turnoff
characteristics. The increase in total current immediatly
after the triggering is due predominantly to an increase in
the DMOST current as a result of modulating R and as
3 ns
discussed previously in Section 5.3.
In Figure 510 we show corresponding SPICE model
currentvoltage curves for the HIGBT. Note that the
triggering points for the hybrid mode of operation are
reliably predicted, as well as the latchup onsets. We
note, however, that although our model modestly simulates
the DMOST region, the predicted conductance in the hybrid
mode is less accurate. This inaccuracy is due in part to
the semiempirical approximate representation (511) of the
modulated DMOST resistance. More physical IJDCS modeling of
this highly nonlinear modulation could be done to improve
the accuracy. However, to effect a generally valid model,
a more physical DMOST module should be developed to replace
the simple SPICE/Level 2 model.
(mA)
127
VA/D
Figure 510. Modelsimulated HIGBT anode/drain current
versus anode/drain voltage for three values
of gate voltage (V =10V, 8V and 6V). The
modelsimulated curves are terminated just
prior to the modelpredicted latchup onset.
128
In Figure 511 we show a modelsimulated transient
turnoff characteristic for the HIGBT. Because the HIGBT
current for our test structure consists mainly of DMOST
drain current, the magnitude of the first phase is quite
large, but the conventional twophase IGBT turnoff
transient is clearly manifested. However, the influence of
RnB' Provides a path for carrier removal during the
transient, needs to be physically characterized so that
design criteria for an optimal HIGBT structure may be
suggested [Fo87], A cursory analysis of how RnB affects
the HIGBT transient turnoff is presented below.
To develop physical insight into how Rnfi affects
transient response, we extend the analysis in Chapter 2 by
adding a term ^vjgB//RnB^ to equation (215), thus
accounting for carrier removal through the drain during
phase two. If we neglect all components of recombination
current, assuming the dominant component of current is
carrier removal through R
differential equation for the charge residing in the base
region during phase two results:
nB, then the following simple
dQ
B
V
dt
JEB
lnB
( 513
If one assumes that VJEB remains relatively constant ()
129
t (ns)
Figure 511. Modelsimulated HIGBT anode/drain current
versus time for a resistive load of 100 G
and offstate voltage of 6 V. The gate
voltage of 10 V falls to zero in 25 ns.
130
during phase two, then the solution to (512) implies a
fast linearly decaying current, inversly proportional to
RnB" 0ur mdel simulations for the HIGBT turnoff
transient (Figure 511) clearly show the predicted linear
nature of the second phase. Experimental corroboration of
this analysis can be inferred from [Go86], where the decay
during phase two is found to be approximately linear in
time. Thus, to effect a fast turnoff, R should be made
ni5
as small as possible, but consistent with the constraint
for a low onset voltage (R _<
nb m3
The circuit topology as depicted in Figure 54, and
used in our simulations, is not capable of maintaining a
latched state (steadystate solution) during transient
operations in SPICE. As a consequence, it is not possible
to observe dynamic latchup directly, i.e., to see the
anode current remain constant with time when the gate
voltage is removed. However, the onset of dynamic latchup
may be indirectly observed by monitoring the current *CNPNf
which represents the injection of electrons by the
parasitic n+pn~ BJT.
We demonstrate the ability of the modeling methodology
to predict the onset of dynamic latchup in Figure 512,
where we have plotted the current, ICNPN/ as a function of
time for a resistively loaded LIGBT turnoff transient.
The sharp increase in IcNPN during the fast turnoff
transient (TFa^=2ns) indicates the onset of dynamic
latchup and is consistent with
(Vui)
131
Figure 512. Modelsimulated ICNPN current versus
time for a resistive load of 125 S and
offstate voltage of 5 V. The gate
voltage (10V) has a fall time (TFall)
of 2 ns for the upper curve and
a T of 200 ns for the lower one.
Fall
132
experimental results. Note that for a slower turnoff
transient (TFal^=200ns), ICNPN remains unchanged during the
time period shown in Figure 512. Eventually, for such a
slow transient, ^cnpn decrease to zero and the onset
of dynamic latchup will not manifest itself. Our
simulations indicate that the primary current responsible
for initiating the onset of dynamic latchup for the above
dQjCi
circuit conditions is the displacement current, Jt'
However, for other circuit conditions the increase in the
transient collector current could be made significant. We
note that the utility of the model to predict the onset of
dynamic latchup will make it useful for optimizing device
design under an actual circuit (transient) environment.
5.5 Summary
We have developed a device modeling methodology needed
for the CAD of HV/P ICs that is also useful for optimal
device (process) design. The methodology is based on a
regional partitioning of LIGBT structures through physical
insight gained from numerical simulations (PISCES) and
experimental results (special test devices). The regional
partitioning of a lateral structure defines an array of new
onedimensional device modules, which properly (physically)
model the unique features of HV/P devices. We have
demonstrated this flexible quasi2D methodology on an
LIGBT test structure for all possible active modes of
133
operation. Both dc and transient measurements, including
static and dynamic latchup, support the modeling
methodolgy. In addition, this study points out the need
for further work in extending previous DMOST models [Su80]
for cases when the enhancementmode device has its bulk
region conductivitymodulated, as is the case for the
LIGBT. Also, the physics underlying the onset of latchup
needs clarification, especially in regards to the
conductivity modulation of prior to latchup.
The constituent chargebased modules, which are easily
implemented into SPICE via UDCSs, allow for a network
representation of the structure that can be used to
simulate the device under actual circuit (transient)
conditions, a feature most device simulators do not have.
Consequently, the methodology may be useful in optimizing
device design under an actual transient environment, in
addition to the CAD capability it affords.
CHAPTER 6
SUMMARY AND CONCLUSIONS WITH RECOMMENDATIONS
6.1 Summary and Conclusions
The culmination of this dissertation manifests itself
in Chapter 5 where we brought together the physical
insights and techniques presented in earlier chapters to
develop a methodology for constructing, and implementing in
SPICE, physical network representations for a general class
of HV/P IC devices exemplified by the LIGBT. We verified
our network models by comparison with PISCES simulations
and by comparison with experimental results obtained from
specially designed test structures. Included in the novel
network representations were several highinjection and
unique effects inherent in HV/P IC devices, heretofore not
represented in more empirical (less accurate) equivalent
circuit models. The effects characterized included
conductivity modulation, enhanced back injection,
multidimensional current flow, and the onset of static and
dynamic latchup.
134
135
In Chapter 2 we presented a general methodology for
modeling lateral (p+pmpn+) structures used in HVICs. The
model, verified by direct comparison with experimental
results obtained from specially designed test structures,
was useful in extending the methodology presented in
Chapters 4 and 5 to include the effects of the
punchthrough shield (buffer region) on the carrier
transport in LIGBT structures. The physical insight gained
in developing a GDS model was later used in Chapters 4 and
5 to develop models for IGBT structures, in particular with
regard to the proper accounting for the PINdiode physics,
which underlies the IGBT operation.
In Chapter 3 a physical quasitwodimensional
analytical model for the IGBT turnoff transient was
developed. The utility of the physical insight gained from
the model was instrumental in suggesting optimal device and
structural parameter values for decreasing the turnoff
time without significant derogation of the onstate current
handling capability. In addition, the phenomenological
insight afforded
by
the model
allowed for
the
identification of
the
significant
charging mechani
sms
controlling the transient response,
and thus permitted
key
simplifications to
be
made in the
development of
the
network models presented
in Chapters
4 and 5.
In Chapter 4
we presented an
initial endeavor
at
devoloping a methodology for modeling an IGBT structure and
for implementing the model in SPICE via UDCSs. The
136
methodology presented was flexible and enabled for the
first time the simulation of the unique effects of
conductivity modulation, latchup (static and dynamic), and
moving boundary conditions; however, it required recourse
to FORTRAN subroutines for the solution of the implicit
nonlinear equations rather than utilizing the nonlinear
equation solver inherent in the SPICE2 source code. Thus,
CPU times required for simulations using the methodology
were considerably longer than those using invalid builtin
SPICE2 models; however, they are not prohibitive for
smallscale circuits, where one or two HV/P IC devices are
used. The preliminary work in Chapter 4 provided the
impetus for developing a more effecient means of problem
formulation and subsequent SPICE2 implementation for HV/P
IC device models. Chapter 5, as discussed above, extended
and refined the work presented in Chapter 4.
6.2 Recommendations
There are several avenues for further research which
would enhance the acceptance of our modeling methodology.
For a complete HV/P IC CAD facility, a library of HP/V
device modules is essential. Ideally, such a library would
include a number of internal SPICE2 HV/P device modules,
consisting of, but not limited to models for the PlNdiode,
the DMOST, the LIGBT, and the widebase BJT. Using our
methodology, a user could then construct his own model
137
(subcircuit) for a particular HV/P structure, without
recourse to UDCSs. We now outline several research areas
essential for the construction of a CAD library for HV/P IC
design.
First, we recommend the extension of our empirical
DMOST model. Since the DMOST is an integral part of many
HV/P devices, it is essential that a simple and accurate
model for this common HV/P device be developed. The device
physics underlying the DMOST when the drain region becomes
conductivity modulated needs clarification. The simple Sun
and Plummer [Su78] model is not applicable to DMOSTs in
which the drain undergoes significant
conductivitymodulation, as in the LIGBT.
Second, we recommend extending our widebase BJT model
(Appendix A) for all regions of operation, thus making it a
viable circuitsimulation tool. In addition, since nearly
all LIGBTs employ punchthrough shields, a more
representative widebase BJT would be a p+n+np structure.
The insights gained from modeling the GDS in Chapter 2
would be helpful in characterizing such a transistor
structure.
Third, we recommend the creation of a standard
PINdiode model for circuit simulation. Many HV/P
structures contain this basic device, and such a model
would be useful for parameterextraction methods involving
optimization techniques, as was done in Chapter 5.
138
Fourth, we recommend extending our firstorder
latchup model used in the LIGBT network representation.
The physics underlying the latchup process, including the
latch current and the holding current, needs clarification.
Fifth, we recommend the incorporation of all device
models into the SPICE code, as we feel that UDCSs are
primarily a means for model development. The inherent
problems of nonstandard coding, nonuniform convergence
criteria, numerical instabilites, and long CPU times
preclude the use of UDCSs for practical circuit simulation
in an industrial environment. For example, the eleven
UDCSs comprising the LIGBT model in Chapter 5 contain
nearly 1500 lines of FORTRAN code (see Appendix B). If the
model were directly implemented into the SPICE code, only a
few dozen lines would be needed. Thus, for universal
acceptance of our modeling methodology, the direct
incorporation of our models into the SPICE code is of
paramount importance.
APPENDIX A
HIGHCURRENT TRANSPORT IN WIDEBASE BJTs
In this appendix we briefly overview carrier transport
in widebase (p+n~p and n+p~n) BJT structures. The
approach is based on an ambipolar transport analysis and
has its historical roots set in PINdiode theory [He68].
Consider a p+n p transistor structure operating in the
forwardactive mode for which high injection (p=n>>ND)
obtains in the n~ base region. A straightforward ambipolar
analysis [He68] can be used to equate the electron
recombination current density in the p+ emitter, JN, to the
electron current density in the n base at the edge (x=0)
of the emitterbase junction spacecharge region
(neglecting any spacecharge region recombination), thereby
yielding the following relation between JN and the total
emitter current density, JE:
N
b
F+T
qDAnf
x=0
(A1 )
139
140
where
increasing
is
the ambipolar di
ffusivity,
dp/dx
i s the
of
the hole
(elect
ron) conce
nt
ration. For
current densi
ties,
the second
term
on the
s j
Lde of Al
will
always bee
ome ne
gligible
i s
proportional
to p( 0
) (p(x): x
= 0
) wh
ereas JN
tional to p(0)
2 [ Gh7
7]. Thus,
at
high
current
the
base current
consis
ts primari
iy
of
emitter
ion
current, as
shown
in Chapter
2,
and
equation
used to to find
a limi
ting value
for
the BJT
current gain:
e
pnp
JE JN
JN
1
B
(A2 )
A similar analysis for an n+p n structure yields a
different high current limit for the gain:
8 b .
Hnpn
(A3 )
Physically, the difference between the highcurrent 8s
for pnp and npn transistors results from the unequal
electron and hole mobilities. Thus typical npn and pnp
BJTs used in HV/P ICs have very different limiting 8s. If
141
carriercarrier scattering effects [Gh77] are taken into
account, the mobility ratio reduces to about two, therefore
the limiting 3s will differ roughly by a factor of four.
The physical insight afforded by this simple analysis can
be used to explain several of the fundamental differences
between n and pchannel IGBTs, such as the lower latchup
onset for pchannel IGBTs.
The details for a rudimentary, firstorder,
highcurrent transport model for a widebase BJT have been
described in chapters 4 and 5. and have been summarized,
pictorially, in Figure 52. Needed additions to that
highcurrent model would include modifications to the
system of implicit model equations to account for the
effects of quasisaturation [Je87] and carrier mobility
reduction due to carriercarrier scattering [Gh77] (refer
to Chapter 2).
APPENDIX B
UDCS/SLICE/SPICE MODEL IMPLEMENTATION
In this appendix we briefly overview a representative
UDCS SLICE/SPICE implementation of a chargebased network
representation for a widebase, low3 pnp BJT, as depicted
in Figure 52.
The general theory and mechanical details behind the
implementation of steadystate UDCS network models into
SLICE/SPICE can be found in the SLICE Manual Rev. 4.08
[Ha84]. The general theory behind the implementation of
transient UDCS network models in SLICE is discussed in
Veeraraghavan et al. [Ve86].
The implicit nature of the network model and the novel
use of numerical derivatives (finite differences) for the
transconductances and transcapacitances are delineated via
comment statements in the following FORTRAN code listing,
which details each UDCS subroutine for the BJT model shown
in Figure 52.
142
c
C**A**AA******************************* *************************
C THE FOLLOWING LISTING IS A SUBROUTINE WHICH CALCULATES
C THE EMITTER CURRENT, IE, GIVEN THE NODE VOLTAGES VBE AND VBC
C THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR THE SPECIAL
C FORMAT USED IN CIRCUIT FILES FOR UDCS DEFINED ELEMENTS
C*AA*AA A*AAA*AA ****************** A********A ************** AAA*A*A
c
SUBROUTINE UIELT1(Y,I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND.NI,JNO,IE1,LA
SPECIAL COFMON BLANK
C0tM0N/BL4NK/X< 64)
GOTQC 50,100,200,300 ) I FLAG52
50 CONTINUE
IF(NC.NE.2> JERROR 99010
GOTO 99910
100 CONTINUE
PHI *=,6
ES=1.035E12
NI1.3E10
UN1350.0
UP480.0
6UN/UP
Q1.6E19
VT.025B6
DA2*VT*UN*UP/< UN+UP)
WB
X(LP+1)
T0
XLP+2)
JNO
XCLP+3)
ND
X(LP+4)
AE1
XCLP+5)
H
XOLP+6)
CF
X(LP+7)
XX2
X(LP+8)
XX3
XLFH9)
VBE
X(LC+1)
VBC
X(LC+2)
TH2*T0
LASQRT(DA*TH)
C
C SET Y VALUE OF IE1
C
c
C CONVERGENCE ENHANCEMENT
C
IF(VBE.GT.0.80)THEN
VBECF*VT*LOG(VBE/VT)
END IF
IF(VBE.LT.0.55ITHEN
P0*4I**2*EXP(VBE/VT)/ND
Y O*AEl*DA/WB*P0
FLOY =0.0
GOTO 98?
END IF
IF((VBE.GT.0.55).AND.(VBE.LT.0.60))
P0NI**2/ND*EXP(VBE/VT)
END IF
FLGY2.0
C
c
W WB (2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
Y (B+l )/B*(AÂ£l*JNO*PO**2/NI**2+Q*DA*AEl*PO/LA/TANH(W/LA) )
C
987 CONTINUE
GOTO 99910
200 CONTINUE
C SET Y VALUE OF DIE1/DVBE
C
IF(FLGY.LT.l.0)THEN
Y Q*AÂ£1*DA/WB*P0/VT
GOTO 876
END IF
Z1 2*(B+1)/B*AE1*JN0*P0**2/NI**2/VT
Z2 (B+l)/B*Q*DA*AEl*PO/LA/VT/TANH(W/LA)
Y Z1 + Z2
876 CONTINUE
GOTO 39910
300 CONTINUE
C
C SET Y VALUE OF DIE1/DVBC BY FINITE DIFFERENCE
C
IFCFLGY.LT.1.0)THEN
Y0 .0
GOTO 765
END IF
W WB <2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
Y1
VBC VBC + H
W WB C2*ES*(PHI+ABS(VBC))/CND*Q))**.3
Y2 IHCW/LA) )
Y (Y2YD/H
VBCVBCH
GOTO 99910
765 CONTINUE
99910 CONTINUE
RETURN
END
C
C THE FOLLOWING LISTING IS A SUBROUTINE WHICH CALCULATES
C THE COLLECTOR CURRENT, IC, GIVEN THE NODE VOLTAGES VBE
C AND VBC THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR
C THE SPECIAL FORMAT USED IN UDCS IMPLEMENTATION
C
SUBROUTINE U1CLT1(Y,IFLAG,LP,NP,LC,NC,JERR0R)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND,NI, JNO,I Cl, LA
SPECIAL COmON BLANK
COPWCN/BLANK/XC 64)
60TOC50,100,200,300),IFLAG+2
50 CONTINUE
IFCNC.NE.2) JERROR 99010
GOTO 99910
100 CONTINUE
PHI.6
ES1.035E12
NI1.3E10
UN1350.0
UP4B0.0
BUN/UP
01.6E19
VT.02586
DA2*VT*UN*UP/( UN+UP )
C
C SET Y VALUE OF I Cl
C
WB
XCLP+l)
T0
XCLP42)
JNO
XCLP+3)
ND
XCLP+4)
AE1*
XCLP+5)
H
XCLP+6)
XXI
XCLP+7)
XX2
XCLP+8)
XX 3
XCLP+9)
VBE
XCLC+1)
VBC
XCLC+2)
TH2*T0
LASORTCDA*TH)
C
C CONVERGENCE ENHANCEMENT
C
IFCVBE.GT.0.80)THÂ£N
VBEVT*LOGC VBE/VT)
END IF
IFCVBE.LT.0.55)THEN
PONI**2*EXPCVBE/VT)/ND
FLGY0.0
Y Q*AE1*DA*P0/WB
GOTO 987
END JF
IFCCVBE.GT.0.35).AND.(VBE.LT.0.80))
PO^C I **2/ND*EXP (VBE/VT)
END IF
FLGY2.0
C
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q>)**.5
Sl AE1*JN0/B*CP0/NI)**2
S2 Q*AE1*DA*PO*CCOSHCW/LA)+B)/LA/SINHCW/LA)/B
Y SI + S2 .
C
987 CONTINUE
GOTO 99910
200 CONTINUE
C
C SET Y VALUE OF DIC1/DVBE
C
IFCFLGY.LT. l.OUHEN
Y Q*AE1*DA*P0/WB/VT
GOTO 878
END IF
21 2*AE1/B/VT*JN0*CPO/NI)**2
Z2 AE1*Q*DA*PO*CCOSHCW/LA)+B)/LA/SINHCW/LA)/VT/B
Y Z1 + Z2
876 CONTINUE
GOTO 99910
300 CONTINUE
C
C
C SET Y VALUE OF DIC1/DVBC
C
IFCFLGY.LT.l.OITHEN
Y 0.0
GOTO 765
END IF
W WB C2*ES*CPHI+ABSCVBC))/(ND*Q))**.5
Y1 Q*AE1*DA*PO*CCOSHCW/LA)+B)/LA/S1NHCW/LA)/B
VBC VBC + H
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
Y2 Q*AE1*DA*PO*(COSHCW/LA)+B)/LA/SINHCW/LA)/B
Y CY2Y1)/H
VBC VBCH
765 CONTINUE
GOTO 99910
99910 CONTINUE
RETURN
END
C THIS SUBROUTINE CALCULATES THE VOLTAGE DROP DUE
C TO CONDUCTIVITY MODULATION IN THE BASE REGION
C AS A FUNCTION OF THE NODE VOLTAGES VBE AND VBC
C THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR
C DETAILS IN USING THIS SUBROUTINE IN A UDCS CIRCUIT
C FILE
SUBROUTINE IVEPTKY IFLAG,LP,NP,LC,NC, JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND,NI,JNO,I El,LA
SPECIAL COMMON BLANK
COHMON/BLANK/X (S4 )
GOTOC 50,100*200,300),IFLAG+2
50 CONTINUE
IF(NC.NE.2) JERROR 99010
GOTO 99910
100 CONTINUE
PHI.S
ES1.035E12
NI1.3E10
UN1330.0
UPA80.0
BUN/UP
VT.02586
Q1.6E19
DA 2*VT*UN*UP/(UN+UP)
C
WBXCLP+1)
TO XC LP+2)
JNO XCLP+3)
NDXCLP+4)
AE1 X(LP+5)
H XCLP+G)
XX1XCLP+7)
XX2X(LP+B)
XX3X(LP+9)
VBE X(LC+1)
VBC X(LC+2)
TH2*T0
LA SQRT(DA*TH)
C
C CONVERGENCE ENHANCEMENT
lF(VBE.GT.O.eO)THEN
VBEVT*LOG (VBE/VT )
END IF
IF(VBE.LT.0.53)THEN
FLGY 0.0
P0NI**2*EXP(VBE/VT)/ND
Y 0.0
GOTO 987
END IF
IF((VBE.8T.0.55).AND.(VBE.LT.0.80))
P0NI**2/ND*EXP(VBE/VT)
END IF
FLGY 2.0
CALCULATE W THE ACTIVE BASE WIDTH AND
CALCULATE XS, THE POINT AT WHICH P(X)ND
W WB (2*ES*(PHI+ABS(VBC))/(ND*Q))** .5
ZZ ND/PO*SINH(W/LA)
XSWLA*LOG(ZZ + SORT(ZZ**2+1))
SET Y VALUE OF VEPI
IE1(B+1)/B*(AE1*JNO*PO**2/NI**2+0*DA*AE1*PO/LA/TANH(W/LA))
VDEMVT*(B1)/(B+1)*LOG(PO/ND)
VEPI VDEMSINH(W/LA)*I El*LA/AEl/Q/( UN+UP)/PO*
8L0G(TANH( (WXS)/LA)/TANH(W/LA) )
Y VEPI
987 CONTINUE
GOTO 99910
200 CONTINUE
C
C SET Y VALUE OF DVEP/DVBE
c
IFCFLGY.LT. l.OUHEN
Y 0.0
GOTO 876
END IF
IFLG1
567 CONTINUE
C
C CALCULATE W THE ACTIVE BASE WIDTH AND
C CALCULATE XS, THE POINT AT WHICH PCXJND
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
ZZ ND/P0*SINH(W/LA)
XSWLA*LOG(ZZ + SQRT(ZZ**2+1))
C
C SET Z VALUE OF VEPI .
C
IE1(B+1)/B*(AE1*JNO*PO**2/NI**2+0*DA*AE1*PO/LA/TANH(W/LA) )
VDEMVT*CB1)/< B+l)*LOGC PO/ND)
VEPI VDEMSINH ( W/LA) I E1*LA/AE1/Q/ ( UN+UP ) /PO*
SLOGCTANHC (WXS)/LA)/TANH(W/LA) )
Z2VEPI
IFCIFLG.EO.DTHEN
ZlVEPI
VBEVBE+H
IFLG2
GOTO 567
END IF
VBEVBEH
YCZ2ZD/H
876 CONTINUE
GOTO 99910
300 CONTINUE
C
C SET Y VALUE OF DVEP/DVBC
C
IFCFLGY.LT.1.0)THEN
Y 0.0
GOTO 765
END IF
IFLG1
789 CONTINUE
C
C CALCULATE W THE ACTIVE BASE WIDTH AND
C CALCULATE XS, THE POINT AT WHICH PCXIND
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
ZZ ND/PO*SINHCW/LA)
XSHJLA*LOGCZZ + SQRTCZZ**2+1) )
C
C SET Z VALUE OF VEPI
IEl( B+l )/B*( AE1*JNO*PO**2/NI**2+Q*DA*AE1*PO/LA/TANH(W/LA) )
VDEMVT*(Bl)/(B+l)*LOG(PO/ND)
VEPIVDEMSINH(W/LA)*IE1*LA/AE1/Q/(UN+UP)/P0*
SLOG(TANH( (WXS)/LA)/TANH(W/LA) )
Z2VEPI
IF(IFLG.EQ.1)THEN
ZlVEPI
VBCVBC+H
IFLG2
GOTO 789
END IF
VBCVBCH
YCZ2ZD/H
765 CONTINUE
GOTO 99910
99910 CONTINUE
RETURN
END
C************ A******* A**** ********* A A A ****** ******
C THIS SUBROUTINE CALCULATES THE CHARGE IN THE BASE
C REGION AS A FUCTION OF THE NODE VOLTAGES VBE &D VBC
C FOR THE CHARACTERIZATION OF THE TRANSIENT CHARGING
C CURRENTS BY A UDCS [VE86]
C* ** ***************** ******** *"* ********** *** A A** *
c
SUBROUTINE UQB1( Y, I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND, JNO.NI.JNOl
SPECIAL COMMON BLANK
COMMON/BLANK/X ( 64 )
COMMON/STATUS/OMEGA ,T1ME, DELTA DELOLDC 7) ,AG(7) ,VT,XNI ,
6 EGFET .MODE .MODEDC I CALC, INITF .METHOD, IORD .MAXORD .NONCON,
6 1TERNO.ITEJMO.NOSOLV
COMMON/KNSTNT/TWOPI.XL0G2.XL0G10.R00T2,RAD,BOLTZ,CHARGE,
& CTOK,GMIN,RELTOL,ABSTOL.UNTOL.TRTOL,CHGTOL,EPSO,EPSSIL,EPSOX
IF(TIME.EQ.O.O) THEN
WBlXILP+l)
TO XCLP+2)
JN01XCLP+3)
NDXCLP+4)
AElX(LP+5)
HXC LP+6)
WBWB1
jnojnoi
A AE1
ENDIF
VT.02586
NI1.3E10
UN1350
UP480
BUN/UP
PHI.6
ES1035E12
Q1.6E19
DA2*VT*UN*UP/( UN+UP)
TH2*T0
LASQRT(DA*TH)
GOTO(50,100,200,300),!FLAG+2
50 CONTINUE
RETURN
100 CONTINUE
149
C INITIALIZE THE VOLTAGES WD MAKE CURRENT 0.0 IN OC CASE
C
VBE XCLC+l)
VBC XCLC+2)
1F(TIME.EQ.0.0)THEN
1RVBE.LT.0.56)THEN
P0 NI**2/ND*EXP(VBE/VT)
Y 0.0
FLGY0.0
GOTO 987
END IF
FLGY 2.0
IF< VBE.GT.0.78)P03E16
IF((VBE.GT.0.36).AND.(VBE.LT.O.7B))
P0NI**2/ND*EXP(VBE/VT)
END IF
WNB(2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
QBlQ*A*LA*P0*(COSH(W/LA)1.0)/SINH(W/LA)
XCLP+8) QB1
Y0.0
X(LP+9)Y
X
XCLP+ll) QB1
X(LP+i2)Y
RETURN
ELSE
C
C UPDATE CHARGE AND CURRENT IF LOCAL TRUNCATION ERROR CRITERIA ARE MET
C
!F( ( INITF.EQ.6) .AND. (DELTA.GE.XCLP+10) ) )THEN
X(LP+8)XCLP+ll)
X(LP+9)*X(LP+12)
END IF
QB1Q*A*LA*P0*(COSH(W/LA)1.0)/SINH(W/LA)
X(LP+11)QB1
X(LP+10)DELTA
IF(DELTA.EQ.O.O)THEN
Y0.0
ELSE
Y((QB1X(LP+8))*2.O/DELTA)X(LP+9)
ENDIF
X(LP+12)Y
ENDIF
C NO ERROR CHECKING
YNOER 0
987 CONTINUE
RETURN
200 CONTINUE
C
C SET Y VALUE OF DQB/DVBE
C
IFCFLGY.LT.1.0)THEN
Y 0.0
GOTO 876
END IF
IFCDELTA.EQ.O.O)THEN
Y0.0
ELSE
y Q*A*LA*PO*(COSH(W/LA)1.0)/SINH(W/LA)/VT
Y 2.0+Y/DELTA
ENDIF
876 CONTINUE
RETURN
300 CONTINUE
C
C SET Y VALUE OF DQB/DVBC
c
IF(FLGY.LT.1.0)THEN
Y 0.0
SOTO 765
END IF
IF(DELTA.EQ.0.0)THEN
Y0.0
ELSE
YQ*A*P0*ES^)D/O^ (2*ES* ( PH I+ABS (VBC))/ND*Q) *. 5
Y 2.0*Y/DELTA
ENDIF
763 CONTINUE
RETURN
END
CA****** ********* A ******* A** ********** *********************
C THIS SUBROUTINE CALCULATES THE CHARGE ASSOCIATED
C WITH THE REVERSEBIASED COLLECTORBASE JUNCTION AS A
C FUNCTION OF THE NODE VOLTAGES VBE AND V8C FOR
C CHARACTERIZATION OF THE TRANSIENT CHARGING CURRENTS
C BY A UDCS IVE86]
C
C*************A *********************************** *********
SUBROUTINE UQJC1(Y,I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND
SPECIAL COMMON BLANK
COMMON/BLANK/X( 64)
COMMON/STATUS/OMEGA,TIME,DELTA,DEL0LDC7) ,AG(7) ,VT,XNI ,
Â£ EGFET .MODE .MODEDC, I CALC, INITF .METHOD IORD ,MAXORD,NONCON,
Â£ ITERNO,ITEMNO,NOSOLV
COMMON/KNSTNT/TWOPI ,XL0G2.XLOGIO,R00T2,RAD,BOLTZ,CHARGE,
Â£ CTOK,GMIN,RELTOL,ABSTOL,VNTOL,TRTOL,CHGTOL,EPSO,EPSSIL,EPSOX
IF(TIME.EQ.O.O) THEN
AC X(LP+1)
ND X(LP+2)
XI X(LP+3)
X2 X(LP+4)
X3XCLP+5)
ENDIF
GOTO!50,100,200).IFLAG+2
30 CONTINUE
RETURN
100 CONTINUE
C
C INITIALIZE THE VOLTAGES AND MAKE CURRENT 0.0 IN DC CASE
C
VBC XCLC+l)
IF(TIME.EQ.O.O)THEN
QJCAC*(2.07E12A1.6E19*ND*ABS(.6+VBC))**.3
QJCY
X(LP+8) QJC
Y0.0
X(LP+9)Y
X
X(LP+11) QJC
X(LP+12)Y
RETURN
ELSE
C
C UPDATE CHARGE AND CURRENT IF LOCAL TRUNCATION ERROR CRITERIA ARE MET
C
IF((INITF.EQ.6).AND.(DELTA.GE.X(LP+10)))THEN
o o o
X(LP+8)X(LP+11)
X(LP+9)X(LP+12)
ENDIF
QJCAC*(2.07E12*1. 6E19*ND*ABS( .6WBC) )**.3
QJCY
X(LP+11)QJC
X(LP+10)DELTA
IF(DELTA.EQ.0.O)THEN
Y0.0
ELSE
YCCQJCX(LP+8))*2.0/DELTA)X
END IF
X(LP+12)Y
ENDIF
C NO ERROR CHECKING
YNOER O
RETURN
200 CONTINUE
SET Y VALUE OF DQJC/DUBC
IF
Y0.0
ELSE
Y AC*.5*(2.07E12*1.GE19*ND)*(ABS<.64VBC)**.3)
Y 2*Y/DELTA
Y0.0
ENDIF
RETURN
END
REFERENCES
[Ap79] J.A. Appels and H.M.J. Vaes, "High Voltage
Thin Layer Devices (RESURF devices)," IEDM
Tech. Dig., pp. 238241, 1979.
[Ba81] B.J. Baliga, "Silicon Power Field Controlled
devices and Integrated Circuits," in Silicon
Integrated Circuits, D. Kahng, Ed., Applied
Solid State Science Series, Supplement 2B.
New York: Academic Press, 1981.
[Ba84a] B.J. Baliga, "Switching Speed Enhancement
in Insulated Gate Transistors by Electron
Irradiation," IEEE Electron Devices, vol.
ED31, pp. 17901795, 1984.
[Ba85] B.J. Baliga, "Analysis of Insulated Gate
Transistor Turnoff Characteristics," IEEE
Electron Device Lett.,vol. EDL6, pp. 7477,
Feb. 1985.
[Ba84b] B.J. Baliga, M.S. Adler, R.P. Love, P.V. Gray,
and N.D. Zommer, "The Insulated Gate
Transistor: A New ThreeTerminal MOSControlled
Bipolar Power Device," IEEE Trans. Electron
Devices, vol. ED31, pp. 821828, 1984.
[Ba84c] B.J. Baliga and D.Y. Chen (eds.), Power
Transistors: Device Design and Applications.
New York: IEEE Press, 1984.
[Ba70] R. Baron and J.W. Mayer, Double Injection in
Semiconductors," in Semiconductors and
Semimetals, vol. 6, pp. 202313. New York:
Academic Press, 1970.
152
153
[ B e 8 5 ]
[Be79]
[Ch70]
[Da84]
t De86 ]
[ F15 7 ]
t Fo77 ]
[Fo86a]
[Fo87 ]
[Fo81 ]
H.W. Becke, "Approaches to Isolation in High
Voltage Integrated Circuits," IEDM Tech. Dig.,
pp. 724727, 1985.
F. Berz, R.W. Copper, and S. Fagg,
"Recombination in the End Regions of PIN
Diodes," SolidState Electron., vol. 22,
pp. 293301, 1979.
S.C. Choo, Effect of Carrier Lifetime on the
Forward Characteristics of HighPower Devices,"
IEE trans. Electron Devices, vol. ED17,
pp. 647652, Sept. 1970.
M. Darwish and K. Board, "Lateral Resurfed
Comfet," Electron. Lett., vol. 20, pp. 519 520,
June 1984.
M.J. Declereq and J.D. Plummer, "Avalanche
Breakdown in High Voltage DMOS Devices,"
IEEE Trans. Electron Devices, vol. ED23,
pp. 16, Jan. 1976.
N.H. Fletcher, "The High Current Limit for
Semiconductor Junction Devices," Proc. IRE,
vol. 22, pp. 862872, June 1957.
J.G. Fossum and F.A. Lindholm, "The Dependence
of OpenCircuit Voltage on Illumination Level
in PN Junction Solar Cells," IEEE Trans.
Electron Devices, vol. ED24, pp. 325329,
April, 1977.
J.G. Fossum and R.J. McDonald, "ChargeControl
Analysis of the COMFET Turnoff Transient,"
IEEE Trans. Electron Devices, vol. Ed33,
pp. 13771382, Sept. 1986.
J.G. Fossum and R.J. McDonald, "Analysis of
the Unique Characteristics of the Hybrid
LIGT/DMOST (HIGT)," IEEE Device Research Conf.
Santa Barbara, CA, June 2224, 1987.
J.G. Fossum and M.A. Shibib, "An Analytic Model
for MinorityCarrier Transport in Heavily
Doped Regions of Silicon Devices," IEEE Trans.
Electron Devices, vol. Ed28, pp. 10181023,
Sept. 1981.
154
[Fo86b]
t Ge78]
[Gh77]
[Go8 3]
[Go87]
[G086]
[Ha85]
[Ha52 ]
t Ha84]
[Ha81]
J.G. Fossum and S. Veeraraghavan, "Partitioned
Charge Based Modeling of Bipolar Transistors
for NonQuasiStatic Circuit Simulation,"
IEEE Electron Device Lett., vol. EDL7,
pp. 652654, Dec. 1986.
I.E. Getreu, Modeling the Bipolar Transistor.
New York: Elsevier, 1978.
S.K. Ghandi, Semiconductor Power Devices.
New York: Wiley, 1977.
A.M. Goodman, J.P. Russel, L.A. Goodman,
C.J. Neuse, and J.M. Neilson, "Improved
COMFET's with Fast Switching Speed and
High Current Capability," IEDM Tech. Dig.
pp. 7982, 1983.
C.A. Goodwin, M.A. Shibib, R.A. Furnanage,
C.Y. Lu, P.C. Riffe, N.S. Tsai, and J.L.
Schmoyer, "A Dielectrically Isolated Bipolar
CMOSDMOS (BCDMOS) Technology for High Voltage
Applications," ECS Symposium, Philadelphia, PA,
May 1015, 1987.
P.A. Gough, M.R. Simpson, and V. Rumennik,
"Fast Switching Lateral Insulated Gate
Transistors," IEDM Tech. Dig., pp. 218221,
1986.
S. Hachad, C. Cros, D. Darees, J. M. Dorkel,
and P. Leturcq, "Latchup Critria in Insulated
Gate pnpn Structures," IEEE Trans. Electron
Devices, vol. ED32, pp. 594598, March 1985.
R.N. Hall, "Power Rectifiers and Transistors,"
Proc. IRE, vol. 40, pp. 15121518, Nov. 1952.
Harris Semiconductor Corp., SLICE Manual Rev.
4.08. Melbourne, FL: Harris Semiconductor
Corp., Jan. 1984.
A.R. Hartman, J.E. Berthold, T.J. Riley,
J.E. Kohl, Y.H. Wong, H.T. Weston, and
R.S. Scott, "530V Integrated Diode Switch
for Telecommunications," IEDM Tech. Dig.
pp. 250257, 1981.
A. Herlet, "Forward Characteristics of
Silicon Power Rectifiers at High Current
Densities," SolidState Electron., vol. 11,
pp. 717742, 1968.
[He68]
155
[Je87]
[Ku85]
[La85]
[ L i 6 7 ]
[Mc87]
[Mc85]
[Mu87]
[Mu77]
[Na75]
[Pi8 4 ]
H. Jeong and J.G. Fossum, "Physical Modeling
of HighCurrent Transients for Bipolar
Transistor Circuit Simulation," IEEE Trans.
Electron Devices, vol. ED34, pp. 848905,
April 1987.
D.S. Kuo, J.Y. Choi, D. Giadomenico, C. Hu,
S.P. Sapp, K.A. Sassaman, and R. Bregar,
"Modeling the Turnoff Characteristics of the
BipolarMOS Transistor," IEEE Electron Device
Lett., vol. EDL6, pp. 211214, May 1985.
J.E. Lary and R.L. Anderson, "Effective Base
Resistances of Bipolar Transistors," IEEE
Trans. Electron Devices, vol. ED32, pp.
25032505, Nov. 1985.
J. Lindmayer and W. Schneider, "Theory of
Lateral Transistors," SolidState Electron.,
vol. 10, pp. 225234, 1967.
R.J. McDonald, J.G. Fossum, "Physical Modeling
of LIGT Structures for SPICE Simulation of Power
Integrated Circuits," ECS Symposium, Philadelphia,
PA, May 1015, 1987.
R.J. McDonald, J.G. Fossum, and M.A. Shibib,
"A Physical Model for the Conductance of
Gated PIN Switches," IEEE Trans. Electron
Devices, vol. ED32, pp. 13141320, July 1985.
S. Mukherjee, M. Amato, and V. Rumennik,
"Influence of Device Structures on the
Transient and Steady State Characteristics
of LIGT," ECS Symposium, Philadelphia, PA,
May 1015, 1987.
R.S. Muller and T.I. Kamins, Device
Electronics for Integrated Circuits.
New York: Wiley, 1977.
L.W. Nagel, "SPXCE2: A Computer Program to
Simulate Semiconductor Circuits," Electronics
Research Lab., University of California,
Berkeley, Memo. ERLM250, May 1975.
M.R. Pinto, C.S. Rafferty, and R.W. Dutton,
PISCESII User's Manual. Stanford,
CA: Stanford University, 1984.
156
[Pa86]
D.N. Pattanayak, A.L. Robinson, T.P. Chow,
M.S. Adler, B.J. Baliga, and E.J. Wildi,
"NChannel Lateral Insulated Gate Transistors:
Part I SteadyState Characteristics," IEEE
Trans. Electron Devices, vol. ED33, pp. 1956
1963, Dec. 1986.
[R086]
A.L. Robinson, D.N. Pattanayak, M.S. Adler,
B.J. Baliga, and E.J. Wildi, "Lateral
Insulated Gate Transistors with Improved
Latching Characteristics," IEEE Electron
Device Lett., vol. EDL7, pp. 6163, Feb. 1986.
[Ru8 3]
J.P. Russel, A.M. Goodman, L.A. Goodman, and
J.M.Neilson, "The COMFET: A New High
Conductance MOSGated Device," IEEE Electron
Device Lett., vol. EDL4, pp. 6365, 1983.
[Sh80]
P.W. Shackle, A.R. Hartman, T.J. Riley,
J.C. North, and J.E. Berthold, "A 500 V
Monolithic Bidirectional 2x2 Crosspoint
Array," ISSCC Tech. Dig. pp. 170171, 1980.
[Si 8 5]
M.R. Simpson, P.A. Gough, F. Hshich, and
V. Rumennik, "Analysis of the Lateral Insulated
Gate Transistor," IEDM Tech. Dig., pp. 740743,
1985.
[Sm82]
R.K. Smith, H.W. Becke, J.C. Gammel, M.A.
Shibib, and Y.H. Wong, "An Analytic Model
for the Forward Characteristics of Gated
PIN Switches Applied to Lateral Structures,"
IEDM Tech. Dig., pp. 1114, 1982.
[Su80]
S.C. Sun and J.D. Plummer, "Modeling of the
OnResistance of LDMOS, VDMOS and VMOS Power
transistors," IEEE Trans. Electron Devices,
vol. ED27, pp. 356367, Feb. 1980.
[Va76]
A. Van der Ziel, Solid State Physical
Electronics. Englewood Cliffs, New Jersey:
PrenticeHall, 1976.
[Ve86]
S. Veeraraghavan, J.G. Fossum, and W.R.
Eisenstadt, "SPICE Simulation of SOI MOSFET
Integrated Circuits," IEEE Trans. Computer
Aided Design of ICAS, vol. CAD5, pp. 653658,
Oct. 1986.
157
[Wa83] R.M. Warner and B.L. Grung, Transistors:
Fundamentals for the IntegratedCircuit
Engineer. New York: Wiley, 1983.
[We82] H.T. Weston, H.W. Becke, J.E. Berthold, J.C.
Gammel, A.R. Hartman, J.E. Kohl, M. A. Shibib,
R.K. Smith, and Y.H. Wong, "Monolithic High
Voltage Gated Diode Crosspoint Array IC," IEDM
Tech. Dig., pp. 14, 1982.
[Yi85] H. Yilmaz, W. Ron Van Dell, K. Owyang, and
M.F. Chang, "Insulated Gate Transistor Physics:
Modeling and Optimization of the OnState
Characteristics," IEEE Trans. Electron Devices,
vol. Ed33, pp. 13771382, Sept. 1986.
BIOGRAPHICAL SKETCH
Robert James McDonald was born in Queens, New York, in
1954. He received the BSEE degree (Magna Cum Laude,
3.75/4.0) from Virginia Tech in 1982 and the ME degree in
electrical engineering from the University of Florida in
1984. His doctoral research involves modeling of HV/P IC
devices.
He received a General Moters Scholarship in 1980, a
Graduate Council Fellowship from the University of Florida
in 1982, and an SRC Fellowship in 1986.
He is a member of Phi Kappa Phi, Eta Kappa Nu, and
IEEE.
158
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
ssum, Cnairman
(e^try G. /Possum, Chairman
Professor of Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Fred A. Lindholm
Professor of Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Arnost Neugro
Professor of
Electrical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Edward K. Walsh
Professor of Engineering Sciences
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Dorothea E. Burk
Associate Professor of Electrical
Engineering
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate
School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December 1987
Dean, Graduate School
r? y
(mA)
127
VA/D
Figure 510. Modelsimulated HIGBT anode/drain current
versus anode/drain voltage for three values
of gate voltage (V =10V, 8V and 6V). The
modelsimulated curves are terminated just
prior to the modelpredicted latchup onset.
141
carriercarrier scattering effects [Gh77] are taken into
account, the mobility ratio reduces to about two, therefore
the limiting 3s will differ roughly by a factor of four.
The physical insight afforded by this simple analysis can
be used to explain several of the fundamental differences
between n and pchannel IGBTs, such as the lower latchup
onset for pchannel IGBTs.
The details for a rudimentary, firstorder,
highcurrent transport model for a widebase BJT have been
described in chapters 4 and 5. and have been summarized,
pictorially, in Figure 52. Needed additions to that
highcurrent model would include modifications to the
system of implicit model equations to account for the
effects of quasisaturation [Je87] and carrier mobility
reduction due to carriercarrier scattering [Gh77] (refer
to Chapter 2).
86
latch during turnoff. Mechanisms that produce latchup in
the IGBT will be simulated and discussed later.
In Figure 45 we show a simulated turnoff transient
for a typical IGBT in Figure 44 with a resistive load.
The turnoff delay reflected by IA(t) results because of
the finite time needed to discharge the gatetocathode
capacitance of the DMOST, and is a function of
GK'
This
discharging time is evident in the VGK(t) decay shown,
which is much slower than the fall of the VG(t) pulse.
Note that VGR(t) influences IA(t) by controlling the
conductance of the DMOST. As shown in Figure 45, the
DMOST transient drain current, ID(t), which, from Figure
42, equals I
+ dQ /dt dQT_/dt, does not begin to
fall until VGR(t) has decreased to a value that causes the
DMOST to saturate (see Figure 43). Further reduction of
V_(t) decreases the DMOST (saturation) current I^(t), and
UI\ D
hence IA(t) as well. Eventually (t) becomes less than
GK'
the DMOST threshold voltage, and ID(t) drops to zero.
IA(t), which includes ID(t), follows the decrease in ID(t)
until it becomes a negligible component, after which lA(t)
decays in accordance with the recombination in the pnp BJT
[Fo86a]. If VGK is reduced very rapidly, for example by
decreasing RGR, then ID falls to zero very quickly,
resulting in the more idealized twophase turnoff
transient [Fo86a,Ba85,Ku85] shown by simulation in Figure
44. In contrast to previous analytical
results
57
Q2
Q IE
n Q0
(316)
where Qq is a constant charge given approximately by
Q0 =
a 2 2 TT ,2
Aq n.(WBxdm)
4inJN0
(317)
With (316), (315) is
firstorder, nonlinear
differential equation for the quasistatic Q (t), which can
P
be solved analytically. If we assume t <
n ri
likely for the asymmetrically doped p+n~ junction, we get
Qp(t)
QpOeXp(
~pOTH [lexp( ^)]
(318)
1 +
Q0Tn
H
where t=0 is now taken as the start of this secondphase
transient. Now I(t) is defined by (313), (314), and
(318), which with (38) yield
Kt)
It exp()
lh
(319)
I1JN0TH
2 2
AK.q nTD
1 p
[1exp()]
H
1 +
(Vui)
131
Figure 512. Modelsimulated ICNPN current versus
time for a resistive load of 125 S and
offstate voltage of 5 V. The gate
voltage (10V) has a fall time (TFall)
of 2 ns for the upper curve and
a T of 200 ns for the lower one.
Fall
62
because V ^ in (33) increases.
For a given t, the
H
turnoff time can be reduced by increasing AI, which
decreases the secondphase decay in I(t) needed to turn off
the device, and by enhancing the significance of the
denominator in (319), which exploits the supraexponential
decay. Physically, these changes lower 0 and make IM0Sr
which is controlled directly and without delay by the gate,
a larger component of the steadyonstate current, and they
make carrier removal through the p+ anode more significant
in the transient. They can be effected by increasing Jnq,
which could be done perhaps by reducing the doping density
and the electron lifetime and/or transit time in the
heavily doped p+anode region [Fo81], The benefit of such
an increase is illustrated in Figure 34. Reducing in
(319), for example by decreasing the BJT collectoremitter
area ratio, would produce similar benefit. We note however
from (33) that if the MOSFET resistances R and R are
ih JD
substantial, then increasing J
NO
and/or decreasing K,
(i.e., reducing 0) could significantly increase RQN.
An n+ punchthrough shield (buffer region), as
described in Chapter 2, may also be used in IGBT
structures. The n+ buffer region reduces the emitter
efficiency of the constituent widebase BJT and, for a
given current level, makes IMqS a larger component of the
steadyonstate current, thus subsequently decreasing the
turnoff time. The methodology for characterizing the
24
where is given by (222). Although not as accurate as
(226), (227) is insightful as we demonstrate later.
We have now defined a simpler analytic model for the
highcurrent J(VA) charactersitic of the GDS. For a given
J, V. is given by (22), in which V is approximated by
(226) or (227), AEpn is approximated by (225), AE^ is
FC
approximated by (214) and (224), and AE?A is approximated
by (212) and (223). We discuss the accuracy of this
model in Section 2.4.
Using the insight accompanying the development of this
model, we now offer a qualitative explanation of the
complete currentvoltage characteristic of the GDS.
Typical measured characteristics are shown in Figure 23.
The data were taken from a GDS test structure having two
anodes placed at different lengths from the cathode.
+
Figure 23 includes plots of I(yPn ) as well as I(V ) for
J +
both anodes. Note that the I(V^n ) characeristics are
virtually coincident.
To explain the characeristics, we consider three
distinct regions of the curves as indicated in Figure 23.
Our models are applicable in region III where
highinjection obtains in the ti region. We note in this
4
region that Iexp(qV^n /kT) except for very high I where
series resistance in the cathode (=352) causes the
+
characteristic to bend.
Further, the I(V^n )
characteristics appears to be independent of W. These
117
conduction mechanisms and the appropriate partitioning of a
particular HIGT depend critically on the device geometry,
as shown in [Mu87], and demonstrated in Section 5.4.
The SPICE model for the hybrid device is shown in
Figure 56. It contains modules for the MOSFET, two
resistors R and R the sum of which is R and a
nS nB epi
single lateral pnp transistor, The value for RnB
(458), which we assume to be constant, is estimated by
noting that it takes about 0.6V (a diode drop) of internal
voltage drop at the trigger current to turn on The
modulation of R .is semiempirically accounted for in R .
epi c 2 nS
which is simulated by a UDCS, as discussed below.
The portion of the DMOST drain resistance associated
with RnS is a function of the total majority carrier
concentration, and thus is a function of the carrier
injection by The variation of RnS with injection level
is modeled by using an average excess hole (electron, p=n)
density, p:
W
5 W J p(x,dx *
VB1
qWA
(510
where p(x) is given by (51), and Qg is given by (57)
We
can use (510) to express Rng:
82
vAk (V)
Simulated IGBT anode current versus
anodecathode voltage for various
gatecathode voltages. The DMOST
threshold voltage is 3 V.
Figure 43.
29
are the corresponding predictions yielded by the model in
Section 2.2 through computeraided numerical solution of
the model equations.
The model parameter values used are listed in Table
21. They were initially estimated from knowledge of the
device structure and of typical ranges of their values,
using the insight afforded by the simpler model in Section
2.3, and then altered such that excellent correlation with
the measured data was obtained. Hence the
experimentaltheoretical agreement not only supports the
model, but also provides estimations of the important
device and material parameters. We stress that these
estimations are not a unique set; relatively small
perturbations about these values do not significantly
change the experimentaltheoretical correlation.
The inferred value Tq=10 psec is not significantly
influenced by bandband Auger recombination [Gh77] because
 17 3
n<10 cm as implied by the calculations. However, the
2 2
values p =920cm /Vsec and p =330cm /Vsec are m
n p
effect average values that reflect significant
carriercarrier scattering [Gh77] at the higher currents,
an effect that we have not explicitly accounted for. This
effect could be incorporated into the model if more exact
parameter determinations were desired, but no additional
insight into the operation of the GDS would be gained
[Ch70] .
135
In Chapter 2 we presented a general methodology for
modeling lateral (p+pmpn+) structures used in HVICs. The
model, verified by direct comparison with experimental
results obtained from specially designed test structures,
was useful in extending the methodology presented in
Chapters 4 and 5 to include the effects of the
punchthrough shield (buffer region) on the carrier
transport in LIGBT structures. The physical insight gained
in developing a GDS model was later used in Chapters 4 and
5 to develop models for IGBT structures, in particular with
regard to the proper accounting for the PINdiode physics,
which underlies the IGBT operation.
In Chapter 3 a physical quasitwodimensional
analytical model for the IGBT turnoff transient was
developed. The utility of the physical insight gained from
the model was instrumental in suggesting optimal device and
structural parameter values for decreasing the turnoff
time without significant derogation of the onstate current
handling capability. In addition, the phenomenological
insight afforded
by
the model
allowed for
the
identification of
the
significant
charging mechani
sms
controlling the transient response,
and thus permitted
key
simplifications to
be
made in the
development of
the
network models presented
in Chapters
4 and 5.
In Chapter 4
we presented an
initial endeavor
at
devoloping a methodology for modeling an IGBT structure and
for implementing the model in SPICE via UDCSs. The
3
(3) the development and experimental verification
of a physical (chargebased) methodology for
modeling HV/P IC structures including the
effects of multidimensional carrier flow,
baseregion conductivity modulation, and
enhanced back injection;
(4) the implementation of the LIGBT model into SPICE
through userdefined controlled sources (UDCSs)
with implicit characterizations and numerical
representations for transconductances and
transcapacitanees.
In Chapter 2, we develop analytic models for the
steadystate forward currentvoltage characteristic of a
(p+pnpn+) gateddiode switch (GDS) [We82]. The models,
which apply generally to gated bipolar switches, are based
on a system of equations derived from basic pindiode
theory. They provide physical insight into GDS operation
and suggest optimal design criteria to minimize the dc and
incremental resistances at high currents. Measured data
taken from a variety of GDS test structures are discussed
in support of the models.
In Chapter 3, a quasistatic chargecontrol analysis
of the unique transient turnoff characteristic of the IGBT
[Be85] is developed. The analysis describes the transient
behavior in terms of steadyonstate current components
that flow in the constituent MOSFET and BJT in the basic
I (A)
28
Figure 24. GDS current versus applied voltage +
(VA) and shieldcathode voltage drop (Vpn )
for two different nregion lengths (W2 J
and ). The solid curves represent
experimental measurements and the points
represent calculations using the
model derived in Section 2.2.
10
Anode Gate Cathode
Figure 21. Gateddiode switch (GDS) cross section and
corresponding onedimensional model.
69
conductivity of the n~ epitaxial region (base) of the IGBT
is modulated by carrier injection from the p+ anode
(emitter), thereby lowering the onresistance but also
increasing the turnoff time because of the excess carrier
storage. The device has been previously modeled [Yi85] by
connecting numerical models for the DMOST and pnp BJT
through a modulated base resitance. Such modeling aids
optimal device design, but is impractical for circuit
simulation and provides little insight into how device
parameters affect the dynamic response of the IGBT in a
circuit, or an HVIC.
We emphasize in this paper the SPICE simulation of the
constituent widebase (lowcurrentgain) pnp BJT and
parasitic npn BJT. We thereby stress the inclusion in the
model of unique characteristics like low BJT gain,
baseregion conductivity modulation, and latchup, which
are not properly accounted for in the builtin SPICE2
models. The DMOST is modeled using a standard level2
SPICE2 MOSFET model [Ha84]. Because of the high level of
conductivity modulation in the n base region, effects of
the parasitic JFET [Yi85] at the drain of the DMOST can, to
first order, be ignored when calculating the onresistance.
The methodolgy presented, however, is flexible enough to
model the JFET effects if desired, but at the cost of
increased model complexity.
22
Therefore for sufficiently high J, (213) and (215)
can be simplified [He68] to
(223)
and
(224)
These simplifications can be easily checked for
selfconsistency with presumed high values of J using the
model in Section 2.2. In fact it can be shown that for a
given J, (223) and (224), with (212) and (214), yield
valid approximations for AE. and ( AE+AE_.T) even when the
diffusion current in the n region, reflected by the second
terms in (13) and (15), is comparable to the drift current.
The approximation (224) enables an additional
simplification regarding AEFn across the p shield.
Combining (14), (18), and (24) yields
(225)
i
I (A)
25
Figure 23. Measured GDS current versus applied voltage
(VA) and shieldcathod voltage drop (V^" )
for two different nregion lengths
and W2). Three distinct regions
(I,II,III) of operation are indicated.
(mA)
122
Figure 57. Modelsimulated (solid) and measured
(dashed) LIGBT anode current versus
anode voltage for three values of gate
voltage (VG = 12V, 10V and 8V from left to
right). The measured curves are terminated
just prior to the onset of latchup; the
modelsimulated curves are terminated just
prior to the predicted latchup onset.
r? y
9
characteristic. The model is more useful as an
engineeringdesign aid than is a direct numerical solution
of the fundamental carrier transport equations [Sm82]
because it is simpler and because it affords physical
insight. The role of the cathode pshield, as well as
those of the n+ cathode, the p+ anode, and the ji region, in
defining I(V^) is clearly described by the model, thereby
aiding optimal GDS design.
The physical insight provided is utilized to develop
an even simpler model, valid for high currents at which RQN
and RDc are of interest, that requires no recourse to
numerical techniques. This model, although not as accurate
as the other, is useful because it enables quick
assessments of possible device design modifications not
only for the GDS, but also, as shown in Appendix A, for the
BJT portion of the LIGBT. The models are supported by
measured data taken from a variety of GDS structures
fabricated at Bell Laboratories (Reading).
2.2 Model Development
The structure of the GDS, fabricated in a "tub" of
dielectrically isolated (DI) silicon, is illustrated in
Figure 21. Because the (anodecathode) length is
typically much longer than the tub thickness, the
onedimensional p+pnpn+ model, also shown in Figure 21,
for the GDS is representative of the basic operation of the
30
5 2
The area A=5xl0 cm of the onedimensional is merely
an effective representation of the actual threedimensional
geometry. It is reasonable because it is comparable to the
actual cathode and anode areas. The anode area is actually
larger than the cathode area, which implies that Jnq and
JpQ are perhaps more comparable in value than shown in
Table 21.
We now discuss measured and predicted resistances of
the GDS. The dc resistance, RDC=VA/I at I=25mA, is plotted
2
versus W in Figure 25. The fact that both the
experimental and theoretical plots become linear for long W
supports in essence our model. This dependence is
explained as follows. From (22) and (227),
R
W
DC
qA(/n+//p)n
1 ,aefa
ql [ 2
AE
FC
AEW
(230)
where I=25mA. We note the actual RDC differs from (230)
C A
by a constant series resistance, (Rg+Rg), associated with
the anode and cathode.
W>3La,
Using (222), we see that for
DC
W2 1 ,6EFA aEFC
qA(//n+i< )LA[n(0)+n(w) ] ql' 2 2
+AEFn>
(231)
81
number [Ge78]. Parameter exractions from latchup
measurements could be done, but would not be straight
forward because of the difficulty in isolating important
current components, e.g., Icp.
4.3 SPICE Simulations and Discussion
In this section we demonstrate the utility of the
modeling methodology used to develop the SPICE IGBT model
in Section 4.2. Results of representative IGBT circuit
simulations on SPICE are presented and discussed. Figure
43 shows simulated dc IGBT currentvoltage characteristics
for various values of gatetocathode voltage, V_v.
Typical parameter values were used for these simulations,
and the results shown are representative of typical
vertical IGBTs. For VGR sufficiently high, the DMOST
operates in the linear region, and the IAVAK relationship,
where VAK is the anodecathode voltage, is linear. This
linearity indicates that the onresistance of the IGBT in
this case is not affected by the nonlinear V ., but is
epi
controlled by the DMOST channel conductance and by contact
resistance. For lower V.,,, I. tends to saturate with
increasing VAK This saturation occurs because the DMOST
is driven to the saturation region, and therefore I^_
(=IB), and hence Icp are limited. For VA less than about
0.6 V, the IGBT does not conduct any appreciable current
because the unmodulated n epi resistance is so large; N
17 epi
XXI
XCLP+7)
XX2
XCLP+8)
XX 3
XCLP+9)
VBE
XCLC+1)
VBC
XCLC+2)
TH2*T0
LASORTCDA*TH)
C
C CONVERGENCE ENHANCEMENT
C
IFCVBE.GT.0.80)THÂ£N
VBEVT*LOGC VBE/VT)
END IF
IFCVBE.LT.0.55)THEN
PONI**2*EXPCVBE/VT)/ND
FLGY0.0
Y Q*AE1*DA*P0/WB
GOTO 987
END JF
IFCCVBE.GT.0.35).AND.(VBE.LT.0.80))
PO^C I **2/ND*EXP (VBE/VT)
END IF
FLGY2.0
C
C
W WB C2*ES*CPHI+ABSCVBC))/CND*Q>)**.5
Sl AE1*JN0/B*CP0/NI)**2
S2 Q*AE1*DA*PO*CCOSHCW/LA)+B)/LA/SINHCW/LA)/B
Y SI + S2 .
C
987 CONTINUE
GOTO 99910
200 CONTINUE
C
C SET Y VALUE OF DIC1/DVBE
C
IFCFLGY.LT. l.OUHEN
Y Q*AE1*DA*P0/WB/VT
GOTO 878
END IF
21 2*AE1/B/VT*JN0*CPO/NI)**2
Z2 AE1*Q*DA*PO*CCOSHCW/LA)+B)/LA/SINHCW/LA)/VT/B
Y Z1 + Z2
876 CONTINUE
GOTO 99910
300 CONTINUE
C
C
C SET Y VALUE OF DIC1/DVBC
C
IFCFLGY.LT.l.OITHEN
Y 0.0
GOTO 765
END IF
W WB C2*ES*CPHI+ABSCVBC))/(ND*Q))**.5
Y1 Q*AE1*DA*PO*CCOSHCW/LA)+B)/LA/S1NHCW/LA)/B
VBC VBC + H
W WB C2*ES*CPHI+ABSCVBC))/CND*Q))**.5
Y2 Q*AE1*DA*PO*(COSHCW/LA)+B)/LA/SINHCW/LA)/B
Y CY2Y1)/H
VBC VBCH
765 CONTINUE
GOTO 99910
99910 CONTINUE
RETURN
END
103
where Wfi is the metallurgical base width and
x^= [ (()+VBC )/qNgpi ] 7 is the (onesided) collectorbase
(step) junction depletionregion width. In writing (51),
we have assumed that the simplified ambipolar transport
equation (p=n) is valid over the entire quasineutral base
region and thus, as done in [Fo77], we have implicitly
neglected the effects of the relatively narrow
lowinjection region near the collector. In addition,
consistent with PISCES simulations for typical operating
conditions, the effects of mobile carriers in the
collectorbase junction spacecharge region, viz.,
quasisaturation [Je87], have been neglected. Indeed in
the widebase transistor, the base widening associated with
quasisaturation is negligible.
In contrast to the GummelPoon model, our (lowp)
module properly accounts for, via (51), possibly
substantial recombination in the base region. Furthermore,
the module must account for possibly substantial
recombination in the p+ emitter region as well as a
currentinduced electric field in the
conductivitymodulated base region which arises to support
the quasineurality. The integral of this electric field
across the base region defines a voltage drop, V i, which
causes the emitterbase junction voltage, VTr,D, to be less
than the applied terminal voltage, V,,D:
Ej JD
100
forwardbias the anode junction and activate the IGBT. The
test structures were fabricated using a
dielectricisolation process [Go78] which eliminates
parasitic substrate effects. The utility of the flexible
and physical modeling is emphasized by SPICE simulations of
the LIGBT which reflects the three possible active modes of
operation. Furthermore, the onset of both static and
dynamic latchup can be be simulated straightforwardly with
the physical SPICE model.
5.2 Modeling Methodolgy
We demonstrate the modeling methology through an
application to the LIGBT structure illustrated in Figure
51. The fabrication of this specially designed device is
described in Section 5.3. To develop a
quasitwodimensional model, we partition the structure
into onedimensional constituent componenets as indicated
in Figure 51. The basis for this partitioning rests upon
physicl insight gained from device measurements in the
various modes of operation (PIN, DMOST, LIGBT, HIGBT) and
from device simulations using PISCES. Subdividing a
multidimensional structure into coupled onedimensional
devices is not uncommon [Li67], but in this case of HV/P
devices the empiricism implied must be minimized through
proper accounting for the underlying physics. The unique
effects of significant back injection, baseregion
conductivity modulation, and the associated low current
46
+ 
where n is
the
drop
across the
underlying p+n
junction; V
J epi
i s
the
vertical
drop across the
(conductivitymodulated) epi
region; IRg
is the drop across
the extrinsic series resistance Rg; and the last term is
the (lateral) drop across the channel of the MOSFET, where,
following [Su80], R and R^ represent effective
lumpedchannel resistances of the "seriesconnected"
enhancement and depletionmode devices. The implicit
formulation in terms of the junction voltages for the
steadystate IGBT transport problem, and its corresponding
numerical solution, are given in chapters 4 and 5.
The conductivity modulation that produces the
excellent steadystate forward currentvoltage
characteristic, viz., low of the IGBT can
ON
unfortunately cause the turnoff time to be much longer
than that of a conventional power MOSFET. A typical IGBT
turnoff transient [Ru83,Ba84b,Ba84a,Ba85,Ku85] is unique
as illustrated in Figure 32. It shows an initial rapid
drop in the forward current, followed by a slower decay,
which reflects the lifetime of the carriers stored in the
epi region. The turnoff time can be shortened by reducing
the carrier lifetime, for example, via electron irradiation
[Ba84a] or intentional metallic impurity doping [Go83].
Such techniques have resulted in turnoff times of less
than 200ns, but with accompanying increases in RQN because
of the reduced carrier injection levels in the epi region.
17
are thus simplified to
P(0)
aefa
n(0) = niexp(2k^) (29)
and
P(W)
aefc
n(W) niexp(y^) (210)
where x=0 and x=W denote the anode and cathode ends of the
ti region, the length of which is W (see Figure 21). The
solution to (27) is then
p(x)
n(0)sinh(WLx) + n(W)sinh(Lx)
= n(x) Aw A (2 11)
sinh(ip)
la
This
solution is coupled to the carrier transport in
the anode and cathode by defining the minoritycarrier
recombination currents in those regions. In the p+p anode,
this current, which can be expressed as [Fo81]
ii
< a
a
AE (212)
JN0eXP( kT >
(212)
85
t(XS)
Figure 45. IGBT anode current, DMOST drain current,
and gatecathode voltage versus time from
simulation of turnoff transient defined
in Figure 44 with resistive load ZL = 35
52 and R = 200 52 (xH = 0.8 /js, Jn0 =
1012 A/cm2) .
136
methodology presented was flexible and enabled for the
first time the simulation of the unique effects of
conductivity modulation, latchup (static and dynamic), and
moving boundary conditions; however, it required recourse
to FORTRAN subroutines for the solution of the implicit
nonlinear equations rather than utilizing the nonlinear
equation solver inherent in the SPICE2 source code. Thus,
CPU times required for simulations using the methodology
were considerably longer than those using invalid builtin
SPICE2 models; however, they are not prohibitive for
smallscale circuits, where one or two HV/P IC devices are
used. The preliminary work in Chapter 4 provided the
impetus for developing a more effecient means of problem
formulation and subsequent SPICE2 implementation for HV/P
IC device models. Chapter 5, as discussed above, extended
and refined the work presented in Chapter 4.
6.2 Recommendations
There are several avenues for further research which
would enhance the acceptance of our modeling methodology.
For a complete HV/P IC CAD facility, a library of HP/V
device modules is essential. Ideally, such a library would
include a number of internal SPICE2 HV/P device modules,
consisting of, but not limited to models for the PlNdiode,
the DMOST, the LIGBT, and the widebase BJT. Using our
methodology, a user could then construct his own model
33
100
80
60
z
o
ce
40
20
0*
Experimental^/
r
/
/
/
/ /
/
/
/
J jf ^Theoretical
/ /
/ v*
7 /
//
1/
i /
f
Rg+R=60
1 L
20 40
W2 (108j.m2)
J L
Figure 26. Measured and calculated incremental
ONresistance versus the square of the
nregion length. The dashed lines
emphasize the linear dependences. The
determination of the extrinsic series
resistance from the extrapolation of the
experimental data is illustrated.
126
approximately a diode drop, V^. The voltage drop across
R then is simply the current through R times R _
nb J nB ns
(VcjRnS/RnB) The total voltage across the HIGBT, just
prior to triggering, may then be expressed as,
V^H+V^(1+Rng/Rn0). Thus the relative magnitudes of RnS and
RnB greatly influence the onset voltage. To effect optimal
HIGBT design (low onset voltage), RnS should be made much
less than RnB* Later we will show that RnB plays an
important role in determining the transient turnoff
characteristics. The increase in total current immediatly
after the triggering is due predominantly to an increase in
the DMOST current as a result of modulating R and as
3 ns
discussed previously in Section 5.3.
In Figure 510 we show corresponding SPICE model
currentvoltage curves for the HIGBT. Note that the
triggering points for the hybrid mode of operation are
reliably predicted, as well as the latchup onsets. We
note, however, that although our model modestly simulates
the DMOST region, the predicted conductance in the hybrid
mode is less accurate. This inaccuracy is due in part to
the semiempirical approximate representation (511) of the
modulated DMOST resistance. More physical IJDCS modeling of
this highly nonlinear modulation could be done to improve
the accuracy. However, to effect a generally valid model,
a more physical DMOST module should be developed to replace
the simple SPICE/Level 2 model.
138
Fourth, we recommend extending our firstorder
latchup model used in the LIGBT network representation.
The physics underlying the latchup process, including the
latch current and the holding current, needs clarification.
Fifth, we recommend the incorporation of all device
models into the SPICE code, as we feel that UDCSs are
primarily a means for model development. The inherent
problems of nonstandard coding, nonuniform convergence
criteria, numerical instabilites, and long CPU times
preclude the use of UDCSs for practical circuit simulation
in an industrial environment. For example, the eleven
UDCSs comprising the LIGBT model in Chapter 5 contain
nearly 1500 lines of FORTRAN code (see Appendix B). If the
model were directly implemented into the SPICE code, only a
few dozen lines would be needed. Thus, for universal
acceptance of our modeling methodology, the direct
incorporation of our models into the SPICE code is of
paramount importance.
c
C**A**AA******************************* *************************
C THE FOLLOWING LISTING IS A SUBROUTINE WHICH CALCULATES
C THE EMITTER CURRENT, IE, GIVEN THE NODE VOLTAGES VBE AND VBC
C THE SLICE USERS MANUAL SHOULD BE CONSULTED FOR THE SPECIAL
C FORMAT USED IN CIRCUIT FILES FOR UDCS DEFINED ELEMENTS
C*AA*AA A*AAA*AA ****************** A********A ************** AAA*A*A
c
SUBROUTINE UIELT1(Y,I FLAG,LP,NP,LC,NC,JERROR)
IMPLICIT DOUBLE PRECISION (AH.OZ)
DOUBLE PRECISION ND.NI,JNO,IE1,LA
SPECIAL COFMON BLANK
C0tM0N/BL4NK/X< 64)
GOTQC 50,100,200,300 ) I FLAG52
50 CONTINUE
IF(NC.NE.2> JERROR 99010
GOTO 99910
100 CONTINUE
PHI *=,6
ES=1.035E12
NI1.3E10
UN1350.0
UP480.0
6UN/UP
Q1.6E19
VT.025B6
DA2*VT*UN*UP/< UN+UP)
WB
X(LP+1)
T0
XLP+2)
JNO
XCLP+3)
ND
X(LP+4)
AE1
XCLP+5)
H
XOLP+6)
CF
X(LP+7)
XX2
X(LP+8)
XX3
XLFH9)
VBE
X(LC+1)
VBC
X(LC+2)
TH2*T0
LASQRT(DA*TH)
C
C SET Y VALUE OF IE1
C
c
C CONVERGENCE ENHANCEMENT
C
IF(VBE.GT.0.80)THEN
VBECF*VT*LOG(VBE/VT)
END IF
IF(VBE.LT.0.55ITHEN
P0*4I**2*EXP(VBE/VT)/ND
Y O*AEl*DA/WB*P0
FLOY =0.0
GOTO 98?
END IF
IF((VBE.GT.0.55).AND.(VBE.LT.0.60))
P0NI**2/ND*EXP(VBE/VT)
END IF
FLGY2.0
C
c
W WB (2*ES*(PHI+ABS(VBC))/(ND*Q))**.5
Y (B+l )/B*(AÂ£l*JNO*PO**2/NI**2+Q*DA*AEl*PO/LA/TANH(W/LA) )
C
987 CONTINUE
GOTO 99910
200 CONTINUE
pasexqpjBAVJOj
' sao
e jog uieaBeip pueqA6jaua
'Z~Z
M 0
Zl
