RELIABILITY OF SILICON BIPOLAR JUNCTION
TRANSISTORS IN INTEGRATED CIRCUITS
By
MICHAEL S. CARROLL
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
1995
ACKNOWLEDGEMENTS
I would like to thank my supervising professors Dr. Arnost Neugroschel and Dr.
ChihTang Sah for their guidance during my doctoral research. I would also like to
thank Dr. Toshikazu Nishida, Dr. Peter Zory, and Dr. L. Elizabeth Seiberling for serving
on my supervisory committee. I also thank Yi Lu, Jack Kavalieros, Michael Han, and
Steven Walstra for helpful discussions, and Kurt Pfaff for assistance in measurements
and data analysis. The financial support from Intel Corporation and the Semiconductor
Research Corporation is also gratefully acknowledged.
TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS................................................................................. ii
A B STR A C T ........................................................................................................... v
CHAPTERS
1. INTRODUCTION TO BIPOLAR JUNCTION TRANSISTOR
RELIABILITY ........................................................................................ 1
1.1. Introduction........................................................................................ 1
1.2. Bipolar Transistor Fabrication.............................................................. 4
1.3. ShockleyReadHall Recombination Theory............................. ... 9
1.4. Shockley Equations for BJT Currents........................... ..................... 11
1.5. SahNoyceShockley Recombination Current................................ 16
1.6. Surface TrapAssisted Tunneling Current............................ ........... 20
1.7. ReverseBias Current in the EmitterBase Junction........................... 25
1.8. Analysis of Base and Collector Currents.................. ... ...... 28
1.9. Theory of HotCarrier OxideSilicon Interface
Trap Generation........................... ......... ..................... 32
1.10. Bipolar Transistor SelfHeating................................ .......... 41
1.11. Summ ary ............................................................................... ............ 45
2. PHYSICAL DEGRADATION MECHANISMS OF SILICON BIPOLAR
JUNCTION TRANSISTORS DURING REVERSE EMITTERBASE
BIA S STRESS........................................................................................ 46
2.1. Introduction......................................................................... 46
2.2. Fundamental Excess Base Current Mechanisms.............................. 52
2.3. Analysis of Hot Carriers During Stress................................ ...... 69
2.4. Analysis of Excess Base Current Kinetics.......................... ....... 78
2.5 Device Models for Excess Base Current............................ ....... 95
2.6. Sum m ary................................................................................. .. .........101
3. CURRENTACCELERATED STRESS METHODOLOGIES
FOR SILICON BIPOLAR JUNCTION TRANSISTORS
UNDER REVERSE EMITTERBASE BIAS STRESS.............................103
3.1. Introduction........................................................................................ 103
3.2. Background and Demonstration of Current Acceleration......................106
3.3. Hot Carrier Analysis During Stress....................................................118
3.4. Demonstration of TTF Extrapolation on Two Technologies.................124
3.5. Sum m ary............................................................................................ 148
4. BASE CURRENT RELAXATION TRANSIENT IN SILICON
BIPOLAR JUNCTION TRANSISTORS AFTER
REVERSE EMITTERBASE BIAS STRESS.....................................150
4.1. Introduction................................. ...................................... .................150
4.2. Experiments and Results............................ .........................................154
4.3. Model for Base Current Relaxation........................................................169
4.4. Sum m ary........................................................... ................................. 186
5. EFFECTS OF HIGH CURRENT DENSITY OPERATION ON SILICON
BIPOLAR JUNCTION TRANSISTOR CHARACTERISTICS..................187
5.1. Introduction........................................................................................ 187
5.2. Experiments and Results......................................................................191
5.3. Model for Current Gain Increase and Emitter Resistance
Decrease.......................................................................................222
5.4. TTF Extrapolation of HighCurrent Stress Data....................................229
5.5. Sum m ary............................................................................................ 237
6. SUMMARY AND CONCLUSIONS...................... ......................................241
6.1. Sum m ary......................................... ................................................... 241
6.2. Oxide/Silicon Interface Reliability....................................................241
6.3. Oxide Charging and Discharging........................................................243
6.4. Polysilicon/Silicon Interface Reliability.............................................244
R EFEREN CES..................................................................................................246
BIOGRAPHICAL SKETCH...........................................................................253
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
RELIABILITY OF SILICON BIPOLAR JUNCTION
TRANSISTORS IN INTEGRATED CIRCUITS
By
MICHAEL S. CARROLL
December 1995
Chairman: Dr. Almost Neugroschel
Cochairman: Dr. ChihTang Sah
Major Department: Electrical and Computer Engineering
The reliability of silicon bipolar junction transistors in integrated circuits is
investigated. The decrease in the commonemitter current gain during bipolar transistor
operation in BiCMOS circuits is analyzed and modeled. The current gain degradation
during reversebias stress of the emitterbase junction is found to be the result of
interface trap generation at the oxide/silicon interface and charging of the oxide layer
near the emitterbase junction perimeter by energetic electrons and holes to increase the
base current. A model for interface trap generation based on the rupture of weak
impurity bonds by hot carriers is presented to explain the measured kinetics of the
increase in interface trap density. A surface electron channel after heavy reversebias
stress is shown to exist over the quasineutral base from positive oxide charging. The
stress voltage thresholds for positive oxide charging are also measured and analyzed.
Accelerated reverse emitterbase bias stress methodologies are presented which
allow for more rapid and accurate determination of bipolar transistor timetofailure at
low power supply voltages. Hot holes are found to be the primary cause of interface
trap generation for low stress voltages. Significant transistor degradation is measured
for stress voltages as low as 2.5V, indicating bipolar transistor reliability will remain an
important concern in the future.
The base current relaxation transient following reverse emitterbase bias stress is
analyzed and attributed to a decrease of trapped positive charge in the oxide layer near
the emitterbase junction perimeter. The trapped holes in the oxide are modeled to
tunnel from oxide traps to the silicon valence band during base current relaxation. The
relaxation transient is found to occur after a certain delay time. The effects of IB
relaxation are also found to decrease at low stress voltages.
The bipolar transistor reliability during operation at high current densities in the
forwardactive mode is investigated. An increase in the current gain is found at
moderate forward emitterbase bias, and this phenomenon is attributed to the passivation
of polysilicon/crystallinesilicon interface traps in the emitter by atomic hydrogen. A
model is presented which explains the measured results in both n/p/n and p/n/p
transistors.
CHAPTER 1
INTRODUCTION TO BIPOLAR JUNCTION TRANSISTOR RELIABILITY
1.1. Introduction
The bipolar junction transistor (BJT) was invented in 1947 at Bell Telephone
Laboratories to become the first solidstate amplifier. The theory of BJT operation was
first proposed by Shockley in 1949 [1]. In the nearly fifty years following the invention
of the BJT, many improvements have been made in device performance through
extensive work on the optimization of the design and fabrication technology. The
original germanium point contact transistors developed in the late 1940s were replaced
by silicon planar diffused transistors in the early 1960s to allow for costeffective mass
production and the thin base layers necessary for highfrequency applications [2]. This
led to the first integrated circuits, which were manufactured at Fairchild Semiconductor
Corporation using silicon bipolar transistors, diodes, and resistors [2]. By the early
1980s, the metal oxide semiconductor transistor (MOST) had replaced the BJT in many
digital logic applications, with complementary metal oxide semiconductor (CMOS)
logic gaining widespread use. However, the advent of bipolarCMOS (BiCMOS) logic
in the mid 1980s suggests BJTs will continue to be important for future VLSI circuit
applications where the superior load capacitance drive of BJTs over MOSTs is
necessary. However, the reliability of submicron, polysiliconemitter BJTs in integrated
circuits still has several important unresolved issues which must be studied for BiCMOS
and other logic designs to reach their full potential.
The decrease in commonemitter current gain (3F) when the emitterbase junction
of a BJT is reverse biased during circuit operation has been studied extensively since it
was first reported by Collins in 1968 [325]. This phenomenon has been determined to
be the limiting factor in BiCMOS circuit reliability in some designs [8], which has
intensified the investigation in recent years. Although a consensus has been reached that
this phenomenon is mainly due to hot carrier degradation of the SiO2/Si interface near
the emitterbase junction, the fundamental mechanisms causing the device degradation
have not been conclusively demonstrated. Several empirical modeling attempts have
had limited success in predicting the BJT OF degradation rate in some cases [8,9,11], but
faster, more accurate, and physicallybased methods of determining the reliability of
new BJT technologies are needed for the lowvoltage (3.3V and 2.5V), deepsubmicron
BiCMOS technologies anticipated in the future.
Operation of polysiliconemitter BJTs in the normal, forwardactive mode at high
current densities has been shown to cause fluctuations in 3F as well as a decrease in the
emitter resistance [2633]. This reliability issue is expected to become more important
as BJT emitter dimensions continue to decrease and current densities surpass ImA/lim2
or 100kA/cm2. A decrease in PF has been measured on many transistor technologies,
and is modeled to be the result of SiO2/Si interface degradation near the emitterbase
junction [2629]. An increase in pF during high current density operation has also been
measured in many instances and is attributed to the capture and release of atomic
hydrogen at grain boundaries in the polysilicon emitter contact and at the
polysilicon/silicon interface in the emitter [3133], by extending the model for boron
acceptor deactivation in ptype silicon developed by Sah [34]. However, only limited
work has been done on the PF instabilities at high current densities, and a detailed
analysis is critical to improve the understanding of this problem.
The reliability issues introduced above will be studied and modeled in this work
in an effort to determine the physical mechanisms involved, improve device timeto
failure (TTF) extrapolation methods, and evaluate the potential reliability problems at
the lowvoltage circuit operation expected in the future. This will serve as an important
step in determining the necessary improvements to submicron BJT designs.
In this introductory chapter, submicron silicon BJT fundamentals for reliability
analysis are presented as a foundation for studying BJT reliability. The important BJT
current components encountered during operation will be characterized, and a model for
trap generation at the SiO2/Si interface from hot carriers will be presented. In Ch.2, the
fundamental PF degradation mechanisms during reverse emitterbase bias stress will be
analyzed and modeled. In Ch.3, two accelerated methods for determining the TTF for
BJTs due to PF degradation during BiCMOS circuit operation will be presented and
demonstrated. This analysis will also determine which degradation mechanisms are the
most important for lowvoltage operation in present and future circuits. In Ch.4, the
post reversebias stress relaxation transient of the base current in submicron BJTs will
be examined and modeled. In Ch.5, the changes in PF and the emitter resistance
decrease during high current density forwardactive operation will be analyzed. Finally,
a summary of this dissertation is given in Ch.6.
1.2. Bipolar Transistor Fabrication
Since the majority of the reliability issues for submicron BJTs have been
attributed to device degradation at the perimeter of the heavily doped emitterbase
junction [333], the characteristics of the emitter and base layers in different BJT
designs must be taken into account when attempting to explain the fundamental
degradation mechanisms. Therefore, the design and fabrication steps to form BJTs in
VLSI applications must be examined. Submicron BJTs are generally fabricated using
polysilicon emitter contacts to enable shallow emitterbase junction depths. BJTs which
are to be integrated into BiCMOS circuits may have a fabrication technology which fits
as closely as possible into the standard CMOS processing steps. In this case, the
technology is referred to as CMOSbased BiCMOS process. If a high performance BJT
is integrated into a CMOS process with little change in the BJT design, the technology
is referred to as a bipolarbased BiCMOS process. In both cases, some compromises to
the device designs must be made to allow costeffective manufacturing. Two designs
have emerged to satisfy this need. The majority of BiCMOS BJTs reported thus far
have consisted of one of these basic designs, possibly with some additional features to
enhance the performance or reliability.
The first design is the selfaligned BJT, which has similar fabrication steps as the
selfaligned MOS transistor. A crosssection of two typical selfaligned polysilicon
emitter bipolar transistors are shown in Fig. 1.1 [35, p.87]. For the single polysilicon
level selfaligned BJT shown in Fig.l.1(a), the ptype intrinsic base is formed by a
boron implant inside an ntype well. A polysilicon layer is then deposited and
implanted with arsenic to form the n+ polysilicon emitter. A nitride layer is deposited
on top of the n+ polysilicon layer. These layers are then patterned to form the active
device area. This is followed by a p+ implant to form the extrinsic base contact. The
base contact is automatically aligned to the active device area, since the polysilicon
emitter contact is used as the implant barrier. The silicon portion of the emitter is
formed by outdiffusion from the n+ polysilicon layer. For the double polysilicon level
selfaligned BJT shown in Fig.l.1(b), a p+ polysilicon layer is used to form the base
contact. A hole is opened in the p+ polysilicon layer to form the active device area. The
n+ polysilicon layer is then added, and the n+ silicon emitter is formed by outdiffusion
from the polysilicon. For both of these processes, sidewall oxide spacers allow for close
alignment of the metal interconnect layers. The collector contact is formed by an n+
implant into the ntype collector layer on the edge of the device. The advantage of the
selfaligned BJT design is that it is easily integrated into a CMOS process and produces
a very compact and high performance transistor design, since the active transistor area is
automatically aligned to the p+ base contact. However, the close proximity of the
highly doped n+ silicon portion of the emitter and the p+ base contact region may
produce a high electric field in this region. This may cause reliability problems in
BiCMOS applications, as will be analyzed in Ch.2. Some processing variations similar
Si02
_ P+ p n+ P
I I\I
n well
p substrate
I I1
n well
p substrate
(b)
Fig.1.1 BJT crosssections for single polysilicon and double polysilicon selfaligned
processes. Adapted from Alvarez [35, p.87].
P+ jn P+
to the lightlydoped drain technology in MOS transistors have been used to decrease the
electric field in this region [21].
The second design will be referred to as a non selfaligned BJT. A typical cross
section is shown in Fig.1.2 [35, p.88]. In this design the ptype base is formed by a
boron implant in a ntype well, and a p+ base contact is implanted at the edge of the p
type base. An oxide layer is then grown, and an opening is etched to form the active
transistor area. The emitter polysilicon is then deposited over the oxide opening and the
silicon emitter is formed by outdiffusion from the polysilicon. An n+ collector contact
is implanted into the ntype collector layer on the other side of the active transistor
region from the base contact. This design is not as compact as the selfaligned BJT,
because more tolerance must be left for alignment of the oxide etch and emitter
polysilicon deposition step which forms the active transistor area. Thus, the ptype base
extends a longer distance between the active transistor area and the p+ base contact.
However, this BJT design may require fewer steps to produce than the selfaligned
process. It also does not place the p+ base contact directly next to the n+ emitter
contact. This decreases the electric field in the emitterbase junction and may increase
the reliability of the transistor during operation in BiCMOS circuits.
For each of the designs mentioned above, a substrate n+ collector (subcollector)
may also be added to the process to improve BJT performance, although this will
increase the complexity of the fabrication due to required epitaxial silicon crystal growth
over the subcollector to form the active device region. The collector technology has not
been found to affect the reliability issues investigated in this work.
SiOo
LP+
_J_ II
n well
p substrate
Fig.l.2 BJT crosssection for a non selfaligned process. Adapted from Alvarez [35,
p.88].
1.3. ShockleyReadHall Recombination Theory
The recombination of electrons and holes in semiconductors determines the
current which flows in p/n junction devices under normal operation. In order to
understand and model BJT operation and reliability, the various recombination
processes which determine the device operation must first be analyzed. The basis for
modeling the recombination kinetics in silicon is the single trap level analysis first
proposed by Shockley and Read [36], which assumes that recombination may be
modeled by a single trap level in the silicon energy gap. The transition rates between
electrons in the conduction band and the traps are the electron capture rate (cn) and
electron emission rate (e ), while the transition rates between holes in the valence band
and the traps are the hole capture rate (Cp) and hole emission rate (ep). The steadystate
rates of electron and hole recombination are then
RN = cNPT eNT (1.1)
and
Rp= pPNT epPT, (1.2)
where N is the density of electrons in the conduction band, P is the density of holes in
the valence band, NT is the density of electrons in traps, and PT is the density of holes in
traps. The quantity NTr is defined as the total number of traps, so PT = NTT NT. It is
assumed that the equilibrium values for cn, cp, en, and ep are good approximations for
the values during steadystate situations. The steadystate rates of electron and hole
recombination are required to be equal such that there is no buildup of charge at the
traps over time. Thus, the electron density in the traps may be found by from Eqs.(1.1)
and (1.2) to be
Nr(eN + e )
N N=(eN + ep) (1.3)
cN + e + + P + e
The result in Eq.(1.3) may be substituted into Eq.(l.1) or Eq.(1.2) to find the net
recombination rate of electrons and holes. For steadystate conditions which are close to
equilibrium, the recombination rate can be further simplified to be
NP n.2
R = 1 (1.4)
(N + N)tp + (P + P1)Cn
where
N = en/c = niexp[(ET' E)/kT] (1.5)
and
P1 = ep/Cp = niexp[(EI ET')/kT]. (1.6)
The quantity ni is the intrinsic electron concentration, ET' is the effective trap energy
which includes trap degeneracy, E1 is the intrinsic Fermi Energy, k is the Boltzmann
constant, and T is the temperature. The quantities =n 1/c NNr and Tp = 1/cpNT are the
steadystate recombination lifetimes of electrons and holes. Eq.(1.4) may be simplified
for the case of ntype silicon where NN >> PN, ni, N1, and P1. In this case, the
recombination rate simplifies to
R = (PN PNo)/tp (1.7)
where PN is the hole concentration in the ntype silicon, and PNo = ni2NN is the
equilibrium hole concentration. Therefore, the recombination rate is found to vary
linearly with the excess minority carrier density in neutral silicon, which is the basis for
Shockley's minority carrier injection theory.
1.4. Shockley Equations for BJT Currents
The important BJT current components for forwardactive operation of a n+/p/n
transistor are shown in Fig.l.3. Ideal expressions for these currents were derived by
Shockley in 1949 [1], and a similar analysis is repeated in this section as a foundation
for modeling BJT reliability. The electron current in the base will be examined first.
The forward bias on the emitterbase junction during forwardactive operation
establishes an injected minority electron concentration, NB, in the ptype base. At the
edge of the emitterbase spacecharge region, x=0g, for lowinjection conditions the
injected electron concentration is related to equilibrium electron concentration in the
base, NBO = ni2/NAA, by
NB(OB) = NBo exp(qVBE/kT), (1.8)
where NAA is the ptype base doping concentration, q is the charge of an electron, and
VBE is the forward emitterbase bias. If the collectorbase junction is assumed to be
shorted (VcB=0) during normal BJT operation, then
NB(XB) = NB0. (1.9)
The steadystate electron transport in the quasineutral base can be approximated by
considering only the diffusion of injected electrons according to the equations
JN = qDBdNB/dx (1.10)
B
OV
1 I,JB
O JPr
JN(OB) J((X)
Jc
JE
+
Jp(OB)
O
Jp(OE)
emitter
XE
JN(OE)
OE OB
base
XB Oc
collector
ovC
OV
. p
Fig. 1.3 Schematic diagram of a BJT showing the important current densities which
contribute to the emitter current, base current, and collector current in
forwardactive operation. Solid dots represent electrons in the conduction
band and circles represent holes in the valence band. Adapted from Sah [42,
p.833].
VBE
E
JN(OC)
dJN/dx = RN = q(NB(X) NBO)/B, (1.11)
where the recombination rate in the quasineutral base is assumed to vary linearly with
the excess injected electron concentration, Ng NBO, as demonstrated in Eq.(1.7). The
quantity Dg is the electron diffusivity in the base, and tB is the electron lifetime in the
base. The solution to Eqs. (1.10) and (1.11) using the boundary conditions in Eq.(1.8)
and (1.9) is
sinh[(XB x)/LB
NB(x) NBO = NBO[exp(qVBE/kT) 1] B (1.12)
where LB = (DBgB)0.5 is the electron diffusion length in the base. The electron currents
in the base at the edges the emitterbase and collectorbase spacecharge regions, x=OB
and x=XB, are found to be
JN(B) = (qNBoDB/LB) [exp(qVBE/kT) 1] ctnh(XB/LB) (1.13)
and
JN(XB) = (qNBODB/LB) [exp(qVBE/kT) 1] csch(XB/LB) (1.14)
by substituting Eq.(1.12) into Eq.(1.lO). The difference of JN(0B) JN(XB) is the
electron current lost to recombination in the base as electrons diffuse from x=OB to
x=XB. An equal hole current must flow into the base to compensate for the holes which
recombine with the electrons. Therefore, the hole current due to carrier recombination
in the base is
[ cosh(XB/LB) 1
JPr = (qNBoD/L)[exp(qVBE/kT) 1] (1.15)
sinh(X BlL B)
The injection of holes into the emitter from the ptype base by the forwardbiased
emitterbase junction also occurs in BJTs. This is the major component of base current,
Ig, in most current BJT designs before aging. The density of injected holes in the
emitter at the edge of the emitterbase spacecharge region, x=0E, is
PE(0E) = PEO exp(qVBE/kT), (1.16)
where PEO = ni2/NDD is the equilibrium hole concentration in the emitter, and NDD is the
emitter doping concentration. The concentration of holes at the emitter contact, x=XE,
generally depends on the contact recombination velocity, SE, for typical submicron
transistors with shallow emitter layers and polysilicon emitter contacts. The
recombination rate of holes at the emitter contact can be modeled to vary linearly with
the excess hole concentration in the emitter at the silicon surface, PE(XE) PEO, such
that
RP(XE) = SE[PE(XE) PEO] (1.17)
The recombination rate of holes at x=XE, Rp(XE), must also be equal to the minority
carrier hole current at x=XE. Therefore,
JP(XE) = SE[PE(XE) PEO' (1.18)
The hole transport in the emitter layer is governed by diffusion such that
dJp/dx = q(PE(x) PEO)/tE, (1.19)
where TE is the hole lifetime in the emitter. The solution of Eq.(1.19) evaluated at x=0E
with the boundary conditions in Eqs.(1.16) and (1.18) is [37]
LE/tEsinh(XE/LE) + SECosh(XE/LE)
Jp(E) = qP[exp(qVBE/kT) 1] + (SEE/DE)(XE/E (1.20)
E O BE cosh(XE/LE) + (SELE/DE)sinh(XE/LE)
where LE = (DETE)0.5 is the hole lifetime in the emitter, and DE is the electron diffusivity
in the emitter. Thus, the hole current injected into the emitter is found to have the same
dependence on VBE as the injected electron current in the base, although the dependence
on SE in the emitter makes the expression in Eq.(1.20) more complicated.
The current in the collector layer is dominated by the current from electrons
which are injected from the emitter into the base and reach the collectorbase space
charge region, JN(XB), which was derived in Eq.(1.14). The collector current, Ic, may
be approximated by multiplying Eq.(1.14) by the emitter area, AE, if interband impact
generation in the collectorbase junction spacecharge region is negligible. Therefore,
Ic = (qAEni2DB/NAAL) [exp(qVBE/kT) 1] csch(XB/LB). (1.21)
The base current, Ig, is the sum of the hole current injected into the emitter from the
base plus the hole current which flows into the base to compensate for recombination of
injected electrons. Therefore, Ig is the sum of the currents in Eq.(1.20) and Eq.(1.15).
However, in devices with very short base layer thicknesses, the hole current injected into
the emitter will dominate Ig' So,
S LE/Esinh(XE/LE) + SEcosh(XE/LE)
IB(qAEni2/ND)[exp(qVBE/kT) 1] .C +( EE E) (1.22)
B 1 DD cosh(XE/LE) + (SELE/DE)sinh(XE/LE)
The emitter current, IE, is simply the sum of the Ic and Ig. An important conclusion
from the above analysis is that the ideal components of Ig and Ic will both be
proportional to exp(qVBE/kT) for forward emitterbase biases. However, the ideal
Shockley BJT equations are not adequate to completely describe device operation, since
the generation and recombination currents associated with the emitterbase and
collectorbase spacecharge regions are ignored.
1.5. SahNoyceShockley Recombination Current
The ideal BJT current equations derived in the last section assume that
recombination in the spacecharge region of the emitterbase junction is negligible
during forwardactive operation compared to the injection of electrons from the emitter
into the base and the recombination of carriers in the quasineutral layers. This may not
be the case in some transistors, and the base current associated with carrier
recombination in the emitterbase spacecharge region, or SahNoyceShockley current,
may be quite important. The increase of the base current due to surface recombination
at the SiO2/Si interface has been found to be an important reliability concern in BJTs [3
31]. The recombination kinetics for a single trap level derived by Shockley, Read, and
Hall can be extended to provide an analysis of recombination in the spacecharge region
of a forwardbiased p/n junction. This was first done by Sah, Noyce, and Shockley in
1957 [38]. Since the assumptions leading to the linear dependence of the recombination
rate on excess minority carrier density in Eq.(1.7) are not valid in the spacecharge
region of a p/n junction, a more detailed analysis must be performed. The electron and
hole distributions vs. energy assuming a Boltzmann distribution are
N = nexp[(FN EI)/kT] (1.23)
and
P = niexp[(E Fp)/kT],
(1.24)
where FN and Fp are the electron and hole quasiFermi energies. Eqs.(1.5), (1.6), (1.23),
and (1.24) can be substituted into Eq.(1.4) to obtain an approximate steadystate
recombination rate in terms of the carrier steadystate lifetimes, the intrinsic Fermi
energy, and quasiFermi energies. If n = Tp = r, Eq.(1.4) becomes
^_R = (n/t) sinh[(FN Fp)/2kT] (1
R = (1.25)
cosh[(Ei FNp)/kT] + exp[(Fp FN)/2kT] cosh[(ET' EI)/kT]
where FNP=(FN + Fp)/2 is the average of the electron and hole quasiFermi energies.
The current due to recombination in the emitterbase spacecharge region is
X EB
JSNS = q Rdx, (1.26)
where XEB is the spacecharge region thickness. An analysis of Eq.(1.25) demonstrates
that the recombination rate in the junction spacecharge region depends nearly
exponentially on three quantities: (1) the difference of the electron and hole quasi
Fermi levels in the spacecharge region or approximately the emitterbase junction
voltage, VBE; (2) the energy difference between the intrinsic Fermi level, EI, and the
average of the quasiFermi levels, FNP; and (3) the energy separation between the trap
level, ET, and the intrinsic Fermi level, E1. Therefore, for a fairly uniform trap density
spatially and vs. energy in the silicon energy gap, the maximum recombination rate will
occur for traps near midgap at the point in the spacecharge region where the average of
the two quasiFermi levels is also near midgap. This is illustrated in Fig. 1.4, where the
maximum recombination point is shown by a solid dot. The total recombination current
in Eq.(1.26) may be approximated by integrating only over the shaded area in Fig.l.4,
since this is where the majority of the recombination takes place. The approximate
n+ Si
pSi
VBE
E 
vB
ov
Fig.1.4 Energy band diagram for the emitterbase junction of a BJT showing the
maximum recombination point (solid dot) in the emitterbase space charge
region according to Eq.(1.25) with T = T'. The SahNoyceShockley current
may be approximated by assuming recombination dominates in the narrow
shaded region near this point. Adapted from Sah et al. [38].
thickness of this recombination region, XR, may be found by calculating the length of
the spacecharge region where IEI FNPI < 3kT. For IE, FNpI > 3kT, the
recombination rate has decreased by a factor of ten from the maximum.
Carrier recombination in the emitterbase spacecharge region of a BJT will
increase IB, as holes are required to flow into the spacecharge region to maintain the
steadystate concentration. In most BJTs, the component of IB due to SahNoyce
Shockley recombination current is dominated by surface recombination at the SiO2/Si
interface. This is because the density of traps at the Si/SiO2 interface, NIT, is usually
much larger than the density of traps in the bulk silicon. Energetic carriers are also
known to increase NIT through impact bondbreaking processes. Therefore, the surface
SahNoyceShockley Ig component produces many of the instability problems
associated with BJTs. An approximate expression for this recombination current may
be obtained by assuming that the current is dominated by recombination in the effective
recombination region, XR. The interface traps near midgap are assumed to dominate the
recombination current. If SN = Sp = SO is the recombination velocity of the interface
traps at the maximum recombination point, then Eq.(1.26) becomes [38]
IBSNs = (qARniSo) [exp(qVBE/2kT) 1] (1.27)
The quantity AR = PEXR is the effective surface recombination area, and PE is the
emitterbase junction perimeter. The recombination velocity and, consequently, IBSNs
is directly proportional to the density of interface traps, NIT, through the relation So =
0.5qni7rCOthNI [39]. Another important point from the above analysis is that the Sah
NoyceShockley surface recombination component of Ig is proportional to
exp(qVBE/2kT), while the IB components due to recombination in the quasineutral base
or emitter were shown to be proportional to exp(qVBE/kT) in the last section. Therefore,
the two Ig components may be distinguished by the measured reciprocal slope factor, n,
of the base current, where IB cc exp(qVBE/nkT). The reciprocal slope factor will be
n=1.0 when IB is dominated by recombination in the quasineutral layers, and n=2 when
IB is dominated by recombination in the emitterbase spacecharge region.
1.6. Surface TrapAssisted Tunneling Current
The injection of electrons from the emitter to the base during forwardactive BJT
operation and the recombination of these injected electrons in the quasineutral base and
emitter and in the emitterbase spacecharge region have been analyzed in the previous
two sections. The recombination processes examined so far involved electron and hole
capture and emission at traps in the silicon energy gap based on ShockleyReadHall
processes. Another possible recombination process involves quantum mechanical
tunneling of electrons from the conduction band in the emitter to traps in the energy gap
in the emitterbase spacecharge region, as shown in Fig. 1.5. A hole is then captured at
the trap to complete the twostep process. Another possible process involves holes in
the valence band of the base tunneling to traps in the energy gap followed by electron
capture. These twostep tunneling processes were analyzed in detail by Sah in 1961 [40]
to explain the excess current in golddoped tunneling diodes. Very similar processes
may occur at the SiO2/Si interface in the emitterbase junction, although the interface
traps are distributed throughout the silicon energy gap. Surface trapassisted tunneling
p Si
n+ Si x) V=q(Vbi VBE)
VBE F NE
Ec
IBT
 .. .. .. Fv OB
Ev OV
Ev
0 Xt XEB
Fig. 1.5 Energy band diagram for the emitterbase junction of a BJT showing the trap
assisted tunneling process during forward bias. The electron tunneling
potential barrier from the conduction band in the emitter to the trap (triangle)
is shown by the shaded region. The average electron tunneling distance is
labeled x,. Adapted from Sah [40].
currents were identified in submicron selfaligned BJTs by Li et al. [41]. If the
tunneling event is the rate limiting step in the twostep tunneling process, then the
current due to trapassisted tunneling will have different characteristics than the
recombination currents based on ShockleyReadHall processes.
The probability for an electron to tunnel from the conduction band in the emitter
to a trap in the emitterbase spacecharge region is determined by the potential barrier
between the conduction band in the emitter and the trap, which is shaded in Fig.1.5.
The approximate potential barrier shape may be calculated for an abrupt, onesided
junction, which is a valid approximation of the emitterbase junction in submicron BJTs.
The potential energy, V, vs. position in the emitterbase spacecharge region using the
depletion approximation is found by applying Gauss's Law and integrating twice to get
[42, p.412]
V(x) = [2qNAA(Vbi VBE)/Si]0.5x + (qNA/2esi)x2, (1.28)
where NAA is the base acceptor impurity concentration, Vbi is the junction builtin
voltage, esi is the silicon permittivity, and x is distance perpendicular to the emitterbase
junction from the emitter edge of the spacecharge region. The potential energy is set to
zero at the emitter edge of the spacecharge region (x=0), and V = q(Vbi VBE) at the
base edge of the spacecharge region (x=XEB). Since the emitterbase spacecharge
region width is
XEB = [2Esi(Vbi VBE)/qNAA0.5, (1.29)
Equation (1.28) may rewritten as
V(x) = 2(Vbi VBE)(x/XEB) + (Vbi VBE)(x/XEB)2. (1.30)
The electron tunneling probability through the potential barrier described by Eq.(1.30)
may be approximated by [42, p.64]
T=exp [2 (x)dx (1.31)
where
a(x) = {2mx[V(x) E] }o05/h. (1.32)
In Eq.(1.32), E is the electron kinetic energy, mx is the electron effective mass in the
tunneling direction, and fi = h/2ic is the normalized Planck constant. The limits of the
integration in Eq.(1.31) are from x=0 to x=xt, where xt is the average tunneling distance
for electrons as shown Fig. 1.5. The current due to the tunnelinglimited recombination
pathway may be approximated by assuming that the tunneling step is rate limiting. This
means the traps involved in the tunneling of electrons may be considered to be mostly
empty since the hole capture event occurs much faster than the electron tunneling step.
Therefore, calculating only the tunneling rate of electrons from the conduction band to
traps in the energy gap will allow the tunnelinglimited recombination current to be
approximated. Only the traps in the energy gap at energies slightly greater than the
bottom edge of the conduction band in the emitter are assumed important, as this is
where the electron density in the conduction band is largest. Since most of the tunneling
electrons have low kinetic energy, E is small in Eq.(1.32) compared to the tunneling
potential barrier height. Equation (1.30) may be substituted into Eq.(1.32) and
integrated in closed form in Eq.(1.31) to produce
T = exp[2(2mx/h2)05 t(Vbi VBE)0.XEBI, (1.33)
where
yt = 0.5[(xt/XEB) 1][(2xt/XEB) (x/XEB)2]05 + 0.5arcsin[l (x/XEB)]. (1.34)
The quantity yt depends on the average tunneling distance from the emitter edge of the
spacecharge region to the trap, xt, in relation to XEB. A constant ratio of xt/XEB is
assumed to allow yt to be independent of VBE and simplify Eq.(1.33). Equation (1.29)
may also be substituted into Eq.(1.33) to yield
T = exp[4(mxesi/i2NA)0.5 t(Vbi VBE)] = exp[(Vb, VBE)/VT]. (1.35)
The surface trapassisted tunneling current is found by integrating the tunneling
probability over the initial and final electron density of states. The initial and final
density of states are assumed not to vary significantly with VBE, which makes the
tunneling current proportional to the tunneling probability such that
IBTs BT exp[(VBE Vbi)/VT], (1.36)
where IBTO and VT are constants. Equation (1.36) will be used in Ch.2 to model the
measured surface trapassisted tunneling current. The value of VT found during least
square fit to the data may be used to calculate the approximate average tunneling
distance for electrons. The constant IBTO will directly depend on the interface trap
density in the emitterbase spacecharge region and the electron density in the emitter
near the spacecharge region. The density of available traps in the spacecharge region
for tunneling will most likely vary as VBE is changed, since NIT is known to vary with
energy in the silicon energy gap. This may cause some small deviations of the measured
current from Eq.(1.36), and may also provide information on the variation of NI with
energy in the top portion of the energy gap.
1.7. ReverseBias Current in the EmitterBase Junction
The leakage current which flows in the n+/p emitterbase junction of submicron
BJTs during reversebias is known to be an important cause of OF degradation [8,9,11].
Therefore, the source of the reversebias emitterbase junction current must be analyzed
to understand BJT Fp degradation. For the heavily doped n+/p junctions in submicron
BJTs, the major source of reversebias current for junction voltages below breakdown is
the interband tunneling of electrons from the valence band in the emitterbase space
charge region to the emitter conduction band. This is shown in Fig.1.6, where the
valenceband electrons are indicated by solid dots surrounded by circles. This notation
emphasizes that the tunneling process leaves behind holes in the valence band of the
spacecharge region as electrons tunnel to the emitter conduction band. The tunneling
process may be direct, phononassisted, or trapassisted. Two trapassisted tunneling
pathways are also shown in Fig.1.6. The tunneling probability for the direct or phonon
assisted pathways for electrons in a reversebiased p/n junction may be approximated by
assuming a triangular potential barrier at the point in the junction where the tunneling
rate is maximum, which is near the emitter edge of the spacecharge region. This
tunneling barrier is shaded in Fig.1.6. The tunneling probability is [42, p.65]
4(2mx)o.5E 1"5
T = exp 4 (2X)5EG ,1 (1.37)
3qhE
where mx is the tunneling electron effective mass in the direction from base to emitter,
EG is the silicon energy gap which determines the height of the triangular potential
tunneling barrier, and E is the electric field in the emitterbase spacecharge region near
secondary
electron
p Si
*B
OV
impact generation
(T)
interband tunneling
(direct or phononassisted)
Fig. 1.6 Energy band diagram for the emitterbase junction of a BJT during reverse
bias showing the tunneling (direct or phononassisted) and trapassisted
tunneling pathways. The shaded area represents the electron tunneling
potential barrier from the valence band in the emitterbase spacecharge region
to the conduction band in the emitter. Interband impact generation and
thermal generation are also shown. Adapted from Neugroschel, et al. [24].
n+ Si
+VEB
E,
the emitter which determines the slope of the triangular potential barrier. The tunneling
current is found by integrating the tunneling probability over initial and final electron
states. Since the tunneling probability is an exponential function of the electric field, the
tunneling rate is dominant at the highest electric field point in the emitterbase space
charge region. Therefore, current may be approximated as being proportional to the
tunneling probability at this point. This gives an emitter current of
IE = IE exp(Vo/E), (1.38)
where IEO and Vo are constants. The value of Vo may be calculated approximately from
the electric field, silicon energy gap, and effective mass. The maximum electric field in
the spacecharge region of a onesided junction may be written as
Emax = Eo(Vbi + VEB),n (1.39)
where Eo is the maximum electric field at equilibrium and n is a constant. For an abrupt
junction n will be approximately 0.5. By assuming the tunneling current is dominated
near the point in the spacecharge region where the electric field is Emax, the tunneling
current in Eq.(1.38) may be rewritten as
IE = IE exp[Vl/(Vbi + VEB)]. (1.40)
A least square fit may be performed on the measured reverse emitter current to find IEO'
V1, Vbi, and n in Eq.(1.40). For the submicron BJTs measured in this work the value for
n has been consistently found to be close to 0.5, indicating the onesided, abrupt
junction approximation made in this and the last section is valid for evaluating the
tunneling currents.
The holes left behind in the emitterbase space charge region may create
additional electronhole pairs through interband impact generation (or avalanche
multiplication) if the holes attain sufficient kinetic energy. This is shown in Fig.l.6.
This process is important only at relatively high VEB, where the carriers in the emitter
base spacecharge region are accelerated to high kinetic energy. The secondary
electrons generated through the impact generation may also create additional electron
hole pairs, and junction breakdown is achieved when the impactgeneration efficiency
approaches unity. Current in the emitterbase junction is also produced from thermal
generation of electronhole pairs, but this current is found to be negligible in submicron
BJTs compared to the tunneling and interband impact generation currents.
1.8. Analysis of Base and Collector Currents
A schematic diagram of a n+/p/n BJT is shown in Fig.1.7. The desired current
flow for forwardactive operation consisting of electrons from the emitter being injected
by the forwardbiased emitterbase junction into the base and collected by the shorted or
reversebiased collectorbase junction into the collector is labeled as the collector
current, Ic. The collector current is affected by the intrinsic transistor area, the base
doping concentration, and by generation of electronhole pairs in the collectorbase
junction, but will generally be expected to remain stable during normal device operation.
The base current, Ig, consists of holes from the ptype base which recombine with
electrons in the base, emitter, or emitterbase spacecharge region. These recombination
mechanisms were analyzed in sections 1.4 and 1.5. Several of these recombination
Fig.l.7 Schematic diagram of a BJT showing the various recombination processes
which contribute to the base current along with the desired electron current
flow from emitter to collector. The diamonds are bulk silicon traps and the
triangles are interface traps at the SiO2/Si or polysilicon/Si interfaces. The
tunneling limited recombination current is not shown. Adapted from
Neugroschel and Sah [22].
n+ Si it p Si Ec
VBE FN
E e E cT
B1Bs
BTs IB2s B
Ev 00
Fig.1.8 Energy band diagram showing the recombination processes in the emitter,
base, and emitterbase space charge region along the silicon surface. The
triangles represent interface traps at the SiO2/Si or polysilicon/Si interfaces.
Adapted from Sah et al. [38].
pathways are illustrated in Fig.1.7 for recombination at either bulk silicon traps
(diamonds) or surface traps at the interface between the silicon and oxide or polysilicon
layers (triangles). Bulk traps are created during crystal growth or device fabrication and
are either due to crystal defects or impurity atoms. Their density is not expected to be
affected by device operation since high temperature or particles with very large kinetic
energy are required to alter the impurity atom concentration or create additional crystal
defects. However, the density of interface traps may increase substantially during
device operation if carriers are accelerated to kinetic energies on the order of several
electronvolts in the vicinity of the interface. Therefore, the base current components
due to surface recombination may change during device operation and cause reliability
problems. In Ch.2, the increase in IB2s will be shown to cause a decrease in pF during
BJT operation in BiCMOS circuits. In Ch.5, the decrease in IB1Es will be shown to
increase OF during operation at high current density.
The location of the recombination is used to differentiate the recombination
pathways in Fig.1.7. The IB2s component is due to surface SahNoyceShockley
recombination in the emitterbase spacecharge region with reciprocal slope factor n=2.
The IBlEb and IB1Bb are the bulk recombination components of Ig in the quasineutral
Emitter and Base with reciprocal slope factor n=l. The surface recombination
components of the base current along with the surface trapassisted tunneling current,
IBTs, are also shown in the energy band diagram in Fig.l.8.
1.9. Theory of HotCarrier OxideSilicon Interface Trap Generation
It is well known that the increase of Ig and decrease of OF during reverse emitter
base bias stress is due to an increase in the surface SahNoyceShockley current as NIT
increases [325]. It has been proposed that the breaking of SiH interface bonds by hot
carriers may be the dominant interface trap generation mechanism for some transistor
technologies. Under this assumption, a model for interface trap generation may be
constructed. This was first done by Hu et al. [43], but many of the details of the model
were not investigated. Thus, a similar model is presented here for use in Ch.2. A
schematic diagram of the model presented here is shown in Fig.1.9. Interface traps are
assumed to be created or passivated through the reaction
SiH Si + H, (1.41)
where Si is a broken SiH bond or interface trap. The quantity H is the atomic
hydrogen concentration near the SiO2/Si interface. The energy for the reaction to
proceed from left to right (generation or increase of NIT) is provided by hot carriers.
The reaction will also proceed from right to left (passivation or reduction of NIT) if there
is sufficient atomic hydrogen near the interface. The rate equation for the net NIT
generation may be written as
dNIT/dt eH(NB NIT) CHNITHI (1.42)
if a first order reaction is assumed. The rate coefficients for NIT generation and
passivation are eH and cH, and Nm is the density of SiH interface bonds which may be
broken by hot carriers. The hot carrier density and kinetic energy will directly affect eH
Fig.1.9 Schematic diagram of the model for SiO2/Si interface trap generation
presented in this chapter. The circled H symbols represent atomic hydrogen
which is emitted and captured at interface traps. The triangles represent
interface traps which are initially passivated by the atomic hydrogen in the
unstressed device. The model is similar to that proposed by Hu et al. [43].
and the rate of NIT generation. The quantity HI is the effective areal hydrogen
concentration near the interface which is defined as
xI
H = Hdx = H(0)XI, (1.43)
where H(0) is the hydrogen concentration very near the SiO2/Si interface, and XI is the
width of the SiO2/Si interface region. For low NIT and HI, the NIT generation process
will be dominant and Eq.(1.42) can be approximated as
NIT = eHNIt. (1.44)
This suggests that if NIT and HI are low at the start of the reversebias stress, then the
rate of NIT generation will be proportional to the stress time. As interface traps are
created during the rupture of SiH bonds, the density of hydrogen also increases near the
interface. In general, HI depends on the rate of interface trap generation and the rate of
hydrogen diffusion away from the interface. This may be modeled by the rate equation
dH/dt = dN,,/dt DHH(O)/Xo, (1.45)
where DH is the hydrogen diffusivity, and Xo is the oxide layer thickness. In Eq.(1.45),
the atomic hydrogen density is assumed to have a linear gradient in the oxide layer as
shown in Fig.l.10. The hydrogen concentration is assumed to be small compared to
H(0) at the top of the oxide layer where the polysilicon emitter overlap acts as a
hydrogen sink. Eq.(1.45) may be rewritten as
dHi/dt = dNr/dt (DH/XIXo)HI (1.46)
A general solution for NIT from Eqs.(1.42) and (1.46) is difficult to obtain analytically.
However, the following discussion lends some insight into the form of the solution. As
H(0)
cO?
I
E JH= DHH(O)/Xo
0
"I
H(X)
I I
o0X1 X /(1cm)
Si SiO2 polysilicon
Fig.1.10 The linear atomic hydrogen concentration gradient in the oxide layer which is
assumed in Eq.(1.45). The hydrogen flux away from the SiO2/Si interface is
JH = DH[H(0) H(Xo)]/Xo = DHH(O)/Xo, since H(0)>>H(Xo).
HI builds up, the rates of generation and passivation of NIT will eventually become
nearly equal, and dNIT/dt and dH/dt will drop to zero if HI remains unchanged. At this
point, the NIT generation is limited by the hydrogen diffusion from the interface. In this
case, the rate of interface trap generation would be equal to the rate of hydrogen
diffusion from the interface, or
dNiT/dt = (DH/XIX)HI. (1.47)
By substituting Eq.(1.47) into Eq.(1.42) and integrating over time, Eq.(1.42) becomes
NIT + (cHXIX2DH)NIT2 = eHNBt, (1.48)
where it is assumed that NIT << NIB. According to Eq.(1.48), the kinetics of NIT
generation would be expected to follow a power law dependence, or NIT o tm, where m
ranges between 1.0 at short stress times and 0.5 at long stress times. Eventually, as NIT
approaches Ng, the NIT generation rate drops to zero, because there are very few weak
interface bonds left to be broken.
A general solution to Eqs.(1.42) and (1.46) may be approximated by converting
the differential equations to difference equations using the Euler approximation. For
simplicity, the initial NIT and HI concentrations are assumed to be negligible, and Nm is
assumed to be much larger than NIT. The results of the general solution for NIT and HI
vs. stress time are shown in Fig. 1.11 for three different hydrogen diffusion rates. For all
of the curves in Fig. .11, the initial rates of NIT and HI generation are proportional to the
stress time, or have a slope of m=1.0 when plotted on logarithmic axes. For low
hydrogen diffusion rate (low DH/XIXo), the NIT generation and passivation rates
eventually become comparable. Therefore, dNIT/dt and dHi/dt drop to nearly zero. At
1012
large DH/XIXo NIT oc to 
moderate DH/XXo .
0^ 1011  small DH/XIXO
C' '
E "
S1010 
Fig.1 To9 x t g a s
: 10 ""
Z 10a
NIT c HI oc t,
HI cct0.5
107 I I
101 1 10 102 103 104
t/(ls)
Fig. 1.11 The approximate general solution for the time dependence of the interface trap
density (NIT, top three curves) and atomic hydrogen concentration at the
interface (HI, bottom three curves) from Eqs.(1.42) and (1.46) is calculated
using the Euler approximation. Three different hydrogen diffusion rates are
shown to demonstrate the effect on NIT and HI. For moderate to high
diffusion rate, the NIT curve is proportional to tm, where m varies between 1.0
and 0.5.
longer time, the hydrogen finally starts to diffuse from the interface, and NIT and HI are
both proportional to t0.5. For the moderate and large hydrogen diffusion rates, the
hydrogen begins to diffuse away from the interface before the NIT generation and
passivation rates become comparable. Therefore, the NIT curves show a smooth
transition from m=1.0 to m=0.5 for NIT, as suggested by the approximate solution in
Eq.(1.48). As shown in Fig.l.12, the approximate solution for NIT in Eq.(1.48) is an
excellent approximation of the calculated general solution for NIT for moderate and high
hydrogen diffusion rates when NIB >> NIT. Only for the low hydrogen diffusion rate
does Eq.(1.48) deviate from the general solution for NIT. If the assumption that NI >>
NIT is removed, then the calculated general solution to NIT shows a drop in dNIT1dt
when NIT approaches Nm, as shown in Fig.l.13. However, Eq.(1.48) does not account
for the drop in the NIT generation rate as NIT approaches NB. Thus, an extra term must
be included in the right side of Eq.(1.48) to give
t
NI + (cHXIXo2DH)NIT2 = eHN H Ndt, (1.49)
which is solved to yield
1 + 1 + (2cHXIX/DH)(eI eH NTdt) 0.5
N = .(1.50)
r CHXIXoDH
The solution for NIT in Eq.(1.50) may be approximated by calculating NIT over a
number of points and using a summation of NIT over time to approximate the integral.
In Fig. 1.13 it is demonstrated that the solution for NIT from Eq.(1.50) is an excellent
approximation, even when NIT approaches NIB. The advantage using Eq.(1.50) rather
C'J
E
0
z
101 1 10 102 103
t/(ls)
Fig.1.12 The calculated general solution for NIT from Eqs.(1.42) and (1.46) is
compared to the approximate result for NIT from Eq.(1.48) for three different
hydrogen diffusion rates. For the moderate and large hydrogen rates,
Eq.(1.48) is shown to provide an excellent approximation of NIT if NIB >>
NIT.
104
10"
u general solution for NIT
E 1010 Eq.(1.50)
109
108
107
101 1 10 102 103 104
t /(s)
Fig.1.13 The calculated general solution for NIT from Eqs.(1.42) and (1.46) is
compared to the approximate computed result for N from Eq.(1.50). The
total number of interface bonds, NIB, is set to 101cm2 to illustrate the
saturation of NIT at long stress time. The result for NIT from Eq.(1.50) is
shown to be an excellent approximation of NIT, even when NIT approaches
NIB
than calculating the general solution for NIT from Eqs.(1.42) and (1.46) is that a much
larger At may be used between the calculated NIT points in Eq.(1.50), which reduces
computing time significantly. The integral in Eq.(1.50) does not become important in
the solution for NIT until NIT becomes comparable to NIB. In Fig. 1.13, NIT from
Eq.(1.50) is calculated at 500 points to maintain a good approximation of the integral,
whereas a minimum of 105 points (maximum At of 0. ls) is required when solving for
the general solution for NIT. Although the theoretical analysis of NIT generation in this
section assumes that broken SiH bonds are the major cause of NIT, the same analysis
may also be applied to other impurity interface bonds using the same rate equations.
1.10. Bipolar Transistor SelfHeating
When BJTs operate at high current densities, the energy losses of carriers through
phonon scattering may locally heat the silicon crystal to temperatures much higher than
the ambient temperature [44]. This is known as transistor selfheating. The amount of
the temperature increase of the device above the ambient temperature, AT, is related to
the total power dissipation, P, by
AT = RhP, (1.51)
where Rth is the thermal resistance of the device. Therefore, the key to predicting the
magnitude of the selfheating in BJTs is to measure Rth
A measurement procedure which is useful for extracting the approximate Rth is to
measure IB vs. reverse collectorbase bias, VCB [45]. If Ig is dominated by
recombination in the emitter, and VcB is well below collectorbase junction breakdown,
then the measured increase in Ig as VCB is increased is strictly due to device selfheating
and is an accurate measurement of the change in device temperature. This measurement
is demonstrated in Fig.l.14 for a 0.81pm x 3.2ptm BJT at VBE=0.64V and an ambient
temperature of 1500C. The data in Fig.1.14 is replotted vs. P in Fig. 1.15, where
P =IcVCE (1.52)
Eq.(1.52) is valid for forwardbias VBE in the low to moderate range where resistive
power losses in the device contacts are negligible, and the majority of the selfheating is
due to phonon scattering in the reversebiased collectorbase junction. For submicron
transistors, it may be difficult to measure significant selfheating without raising VBE to
large values at room temperature. Thus, the measurement is performed at elevated
ambient temperature to solve this problem. Since Ig is an exponential function of device
temperature and is not a function of VCB for voltages well below junction breakdown
[45],
a(AIB/IB)/aP = Rth (ln[IB])/T. (1.53)
Thus, Rt may be solved to be
Rt = [(kT2)/(EG qVBE)][(AIB/IB)/P], (1.54)
where EG is the silicon energy gap. The value of Rth is obtained from the slope of the
curve in Fig.l.15, and is found to be Rth=0.95K/mW.
In Ch.5, the transistor selfheating must be calculated for very large values of
VBE, where the transistor current is limited by the emitter series resistance rather than
minority carrier injection. In this case, the power dissipation is
P = IEAVBEO + IC(VCE AVBEO) (1.55)
43
1.66
T=150C
1.65 VBE=0.64V
1.64
(CD
1.63
._ 1.62
1.61
1.60 I I
0 1 2 3 4
VBC /(1 V)
Fig.1.14 The base current vs. reverse collectorbase bias at 1500C and forward emitter
base bias of VBE=0.64V. The increase in IB is caused by transistor self
heating as the power dissipation increases.
m 0.01 a(AIB/IB)/P = 0.028mW'
0.0 
0.01
0 1 2
P/(1 mW)
Fig.1.15 The percent change of the base current vs. transistor power dissipation at
1500C and VBE=0.64V. The slope of the curve is found to be 0.028mW,
which yields Rt=0.95K/mW from Eq.(1.54). This measurement technique is
from Reisch [45].
where AVBEO is the voltage drop in the emitter contact. Eq.(1.55) is approximately
equal to Eq.(1.52) if IE = IC.
1.11. Summary
The background necessary for the analysis of BJT reliability in the subsequent
chapters of this dissertation was given. An introduction to the common fabrication
procedures was given in section 1.2. In the next four sections, theoretical expressions
for the measured transistor currents during forwardactive operation were presented. In
section 1.7, the reversebias leakage current in the emitterbase junction was examined.
A model for trap generation at the SiO/Si interface from the rupture of SiH bonds was
presented in section 1.9. Finally, transistor selfheating was analyzed in section 1.10.
CHAPTER 2
PHYSICAL DEGRADATION MECHANISMS OF
SILICON BIPOLAR JUNCTION TRANSISTORS
DURING REVERSE EMITTERBASE BIAS STRESS
2.1. Introduction
It has been known since the 1960s that the electrical characteristics of oxide
passivated silicon bipolar junction transistors (BJTs) change during operation. A
reduction of the commonemitter current gain (3F or hFE) due to an increase of the
transistor base current, Ig, during an application of reverse emitterbase bias to near the
junction breakdown voltage was first reported by Collins [3,4] in 1968. He performed
reversebias stress experiments at various current levels and temperatures and proposed
that degradation of the SiO2/Si interface near the emitterbase junction was the probable
cause of the pF decrease. He also demonstrated that junction breakdown was not
necessary for PF degradation and found no significant temperature dependence of the
degradation rate. Additional studies were performed by Verwey [5] in 1969 and
McDonald [6] in 1970. The increase in Ig was attributed to an increase in the surface
recombination velocity at the SiO2/Si interface at the emitterbase junction perimeter
and charge injection into the oxide. The increase in the surface recombination is caused
by the breaking of interface bonds by hot electrons and holes generated during the
reversebias stress to increase the interface trap density, NIT. Experiments with a field
gate over the emitterbase junction [5,6] showed that both electrons and holes can be
injected and trapped in the oxide, depending on the polarity of the gate voltage applied
during the stress. These experiments also showed that the stressinduced excess base
current, AIB, was a function of the silicon surface potential. The gatecontrolled BJT
was first described by Sah [46] who studied the base current mechanisms in detail [47].
The gatebase voltage controls the surface potential and recombination rate at the
surface of the emitterbase spacecharge region as well as the size of the induced surface
channel in the quasineutral base, and thus controls the BJT base current and pF [47,48].
A principle result obtained by Sah was that if a surface channel is induced by the gate
potential, the channel current due to the recombination either in the channel bulk space
charge region or the SiO2/Si interface can give a reciprocal slope factor (diode ideality
factor) n for the base current larger than 2.0 in the current relation, Ig exp(qVBE/nkT).
This exceeds the slope factor for SahNoyceShockley recombination current in the bulk
emitterbase spacecharge region which requires 1.0_n<2.0 [38]. Thus, the measured
slope factor of the base current can be an important indicator of the surface channel
presence in VLSI transistors without the gate electrode.
The effects of reversebias stress on the characteristics of advanced BJTs received
renewed attention in the last decade from a number of investigators [725] as the use of
BiCMOS logic became widespread. In 1985, Petersen and Li [7] demonstrated that the
large reversebias leakage current in heavilydoped n+/p emitterbase junctions in
submicron BJTs can degrade pp even at reversebias voltages much less than
breakdown, and avalanche was not a necessary condition for BJT degradation as was
found in earlier studies on larger transistors. They also showed through the use of light
to generate carriers in the base that the increase in AIB or degradation of 3F may be
accelerated by the injection of additional electrons into the emitterbase junction during
reversebias stress. In 1987, Joshi et al. [8] were the first to demonstrate that significant
PF degradation may occur from the transient reverse emitterbase bias stress of the pull
up BJT in a BiCMOS inverter during output node transition from high to low. They
showed that the AIB increase was directly related to the current flowing in the emitter
base junction during stress, and that device failure may be predicted by measuring the
cumulative stress charge. They also suggested that the reliability of BiCMOS circuits
may be limited by the BJT reliability from reverse emitterbase bias stress. In 1988,
Tang and Hackbarth [9] proposed a model for the rate of AIB increase based on a single
firstorder rate equation for NIT generation and annihilation in the emitterbase space
charge region. The model was demonstrated to fit the data measured in their work, but
was not able to predict the time dependence of the increase in AIB in some other
technologies or stress conditions. Hackbarth and Tang [10] also demonstrated that the
reversebias leakage current in the emitterbase junction may also increase during
reversebias stress. Also in 1988, Burnett and Hu [11] developed a largely empirical
degradation rate model for AIB based on a measured power law dependence of AIB on
stress charge. They measured BJT degradation for a small range of reversebias stress
voltages using constant current stress, and found good agreement with their power law
model. Hu et al. [43] had used a similar model for MOS transistor (MOST) degradation
in earlier studies. In this work, a NIT generation model was developed in which the
rupture of HSi bonds was assumed to be responsible for the majority of the NIT
increase, and the diffusion of hydrogen was considered along with the generation of NIT
by hot carriers and the annihilation of NIT by hydrogen recapture at the interface to
account for the measured kinetics. The model by Burnett and Hu [11] proved to be
convenient for BJT reliability analysis, but the accuracy of the model over a wide range
of stress voltages has not been proven. The model also lacked a physical basis for the
power law dependence of AIB on stress charge, thus making the extrapolation to low
stress voltages questionable. Furthermore, this model is based on constant reversebias
current stress rather than constant reversebias voltage stress. As will be demonstrated
in this chapter, constant current stress is physically incorrect for analyzing hot carrier
effects, because it does not maintain a constant hot carrier kinetic energy during stress.
In Ch.3, it will be demonstrated that the hot carrier kinetic energy is the fundamental
parameter responsible for interface trap generation.
In 1991, Niitsu et al. [12] measured anomalous rates of AIB increase which were
not consistent with those predicted in the model by Burnett and Hu [10], and these
effects were qualitatively attributed to oxide charging. In 1993, Kosier et al. [13]
measured a similar superlinear AIB timedependence in radiationinduced BJT
degradation. This effect was also attributed to oxide charging, but the radiationinduced
oxide charging is expected to differ from hotcarrier oxide charging in magnitude and
location. In 1995, Maugain et al. [14] used a quantitative model to explain the
anomalous AIB increase. They extended the model by Burnett and Hu [11] to include a
modulation of AIB due to the change in silicon surface potential from positive oxide
charging, but no justification for the assumed exponential dependence of AIB on surface
potential was presented. They also used constant current stress over a very narrow range
of reversebias stress voltages near junction breakdown to examine the AIB increase, and
did not propose a model for positive oxide charging or attempt measure a threshold
voltage below which positive oxide charging will not occur.
In 1993, Huang et al. [18] also extended the model by Burnett and Hu to include
the temperature dependence of reversebias stress in submicron BJTs. The rate of AIB
generation was found to be inversely proportional to temperature for the stress
conditions and BJT technology investigated in their work. This was explained by a
higher NIT annihilation rate, or larger hydrogen capture rate according to Hu's model
[43] at higher temperatures. In 1994, Momose et al. [19] performed similar
measurements and found that the peak degradation rate occurred at approximately 500C,
suggesting that the temperature dependence of AIB generation is technology dependent.
The first significant investigation into the microscopic mechanisms for BJT
degradation at stress voltages much less than breakdown was performed by Kizilyalli
and Bude [20] in 1994. They suggested that to explain the current gain degradation
during reversebias stress in heavily doped n+/p emitterbase junctions, the effect of
both interband tunneling generated hot holes and interband impact generated secondary
hot electrons must be considered. They also speculated that holes injected into the oxide
could be responsible for interface trap generation. Recent efforts in reliability modeling
have also focused on determination of the 10year timetofailure (TTF) using a voltage
acceleration method [21]. Using this method, TTF is measured at stress voltages higher
than those encountered during operation, and the results are extrapolated to the lower
operating voltages using an empirical curve fit.
In spite of these extensive investigations of BJT degradation during reversebias
stress, detailed microscopic models of the dominant degradation mechanisms and their
geometrical locations are still not well understood. Even the source of the hot carriers
causing the increase in IB has not been conclusively determined. The purpose of this
chapter is to report a systematic experimental delineation of the (3F degradation
phenomena under reverse emitterbase bias stress in submicron Si BJTs and model their
effects on BJT degradation rate. In particular, the microscopic mechanisms of NIT
generation and positive and negative oxide charge buildup during reversebias stress
and their effects on surface recombination are discussed in detail. The reversebias
stress voltage thresholds necessary for positive and negative oxide charge will also be
presented. It will be noted that the fundamental BJT degradation mechanisms are
identical to those which cause instabilities in the silicon MOS transistor (MOST) [49
51] with only modification of spatial distribution of the carrier recombination sites
because of different BJT and MOST geometries. The study shows that the location of
AI, is a very important factor in determining the degradation rate. It is further shown
that the device models accounting for the degradation are exactly those studied before,
i.e. interface trap generation at the SiO2/Si interface of the oxide passivated surface of
the ptype base of the n+/p/n Si BJT and the ntype surface channel on the ptype base
[4648]. Measured results will show that AIB after heavy stress cannot be explained
entirely by an increase in the recombination rate at the narrow emitterbase junction
spacecharge region, and requires an electron surface channel on the ptype base which
is induced by positive oxide charge. The effects of both positive and negative oxide
charging on the rate of AIB increase are also modeled. The device models presented
here originated from previous investigations by Sah which were described in a research
report by Neugroschel [22].
Experimental results and fundamental mechanisms of AIB generation are
described in section 2.2. The analysis of hot carrier kinetic energy and the location of
interface trap generation and oxide charging are described in section 2.3 The measured
kinetics of AIB generation are examined and modeled in section 2.4. Finally, the device
models explaining AIB are described in section 2.5.
2.2. Fundamental Excess Base Current Mechanisms
Most of the results in this work were obtained from non selfaligned n+/p/n BJTs
fabricated by CMOSbaseline BiCMOS technology. Fig.2.1 shows a schematic cross
sectional view of the device. Its n+ polysilicon emitter contact overlaps the oxidized
surface of the extrinsic ptype base and creates a MOS capacitor with gatebase voltage
equal to the emitterbase voltage (VEB = VGB). This emitter polysilicon overlap
experimentally controls the surface electric field at emitterbase junction and the ptype
base in this device, which are important parameters in determining the transistor
degradation rate. The results and the analysis presented below are, however, very
general and apply to BJTs fabricated by other technologies, such as selfaligned BJT
baseline BiCMOS processes.
VBE
n+ potySi
A A Al
ov
9B
SiO2
A NIT A
n+ emitter
2 B2s '/ BBs
1 Es 'lEb p base
B2b 113 Eb
I +
n collector_ I
p+Base
contact
O
O
ovt C
OV
Fig.2.1 Schematic cross section of a BJT showing the recombination processes which
contribute to the base current. The diamonds are bulk silicon traps, and the
triangles are interface traps at the SiO2/Si or polysilicon/Si interfaces.
Adapted from Neugroschel and Sah [22].
The observed degradation phenomena in submicron silicon n+/p/n BJTs are
illustrated in Figs.2.2 through 2.10. Fig.2.2 shows the collector and base currents, Ic
and IB' measured as a function of the forward emitterbase bias, VBE, before and after
increasing reverse emitterbase bias stress. They show that the prestressed Ic and Ig
are nearly ideal, i.e. following Shockley's ideal theory [1] of Ic and Ig c exp(qVBE/kT)
for VBE>0.4V. The reciprocal slope factor, n, is nearly equal to that predicted by
Shockley's ideal minoritycarrier injection theory, where n=n1l.0, and
F=IC/IB =constant (independent of VBE or Ic). After successive reverse emitterbase
stresses, Fig.2.2 shows that IC does not change, as predicted by the ideal theory.
However, IB increases with stress by greater than four orders of magnitude at low VBE
due to the increase of a stressinduced excess base current component, AIB, with
reciprocal slope factor of n=n2=2. The increase of AIB is generally attributed to an
increase in the SahNoyceShockley spacecharge region surface recombination current,
shown as IB2s in Fig.2.1, due to an increase in the interface trap density, NIT in the
emitterbase spacecharge region. For long stress times, an additional AIB component
with n=n4=4 appears for VBE<0.3V. This Ig component was previously measured in the
gated BJT in the 19612 studies by Sah [46,47] and was explained by the formation of a
surface electron channel connected to the emitterbase junction. A surface electron
channel is created when the surface of the ptype quasineutral base layer is depleted or
inverted by a positive voltage on the gate or by trapped positive oxide charge to allow
electron conduction prior to electronhole recombination. The existence of a AIB
component with n=4 is a key experimental hint which suggests that positive oxide
104
Stress: VBE=5.5V for 104s IC
1 0'
1010 n=4
 n=l
1012
0.0 0.2 0.4 0.6 0.8 1.0
VBE /(1V)
Fig.2.2 Base and collector current vs. emitterbase voltage for a n+/p/n BJT before
and after several periods of reversebias emitterbase stress. The stress
consisted of VBE=5.5V for a total of 104s. The measured curves for IB are at
20, 50, 100, 2000, 5000, and 104s of stress time. The excess base current, AIB,
is defined as the difference between in base current before and after stress.
charging must be included in the model for AIB presented in section 2.5. Quantitative
analysis will also show that the greater than four orders of magnitude increase in Ig in
Fig.2.2 at low VBE cannot be accounted for entirely by an increase in NIT in the thin
emitterbase spacecharge layer, further supporting the presence of a surface channel.
The temperature dependence of Ic and IB vs. VBE before stress and after moderate
and heavy reversebias stress is shown in Figs.2.3 through 2.6, and an activation energy
plot from the data in Fig.2.6 is given in Fig.2.7. Figs.2.8 and 2.9 show the temperature
dependence of the reversebias emitter current, IE, before and after stress. As shown in
Figs.2.3 and 2.4, both Ic and IB maintain a nearly ideal reciprocal slope factor of n=1.0
for the temperature range from 291K to 77K before stress. After a moderate stress of
VEBstress=5.5V for 100s, Fig.2.5 shows that Ig contains a stressinduced AIB component
for the entire temperature range. Since AIB has a reciprocal slope factor of n=2 at 291K,
it is often interpreted as strictly due to SahNoyceShockley surface recombination in
the emitterbase spacecharge region. However, AIB is shown to deviate severely from
the SahNoyceShockley theory at low temperatures, where the reciprocal slope factor
would be calculated to be n=8 from the measured data at 77K. At low temperature, AIB
is instead modeled accurately by a forwardbias surface trapassisted tunneling
expression, where
IBTs O exp[(VBE Vbi)/VT] (2.1)
as derived in Ch.1 as Eq.(1.36). This tunneling mechanism is similar to the excess
tunneling current mechanisms analyzed by Chynoweth et al. [52] and Sah [40] in tunnel
diodes, except the traps involved are interface traps and, therefore, are distributed in the
Sn=1.0
VBE/(.V)
108
12291K.
77K
1010
1012 I
0.0 0.2 0.4 0.6 0.8 1.0 1.2
VBE /(l V)
Fig.2.3 Base current for an unstressed BJT vs. emitterbase voltage measured at
several temperatures from 77K to 291K. The measured curves are at 77, 95,
125, 155, 195, 240, 265, and 291K.
=n=1.0
S108
291K
1010 77K
1012
0.0 0.2 0.4 0.6 0.8 1.0 1.2
VBE /(1V)
Fig.2.4 Collector current vs. emitterbase voltage measured at several temperatures
from 77K to 291K. The measured curves are at 77, 95, 125, 155, 195, 240,
265, and 291K.
m
1011 I \X l \ I I I I I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2
VBE /(1V)
Fig.2.5 Base current measured at several temperatures from 77K to 291K vs. emitter
base voltage after a moderate reversebias emitterbase stress of VBE=5.5V
for 100s. The measured curves are at 77, 95, 125, 155, 195, 240, 265, and
291K.
m
101
10
0.0 0.2 0.4 0.6 0.8 1.0
1.2
VBE /(1V)
Fig.2.6 Base current measured at several temperatures from 77K to 291K vs. emitter
base voltage after a heavy reversebias emitterbase stress of VBE=6.0V for
1000s. The measured curves are at 77, 95, 125, 155, 195, 240, 265, and 291K.
61
Stress: VBE=6.0V for 1000s
C Y VBE=0.8V
C1) 102
Co)
12EA=O.l 1eV
103
N
4 104 0
EA=0.20eV
o 105
C 1 A IB4s after stress
0 1 66 0 IB2s after stress
10 c EA=0.40eV
107 I I I I
3 4 5 6 7 8
1000/T /(1 K1)
Fig.2.7 Activation of plot of I, IB2s' IB4s from Fig.2.6 vs. 1000/T after heavy stress.
silicon energy gap. This perimeter tunneling current has also been identified in self
aligned BJTs [41]. The value of VT at 77K is found to be 0.0521V from a leastsquare
fit to the data, as shown in Fig.2.5. If the base impurity concentration is
NAA=2x1018cm3, the electron tunneling effective mass is mx=0.20mo, and the average
electron tunneling distance is xt=0.26XEB (26% of spacecharge region thickness), then
the value of VT=0.0521V is also calculated theoretically. At room temperature, AIB is a
combination of surface recombination and surface trapassisted tunneling, thus
explaining the reciprocal slope factor slightly greater than 2.0. The measured data
indicates that for the moderate stress case NIT in the emitterbase spacecharge region
has increased which increases both IB_2s and IBTs. However, no significant change in
the electric field in emitterbase junction at the silicon surface due to oxide charging is
suggested at this stress level.
After additional heavy stress at VEBstress=6.0V for 1000s on the same device,
Fig.2.6 shows that AIB has increased such that it dominates IB for the entire forward
emitterbase bias range. The primary AIg mechanism has changed after heavy stress
such that it follows the SahNoyceShockley spacecharge layer surface recombination
theory with n=2 much more closely for the entire temperature range. The reciprocal
slope factor gradually increases from n=2.0 at 291K to n=2.8 at 77K, which indicates a
slight deviation from the ideal recombination theory. However, this deviation is much
less than that measured after moderate stress in Fig.2.5, and does not suggest any
significant contribution from the surface trapassisted tunneling mechanism. Instead
this deviation from the SahNoyceShockley theory at low temperatures is explained by
electron conduction in a stressinduced surface channel before recombination. For low
current levels at the higher temperatures in Fig.2.6, an additional AIB component with
n=4 is measured due to this same surface channel electron conduction before
recombination. The surface trapassisted tunneling current which was dominant at low
temperatures after moderate stress has decreased dramatically after heavy stress such
that it is nearly insignificant.
There are two possible reasons for the large decrease in the trapassisted tunneling
current. The first is a decrease in the density of available interface traps for tunneling in
the emitterbase spacecharge region. However, this disagrees with the large increase in
the SahNoyceShockley recombination current which suggests a large increase in NIT
in the spacecharge region. The second possibility is an increase in the tunneling
potential barrier related to a decrease in the emitterbase junction electric field or
increase in the tunneling distance. This will decrease the trapassisted tunneling current
drastically, and may be modeled by a change in VT in the Eq.(2.1). The decrease in the
electric field at the surface of the emitterbase junction spacecharge region is consistent
with the formation of a surface electron channel during heavy reversebias stress,
already suggested by the AIg measurements as mentioned above. The thickness of the
emitterbase spacecharge region at the silicon surface is increased as positive oxide
charging depletes the surface of the quasineutral base. This same effect will be shown
to increase the SahNoyceShockley surface recombination current in addition to
decreasing the surface trapassisted tunneling current.
An activation plot of Ic and Ig after heavy stress is shown in Fig.2.7. The ideal Ic
is shown to have an activation energy of EA=0.40eV at VBE=0.8V, or Ic O
ni2exp(qVBE/kT) cc exp(0.40/kT). This is consistent with the fact that ni2 =
NcNvexp(EG/kT) = exp(EG'/kT), where EG'= 1.20eV for the temperature range in
Fig.2.7, and qVBE EG' = 0.8eV 1.20eV = 0.40eV = EA. The activation energy for
the stressinduced AIB at VBE=0.8V is EA=0.20eV for the higher temperatures, which
corresponds to a niexp(qVBE/2kT) temperature dependence since ni = exp(0.60/kT).
This temperature dependence for AIB is expected for SahNoyceShockley
recombination [38]. However, at low temperatures the temperature dependence of AIB
decreases, due to a deviation from the SahNoyceShockley theory as surface channel
electron conduction becomes more important. The surface channel recombination
component of Ig with n=4 at low current levels for the higher temperatures can be
decomposed from the measured total AIB. This current component is labeled IB4s in
Fig.2.7 and is found to have an activation energy of EA=0.1 leV or approximately a
ni.5exp(qVBE/4kT) temperature dependence. This current component drops below the
noise level for lower temperatures. The measured temperature dependence in Fig.2.7 for
the surface channel recombination current is consistent with the surface channel currents
measured in gate controlled BJTs by Sah [47].
The reversebias emitter current, IE, in the unstressed device is shown in Fig.2.8.
The major mechanism for IE in the heavily doped n+/p emitterbase junction at voltages
much less than breakdown is expected to be interband tunneling of valenceband
65
104 I I I I
interband impact
generation 
6_ (avalanche)
interband
tunneling
108
CI)
1010 / 39.4 /
IET oc exp (1.1 .54 
(1.1 + VEB)""'
1012
0 1 2 3 4 5 6
VEB /(1 V)
Fig.2.8 Reversebias stress current, IEstress, vs. emitterbase voltage for an unstressed
BJT. For VEB stress<4.5V, the stress current may be modeled by the interband
tunneling formula shown, as shown by the leastsquare fit of Eq.(2. 1) to the
data (dashed line). For VEBstress>4.5V, interband impact generation current
becomes important.
10 0 l ,J, I tS J I V y, l u L,, I i
Unstressed device
291K
 I77K
'I 1010
1 0 interband
tunneling
1012
0 1 2 3 4 5
VEB /(1V)
Fig.2.9 Reversebias stress current, IEstress' vs. emitterbase voltage for an unstressed
BJT at various temperatures from 77K to 291K. The measured curves are at
77, 95, 125, 155, 195, 240, 265, and 291K.
67
106 T=77,95,125,155,195,240,265,291K
Stress: VBE=6.0V for 1000s
291 K
< 108
surface
trapassisted
S_ tunneling 77K
CO
4
1012
0 1 2 3 4 5
VEB /(1V)
Fig.2.10 Reversebias stress current, IEstress, after heavy stress at various temperatures
from 77K to 291K. The measured curves are at 77, 95, 125, 155, 195, 240,
265, and 291K. The interband tunneling current is still dominant for
VEBstress>3.0V and for all VEBstress at low temperatures. An additional trap
assisted tunneling current is important heavily stressed devices for
VEBstress<30V
electrons in the spacecharge region to the quasineutral emitter conduction band, or
Zener tunneling. The excellent fit of IE to the interband tunneling expression [53],
IET exp[Vl/(VEB + Vbi)m], (2.2)
suggests that this mechanism indeed dominates for stress voltages below =4.5V in
Fig.2.8. The derivation of the simplified expression in Eq.(2.2) appears in Ch.l. The
values in Eq.(2.2) used in the leastsquare fit to the data in Fig.2.8 are Vbi=1.1V,
V,=39.4V, and n=0.54. The fact that m is close to 0.50 indicates that the onesided,
abrupt junction approximation is valid for the emitterbase junction in reverse bias. If
the base doping concentration is assumed to be NAA=2x1018cm3 and the tunneling
effective mass is mx=0.20mo, then Vbi=1.1V and V1=39V, which are close to the values
used in the leastsquare fit. At reversebias emitterbase voltages approaching junction
breakdown, the interband impact generation of electronhole pairs or avalanche
multiplication also contributes to the measured IE'
The temperature dependence of the reversebias emitter current before stress is
shown in Fig.2.9. The small temperature dependence for IE is further support of the
interband tunneling mechanism. After heavy stress, as shown in Fig.2.10, the reverse
bias IE contains an additional stressinduced component for VEB<3.0V. The larger
temperature dependence of this stressinduced IE along with its increase during reverse
bias stress suggests that it is due to reversebias surface trapassisted tunneling, which is
the inverse of the twostep process involved in forwardbias trapassisted tunneling.
This reversebias trapassisted tunneling current component may be an important source
of hot carriers at stress voltages less than 3.0V in devices with large interface trap
density.
2.3. Analysis of Hot Carriers During Stress
In Fig.2.11, the schematic crosssection of a BJT under reversebias stress is
shown. As was discussed in section 2.2, the major reversebias current mechanism for
VEBstress<4.5V is interband tunneling, labeled (T) in Fig.2.11. The maximum tunneling
probability occurs at the maximum electric field point in the emitterbase junction,
which is near the emitter edge of the emitterbase spacecharge region and also near the
SiO2/Si interface for a typical base doping profile in which the peak of the boron
distribution is near the interface [21]. This locates the reversebias tunneling current
near the SiO2/Si interface where the BJT degradation is known to occur. The valence
band electrons which tunnel to the emitter conduction band are generally not energetic
enough to break interface bonds or charge the oxide after tunneling, as shown in the
energy band diagram for the reversebiased n+/p emitterbase junction in Fig.2.12. This
is because the electron tunneling is concentrated very close to the quasineutral emitter,
as shown in Fig.2.12. Although the tunneling electrons are not energetic, the holes left
behind in the valence band of the emitterbase spacecharge region after electron
tunneling are accelerated toward the base by the junction electric field and may become
energetic (hot) holes. Since the electron and hole quasiFermi levels are very near the
conduction and valence band edges for typical n+/p emitterbase junctions, the hot holes
may attain a maximum kinetic energy of =qVEBstress as they reach the quasineutral
+VEBstress
E En+ polySi
A\ A
SiO2
n+ emitter y
p
 (
xzzzzzzz zZ
p base
_1 ^ 
n collector
Open
Open
OV
B
p+Bs 'iB
p+Base
contact
 B
Fig.2.11 Schematic cross section of a BJT during reversebias stress with open
collector or reversebiased collectorbase junction. The interband tunneling
(T) and interband impact generation (I) processes which make up the
measured emitter current are shown. Adapted from Neugroschel et al. [24].
A
secondary
hot electron
n+ Si
EMITTER
interband
tunneling
pSi
BASE
eB
OV
primary
hot hole
E
X
Fig.2.12 Energy band diagram of a reversebiased emitterbase junction indicating
interband tunneling (T) and interband impact generation (I). Tunneling
generated hot holes, impact generated secondary hot electrons, and thermally
generated hot electrons are shown. The hot holes are shown to acquire a
maximum kinetic energy of Ekmax = qVEBstress at the base edge of the
emitterbase spacecharge region. Adapted from Neugroschel et al. [24].
I
n+ Si __ B
IBOV
X
Fig.2.13 Magnified schematic diagram of near the emitterbase junction indicating the
interface trap generation and oxide charging pathways. Interface trap
generation by hot holes and electrons is indicated by an asterisk. The solid
triangles are unbroken interface bonds and the empty triangles are broken
interface bonds. The pathways for positive charging of oxide hole traps
(hexagons) and negative charging of oxide electron traps (squares) are also
indicated. The letters denoting the oxide charging pathways correspond the
processes in Fig.2.14. Adapted from Neugroschel et al. [24].
p Si
Ec
 B
Ev OV
(C) (d) (e)
QOT
+VEBstress FN Si02 (g
Ec A
Ev (b)
n+ polySi +oT
(h) (a)
/I x
Y
Fig.2.14 Energy band diagram along the direction perpendicular to the SiO2/Si
interface near the reversebiased emitterbase junction of a n+/p/n BJT. The
injection of hot holes into the SiO2 valence band and capture at oxide hole
traps (hexagons) is shown as process (a). The direct tunneling of hot holes to
oxide hole traps is shown as process (b). The injection of hot electrons into
the SiO2 conduction band and capture at oxide electron traps (squares) is
shown as process (c). The tunneling of hot electrons into the SiO2 conduction
band or to oxide electron traps is shown as processes (d) and (e). The impact
generation of electron hole pairs in the polysilicon emitter contact overlap and
the back injection and capture of hot holes at oxide hole traps and SiO2/Si
interface traps are shown as processes (f) and (g). Process (h) is similar to (g),
but involves direct tunneling to oxide hole traps. Adapted from Sah [54,
p.397].
base, as demonstrated in Fig.2.12. The hot holes may break strained interface bonds to
increase NIT through an impact process, represented by the star in the magnified
schematic diagram of the emitterbase junction in Fig.2.13. The open triangles represent
interface traps, and the filled triangles represent unbroken weak interface bonds. Since
interface trap generation is known to have a strong kinetic energy dependence, NIT will
vary along the SiO2/Si interface with the maximum located near quasineutral base
during reversebias. The hot holes with kinetic energy greater than 4.3eV (the SiO2/Si
valence band barrier height) may be injected into the oxide valence band and trapped at
oxide hole traps (hexagons) to positively charge the oxide, as shown in Fig.2.13 and in
Fig.2.14 as process (a). The hot holes will acquire the necessary kinetic energy of 4.3eV
as they near the base edge of the spacecharge region. Therefore, both NIT and +QoT
generated from hot holes are expected to be maximized near the edge of the quasi
neutral base. Since the hot hole mean free path is h=5nm, the average energy loss is in
the =60nm spacecharge region during stress is less than 0.75eV for hot holes, since the
maximum optical phonon energy is =60meV. Interband impact electronhole pair
generation may cause substantially larger energy losses, but this only affects a small
percentage of the hot holes until VEBstress nears junction breakdown. Hot holes with
kinetic energy less than 4.3eV may tunnel to oxide hole traps close to the SiO2/Si
interface, as shown in Fig.2.14 as process (b), but this process will produce only small
amounts of +QoT. It should also be noted that interface traps generated at the surface of
the quasineutral base will give positive interface charge, +QIT, due to the empty donor
like interface states, which will deplete the surface of the ptype base. This will enhance
the effects of +QoT in forming a surface channel in the quasineutral base.
For stress voltages approaching junction breakdown, the interband impact
generation of electronhole pairs becomes an important contribution to the measured
reversebias current. At lower VEBstress' impact generation may still be an important
source of hot electrons, compared to the density of thermally generated electrons in the
spacecharge region. The impact generated hot holes, however, will be of much smaller
density than the interband tunneling generated hot holes until VEBstress nears junction
breakdown. The impact generation mechanism is labeled (I) in Figs.2.11 and 2.12. The
impactgenerated secondary electrons may also break interface bonds through an impact
process in a similar manner as hot holes, as shown in Fig.2.13. The secondary hot
electrons will produce the largest NIT very near the edge of the quasineutral emitter,
since this is where they attain their maximum kinetic energy. Secondary hot electrons
with kinetic energy greater than 3.13eV (the SiO2/Si conduction band barrier height)
may be injected into the oxide and negatively charge oxide electron traps (squares), as
shown in Fig.2.13 and in Fig.2.14 as process (c). Hot electrons with kinetic energy less
than 3.13eV may also tunnel to the oxide conduction band or directly to oxide electron
traps, as shown in Fig.2.14 as processes (d) and (e). Hot electrons which are injected
into the oxide but not captured at oxide hole traps may also impact generate hot holes in
the polysilicon emitter contact overlap. The impactgenerated hot holes in the emitter
polysilicon may be back injected into the oxide and trapped at oxide hole traps to
positively charge the oxide [54, p.397], which is labeled (f) in Fig.2.14. This positive
oxide charge generation mechanism during electron injection into the oxide was recently
proposed, analyzed, and experimentally verified in thin oxide MOS transistors [55,56].
Hot electrons may significantly contribute to BJT degradation if their density is
comparable to hot holes. However, the location of the NIT, QoT and +QOT generated
from hot electrons is near the quasineutral emitter, which differs from the location of
the NIT and +QoT generated from hot holes near the base. Since the majority of the
surface recombination in the emitterbase spacecharge region during forward bias takes
place in a narrow portion of the spacecharge region, the location of NIT and QOT is very
important in determining their relative contributions.
The fundamental VEBstress thresholds for oxide charging are determined by
considering the kinetic energy requirements of hot carriers to be injected into the oxide
[54, p.408]. As mentioned above, the kinetic energy threshold for hole injection into the
oxide valence band is =4.3eV, based on the valence band potential barrier at the SiOz/Si
interface. Since the maximum hot hole kinetic energy is =qVEBstress for the interband
tunneling generated hot holes, as shown in Fig.2.12, the minimum stress voltage for
positive oxide charging from direct injection of hot holes, as shown by process (a) in
Fig.2.14, is VEBstress=4.3V. Although the conduction of holes in the oxide valence band
may be limited by the opposing electric field during stress as shown in Fig.2.14, the
injection and trapping of holes will still occur. For thicker oxides in selfaligned BJTs,
the field in the oxide may be much less than that shown in Fig.2.14. The minimum
stress voltage for impact generation of hot holes in the polysilicon emitter contact
overlap and back injection of the hot holes into the oxide, as shown in process (f) in
Fig.2.14, is also VEBstress=4.3V [5456]. This is easily estimated by considering the
minimum energy required for electrons in the polysilicon layer to impact generate hot
holes with kinetic energy greater than =4.3eV such that they may be injected into the
oxide valence band. Thus, the two important sources of positive charge initiated by both
hot holes and hot electrons are cut off for VEBstress<4.3V. Therefore, the anomalous AIB
increase associated with positive oxide charging [1214] is not expected for
VEBstress<4.3V. This is confirmed by the measurement of the AIB generation kinetics at
VEBstress=4.0V in Fig.2.15 which shows no anomalous increase in the AIB generation
rate. Limited positive oxide charging very near the SiO2/Si interface may be measured
for VEBstress<4.3V for the case of direct hole tunneling to traps in the SiO2, as shown in
process (b) in Fig.2.14. However, the amount of positive charging will be small due to
the exponential dependence of the tunneling probability on distance. This phenomenon
will be encountered in the model for the Ig relaxation transient in Ch.4. The threshold
for negative oxide charging is determined by the =3.13eV conduction band potential
barrier at the SiO2/Si interface. However, since the majority of hot electrons are
generated as a result of interband impact generation, this kinetic energy threshold is not
easily translated to VEBstress. At VEBstress<4V, the density of impact generated
secondary hot electrons will be small and significant negative oxide charging will also
be expected to cease.
The SiO2/Si interface traps are generated by two mechanisms of breaking the
strained SiSi, SiO, or SiH bonds: (1) the direct impact by energetic holes and
electrons in the emitterbase spacecharge region already mentioned above and shown
schematically in Fig.2.11, and (2) the holecapture energy of holes back injected into the
SiO2 as they are captured at SiO2 interface traps [54, p.397]. This is shown by process
(g) in Fig.2.14. As will be explained in section 2.5, the large increase (>104) in the
magnitude of the stressinduced AIB as shown in Figs.2.2 and 2.5 cannot be explained
exclusively by an increase in NTr in the very narrow emitterbase spacecharge region by
the two mechanisms just described. Instead, positive oxide charging over the quasi
neutral base is necessary to induce a surface channel which increases the recombination
area.
2.4. Analysis of Excess Base Current Kinetics
The fundamental recombination and tunneling mechanisms causing the IB
increase and PF decrease have been delineated, and the hot carriers created during stress
have been examined. The time dependence or kinetics of the AIB increase, which
directly determines the device timetofailure, will now be analyzed. Further support for
the AIB mechanisms measured in section 2.2 will be obtained. One method for quickly
measuring the effects of a reversebias stress on AIB is to measure Ig and Ic at a single
forward emitterbase bias, VBEmeas, which corresponds to the expected operating point
in the circuit. This method allows for frequent sampling of Ig and Ic without significant
interruption of the reversebias stress, and provides a true worstcase measurement of
device degradation. A constant reversebias stress voltage, VEBstress' is used in all
measurements of the AIB kinetics. Constant current stress has been used during reverse
bias stress by other investigators [11,12,14], but this method obscures the measurement
of detailed kinetics since the stress voltage and hot carrier kinetic energy are changing
during stress.
The AIB kinetics measured at VBEmeas=0.6V during reversebias stress varying
from VEBstress=4.0V to 6.OV is shown in Fig.2.15. The percent change of IB or AIB/IBO
is plotted vs. the stress time. An accelerated stress method involving the use of base
layer punch through current during reversebias stress is used at VEBstress=4.0V to
accelerate the stress current and reduce the stress time by approximately 100 times [23].
The measured data in Fig.2.15 indicates that the AIB increase is initially proportional to
the stress time, or AIgB c t at short stress times. For moderate stress times, the rate of AIB
increase slows such that AIgB to5, and may slow further at longer stress times to AIB c
t03. For VEBstress>4.3V in Fig.2.15, the rate of AIB generation is shown to suddenly
increase such that AIB o t1.4 at long stress times. This anomalous or superlinear AIB
increase has been measured by other investigators during both reversebias stress and
radiation stress, and has been modeled to be the result of positive oxide charging near
the emitterbase junction during stress [1214]. Eventually, the rate of AIB increase
slows and then saturates as the various processes involved in the AIB increase reach
steadystate. The AIB kinetics at short to moderate stress times may be explained
adequately by a simple firstorder interface bond breaking model [11,43], but the
deviation from this model may only be explained by also considering both positive and
negative oxide charging near the emitterbase spacecharge region as demonstrated in
this chapter.
10 1 1 l l I I l
VBEmeas=0.6V
102
/  t.4
S10 VEBstress=6.Os s s5.V
2 4.0V
101 10 103 10 10 109
t /( s)
Fig.2.15 The percent change of the stressinduced excess base current, AIB/IBO,
measured at VBE=0.6V is plotted vs. time while being stressed at varying
VEBstress from 4.0V to 6.0V. AI is shown to be proportional to tm, where m
varies during stress. The slope m is initially close to 1.0 for short stress time.
It drops to 0.5 at moderate stress time, and as low as 0.3 for longer stress time.
For VEB stress>4.0V, m increases suddenly to 1.4 before AIB saturates to a
nearly constant value. The accelerated stress is performed with basecollector
shorted to provide stress current acceleration.
A model for interface trap generation based on the release and diffusion of atomic
hydrogen from the SiO2/Si interface by hot carriers was proposed by Hu [43] and used
by Burnett and Hu [11] to explain the measured effects of BJT degradation over a
limited reversebias voltage range. A similar model for interface trap generation along
with some additional details of solving the rate equations for interface bond breaking
and hydrogen diffusion in general were explained in Ch.1. The resulting approximate
equation for the case of sufficient hydrogen diffusion that the rate of NIT generation
does not saturate before becoming diffusion limited is
Nrr + (CHXIX2DH)N2 = eH t eH dt (2.3)
where NIT is the interface trap density, NIB is the total number of hydrogen passivated
interface traps or total number of HSi bonds, eH and cH are the emission and capture
rates of hydrogen at the interface traps which are a function of the stress voltage, XI is
the SiO2/Si interface thickness where the atomic hydrogen can react with the interface
traps, Xo is the oxide thickness, and DH is the diffusivity of atomic hydrogen. The
solution for NIT from Eq.(2.3) may be easily approximated numerically to yield NIT as a
function of stress time. The stressinduced AIB may be assumed to be directly
proportional to the change in surface recombination velocity, ASo, and the
corresponding change in interface trap density, ANIT, during stress by the relation [38]
AIB = qARniASoexp(qVBE/2kT) = 4.8x10ANIT (2.4)
where [39]
ASo = 0.57thANIT = 1.5x107AN .
(2.5)
In Eqs.(2.4) and (2.5), AR = PEXR is the effective emitterbase spacecharge region area
where surface recombination is important, PE is the emitter perimeter, c is the capture
cross section of the interface traps, 0th is the thermal velocity, and the reciprocal slope
factor is assumed to be n=2. The numerical result relating AIB and ANIT in Eq.(2.4) uses
reasonable values of XR=3nm, a=1014cm2, 0th=107cm/s, and assumes that
VBEmeas=0.6V as in Fig.2.15. The value of XR=3nm is estimated by considering the
width required for 3kT variation of the potential on either side of the maximum
recombination point in the emitterbase spacecharge region, where FNp = (FN + Fp)/2 =
Er. An abrupt junction approximation is used in the calculation with total spacecharge
region thickness of XEB=18nm at VBE=0.6V. The theoretical fit to the measured data in
Fig.2.15 using Eqs.(2.3) and (2.4) is shown by the dashed lines in Fig.2.16. The values
for Ng, eH, and CHXIXo/DH used to obtain the fit in Fig.2.16 are listed in Table 2.1. It
is evident from Fig.2.16 that the theoretical model for NIT generation results in an
adequate fit to AIB for short to moderate stress times, but fails to properly model the AIB
kinetics for long stress times.
It has been suggested that a more accurate theoretical basis for the measured data
in Fig.2.15 at long stress times may be obtained by including the effects of oxide
charging near the emitterbase junction during stress [1214]. However, no detailed
models have been presented which account for the location and pathways of the oxide
charging, as described in the last section. Both positive and negative oxide charging
may be modeled individually by first order models [50], where
QOT = QOT[1 exp(oNINJ)] = QoT[1 exp(t/T)]. (2.6)
0
m
m
101 10 103 105 107
t /(1 s)
Fig.2.16 The theoretical fit from Eqs.(2.3) and (2.4) which model the generation of
interface traps is compared to the measured AIB/IBO from Fig.2.15. The values
for the parameters in Eq.(2.3) used to fit the measured data are given in Table
2.1.
109
Table 2.1 The values of the parameters used in Eq.(2.3) for fitting the data in Fig.2.15
vs. stress voltage. The result of the fit is shown in Fig.2.16.
VEBstress /(1V)
4.0
4.5
5.0
5.5
6.0
NB /(1cm2eV1)
1.3x1013
1.3x1013
1.3x1013
2.2x1013
3.0x1013
eH /(s1)
4.5x106
8.1x105
5.1x104
3.0x103
3.2x102
CHXXo/DH /(1cm2)
1.5x1010
1.9x10"
4.5x1012
2.3x1012
2.4x1012
Note:
Nrr(t4)= =~rr(t66)=NIB
The quantity QOT, is related to the total number of oxide electron or hole traps, a is the
oxide electron or hole trap cross section, and NINJ is the electron or hole fluence passing
through the oxide. The fluence may be assumed to be proportional to the stress time
(oNINJ = oJt/q = t/h) if the current injected into the oxide does not vary significantly
with time. Using the depletion approximation for a MOS capacitor [42, p.338], the
surface potential may be calculated to be
Vs = [(VG MS + Q oTCO + QITC + VAA)0.5 VAA0.5]2 (2.7)
where VAA=EsqNAA/2Co2, s is the silicon perimittivity, NAA is the base impurity
concentration, Co is the oxide capacitance, and (MS is work function difference between
n+ polysilicon and ptype base.
It is well known from SahNoyceShockley recombination theory and gated BJT
measurements that the surface recombination rate is an exponential function of the
silicon surface potential, Vs, if the surface is depleted, in addition to being proportional
to NIT [38,4648,57]. This is demonstrated by measuring the base current due to
recombination at the surface of the quasineutral base while sweeping the gatebase
voltage in a gated BJT structure as shown in Fig.2.17. If there is oxide charging during
reversebias stress, this effectively shifts the Ig vs. VGB curve in Fig.2.17 to the left for
positive charging or to the right for negative charging. This measurement is a basis for
separation of the effects of QIT and QOT in MOSTs and BJTs [57]. It was assumed by
Maugain et al. [14] in their quantitative analysis of the effects of oxide charging on AI,
that oxide charging near the emitterbase spacecharge region associated with hot carrier
injection into the oxide would provide the same modulation of the total recombination
IB oc exp(qVs/kT)
. 400 AIB
after SHEi
200 stress
unstressed
1.0 0.5 0.0 0.5 1.0
VGB /(1V)
Fig.2.17 The base current vs. gatebase voltage in a BiMOS device, which is similar to
gated BJT as described by Nishida [49]. The base current is shown to have an
exponential dependence on surface potential, Vs, as the gatebase voltage is
changed. In a BJT without a gate, the oxide charge may modulate Ig in a
similar manner.
rate in the spacecharge region, and the measured AIB would, therefore, be proportional
to exp(qVs/kT). However, no theoretical basis was given to justify this model. Since
AIB is proportional to the integrated recombination rate in the emitterbase spacecharge
region, the exponential dependence of AIB on oxide charging is not necessarily
expected. If NIT is fairly uniform throughout the spacecharge region, then a small
change in Vs due to oxide charging near the emitterbase junction will change the point
in the spacecharge region where the recombination rate is maximum, where FNp = (FN
+ Fp)/2 = EI. However, the total AIB will not vary exponentially with Vs. This is
demonstrated Figs.2.18 and 2.19, where the distortion of the surface potential due to
positive oxide charging during reversebias stress is demonstrated to change the point of
maximum recombination rate shown by a solid dot, but does not increase IB
significantly.
The positive oxide charge from hot holes and hot electrons will be located in the
vicinity of the emitterbase spacecharge region during stress. This means that the
positive charge extends into quasineutral base during forwardbias, since the space
charge thickness during forwardbias is smaller than during reversebias as
demonstrated in Fig.2.20. Thus, the significant positive oxide charging for up to
= 100nm over the quasineutral base will deplete the silicon surface in this region.
In order to present a firstorder quantitative model for the AIB increase from
positive charging, a situation is presented in which AIB is nearly an exponential function
of AVs, as assumed by Maugain [14]. If the large density of +QIT and +QoT generated
during stress depletes the surface of the quasineutral base such that it is nearly intrinsic,
tIE
0 IB2s
n+ Si  Si
I:B
I, _ "']
n+ Si p Si
EvE
VBE FN (F+Fp)/2
FF   ,\ El
F A 
SXR
Fig.2.18 The schematic diagram and energy band diagram along the silicon surface
near the emitterbase junction before stress or at short stress times with
negligible positive oxide charge. The point of maximum recombination is
designated by a dot, and the effective recombination thickness is shaded and
labeled XR. Adapted from Sah et al. [38].
E
B H ) M +QoT SiO2
AAA A A A A A+QIT .
13 IB2s
n+ Si PB Si
......  I B
n+ Si p Si
Ec
EE FNN (FN+Fp)/2
E"c V, '..FN
E.   / oF
.. ........ . .............. B
v OV
Ev 
XR
Fig.2.19 The schematic diagram and energy band diagram along the silicon surface
near the emitterbase junction after moderate stress and moderate oxide
charging such that the quasineutral base is slightly depleted. The point of
maximum recombination has shifted to the right from Fig.2.18. Adapted from
Neugroschel and Sah [22].
EVBE
N, Si02
O B2s
n+ Si P Si 6 B
_ IB OV
(a)
+VEBstress
+IE
N,T ^ITA A+QOT Si02
IET<
n+ Si p Si B
'IB OV
(b)
Fig.2.20 The energy band diagram along the silicon surface near the emitterbase
junction during (a) forward bias and (b) reversebias. The major current
pathways are also shown. Adapted from Neugroschel et al. [24].
Ettl
8 8 0 +QOT Si02
A AAAAAAA+QIT
n+ Si B4s IB2s p Si B
SIB
n+ Si p Si
(FN+Fp)/2 PEc
VBE FN ......
E FE
,.   E
F' Pv 0V
E...... 
S OV
EXR
Fig.2.21 The schematic diagram and energy band diagram along the silicon surface
near the emitterbase junction after heavy reversebias stress and heavy oxide
charging such that the surface of the quasineutral base has become nearly
intrinsic. The effective recombination area is shaded and designated by XR.
Adapted from Neugroschel and Sah [22].
as shown in Fig.2.21, the surface recombination there will dominate the measured AIB.
In this case, the modulation of the surface potential, AVs, from further positive oxide
charging will have a strong effect on the measured AIB. This model is supported by the
measurements in section 2.2 which suggested the presence of a surface electron channel
over the ptype base. Thus, it is assumed to be a valid model for the devices in this
work. The expression for AIB in Eq.(2.4) may be extended to account for the surface
potential modulation as
AIB = 4.8xlO18ANiexp(qAVs/kT), (2.8)
where the recombination rate at the surface of the quasineutral base is assumed to be
nearly an exponential function of Vs. For small AVs when the surface of the quasi
neutral base is nearly intrinsic, this approximation is valid. Using Eq.(2.8), the
theoretical fit to the data in Fig.2.15 is shown in Fig.2.22. The model in Eq.(2.8)
predicts that the rate of AIB generation will increase with positive oxide charging and
decrease with negative oxide charging. With both positive and negative oxide charging
included, the theoretical fit is able to accurately model the AIB kinetics for the entire
range of stress time. The values of NIB, eH, and CHXIXo/DH for NIT generation are the
same as those used in the fit in Fig.2.16 and listed in Table 2.1. The additional
parameters involving positive and negative oxide charge which are QOT+I/CO'
QOTj/Co, '+, and T_ are listed in Table 2.2, where the symbols with + and refer to
+QOT and QOT respectively.
The onedimensional model used to generate the theoretical fit in Fig.2.22 can
only roughly approximate the two dimensional effects of interface trap generation and
oxide charging included
10  experiment
I
VEBstress=6.0V
o 10 5.ov
m 4.5V,
'4.0V
1 0
1 0 ,,/ 
/ normal accelerated
/I, stress stress
10'
101 10 103 105 107 109
t/(ls)
Fig.2.22 The theoretical fit from Eqs.(2.3) though (2.7) which model the generation of
interface traps and oxide charge is compared to the measured AIB/IBO from
Fig.2.15. The values for the parameters in Eqs.(2.3) and (2.6) used to fit the
measured data are given in Tables 2.1 and 2.2.
Table 2.2 The values of the parameters used in Eqs.(2.6) through (2.8) for fitting the
data in Fig.2.15 vs. stress voltage. The result of the fit is shown in Fig.2.22.
VEBstress /(V) NOT+ /(lcm2)
4.0 0
4.5 2.5x1012
5.0 2.6x1012
5.5 2.4x1012
6.0 2.3x1012
T+ /(ls)
6.3x105
4.7x104
2.7x103
1.3x102
NoT /(1cm2)
9.5x101
9.5x101
9.5x10'
9.5x101
9.5x101
Note:
N0T=Q0TIq
z_ /(ls)
8.9x106
1.3x105
6.0x103
2.1x102
2.9x101
