Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UF00082293/00001
## Material Information- Title:
- Hot-electron noise in gallium arsenide aluminum gallium arsenide heterojunction interfaces
- Creator:
- Whiteside, Christopher Francis, 1959- (
*Dissertant*) Bosman, G. (*Thesis advisor*) van der Ziel, A. (*Reviewer*) van Vliet, C. M. (*Reviewer*) Neugroschel, Arnost (*Reviewer*) Anderson, Timothy J. (*Reviewer*) - Place of Publication:
- Gainesville, Fla.
- Publisher:
- University of Florida
- Publication Date:
- 1987
- Copyright Date:
- 1987
- Language:
- English
- Physical Description:
- v, 144 leaves : ill. ; 28 cm.
## Subjects- Subjects / Keywords:
- Diffusion coefficient ( jstor )
Electric current ( jstor ) Electric fields ( jstor ) Electric potential ( jstor ) Electrons ( jstor ) MODFETS ( jstor ) Noise temperature ( jstor ) Phonons ( jstor ) Spectral energy distribution ( jstor ) Velocity ( jstor ) Dissertations, Academic -- Electrical Engineering -- UF Electrical Engineering thesis Ph. D Gallium arsenide semiconductors -- Noise ( lcsh ) Hot carriers ( lcsh ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Abstract:
- In recent years much attention has been paid to the study of semi-conductor heterojunction interfaces. An interest in the hot-electron behavior of electron transport parallel to the interface has arisen. in this dissertation the charge-transport noise in the direction parallel with the GaAs/AlGaAs interface is studied. Monte Carlo calculations of the electron transport properties of bulk GaAs are fitted to recent experimental data of the field-dependent diffusion coefficient. This method provides a better theoretical value of the T-I, intervalley coupling constant. The effects of GaAs device length on the velocity fluctuation spectrum are investigated using the Monte Carlo technique. In addition, an experimental investigating of the velocity fluctuation spectrum as a function of electric field and length for different AlGaAs/GaAs heterjunctions is completed. finally, the dc, ac, and noise properties of the AlGaAs/GaAs MODFET channel are investigated both experimentally and theoretically using the impedance field method.
- Thesis:
- Thesis (Ph. D.)--University of Florida, 1987.
- Bibliography:
- Bibliography: leaves 141-143.
- General Note:
- Typescript.
- General Note:
- Vita.
- Statement of Responsibility:
- by Christopher Francis Whiteside.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Christopher Francis Whiteside. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 030367795 ( ALEPH )
16865103 ( OCLC ) AEQ8989 ( NOTIS )
## UFDC Membership |

Downloads |

## This item has the following downloads:
UF00082293_00001.pdf
00006.txt 00026.txt 00047.txt 00080.txt 00058.txt 00105.txt 00060.txt 00054.txt 00092.txt 00051.txt 00055.txt 00061.txt 00137.txt 00067.txt 00142.txt 00037.txt 00033.txt 00100.txt 00096.txt 00145.txt 00108.txt 00062.txt 00002.txt 00112.txt 00146.txt 00076.txt 00057.txt 00148.txt 00087.txt 00066.txt 00073.txt 00075.txt 00007.txt 00127.txt 00027.txt 00063.txt 00114.txt 00091.txt 00071.txt 00120.txt 00059.txt 00136.txt 00150.txt 00042.txt 00012.txt 00125.txt 00023.txt 00039.txt 00122.txt 00133.txt 00072.txt 00081.txt 00020.txt 00038.txt 00151.txt 00101.txt 00011.txt 00034.txt 00010.txt 00083.txt UF00082293_00001_pdf.txt 00143.txt 00024.txt 00110.txt 00093.txt 00117.txt 00022.txt 00119.txt 00111.txt 00019.txt 00126.txt 00135.txt 00070.txt 00032.txt 00138.txt 00068.txt 00107.txt 00128.txt 00140.txt 00064.txt 00008.txt 00035.txt 00095.txt 00090.txt 00016.txt 00116.txt 00118.txt 00005.txt 00103.txt 00017.txt 00139.txt oai_xml.txt 00097.txt 00050.txt 00121.txt 00085.txt 00018.txt 00098.txt 00113.txt 00052.txt 00144.txt 00084.txt 00069.txt 00134.txt 00004.txt 00088.txt 00029.txt 00074.txt 00132.txt 00077.txt 00041.txt 00053.txt 00104.txt 00115.txt 00078.txt 00149.txt 00141.txt 00131.txt 00021.txt 00028.txt 00031.txt 00009.txt 00046.txt 00147.txt 00044.txt 00013.txt 00001.txt 00109.txt 00099.txt 00102.txt 00040.txt 00129.txt 00094.txt 00014.txt 00086.txt 00130.txt 00049.txt 00079.txt 00048.txt 00123.txt 00065.txt 00106.txt 00015.txt 00056.txt 00045.txt 00030.txt 00089.txt 00082.txt 00036.txt 00124.txt 00043.txt 00025.txt 00003.txt |

Full Text |

HOT-ELECTRON NOISE IN GALLIUM ARSENIDE/ALUMINUM GALLIUM ARSENIDE HETEROJUNCTION INTERFACES By CHRISTOPHER FRANCIS WHITESIDE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1987 .. ACKNOWLEDGMENTS The author wishes to express his sincere gratitude to Dr. G. Bosman for his research guidance and many helpful discussions and also to Dr. C.M. Van Vliet and Dr. A. van der Ziel for their support and encouragement. The services of Dr. Morkoc at the University of Illinois in supplying the heterostructures for the experiments are greatly appreciated. He also wishes to thank his fellow students in the Noise Research Laboratory for their help and many interesting discussions and Miss Katie Beard for the editing and typing of the manuscript. Special thanks go to his wife, Susan, and his family, who have supported and encouraged him over the years. .. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii ABSTRACT V CHAPTER I. INTRODUCTION 1 1.1. Band Structure of AlGaAs/GaAs 2 1.2. Hot-Electron Effects 4 1.3. Noise Characterization of Hot-Electron Phenomena 7 1.4. Device Applications of Heterojunctions. 14 II. MONTE CARLO MODELING OF HOT-ELECTRON TRANSPORT 18 2.1. Description of Physical Model 19 2.2. Determination of P-L Intervalley Coupling Constant and its Relation to the Diffusion-Field Characteristics 32 2.3. Monte Carlo Spectral Analysis of Velocity Fluctuations 39 2.4. Position Monitoring and Boundary Conditions in Monte Carlo Programming 49 2.4.1. Program algorithm 52 2.4.2. Simulation results 57 III. EXPERIMENTS ON ALGAAS/GAAS INTERFACES 63 3.1. Description of Device Structures 63 3.2. Noise Temperature Measurement Setup and Experimental Procedures 65 3.3. Experimental Results 71 3.4. Discussion of Results 83 IV. THE DC, AC AND NOISE CHARACTERIZATION OF THE ALGAAS/GAAS MODFET CHANNEL 89 4.1. Impedance Field Modeling 90 4.1.1. Review of impedance field method 90 4.1.2. Application of the impedance field method to the MODFET 94 4.2. Charge-Voltage Dependence.99 4.3. Device Description .o.o.103 4.4. Measurement Procedure . 103 4.5. Results and Discussion 107 4.6. Conclusions 115 iii .. V. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 118 5.1. Monte Carlo Transport Modeling 118 5.2. Experimental Characterization of Heterostructures 119 5.3. MODFET Characterization 120 APPENDICES A. MONTE CARLO ELECTRON TRANSPORT ALGORITHM 121 B. VELOCITY TIME SERIES ALGORITHM 122 C. POSITION-MONITORING ALGORITHM 123 D. MONTE CARLO COMPUTER PROGRAM 124 REFERENCES 141 BIOGRAPHICAL SKETCH 144 .. 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 HOT-ELECTRON NOISE IN GALLIUM ARSENIDE/ALUMINUM GALLIUM ARSENIDE HETEROJUNCTION INTERFACES By Christopher Francis Whiteside May 1987 Chairperson: G. Bosman Major Department: Electrical Engineering In recent years much attention has been paid to the study of semiconductor heterojunction interfaces. An interest in the hot-electron behavior of electron transport parallel to the interface has arisen. In this dissertation the charge-transport noise in the direction parallel with the GaAs/AlGaAs interface is studied. Monte Carlo calculations of the electron transport properties of bulk GaAs are fitted to recent experimental data of the field-dependent diffusion coefficient. This method provides a better theoretical value of the F-L intervalley coupling constant. The effects of GaAs device length on the velocity fluctuation spectrum are investigated using the Monte Carlo technique. In addition, an experimental investigation of the velocity fluctuation spectrum as a function of electric field and length for different AlGaAs/GaAs heterojunctions is completed. Finally, the dc, ac and noise properties of the AlGaAs/GaAs MODFET channel are investigated both experimentally and theoretically using the impedance field method. .. CHAPTER I INTRODUCTION In recent years much attention has been paid to the study of semiconductor heterojunction interfaces. Due to increased processing capabilities, novel semiconductor heterojunctions of various material compositions can be manufactured. This opens many new possibilities in the development of existing and novel semiconductor devices and their applications. In order to take full advantage of these new heterojunctions, more information on the charge-transport properties must be attained. In this dissertation the charge-transport noise in the direction parallel with the GaAs/AlGaAs interface is studied. Monte Carlo calculations of the electron transport properties of bulk GaAs are fitted to recent experimental data of the field-dependent diffusion coefficient. This method provides a better theoretical value of the r-L intervalley coupling constant. The effects of GaAs device length on the velocity fluctuation spectrum are investigated using the Monte Carlo technique. In addition, an experimental investigation of the velocity fluctuation spectrum as a function of electric field and length for different AlGaAs/GaAs heterojunctions is completed. Finally, the dc, ac and noise properties of the AIGaAs/GaAs MODFET channel are investigated both experimentally and analytically using the impedance field method. In this introductory chapter the band structure of the AlGaAs/GaAs system is reviewed, including energy band lineup and modulation-doping .. techniques. The second section of this chapter outlines some of the effects of hot electron behavior on charge transport, such as realspace-charge transfer vs. intervalley transfer, in providing negative differential mobility. The length of the active device region can have a significant effect on the charge-transport properties of GaAs in the hot electron regime, and this effect is discussed. Noise measurements have been used for many years as a method for investigating charge transport properties in materials and devices. A review of both analytical and computational methods of noise modeling is presented. Device applications of the AlGaAs/GaAs heterojunction, such as the heterojunction bipolar transistor (HBT) [11 and the modulationdoped field-effect transistor (MODFET) [2], are discussed. 1.1. Band Structure of A1GaAs/GaAs The alloy system AlxGal_xAs/GaAs is of great importance in highspeed electronic devices since it allows the possibility of bandgap engineering. The lattice constants between the two materials are closely matched. If properly grown, this small lattice constant difference results in high-quality interfaces between GaAs and AlGaAs with an insignificant concentration of interface states. The most important device parameter of interest in AlxGailxAs is the energy bandgap dependence on the alloy composition. The energy gap as a function of the mole fraction x can be expressed by [3,4] E (x) = 1.424 + 1.247x(O < x 4 .45) (1.la) g E (x) = 1.900 + 0.125x + 0.143x2(0.45 4 x < 1.0) (1.lb) g and the units are in eV. For mole fractions less than approximately 0.45, the AlGaAs has a direct bandgap. For larger mole fractions, the .. alloy bandgap is indirect, with the X-valley having the lowest energy. The L-valley lies between the r- and X-valleys for mole fractions larger than 0.45. The sum of the valence- and conduction-band discontinuities must equal the energy bandgap difference between the GaAs and AlGaAs. Originally, it was believed that the conduction-band discontinuity was 0.85 E (x) [5]. However, more recent measurements [61 have shown that sixty-five percent of the bandgap difference lies in the conduction band for x 4 0.45. Then the conduction-band discontinuity follows from AE = 0.81x (eV) for x 4.0.45 (1.2) c From measurements of the valence-band discontinuity as a function of mole fraction, it was determined that the maximum conduction-band discontinuity lies in the vicinity of x = 0.45 [7]. A further increase of the mole fraction results in a decrease in the conduction-band discontinuity with a corresponding larger increase in the valence-band discontinuity. Of special interest in the A1GaAs/GaAs system is the method of modulation doping. In this doping process, the GaAs layer is undoped and the dopant atoms (usually silicon atoms for n-type) are deposited in the AlGaAs layer. In equilibrium the Fermi level must be constant across the interface. Consequently, the electrons from the donors near the interface transfer to the lower energy GaAs conduction band. In this way, the electrons become spacially separated from the parent donor atoms, causing an electric field normal to the interface. The electric field leads to energy band bending in both the AlGaAs and the GaAs in the vicinity of the heterojunction. This band bending forms a quasi- .. triangular potential well for the electrons in the GaAs. If the electric field is large enough, the width of the triangular potential well may be smaller than the carrier deBroglie wave length. The momentum vector perpendicular to the interface then becomes quantized. Shown in Figure 1.1 Is an example of a heterojunction where the A1GaAs is doped n-type and the GaAs is slightly p-type. The modulation-doping process was developed to increase the lowfield mobility of electrons in the direction parallel to the interface. At room temperature (300K), the dominant scattering mechanism is polar optical phonon scattering. At lower temperatures, however, the dominant scattering mechanism becomes ionized impurity scattering. Because the electrons are spacially separated from the donor atoms, a reduction of ionized impurity scattering is obtained, leading to a higher electron mobility. The inclusion of a thin spacer layer of undoped AlGaAs between the doped AlGaAs and GaAs reduces even further the coulombic interaction between the donor atoms and free carriers [8]. 1.2. Hot-Electron Effects With microelectronic devices approaching submicron dimensions, even moderate applied voltages result in very high electric fields. These large fields cause the average carrier energy to increase significantly beyond the thermal equilibrium value. This increase in energy leads to nonlinear charge transport (i.e., deviations from Ohm's Law), also known as hot-electron transport. To improve the modeling and performance of electron devices, high-field transport properties need a more thorough understanding. An interesting hot-electron effect is the occurrence of a negative differential mobility regime in bulk GaAs. This phenomenon, commonly .. GaAs EC -EF spacer layer I I AlGaAs/GaAs heterojunction at equilibrium. AIGaAs Fig. 1. 1. .. known as the Gunn effect [9], is due to the transfer of electrons from the high-mobility central r-valley to the low-mobility satellite L and X valleys. At low fields the electron velocity increases in proportion to the electric field. At higher field strengths, the electrons partially occupy the low-mobility satellite valleys, and the average velocity is lowered. This net decrease in velocity with increasing field gives rise to the negative differential mobility in GaAs. From the measurements by Ruch and Kino [10] on bulk GaAs, it was found that the diffusion coefficient shows a sharp increase in the same field range as the onset of transfer of electrons to the satellite valleys. Since the diffusion coefficient is closely related to the velocity fluctuations caused by random scattering, in formation ahout the scattering process can be obtained. The increase in diffusion is very sensitive to the intervalley coupling constant DrFL* Thus, accurate measurements of the field dependence of the diffusion coefficient can provide a more accurate value for this constant. Since the L valley is located .33 eV above the conduction-band minimum, it takes time for most electrons to gain sufficient energy under an applied field to undergo intervalley transfer. If the device length is short, few electrons will transfer to the satellite valleys before being collected by the contact. The large changes in velocity associated with intervalley transfer will not occur and less noise will be produced in the external circuit. A description of a Monte Carlo experiment to observe this effect is outlined in Chapter II. In the AlGaAs/GaAs interface there are two mechanisms that can produce negative differential mobility at high electric fields. The first is the Gunn effect just outlined for bulk GaAs. The second .. mechanism is called real-space-charge transfer, which stands for the following physical process. Electrons in the high-mobility GaAs gain energy as they drift under an applied electric field parallel to the interface. When the energy becomes comparable to the conduction-band difference, there is the possibility of transferring to the AlGaAs. Because of the high doping concentration, which introduces a significant amount of ionized impurity scattering in the AIGaAs layer, the electron mobility in this layer is lower than in the GaAs layer. The increasing percentage of electrons transferring to the AlGaAs layer with increasing field causes the drift velocity to decrease, similar to the Gunn effect. Experimentally, real-space-charge transfer has been shown to be the cause of negative differential device conductance of specially made heterostructures [11i]. However, accurate modeling of the processes involved is difficult, and even getting experimental verification of negative conductance is rather involved. The length of the heterostructure may also play a role in the transfer of carriers. Investigation of the field-dependent diffusion coefficient in conjunction with velocity-field measurements should provide information on the hot-electron behavior of the GaAs/AlGaAs interface system. In Chapter III these measurements will be presented for different interface compositions and compared with bulk GaAs. 1.3. Noise Characterization of Hot-Electron Phenomena Noise measurements are used to provide information on chargetransport processes in semiconductors. In this section the methods of characterizing hot-electron effects by noise measurements are reviewed. There are basically three types of noise in semiconductor devices: 1/f, generation-recombination (g-r) and velocity-fluctuation. At low .. frequencies 1/f and g-r noise, caused by fluctuations in the sample resistance, can be observed by the passage of a current through the sample. The 1/f noise mechanism has been attributed to mobility and number fluctuations. Generation-recombination noise is caused by the interaction of carriers with trapping states in the forbidden energy band. The trapping process gives rise to fluctuations in the number of free carriers available for conduction. Velocity fluctuations are a result of carrier interactions with the scattering mechanisms associated with the thermal vibrations of the host crystal. Since the mean intercollision time of the carriers in high-mobility semiconductors is very small, the velocity-fluctuation spectrum extends to very high frequencies. The emphasis in this dissertation is placed on the hot-electron effects that are associated with the various scattering mechanisms. Therefore, velocity fluctuation noise, also known as thermal or diffusion noise, is used as a tool for probing these effects. Consider a one-port network biased by an arbitrary dc voltage V0 with a dc current 10 flowing through it. The small-signal Thevenin and Norton equivalent circuits, evaluated around the bias point, are depicted in Figure 1.2. In general, the small-signal impedance Z(V0,f) and admittance Y(V0,f) are functions of bias and frequency. The voltage and current noise generators represent the noise mechanisms in the network. The mean square voltage fluctuations AV2 can be expressed in terms of the voltage spectral density SAV by AV = f SAv(Vo,f)df (1.3) 0 where f denotes frequency. A similar relation, 00 A2 = f SA(V,f)df (1.4) 0 .. z Fig. 1.2. Thevenin and Norton small-signal equivalent circuits. .. holds for mean square current fluctuations in terms of current noise spectral density. One can now define the concept of an ac noise temperature T (Vf) n 0f of the network in analogy with the Nyquist relation in the following way: S AV(V 0f) =4kBT (V 0 )eZVJf (1.5) S AI(VNJ) = 4k B Tn(VO0 f)Re{Y(Vo,f)} (1.6) where kB is Boltzmann's constant and Re {Istands for the "real part of ." It should be noted that the noise temperature is an electrical parameter of the network and has nothing to do with the electron temperature. By connecting a conjugately matched load to the network, the maximum available power is delivered to the load. This maximum available power has the value P av=k BT n V9f'Af(17 where Af is the bandwidth of the measuring system. Therefore, T n has physical meaning and can be measured. At high frequencies (f > 10 MHz)measurements of T nare preferred because it is much easier to measure power flow than terminal voltages and currents. The above definitions are valid for every one-port network whether it is linear or nonlinear. The following discussion is restricted to homogeneous semiconductor samples for which a one-dimensional treatment is warranted. The link between diffusion coefficient and velocity fluctuations is outlined. It should be noted that the quantum correction factor for thermal noise is neglected [12]. .. Let the instantaneous velocity of a carrier i at time t be (t = ) + AVi(t) (1.8) ++ where Vd(E) is the average drift velocity and E is the electric field. + The term Av i(t) represents the fluctuations in the velocity about vd(E), with the average Av-(t) = 0. By definition [12] the diffusion d i coefficient is related to the spectrum of velocity fluctuations by DEf= AV (~)-1C j2TF dT (1.9) S('f4 2 f Av(t)Av(t+T) e-2 ft where the term Av(t)Av(t+T) is the autocorrelation function of the velocity fluctuations. At low frequencies eq. (1.9) reduces to the well-known Einstein formula for diffusion Ax = 2Dt (1.10) for sufficiently long t. Consider a semiconductor sample of length L and cross-sectional area A with ohmic contacts. An electron with velocity Avi (t) gives rise to a current Ai (t) in the external circuit such that qAv i(t) iL and the corresponding spectrum of current fluctuations is 2 2 SAi(f) = _q_ S (f) = 4 L- D(f) (1.12) AL2 Av L 2 If the electron gas in nondegenerate and there are nAL electrons in the .. sample, then the total noise current spectral density becomes S (f)- nAL5(f) 2 nA SAI(f) = hAL SAi(f) = 4q D(f) (1.13) Using eq. (1.6), one obtains kBTn(f)L D(f) = Re(Y) (1.14) q nA Recognizing that Re(Y) = Re(u')qnA/L, one arrives at the generalized Einstein relationship kBTn(E,f) D(E,f) = B n Re(') (1.15) q where V' is the differential mobility. This equation is valid for all cases in which the field remains uniform throughout the sample. As the electric field approaches zero, the noise temperature becomes equal to the lattice temperature, and the Einstein relation reduces to the familiar form in equilibrium kBT D k B 0 (1.16) q O If the electron gas is degenerate, as in heavily doped semiconductors or metals, electron-electron interactions can no longer be ignored. In this case, electrons cannot be treated as statistically independent particles, and cross-correlation terms must be included in the spectrum. Van Vliet and van der Ziel [13] have extended the relation for current spectral density using statistical mechanics and derived .. (f) = L4q D(f)kBT( F ) T (1.17) The expression for diffusion in terms of mobility for degenerate semiconductors then becomes 3 log nqD(f) ( ao F) = Re(v') (1.18) EF Once the sources of noise in semiconductors have been determined, it is possible to characterize the noise at the terminals of solid-state devices. Three methods are used in hot-electron problems: the Langevin, the impedance field, and the transfer impedance. First, in all three methods the equations describing the device behavior are formulated. Then each variable involved is set equal to Q = Q0 + AQ exp(jwt) The zero-order terms give the dc characteristics. The first-order terms give the ac equations. In the Langevin method [14], the appropriate white noise source is added to each ac equation. Auxiliary variables are then eliminated to get a relationship between the ac current AI and the ac field AE. Writing the solution of AE in terms of the other variables and integrating over the device length, one gets the ac voltage across the terminals. By setting the noise sources to zero, the device impedance is obtained. Conversely, when AI = 0, multiplying by the complex conjugate AV results in the ac voltage noise around the bias point. An extensive review of this method was given by Nicolet et al. [151, in application to single-injection diodes. The impedance-field method was developed by Shockley et al. [16] to describe diffusion noise in devices. In this method the transfer .. function between the position-dependent ac current noise sources and the ac voltage at the terminals is derived. Once the transfer function has been obtained, the impedance and noise characteristics easily follow. A general outline of this method applied to a MODFET is reviewed in Chapter IV. When the variables used to describe the ac properties of a device are written in terms of current AI and electric field AE, the most general technique for calculating the impedence and noise properties is the transfer impedance method. Van Vliet et al. [17] developed this method to describe the noise behavior in space-charge limited-current (SCLC) solid-state diodes. It was found that the transfer impedance method is quite general and encompasses the impedance-field technique. Its ability was recently utilized by Tehrani et al. [18] in SCLC silicon carbide devices. As device dimensions continue to shrink, traditional analytical methods of characterizing solid-state devices become questionable. Transient transport effects and boundary conditions will become increasingly important in device modeling. Computer methods for obtaining device noise characteristics are beginning to emerge. In these methods fewer approximations are made concerning carrier transport phenomena; consequently, these methods are expected to lead to more accurate results. In Chapter II the use of the Monte Carlo method to calculate velocity-fluctuation noise is outlined. The technique is then used in modeling noise behavior of very short GaAs diodes. 1.4. Device Applications of Heterojunctions In the following, two well-known examples of devices based on AlGaAs/GaAs heterojunction operation are discussed. .. There are essentially two main parameters that influence the common-emitter current gain a in bipolar transistors; they are the emitter efficiency y and the base transport factor. The base transport factor determines how many carriers injected from the emitter into the base reach the collector before recombination occurs. With the short base regions achievable with present processing capabilities, recombination becomes negligible. Then the emitter efficiency, caused by back injection of carriers from the base to the emitter, dominates the current gain. In homojunction technology, the emitter is heavily doped with a lightly doped base region to decrease the back injection. However, the high resistance of the lightly doped base severely limits the high frequency and noise performance of bipolar devices. Doping the base more heavily would lower the resistance but degrade emitter efficiency. To circumvent these effects, it was proposed by Kroemer [191 that a heterojunction at the emitter-base junction be used. Using a wide bandgap emitter would allow the base region to be heavily doped, thus lowering the base resistance while maintaining high emitter efficiency. This is the basic premise of the heterojunction bipolar transistor (HBT). Much research is currently being pursued on this interesting device topic. Although the technology is available to make heterojunction bipolar transistors today, the processing of integrated circuits is difficult due to layout and interconnection problems. Heterojunctions have also improved field-effect transistor technology. The Si-SiO2 interface has been used to make MOSFETs for years. However, the interface is often degraded due to surface roughness and interface states. The AlGaAs/GaAs heterojunction does not have .. these problems if properly grown. The modulation-doped field-effect transistor (MODFET), also known as the high electron mobility transistor (HEMT), was developed for high-speed applications. In this case the carrier transport is parallel to the interface. The MODFET fabrication process begins with a semi-insulating GaAs substrate on which an undoped buffer layer of GaAs is grown. A doped AlGaAs layer is then deposited on top of the buffer layer. After ohmic contacts are defined for the source and drain pads, the AlGaAs layer is etched down to provide a Schottky-type gate. The depletion region of the gate is made to overlap the depleted area in the AlGaAs adjacent to the GaAs/AlGaAs interface. Careful control of the gate to interface spacing determines the threshold voltage of the FET structure. A typical MODFET conduction band diagram showing the overlapping depletion regions is shown in Figure 1.3. The MODFET has shown excellent gain and noise figure characteristics at high frequencies and will probably exceed conventional MESFET capabilities into the millimeter-wave region. In Chapter IV the dc, ac and noise properties of the MODFET channel are derived and experimentally verified. .. AIGaAs Doped 4 GaAs EF Undoped Fig. 1.3. MODFET conduction band diagram. q 4b .. CHAPTER II MONTE CARLO MODELING OF HOT ELECTRON TRANSPORT The semiclassical Boltzmann transport equation (ETE) describes the evolution of the distribution function in phase space. Once the distribution function is known, the pertinent transport parameters can be obtained by taking the appropriate moments of this function. Solutions of the integro-differential Boltzmann equation can be difficult to obtain analytically. In seeking solutions in the hot-electron regime, drastic approximations have to be made for analytical results. Monte Carlo techniques were first devised as a computational tool for calculating difficult integral expressions. The general principles have been applied to the solution of differential equations and many other problems in the applied sciences. In this chapter the method of Monte Carlo simulation of electron transport properties in GaAs is examined. The method is very versatile since steady-state as well as transient phenomena can be simulated in situations near as well as far from equilibrium. A main disadvantage of the method is, however, that it requires large amounts of computer time to obtain sufficient stat istical accuracy. Therefore, the Monte Carlo technique is not always the most efficient means of investigating a problem. First, a description of the physical modeling of transport in semiconductors and an explanation of how the Monte Carlo methods are used to describe stochastic processes will be given. Subsequently, the band structure of GaAs in k space and the electron-phonon scattering .. mechanisms are reviewed. The sensitivity of the diffusion-field and velocity-field characteristics on the r-L intervalley-scattering coupling constant is examined. The proper r-L coupling constant is found from fitting the calculated diffusion-field characteristics to recently measured data on GaAs obtained from noise measurements. Next, the techniques used to obtain the velocity fluctuation spectrum from a velocity time series are described, and results obtained for GaAs under high-field conditions are presented. As the device length shortens, it is expected that transport behavior becomes more dependent on the imposed boundary conditions. To study the effects of boundary conditions, the Monte Carlo program was modified in such a way that the active device length and initial electron velocity could be adjusted. The effects of the length and boundary conditions on the calculated velocity fluctuation spectrum are examined and compared with bulk behavior. 2.1. Description of Physical Model The Monte Carlo method can be applied to many physical systems whose parameters are governed by probability distributions. The ability to map simple pseudo-random distributions, available in most computers, into more complex ones is very powerful. The mapping process begins by equating the areas under the different distribution functions. Solving the equations allows one to obtain the physical variable of interest from the known, compute r-generat ed distribution. In the example given by Boardman [20], p(r) and p( ) are the respective probability densities, where r is associated with the pseudo-random computer distribution and is the physical quantity to be obtained from the mapping. Equating the cumulative distributions .. 0r f p(4')do' = f p(r')dr' (2.1) 0 0 and using a uniform distribution for p(r) = 1, r f p(0')dp' (2.2) 0 Evaluating the integral of eq. 2.2, one obtains 0 in terms of r. In the following Monte Carlo program, this method of obtaining random variables is used to generate free-flight times, choose between scattering mechan+ isms, and select the final k-space position after scattering. In addition, the energy of the electrons injected into the active device region is calculated using random numbers. The program to be described is built upon the Fortran version outlined by Boardman [20]. The original Boardman program only allowed for a central valley and one type of satellite valley in the energywavevector dispersion relation E(k) for electrons in the conduction band. Originally, it was believed that the ordering in energy of the conduction-band valleys was r X L for GaAs in increasing order of electron energy. For this reason the original version included only the r and X valleys, since the L valley population in this model could be neglected. More recently, it was discovered that the ordering of the valleys is F L X [211. The program was rewritten to include all three valleys in the appropriate order. The values for intervalleyscattering coupling constants and energy offsets between valleys were taken from Pozhela and Reklaitis [221. Figure 2.1 shows the energywavevector relationship for the GaAs conduction band. Each valley is taken to be parabolic. .. E(k) 0.52eV Fig. 2.1. Energy-wavevector relation for GaAs. [111 I0003 1100] k .. + Electron motion is most easily described in k space. In simple semiconductors the electrons are regarded as free particles with an effective mass m* of the appropriate valley. The electron energy is then given by 2+2 E(i) = (2.3) 2m + where k is the reduced wavevector of the electron. To simulate electron motion, one first generates a random number based on the scattering rates of the valley occupied by the electron. This number is then used to calculate the flight time between colli+ sions. The wavevector k changes during the collision free-flight time in proportion to the applied electric field. If the electric field is in the -z direction, only the k component of wavevector increases z linearly with time during the free flight as indicated by kzi (t) = kf +R t (2.4) The subscript i refers to the initial state before scattering and f denotes the final state after the previous scattering event. During the free flight the wavevector component kp perpendicular to the z axis does not change. Upon scattering, however, both the k. and kp components may change and obtain values determined by the particular scattering mechanism involved. This process is shown pictorially in Fig. 2.2. Having outlined the band structure and concept of electron motion in GaAs, the electron-phonon scattering mechanisms will be reviewed. The program accounts for the following electron-phonon interactions: acoustic phonon (intravalley), polar optical phonon (intravalley), .. -S - -/ / / / / I I / kZ elec. field E Electron motion in k space. do Fig. 2.2. .. equivalent intervalley (L L or X X), and nonequivalent intervalley. (L X, etc.). Intravalley scattering means that the initial and final states before and after scattering are in the same valley, and intervalley scattering means that the two states are in different valleys. Both types of intervalley scattering are via optical phonons since acoustic and polar optical phonon scattering does not allow for large changes in the wavevector. For all intravalley scattering processes involving optical phonon fields, the energy state after scattering must satisfy the relation E(k') = E(k) Aw (2.5) where w is the radian frequency of the lattice vibration, the plus sign indicates absorption, and the minus sign emission of an optical phonon. Acoustic phonon scattering, however, is treated as an elastic process and therefore E(k') = E(k) The energy of the electron is measured with respect to the minimum of the valley it occupies. Therefore, when a nonequivalent intervalley transition occurs, the energy difference between valleys must be accounted for. When the transition is such that the final state is in a valley with a minimum higher in energy than the initial valley, the energy of the electron becomes E(k') = E(k) I fl A (2.6) where A is the energy difference between the valley minima and %w is the optical phonon energy. If the transition is to a valley with a lower minima, then the energy difference is added to the final energy. .. Each process that can scatter an electron at the end of a collision free flight is characterized by a transition rate S n(k,k'), which is equal to the probability per unit time that an electron is scattered from the state k to a state k'. The subscript n denotes a particular scattering process. The scattering rate X (k) from state k to any state k' due to the nh process is found by integrating over all possible final states k'. Hence The total scattering rate is then found from a summation over all processes X =k ) (k). (2.8) n=1 The scattering rates for each process are listed in Table 2.1, where the rates are presented in terms of energy rather than in terms of wavevector. The values of the physical constants used to fit experimental data are listed in Table 2.2. The scattering rates for the central (r') valley are depicted in Fig. 2.3. Polar optical phonon absorption dominates over acoustic phonon scattering at low energy levels. Once the electron energy exceeds an energy of 0.035 eV, it becomes possible to emit a polar optical phonon. The scattering rates for polar optical phonons become smaller as the electron energy increases due to the coulombic nature of the interaction. The dominance of polar optical phonon scattering in GaAs is responsible for the polar runaway phenomena to be discussed later. When the electron energy approaches the energy of the satellite valleys, intervalley transfer plays a role in the total scattering rates. As seen in Fig. 2.3, polar optical phonons still dominate up to .. TABLE 2.1 Scattering Rates Mechanism Scattering Rates A(E) "* 3/2k 2 1/ Acoustic phonon (2m ) kT D2 E1/2 (intravalley) B a 41Tps2 A 4 Polar optical Yq2 .1/2 E/E 1/ 0 E 1/2 phonon- .( l g 1/ (intravalley) 4rK 0(2E) 0 o EI E,1/2 Y = N absorption 0 + 1 emission N0 = [exp(%w0/kBT) I]-' Equivalent intervalley (G-l)m 2D2 E,1/2Y (satellite satellite) e /2 Tp e 433 eG = 3 for X valley G = 4 for L valley Y = Ne absorption (N_+i) emission Ne [exp(%we/kBT) 11-1 Nonequivalent Gm Di2E11/2y i nt ervalley ii ntv e TrPW n3 G = 1 for r valley G = 3 for X valley G = 4 for L valley Y = Nn absorption = Nn+l emission Nn = [exp( n /k BT) - p = material density s = sound velocity N = phonon occupation number KO = permitivity of free space CO6 0 = high frequency, static dielectric constants Da = acoustic deformation potential De = equivalent intervalley coupling constant DiJ = nonequivalent intervalley coupling constant E = energy of initial state E' = energy of final state G = parameter associated with the symmetry of the valleys .. TABLE 2.2 Physical Constants 1. Material density (g/cm3) 5.37 2. Sound velocity (105cm/s) 5.22 3. High-frequency dielectric constant 10.82 4. Low-frequency dielectric constant 12.53 5. Optical phonon frequency (1013rad/sec) 5.37 6. Intervalley phonon frequency (1013rad/sec) 4.54 7. Acoustic deformation potential (eV) 7.0 8. Intervalley coupling constants (109eV/cm): r L 0.325 r-X 1.0 L-X 0.1 L-L 0.5 x-x 1.0 9. Energy separation between valleys (eV): r L .33 r x .52 10. Effective mass (m*/m0): r .063 L .17 X .58 .. 14 ''k., 10 T=300 K XE (s-') X c 10 PI 012 1Q- P0 Li AC I0 0 .2 .4 .6 .8 1.0 Energy (eV) Fig. 2.3. Scattering rates for r valley. .. about 0.5 eV. Above 0.5 eV the 1- to X-valley transitions dominate. The scattering rates in the L and X valleys are shown in Figs. 2.4 and 2.5, respectively. As mentioned previously, one must generate collision free-flight times from the scattering rates. If p(t) is the probability per unit time that an electron has a flight, of duration t, and subsequently scatters, then the flight time t is found from t r = f p(t')dt' (2.9) 0 where r is the uniformly distributed random number. As shown in Boardman [20], eq. (2.9) can be written as t r = 1 exp{- f X(i+)dt'} (2.10) 0 The integral cannot be evaluated analytically and thus requires numerical evaluation. This involves a significant amount of computer CPJ time for each flight. To circumvent this problem, Boardman et al. [23] developed the concept of virtual scatterings. In a virtual scattering event, the state of the electron does not change. The scattering rate for the electron, including virtual scattering, becomes equal to GAMMA = XT(k) = X(k) + XV (k) (2.11) where GAMMA is the nomenclature used by Boardman, and XV is the virtual scattering rate. Since GA1MA is a constant, the integral in eq. (2.10) can be easily evaluated, and one finds for t t = -log(r)/GAMMA (2.12) The value of GAMMA is usually taken to be equal to the maximum electron real scattering rate evaluated over the possible electron energy range. .. 1~4 101 T=300 K (S-) TO 1013 P PO EQ PO EQ 12 AC 10 X rE r c 0 .2 .4 .6 .8 1.0 Energy (eV) Scattering rates for L valley. Fig. 2.4. .. (s-') EQ 13 PO PO r 1012 r I0 L 0 .2 4 .6 .8 1.0 Energy (eV) Fig. 2.5. Scattering rates for X valley. .. At the end of a collision free flight, the electron is scattered by one of the real processes or by a virtual process. The scattering rate for each process is evaluated and normalized to unity by dividing by GAMMA. A random number is generated uniformly between 0 and 1 to choose between scattering mechanisms. If a virtual scattering mechanism is chosen, the wavevector k remains the same and the program proceeds to generate a new flight time. However, if a real scattering mechanism is chosen, a new wavevector must be stochastically determined before a new f light time can be produced. A block diagram of the electron transport simulation is outlined in Appendix A. At the end of a sufficiently long time interval to obtain convergence, the quantities of interest such as the mean velocity, the diffusion coefficient, etc., are evaluated and outputed. More details can be found in Boardman [20]. 2.2. Determination of r-L Intervalley Coupling Constant and its Relation to the Diffusion-Field Characteristics Recently obtained experimental data [24,25] of the field-dependent diffusion coefficient of GaAs at room temperature can be combined with Monte Carlo calculations to investigate transport parameters. Input variables to the program such as effective masses, valley separations in energy, deformation potentials, etc., can be adjusted to give a proper fit to experimental data. The most uncertain of these transport parameters are the intervalley scattering coupling constants, which represent the strength of the electron transfer mechanism resulting in intervalley transitions via a deformation potential. According to recent literature [51, these constants have values that range from 108 to 109 eV/cm for GaAs. .. At low electric fields the intervalley transitions play a minor role in transport since most of the electrons stay in the central (r) valley. With larger fields present, the electrons move to higher energies in the conduction band, thus enabling the intervalley transfer from r to L valleys. This intervalley transfer to the low-mobility satellite valleys is the cause of the negative differential mobility regime in bulk GaAs. Shown in Fig. 2.6 is the variation of the velocity-field characteristic as a function of the r-L intervalley coupling constant. The minimum and maximum values of the constant were obtained from other Monte Carlo simulations of bulk GaAs [20,221. It can be seen that the maximum sensitivity of the velocity-field relationship lies in the 3 to 5 kV/cm range. This is the same range where Gunn oscillations of bulk GaAs make accurate measurements almost impossible. Figure 2.7 unveils the effect of changing the P-L intervalley coupling constant on the field-dependent, low-frequency diffusion coefficient of GaAs. Measurements, utilizing noise techniques, of the diffusion coefficient of GaAs done by Bareikis et al. [241 and Gasquet et al. [25] are included in the figure. Accurate noise measurements can be done below 3 kV/cm without the problems associated with Gunn domain formation. There is a strong peak in the diffusion coefficient around 3 kV/cm that is very sensitive (much more so than the velocity) to the r-L intervalley coupling strength. The value of 0.325 x 109 eV/cm gives the best fit to the experiments. The increase in the diffusion coefficient with electric field in bulk GaAs has been attributed to two mechanisms, intervalley transfer .. 2.0 V (I 07c m/s) 1.0 0/ 0 Fig. 2.6. 2 4 6 E(kV/cm)8 Velocity-field characteristics of bulk GaAs vs4, F-L intervalley coupling constant. .. 5 4 3 2 0 2 Fig. 2.7. D Do 2 4 6 8 E (kV/c m) Normalized diffusion-field characteristics of bulk GaAs vs. r-L intervalley coupling constant. Measured values indicated by circles and squares are from Bareikis et al. [24] and Gasquet et al. [25], respectively. .. and polar runaway. In both of these mechanisms the intervalley coupling strength has an effect on the diffusion coefficient. Electrons undergoing intervalley transfer experience large changes in velocity due to the randomizing nature of the intervalley process and due to the change in effective mass., These large fluctuations in velocity might be responsible for the increased diffusion coefficient. As can be seen in Fig. 2.8, the population of the L valley starts to increase, due to intervalley transfer, in the same field range where the diffusion coefficient increases. Polar runaway is a term used to describe a process attributed to semiconductors in which polar optical phonon scattering dominates [261. Since polar optical phonons emphasize small-angle scattering, the electrons heat up fast. In addition, the process becomes less efficient with increasing electron energy. Consequently, fast electrons move even faster. This causes the velocity distribution to widen, corresponding 2 to an increase in Av Assuming that the correlation time of velocity fluctuations is not significantly altered in this process, the lowfrequency diffusion coefficient (plateau value) will increase with electric field (see eq. 1.9). Figure 2.9 shows the results of a Monte Carlo simulation of the frequency dependence of the diffusion spectrum for different electric field strengths. In this simulation all electrons were confined to the central valley as no intervalley transfer was allowed. As Fia. 2.3 indicates, polar optical phonon scattering dominates in this case. The spectral shape remains essentially unaltered while the plateau value increases with.field strength. This confirms the fact that the velocity distribution spreads (Av 2 increases), while the time dependence of the .. 00 pop(%) 80 60 40 20 0 2 4 6 8 E (kV/cm) Fig. 2.8. Average L and X valley population of bulk GaAs vs. r-L intervalley coupling constant. .. 10 5 D(f) (cm2/s) 10 2 101 101 Fig. 2.9. f (GHz) Diffusion spectra vs. electric field for electrons in r valley (polar runaway). .. velocity autocorrelation function experiences little change. Section 2.3 will explain how the calculations of the spectrum are made. It is expected that when all three valleys are included in the simulation, a decrease of the r-L intervalley coupling constant will cause the electrons in the central valley to have a smaller probability of scattering to the L valley. Since the probability of intervalley scattering is smaller, the electrons spend more time, on the average, in the central valley where polar optical phonon scattering dominates. If polar runaway is the cause of increased diffusion, then decreasing the P-L intervalley coupling strengths would result in an increase in the diffusion coefficient as indicated in Fig. 2.7. However, when one observes that the decreased coupling constant gives rise to a larger, average electron population in the L valleys, the effects of polar runaway are not as clear. As a result of the decreased coupling strength, once the electron scatters to the L valley there is a small probability of returning to the central valley. This is the cause of the average L valley population increase. 2.3. Monte Carlo Spectral Analysis of Velocity Fluctuations Since the diffusion coefficient is a frequency-dependent parameter as shown by eq. (1.9), it is interesting to investigate the velocityfluctuation spectrum to gain insight into transport processes. En this section the process of how to generate the velocity time series in the Monte Carlo program is described, including the selection of sampling rate. The definition of spectral density is reviewed, and the calculation of the spectrum from discretely sampled signals is explained. Results for bulk GaAs are presented, and they indicate the effects of a dominant scattering process on the spectrum. .. The Nyquist sampling theorem states that the sampling rate f = 1/At must be at least twice the highest frequency component of the s waveform being sampled. Here, At is the length of time between samples. If the sampling rate is less than twice the highest frequency present, then aliasing will occur. In other words, the sampling time At used in the Monte Carlo program must be much smaller than the intercollision time. After considering the scattering rates in GaAs (see Figs. 2.3 2.5), the sampling time of 5 x 10- 15sec was chosen, reducing aliasing to a negligible effect. However, after observing the spectral character-14 istics of GaAs, the sampling time was increased to 2.5 x 10 sec to reduce the time-series length. To obtain the velocity time series, the program first generates the free-flight time of the electron between scattering events, as described in section 2.1. The collision free-flight time is then broken up into smaller subflights of duration At. The subflights are treated similarly to the virtual scattering process. At the end of each subflight, the velocity of the electron is calculated from the knowledge of the wavevector component k. in the direction of the applied field. In principle one could also sample the velocity components normal to the field direction. This would allow characterization of the transverse diffusion coefficients. The velocity of the electron in one dimension is given by 1 3E(k) 1kz Vz W k (2.13) z m These subflights continue until the end of the free flight or the time window length T (= NAt) has been reached. s .. The actual algorithm of the process is described below and outlined in the f low chart of Appendix B. Since scattering events occur, in general, between the sampling times, the computer must keep track of when it last took a sample. The program labels the time passed since the last sample was taken as TIMEX. When the free-flight time between scattering events (TIME) is generated, the algorithm first determines whether the generated time (TIME) plus the time remaining since the last sample (TIMEX) is long enough to reach the next sampling time. If it is not, the flight time is added to TIMEX to become the new TIMEX, and the program proceeds to the next scattering selection without taking a sample of the velocity. When the generated free-flight time plus TIMEX is greater than the sampling time At, the program advances to the next sampling time by the time labeled TIMEV = At TIMEX. The velocity of the electron is then calculated using eq. (2.13) and stored in the time series. Figure 2.10 pictorially represents the relationship of the times in the sampling process. The number of samples in the time series that can be taken in the remaining free-flight time is designated by NN. The value of "N. is an integer number and is determined by dividing the remaining flight time by At and truncating any fractional quantity. When NN is equal to zero, the remaining time is not long enough to reach the next sampling time, so the remaining time becomes TIMEX. The program then goes to the next scattering selection. For NN greater than zero, the algorithm loops through NN subflights, generating additional time-series data. At the end of the NN loop the new value of TIMEX is updated by the remaining time before the loop minus the loop time. The program then proceeds to the next scattering selection. .. TIME H- TIMEV I- NNxAt r5- TIMEX scattering event scattering event Fig. 2.10. Representation of times used to generate velocity time series. , ! i I .. The number of samples N in the time series is monitored at each sampling time. When the number reaches T /At, the program stops s sampling and proceeds to the FFT algorithm. The methods of calculating the velocity-fluctuation spectral density from the time series will now be reviewed. Here we follow the outline given by Tehrani [271. Let a random signal x(t) in the interval 0 < t < Ts be defined in terms of a Fourier series O j 2Trft x(t) = I aKe (2.14) K=-om K where fK =T- (K = 0, ;1, +2 .) and aK is the Fourier coefficient of T s x(t) at fK" The discrete Fourier coefficients aK are defined as i N-I a K = NA At x(nAt) e-j2wKAfnAt (2.15) n=0 where x(nAt) is the sampled time data, Af is the frequency spacing defined as Af = 1/NAt, and K denotes the frequency component f = K k NAt KAf. The Fourier component XK of x(t), having a frequency fK, is given by 2fKt -j2 rfKt XK = aKe + aK e (2.16) The ensemble average of X is found to be = 2 aa (2.17) since the Fourier coefficients have an arbitrary phase resulting in .. a K = aK = 0, and since for a real signal x(t) a_ =a (2.18) -K K Writing the ensemble average in terms of the discrete Fourier transform results in N-I N-I XK = 2 aa 2 n 0 (At)2 x(n)x(m) exp(j21TfK(m-n)At) K K K (NAt) 2n=0 m=0 (2.19) For a stationary process and setting s = m-n, the two summations can be decoupled as shown in [27], resulting in X2 = At x(n)x(n+s) exp(j27f SAt) (2.20) K NAt s=-MK Since x(n+s) = 0 for s>M and if N>X, the limits of summation change such that 2~ 2 XK = 7 t At x(nx(n+s) exp(j2TfKSAt) (2.21) NAt s =-00 The spectral density of x(t) can be defined by the discretized WienerKhintchine theorem, S x(fK) = 2 1 At x(n)x(n+s) exp(j2rf KsAt) (2.22) 5 =-.0 which is essentially the Fourier transform of the discretized autocorrelation function x(n)x(n+s) of the process x(t). Since Af is the frequency interval between adjacent fk's, the spectral density can be written as .. X 2 a a S (f ) = K (2.23) x K Af Af Equations (2.22) and (2.23) show that there are two routes that can be taken to calculate the spectral density of a signal. One can either generate the discretized autocorrelation function from the time series and then compute the Fourier transform, or one can calculate the Fourier coefficients aK directly by fast Fourier transform (FFT) and average each spectrum. The latter method was preferred in this case since it involves calling only one of the standard library subroutines available on the Harris 800 computer system. Computing the spectrum from the autocorrelation function would require calling two subroutines, one to compute the autocorrelation function and another to take the Fourier transform. This method would be more time consuming. The Harris subroutine used is named FFTRC. This subroutine computes the fast Fourier transform of a real valued sequence. Time-series lengths up to N = 20,000 have been transformed by the subroutine very quickly and without any problems. All variables transferred to the subroutine must be defined in single precision. Since many of the variables used in the Monte Carlo program are implemented in double precision for accuracy, the data to be passed on are stored in single-precision variables before calling the subroutine. The computer program proceeds as follows. First, the program comI putes the average value of the velocity time series and subtracts it from the data. This new time series is then stored in the singleprecision real vector A(G). A running average of the average velocity is made for each time series. The vector A(G) is the data to be transformed by the FFT. The output is expressed in the complex vector X(G). .. The FFT algorithm computes the following summation: N-I JT X(T = J A(-)J e12 JKJ/N (2.24) s J=0 K Therefore, the spectral density at frequency f- of the time series is K s K found by multiplying X(T-) by its complex conjugate X(-), then multis S plying the result by 2Ts/N2 and averaging over many time series. The velocity-fluctuation spectral density is then calculated from 2 T S(!L) = X(E-X(-- (2.25) AV N 2 T sX( In order to obtain the diffusion coefficient, one simply divides the velocity-fluctuation spectral density by 4, as indicated in eq. (1.9). The average diffusion spectrum is stored in the vector AV(G). The constant 2Ts /4N2 is lumped into a single number to improve computation time. Although the first N/2 + 1 coefficients of the Fourier transform are available, only the first 400 frequencies were outputed for our purposes. The time window Ts was chosen to be 100 ps, giving a frequency resolution Af(= 1/T ) of 10 GHz. S We are now in a position to calculate the velocity-fluctuation spectral density of bulk GaAs at room temperature (300 K). Calculations of the low-frequency diffusion coefficient D(E,0) as a function of electric field, using the time-of-flight and spectral-density methods, show good agreement. At each field strength the spectra have been normalized to their low-frequency plateau level so that the relative spectral shapes can be compared, as shown in Figs. 2.11 and 2.12. For the low-field range, .. 10 D(f) T=300 K D(O) ~3 kV/cr m'' 5 kV/cm .0 1 I I I I I I ,,,l 10 102 f(GHz) IO Fig. 2.11. Normalized diffusion coefficient spectral density for 3 and 5 kV/cm. .. I0= T=300 K D(f) D(O) 7 kV/cm ---10 kV/cm S.--------- 20 kV/cm .0 11 2 il 1 3I , 10 10 f(GHz)103 Fig. 2.12. Normalized diffusion coefficient spectral density for 7, 10, and 20 kV/cm. .. between 1 and 3 kV/cm, the spectrum has a Lorentzian shape with a halfpower bandwidth on the order of 500 GHz. At 5 kV/cm a peak shows up in the spectral characteristics around 300 GHz. As indicated in Fig. 2.12, the peak in the spectra moves gradually to higher frequencies as the field increases. The presence of a peak in the spectrum was first observed in Monte Carlo simulations of InP and explained by Hill et al. [28]. The peak has also been observed in simulations of GaAs done by Fauquembergue et al. [29] and Grondin et al. [30]. The observed peak in the spectrum has been attributed [28] to a strong scattering cycle of electrons from a satellite valley back to the central valley with a velocity in the direction negative to the motion under the applied field. The electrons are then accelerated under the applied field through the valley minima and travel almost ballistically until they scatter once again to the satellite valley. This scattering process is pictorially shown in Fig. 2.13. The ballistic motion is characterized by an almost sawtooth-like velocity waveform as indicated in Fig. 2.14, where the associated Fourier spectrum of this waveform is also presented. As the electric field increases, the motion through the central valley becomes faster, causing the peak in the spectrum to move higher in frequency as displayed in Fig. 2.12. 2.4. Position Monitoring and Boundary Conditions in Monte Carlo Programming It is expected that as device dimensions shrink to submicron levels, the boundary conditions and the length of the active region will have significant effects on the charge-transport characteristics of these devices. To investigate these phenomena, the Monte Carlo program .. - - - E~ik) Scattering process responsible for spectral peak. Fig. 2.13. .. SA 2 4 6 Fig. 2.14. 8 10 Dominant scattering process: a) velocity waveform; b) spectral characteristics. Y(-E) .. was rewritten to monitor the electron position in real space. Electrons can be injected from a cathode at some well-defined position (z = 0) and removed at the anode after drifting some fixed length L. The injected electron energy at the cathode can be tailored to any probability distribution desired. The program still contains the velocity time-series capability so that the velocity spectral density information of short-channel devices is obtained. This method is physically satisfying, in that it is analogous to the measurement of noise in actual devices. The program does not, however, account for noise associated with the injection process. Also, the effects of space charge are neglected by assuming a uniform electric field throughout the active device region. An outline of the algorithm to monitor the position of the electron in real space is given below. This will include a description of the back scattering of electrons from the active region into the cathode. Although the back-scattered electrons do not contribute to the dc characteristics, they do have an effect on the velocity spectrum. Thus, it is important to include the back scattering in the simulation. When an electron reaches the anode or returns to the cathode, a new electron is injected. The injected electron velocity is derived from a modified Maxwellian velocity distribution [311. After explaining how the program functions, results for differentlength GaAs devices will be presented. The experimental data of Andrian [32] on 1.1 Pm GaAs diodes will then be compared with the simulations. 2.4.1. Program algorithm The equations describing electron motion, in one direction, during the free-flight time between collisions can be expressed most simply in .. terms of a classical velocity v V 0+ at (2.26) and position Z z + v t +-at 2(2.27) 0 0 2 where t is time, vo is the initial velocity, z0 is the initial position, and the acceleration a is given by ql+l/m*. At the beginning of the simulation, an electron is injected with some positive initial velocity, derived from the modified Maxwellian velocity distribution, at the position z = 0. The Monte Carlo program then generates the collision freeflight time according to the standard procedure as outlined in section 2.1. The first thing that has to be determined at the beginning of each collision free flight is whether at any time during the flight the electron ever goes back into the cathode. In other words, a check is made to see if the electron position becomes negative (z < 0). The position of the electron obeys a quadratic equation (2.27) in time and depends on the direction of the initial velocity. If the initial velocity is positive, then the electron position only increases with time. However, when the initial velocity is negative, the position first decreases and then increases given that the flight time is long enough. Therefore, to determine if the electron ever goes back into the cathode, the program only has to check those flights in which the initial velocity is less than zero. With a negative initial velocity, the program first calculates the time in which the electron velocity v z is equal to zero. This time, .. labeled TMIN, corresponds to the minimum position of the particle during the flight if the flight time is at least that long. The value of TMIN is determined by TMIN = 0 (2.28) a A check is made to determine whether the flight time (TIME) is less than TMIN. If it is less than TMIN, the minimum position is determined by the flight time. The minimum position ZMIN, during the electron flight, is now calculated from (2.27) using TMIN or TIME, whichever is smaller. When ZMIN is less than zero (ZMIN < 0), the program calculates at what time during the flight ZMIN = 0. Solving (2.27) for the time when z = 0, one obtains -v0 [v2 2az0 ]1/2 t 0 0, (2.29) a since the smaller of the two roots of the quadratic equation corresponds to the first time the electron crosses the boundary. This new calculated time (2.29) is the actual flight time of the electron in the active region. Now the velocity time series can be updated for this flight. A flag in the program, labeled IFLAG, is set equal to 1 each time that ZMIN is found to be less than zero. This flag causes the program to reinject another electron from the cathode after the time series has been updated. The value of 1 is assigned to the flag to keep track of how many electrons scatter back into the cathode during the simulation. The number of back-scattered electrons is stored in the variable ILTO. .. When the initial velocity is positive or the minimum position is found to be still in the active region, the program determines the final position from (2.27), using the free-flight time. This final position is compared to device length L to see if the electron was collected by the anode. When z < L, the time series is updated during the free flight and then proceeds to the next scattering selection. If the final position is greater than L, the exact time that the electron passed the anode boundary must be calculated. This new flight time is + v2 -2z LJ1/2 + 0 v0 2z0-) (2.30) and is used in updating the time series. As bef ore, the f lag is set when the electron reaches the anode, indicating injection of another electron from the cathode. This time, though, the flag value is equal to 2 so as not to interfere with keeping track of the number of back scattering. A block diagram of the position-monitoring algorithm is given in Appendix C. During the process of evaluating the velocity time series, the counter N is monitored. When the appropriate time window length T (= NAt) is reached, the program proceeds with the spectral density S calculations as outlined in section 2.3. Every time the electron arrives at the anode or scatters back to the cathode, a new, central-valley electron is injected into the active region to maintain constant space charge. The electrons injected in the z direction obey a modified Maxwellian distribution [311. The probability that an electron is emitted with a velocity between vzand v + Av is z .. 1 2 1 2 AP(vZ) = exp( k T 2 (2.31) where T is the lattice temperature. The modified Maxwellian distribution can be generated from a uniform distribution with the techniques of section 2.1. Here the variable EZ, associated with the energy due to the vz component, is randomly generated from r, using EZ = -k BT log(r) (2.32) The average value of this distribution is kBT. The wavevector (or velocity) component is found directly from EZ by 1/2 k = (2m EZ (2.33) z -.2 Only the positive root need be taken since negative values signify electron motion back into the cathode. The emitted electrons also have velocity components perpendicular to the field direction. These electrons obey a Maxwellian distribution in each direction. The energy distribution associated with the perpendicular velocity components can be expressed in a form similar to (2.31), so the wavevector component kp is determined in much the same way using (2.32) and (2.33). The actual magnitudes of the two perpendicular components kx and ky are not needed since the program simulation considers the x-y dimensions to be infinite. However, the two components can be determined by generating a random phase angle between 0 and 2w once the magnitude of the k wavevector is known. This would need to be done to gain information on the transverse diffusion coefficient. .. Both perpendicular components have an average energy equal to -1 k T 2 BT Therefore, the total average energy of injected electrons into the active region is 2 kBT [311. An integer variable named IINJ is used to keep track of how many electrons are injected from the cathode. The difference between EINJ and the number of electrons returning to the cathode ILTO gives the number of electrons traversing the entire length of the active region to the anode. A copy of the entire program is listed in Appendix D. 2.4.2. Simulation results The program was run for GaAs at room temperature (300 K) with the same intervalley coupling parameters used to fit the bulk experiments in section 2.2. The length of the active region was varied from 0.25 to 4 i'm, and the values at the electric f ield were chosen between 1 and 3 kV/cm. A number of interesting effects on transport behavior versus device length can be observed in the results presented in Table 2.3. First, when the electrons are injected into the active region, they are rapidly accelerated by the electric field to very high velocities. If the device length is short, the electron velocity has insufficient time to relax to the steady-state bulk velocity before being collected by the anode. This transient velocity phenomenon is termed velocity overshoot 1331. As shown in Table 2.3, for a given field value as the device length is reduced, the average velocity throughout the active region increases. This increase in average velocity signifies the occurrence of velocity overshoot near the cathode. Second, the amount of intervalley transfer, from r to L valleys, is reduced in short devices. In Fig. 2.15 the average fraction of time spent in the L valley during the simulation of 3 kV/cm as a function of .. TABLE 2.3 Simulation Results for Short-Length GaAs Length Electric Field v SAv(0)/4 (Om) (kV/cm) (107 cm/s) (cm2/s) .25 1 1.59 113 2 2.16 124 3 2.55 128 .5 1 1.33 162 2 1.96 172 3 2.45 181 1.0 1 1.16 208 2 1.84 219 3 2.46 258 2.0 1 1.07 238 2 1.80 270 3 2.40 384 3.0 1 1.03 248 2 1.80 293 3 2.21 425 4.0 1 1.02 260 2 1.77 300 3 2.09 500 Bulk 1 0.96 250 2 1.73 326 3 1.82 508 .. active region length is presented and compared to the bulk GaAs value. Injected electrons with high energies, near the F-L energy offset of 0.33 eV, can undergo intervalley transfer after traveling over short distances. However, since most of the injected electrons have low initial energy (Eav "4 2 kIBT), they must travel farther into the active region before gaining sufficient energy for F-L intervalley transitions to commence [34]. Therefore, as the length of the active region decreases, a higher fraction of the injected electrons are swept out at the anode before transferring to the L valley. The velocity fluctuation spectrum is also determined as a function of device length. Table 2.3 gives the low-frequency plateau value of the spectrum for each length and field. As mentioned before, shot noise behavior associated with the random injection of electrons from the cathode is not taken into account. Often in real device structures the injection noise levels are reduced due to space-charge suppression [35]. Only the effects of the velocity spectrum in the active region are calculated and presented. The spectrum plateau levels are normalized to the low-field value at each length and depicted in Fig. 2.16. This figure shows the relative increase in the noise characteristics versus field strength for various device lengths, as well as for a bulk device. Also included in the figure are the normalized diffusion coefficient measurements of a n +-n-n +GaAs mesa structure, performed by Andrian [321. The donor concentration in the 1.1 p'm active n-layer was 1015 cnf3. The Monte Carlo data support the measurements, showing that the relative increase in the current-noise spectral density measured in short GaAs regions is not as large as for bulk GaAs. .. 30 20 I0 0 2 3 4 L(pm) Fig. 2.15. Fraction of time electrons spent in L valleys at 3 kV/cm as a function of active region length. bulk/ 0 0 0 0m ( 0 .. T=300 K I / / bulk,4pm 2pm Ipm .5pm o I.Ijim meas. 1( ) I 2 3 E (kV/cm) Fig. 2.16. Relative increase in GaAs low-frequency velocity spectral density versus electric field for several active region lengths. Sv Svo I I .. 62 Again, the mechanisms causing the increase in the low-frequency velocity spectrum with increasing field can be due to intervalley transfer or polar runaway. In very short active regions, the lower noise produced could be attributed to the decrease in intervalley transfer. It can also be argued that for the short regions there is insufficient scattering before the electrons are removed at the anode, so the spread in the velocity distribution attributed to polar runaway cannot be attained. .. CHAPTER III EXPERIMENTS ON AlGaAs/GaAs INTERFACES In this chapter, we will discuss the experiments which are done to determine the dc, ac and noise properties in the hot-electron regime of AlGaAs/GaAs heterojunction interfaces. Two device structures with different characteristics, such as length, fraction of aluminum content, sheet-carrier concentration, etc., are used in the experiments. In this dissertation the emphasis is on noise characterization, so first a review of the methods of measuring the device ac noise temperature Tn is given. With the use of noise temperature data, the diffusion coefficient can be determined as a function of electric field for transport parallel to the AlGaAs/GaAs interface. The differences in the experimental results between the two interfaces are examined and compared to bulk GaAs behavior. 3.1. Description of Device Structures The devices used in the experiments were modulation-doped fieldeffect transistor structures without the gate metalization. The advantage of these structures was that they were readily suitable for highfrequency measurements and device-mounting procedures. A diagram of the gateless MODFET device structure is presented in Fig. 3.1. These MODFET structures were fabricated by Dr. Morkoc of the University of Illinois. The devices are grown on a semi-insulating (SI) GaAs substrate starting with an undoped GaAs buffer layer. This buffer layer is grown to smooth out any defect properties associated with the .. GaAs Diagram of AlGaAs/GaAs structures. i Fig. 3. 1. .. surface of the SI substrate and to provide a relatively pure GaAs region for electron transport. It also provides a means for obtaining an uninterrupted growth cycle at the AlGaAs/GaAs interface. An undoped AlGaAs spacer layer is incorporated to provide greater separation between the parent donor atoms and the free electrons at the interface. A silicon-doped AlGaAs layer is grown next. The doping level, as well as the spacer layer thickness and conduction-band difference, determine the quasi-two-dimensional electron sheet carrier concentration n s at the interface. A, thin, highly doped n+ cap layer of GaAs is grown to facilitate ohmic contact formation. Source and drain regions are defined by photolithography, and gold is deposited for contact pads. Details of each structure are found in Table 3.1 for the two wafers numbered 1483 and 1885. Also included are the geometrical width w and length L of each device. The contact resistance R c associated with the ohmic contact to the active device region is given because of its importance in interpretation of the experimental data. 3.2. Noise Temperature Measurement Setup and Experimental Procedures Since our investigation is concerned with the determination of the field-dependent diffusion coefficient, the noise component associated with the velocity fluctuations needs to be measured. To measure the velocity fluctuation spectrum, experiments have to be done at frequencies high enough to avoid the g-r and 1/f noise contributions. At high frequencies it becomes difficult to measure the actual terminal voltages and/or currents, so it is easier to measure the available power from the network. This, available noise power is related to the noise temperature T n as described in Chapter I. .. TABLE 3.1 Device Structure Parameters #1483 #1885 1. Cap layer thickness (A) 50 50 2. Cap layer doping level (cm-3) 2.5xi0 18 2.5x1018 3. Doped AlGaAs thickness (A) 600 350 4. AlGaAs doping level (cm-3) 2.5xi018 2.5x1018 5. Aluminum mole fraction x .28 .23 6. Undoped spacer thickness (A) 30 15 7. GaAs buffer thickness (pm) 1 2 8. Contact resistance Rc () 8 11 9. Width w (pm) 145 75 10. Length L (pm) 4 2,8 .. The technique used to measure the noise temperature of the device under test (DUT) is similar to the method developed by Gasquet et al. [36]. The main advantage of this particular scheme is that it allows measurement of the noise temperature without the need to match the DUT to the characteristic impedance (50 SI) at each bias and frequency. Not only can matching be a tedious task, but the stub tuners used in matching can have different resistive losses depending on the particular stub settings. The variability of these losses degrades measurement accuracy. The experimental setup to measure DUT noise temperature over the frequency range 500 MHz to 12 GHz is depicted in Fig. 3.2. This broad range of frequency coverage is obtained by using circulators with octave bandwidths and broad-band low-noise amplifiers. Frequency selection is attained with the spectrum analyzer (HP8559A), which is capable of receiving input frequencies from 10 MHz to 22 GHz. The noise source (HP346B) is also broad-band covering 10 MHz to 18 GHz with an effective noise ratio of 15 dB (T = 9170 K). Amplification and power detection are performed at the intermediate frequency (21.4 MHz) of the spectrum analyzer. The experimental procedure consists of four measurements to determine the noise temperature Tn of the DUT. These measurements also make available the power reflection coefficient Irl2 at port 2 of the circulator, the noise temperature Ta of the measuring system, and the gain bandwidth product GB of the system. The first measurement M1 consists of a reference temperature signal Tc flowing from port 1 in the preferred direction to port 2, where a short-circuit termination is placed. The reference signal is totally .. SWITCH DET SYNCH Fig. 3.2. Noise temperature measurement setup. .. reflected by this short circuit and proceeds to the amplifier stages at port 3. The amplifier system provides proper impedance termination at port 3. The measured power is then proportional to M1 =k GB(T a+ T) (3.1) where kB is the Boltzmann constant. The second measurement M2 is essentially the same except that the reference temperature is now T h, where T h > Tc giving M2 =k GB(T a+T) h (3.2) Now, the short circuit at port 2 is replaced by the DUT which is biased to the dc voltage of interest. The reflection coefficient between the DUT and circulator is defined in terms of the DUT impedance Z DTand the-characteristic impedance Z 00 by the relation r-ZDUT Z00 (3.3) ZDUT +Z00 Since the DUT has, in general, an impedance different from the characteristic impedance of the circulator, the available noise power from the DUT is reduced by the factor (1 Jrf 2 This property is exploited in the next two measurements. The noise source temperature is again set to Tc for the third measurement. Since the low-noise amplifier sees a constant impedance looking into port 3 regardless of the impedance change at port 2, the system noise temperature Ta remains the same. Also, the reference temperature is partially reflected at port 2 because of the mismatch, so the measured power is proportional to .. M3 = kBGB(Ta + Tn(l Irl 2) + TCIn2) (3.4) A final reading is done with the reference temperature at Th providing M4 = kBGB(Ta + Tn(l IFl2) + Thl 2 ) (3.5) Manipulating these four measurements, one obtains the unknown device noise temperature T h(M3 MI) + T (M2 M4) T hc (3.6) n M3 M1 + M2 M4 and the power reflection coefficient as I2 M4 M3 IrI = M2 M1 (3.7) It should be pointed out that the parameters determined by (3.6) and (3.7) are associated with the network connected at the reference plane of port 2 of the circulator. If there are no resistive or radiative losses between the actual DUT and the circulator port, then Tn is the actual device noise temperature. Any known losses between the DUT and circulator can be easily corrected. Also, the loss between ports I and 2 only affect the values of the reference temperatures Tc and Th. Correspondingly, the loss between ports 2 and 3 affect only the system noise temperature Ta. The system noise temperature can be determined from MITh M2T T M (3.8) a M2- Ml and the gain bandwidth of the system is given by .. 71 1 M2 Ml GB = I.M2 l (3.9) kB Th T c Another advantage of this measuring technique is that it allows the determination of device noise temperature using either a continuous or pulse bias. When the device is biased into the hot-electron regime, significant Joule heating of the lattice occurs. A pulse bias at lowduty cycle is then required to keep the average power dissipation to a minimum. A pin-diode RF switch is used in the IF section to make sure that only the noise power produced during the bias time is detected. The actual length of bias pulse time is determined by the time constants associated with the bias tee network and the DUT impedance. The bias tee provides the necessary dc and RF isolations. 3.3. Experimental Results Both device structures used for the measurements were mounted in a 50 microstrip transmission line test fixture. The microstrip line was made from a 25-mil.-thick alumina substrate and attached to SMA coaxial connectors. All measurements were made with a covered mount to keep the device in the dark. The first device to be measured was wafer #1483. Measurements were done with a pulse bias time of 4 ms and a 3% duty cycle at room temperature (300 K). The dc current-voltage characteristic for this 4 um heterostructure is depicted in Figure 3.3. The low-field equilibrium resistance is found to be 31 ohms. As can be seen in the figure, the I-V characteristic begins to deviate from Ohm's law around 600 mV. This nonlinear behavior is an indication of hot-electron effects in the channel. Changing the polarity of the voltage had no .. I(A) 100 V(V) Current-voltage characteristic of #1483. 101 Fig. 3.3. .. effect on the I-V relationship, indicating that the contacts were indeed ohmic and had no rectifying properties. From the I-V characteristic one can obtain the dc mobility as a function of electric field. The electric field in the channel is assumed to be uniform and found by taking the voltage drop across the active region and dividing it by the length. The definition of dc mobility is given by 11(E) = (3.10) Figure 3.4 shows the dc mobility as a function of electric field, normalized to its equilibrium value ip0 after correcting for a contact resistance of 8 ohms. The advantage of normalization is that a better comparison with other heterostructures can be made since it removes any differences in the actual thermal equilibrium mobility values. Also included in the figure are other published experimental results on similar heterostructures [37-39]. Since no other means of obtaining the contact resistance for this structure was available, the value of 8Q2 was derived by lining up the data with the previously published results in the figure. Next the noise temperature of #1483 was measured in the frequency range 500 MHz to 1 GHz. No frequency dependence in the noise temperature as a function of bias was observed, indicating the absence of any 1/f or g-r noise components. Therefore, the noise temperature was associated with velocity fluctuations. The actual noise temperature of the active region measured between .5 and 1 GHz and as a function of electric field is displayed in Figure 3.5. It can be seen here how quickly the noise temperature increases for fields far from equilibrium. .. 3 12 io Oo Fig. 3.4. 2 3 2 6 (104 E (V/cm) Normalized dc mobility as a function of electric field. Circles indicate ungated MODFET #1483, inverted triangles indicate Tsubaki et al. [371, right-side-up triangles indicate Masselink et al. [38], and squares indicate van Welzenis et al. [39]. 0 0:14 V 102 .. 3 2- 1483 T=300 K Tn(K) 0 7 0 0 7- 00 0 3- 0 0000 2 12 102 2 3 7103 23 7104 E (V/c m) Noise temperature vs. electric field for #1483. Fig. 3.5. .. The differential mobility is obtained from a measurement of the admittance of the DUT. First, the conductance or Re(Y) can be calculated from the derivative of the I-V characteristic. This method works well as long as the Re(Y).is not frequency dependent in the range of interest. The admittance can also be measured with the use of an Sparameter test set (HP 8410). The drawback of this measurement technique is that it has to be done with a continuous bias. Finally, the magnitude of the reflection coefficient is determined during the noise temperature measurement (3.7). When the susceptive elements are negligible, the Re(Y) can be found from the magnitude of the reflection coefficient. Whenever possible, all three methods are combined. For #1483 all methods showed good agreement in the Re(Y) since the parasitic susceptive elements were small compared to the channel conductance. The diffusion coefficient in the active region of #1483 can now be determined from the generalized Einstein relation k BT n(E) D(E) = -n Re(P') .(3.11) q Normalizing the diffusion coefficient to the equilibrium value Do, one obtains from the measured data D(E) n ()RY (3.12) D 0 T Re(Y 0) where T is the lattice temperature and YO is the equilibrium admittance. A constant carrier concentration in the channel is assumed. The normalized diffusion coefficient as a function of electric field for #1483 is presented in Figure 3.6. Also included in the figure are the .. 7' D0 I0o 7 31 i - 102 2 3 25 7104 E (V/cm) Fig. 3.6. Normalized diffusion coefficient for #1483 as a function of electric field. Circles indicate ungated NODFET, squares indicate Ruch and Kino [101, inverted triangles indicate Gasquet et al. [251, and the rightside-up triangles indicate Bareikis et al. [241. AV 0 AV .0.Oo- 0 O- 0-00ooc I I I I I I 2 I .. normalized diffusion coefficient measurements of bulk GaAs [10,24,25]. It can be seen that the diffusion coefficient of the heterostructure does not increase as significantly as the bulk GaAs results. Device structure 41885 was measured next. One of the main advantages of this structure was that on the same wafer different-length devices were available for measurement. In this way the contact resistance could be determined more accurately. The low-field ohmic resistance as a function of device length is plotted in Fig. 3.7. The circles indicate the data obtained by using the wafer probe station and the triangles indicate the actual wire bonded values. The discrepancy between the two different measurements is attributed to the contacting problems associated with the wafer probes. However, both sets of data extrapolate to the same value at the origin (L =0) giving a contact resistance of 11Q2. The current-voltage characteristics of #1885 for lengths of 2 and 8 jim are shown in Figs. 3.8 and 3.9, respectively. Both devices showed hot-electron effects at high bias. Having the I-V characteristics and the contact resistance, it is again possible to find the dc mobility versus electric field. The normalized dc mobility of #1885 is given in Figure 3.10. There was no difference found in the dc mobility for the two lengths measured. Also, the dc mobility behavior of #1885 is very similar to that of #1483. Obtaining the Re(Y) from measurements at high frequencies was difficult for this structure. The measured admittance data at low frequencies (f < 500 MHz) showed reasonable behavior, but became quite difficult to model at high frequencies (f > 1 GHz). Because of the large wafer size associated with this structure, very long bonding wires had to be used to make connections to the actual DUT. These long .. 160 R(fl) 120 80 40 10 Resistance vs. length for #1885 to determine contact resistance. Circles indicate waferprobed values whereas triangles indicate wirebond values. 2 46 8 L (pm) Fig. 3.7. .. - T=300 K 1885 2pm '00 ,o0 /0 0 / o /0 0. 0/ 0/ ! I I I ll111 1(0t I I 11111 I I I I v (V) 100 Current-voltage characteristic of #1885 (L = 2 pm). I(A) i06 Fig. 3.8. .. '0-1 1885 8pm I(A) T=300K / -(5 /0 / /00 0 00 o,O / / I c 5 3-'5/,' I I i t i I I 1 1 0 i00 V(V) 101 Fig. 3.9. Current-voltage characteristic of #1885 (L = 8 im). .. .1 .I E (V/cm) Fig. 3.10. Normalized dc mobility vs. electric field for #1885. 103 1885 T=300 K I I [ f ill I I i l lII 102 .. bonding wires made it difficult to obtain a good high-frequency ground, and the large wafer may introduce other unaccounted for parasitics. As a result, the Re(Y) of the DUT was determined from dI/dV, and we assumed that it is frequency independent in the range of interest. The noise temperature of #1885 was measured from .5 to 12 GHz. After accounting for all known losses between the circulator and DUT, the noise temperature showed a slight decrease for frequencies greater than 2 GHz (see Fig. 3.11). This slight decrease was associated with losses in the parasitics that could not be well defined. At other bias values, similar behavior of Tn versus frequency was observed. Taking the data between .5 and 1 GHz to be accurate, the noise temperature of the active region versus electric field for #1885 is depicted in Fig. 3.12. Again it can be seen that the noise temperature increases with electric field, but not as rapidly as that of #1483. The normalized diffusion coefficient as a function of electric field is given in Fig. 3.13 for both 2 and 8 Pm structures. The Re(Y) is determined from dI/dV. Both device lengths show the same decrease in the diffusion coefficient with field, indicating that there is no noticeable dependence on device length in this range. 3.4. Discussion of Results In this section we will discuss the hot-electron behavior of the AlGaAs/GaAs interfaces and compare the results to those of bulk GaAs. Only qualitative explanations can be given due to the lack of sufficiently developed analytical models for parallel transport in the heterojunctions or the availability of complex Monte Carlo programs. Clearly, the first observation that can be made is the similarity in the dc characteristics of different heterointerfaces. The dc .. T=300 K 1885 2 pm V=600mV 0 0 000 I I I iiiiil 108 ! I I I 1 11 f (Hz) Noise temperature vs. frequency for #1885. Tn(K) 1010 I I I 1 I i I I I . . Fig. 3. 11. .. Tn(K) T=300K 1885 103 0 0 000 00 _00 0 0 0 0000 0 10 2 1u , , 102 I03 E(V/cm) I( Fig. 3.12. Noise temperature vs. electric field for #1885. .. E (V/cm) Fig. 3.13. Normalized diffusion coefficient vs. electric field for #1885. Squares and circles indicate 2 and 8 um data, respectively. D Do 102 1885 T=300 K 000 0000 0 II I I1 I I I1 I I I1 I1I I .. mobility of both #1483 and #1885 decreases with increasing field strength in the hot-electron regime, which also agrees with the previously published results. However, there does seem to be differences in the noise behavior between different heterointerface compositions. For device #1483 the diffusion coefficient (or velocity fluctuation spectral density) remains nearly constant with increasing field, whereas #1885 shows a slight decrease in the hot-electron regime. This difference in diffusion coefficients results mainly from the lower noise temperature measured in #1885. Both heterojunction interface structures show a clearly different noise behavior than bulk GaAs. In bulk, the increase in the diffusion coefficient with field was attributed to polar runaway and intervalley transfer (sec. 2.2). A decrease in the importance of one or both of these mechanisms in the heterointerfaces might be responsible for the observed D(E) dependence. Differences due to device length are not suspected since no noticeable length dependence of D(E) is observed in the diffusion coefficient measurements of the 2 and 8 um channels of #1885 presented in Fig. 3.13. Yokoyama and Hess [40] calculate the two-dimensional scattering rates for electrons in the first five subbands of a quasi-triangular potential well at the AlGaAs/GaAs interface. Their results show lower scattering rates for polar optical phonons as compared to the rates for bulk GaAs at room temperature. Since the polar-optical phonon scattering rates are reduced in two-dimensional systems, the effects of the polar runaway phenomenon may be less significant. .. The second contributing factor to the diffusion coefficient in bulk GaAs is intervalley transfer. In the case of interfaces, this process is difficult to model because of the real-space-charge transfer from the GaAs to the AlGaAs. An electron might cross the energy barrier at the interface before gaining enough energy to undergo intervalley transfer. Indeed, the conduction-band difference at the interface is smaller for device #1885 by 40 meV, which is the structure that shows the decreasing diffusion coefficient with electric field. Since there is a lack of experimental data on the AlGaAs system, it is very difficult to model or otherwise evaluate hot-electron properties in this region or its effect on real-space-charge transfer. The only analytical support for the diffusion coefficient behavior in the heterointerfaces is from the Monte Carlo model of van Rheenen and Bosman [411. In their model they use an infinitely high, square potential well to simulate the two-dimensional transport behavior of a twovalley GaAs channel. The diffusion coefficient in this simulation shows a decrease with increasing electric field as opposed to the increase in diffusion observed in their bulk simulation. Therefore, the decrease in the diffusion coefficient with increasing field in the heterostructures is possibly linked to the two-dimensionality of the electron gas. .. CHAPTER IV THE DC, AC AND NOISE CHARACTERIZATION OF THE ALGAAS/GAAS MODFET CHANNEL In recent years much attention has been paid to AlGaAs/GaAs modulation-doped field-effect transistors (MODFETs) for potential use in high-speed logic circuits. The very high transconductance gm and high cut-off frequencies fT also make them of interest for low-noise microwave amplification. Excellent articles by Solomon and Morkoc [2] and Drummond et al. [42] have been written reviewing the characteristics of these new transistors. Since the first report of the noise figure of these devices in the microwave frequency range, an interest in the noise behavior has developed. The noise figures of various MODFETs have been reported recently and show improvements over conventional GaAs MESFETs of comparable gate lengths. Up to now only noise-figure measurements have been reported in the microwave frequency range. In this chapter we will not focus on the noise figure, but instead report on the noise characteristics of the FET channel. At intermediate frequencies (0.5 < f < 10 GHz) the channel noise is due to fluctuations of the free-carrier velocity and is the major contributor to the overall device noise. Measurements of the thermal noise (i.e. velocity fluctuation noise) as a function of bias are discussed in this chapter. In section 4.1 we will outline the theory of the impedance field method, which is used to obtain the ac and noise properties of the MODFET channel. Section 4.2 explains the methods of obtaining the charge-voltage relationship for the devices used in our experiments. Some of the methods of obtaining the charge-voltage relationship involve .. only low-bias data while other methods involve high-bias data. Comparing the results of the different methods can help determine the presence or absence of real-space-charge transfer. Section 4.3 describes the MODET structures to be considered. Measurement procedures are discussed in section 4.4. The experimental results will then be presented and discussed in section 4.5, followed by conclusions in section 4.6. 4.1. Impedance Field Modeling In this section the procedure for obtaining the position-dependent ac channel voltage in terms of the Green's function for a MODFET channel is discussed. It will be shown how the Green's function is related to the impedance field [16,17]. Once the impedance field is obtained, the ac and noise properties can be easily calculated. Van Vliet [43] and Nougier [44] have outlined this method for the case of the junction field-effect transistor (JFET). In this chapter the impedance field for a MODFET is calculated using the proper transport equations, and the ac and noise properties of the MODFET are derived. 4.1.1. Review of impedance field method The procedure begins by considering the device transport equations. Small-signal variations around the steady-state values of all of the variables are introduced. Having done this, and neglecting secondorder and higher terms, the ac and dc equations can be separated. The dc equation can be used to obtain the steady-state current-voltage characteristic of the device. The ac equation has some interesting properties. Generally, the ac equation involves the position-dependent steady-state parameters. This equation can be written as follows: HAV(x) = AI(x) (4.1) .. where H is a linear operator and AV and AI are the small-signal ac channel voltage and current respectively. By letting z(x,x',f) be the Green's function of H, i.e. Hz(x,x',f) = S(x-x'), (4.2) where 6(x-x') is the Dirac delta function and f denotes frequency, the total ac voltage at position x can be calculated from L AVT(x) = f z(x,x',f)AI(x')dx' (4.3) 0 The integration is taken over the entire length of the device. The total ac voltage at x given by eq. (4.3) is simply the summation over all of the small-signal current sources properly weighted by the terms z(x,x',f).dx'. Depending on the charge transport mechanisms involved, some of the terms z(x,x',f) might be zero. This point will be illustrated when the equations are developed for the MODFET. Of course, one is mainly interested in the values of the small-signal quantities at the device terminals, since these can be measured. The total small signal voltage at the device terminal (x L) is L AVT(L) = f z(L,x',f)AI(x')dx' (4.4) 0 The one-dimensional device shown in Fig. 4.1 is grounded at x = 0 and has an arbitrary steady-state dc bias applied at x = L. Suppose a current of value AI(x) is introduced at position x + Ax and extracted at x. AI(x) will produce an open-circuit voltage response AV(L) at the terminal (x = L). If the ac impedance between position x and ground (x = 0) is given by Z(x), then the voltage response at L can be expressed as .. AKx) 10 AV( x=O AX x=L Fig. 4.1. A small signal current AI(x) produces a voltage response AV(L) at the terminal x = L. Steadydc current 10 and voltage V0 are indicated. 40 :L) .. AV(L) = [Z(x+Ax,f) Z(x,f)]AI(x) (4.5) For small Ax Z(x+Ax,f) = Z(x,f) + dZ(x,f) Ax (4.6) dx and one obtains AV(L) = VZ(x,f)AI(x)Ax (4.7) The term VZ(x,f) is known as the impedance field and was first introduced by Shockley et al. [16]. The impedance field relates the ac current inside the device to the voltage response at the terminals. In the limit Ax + dx the total ac voltage at L is given by L AVT(L) = f VZ(x',f)AI(x')dx' (4.8) 0 Comparing eqs. (4.8) and (4.4), one sees that VZ(x',f) = z(L,x',f) (4.9) To find the total device impedance at the terminals, one makes use of the fact that the ac current is conserved. Then AI(x) = AI, and consequently AVT(L) L L Z(L) = AT = f VZ(x',f)dx' = L z(L,x',f)dx' (4.10) 0 0 Using the impedance field, one can express the noise in terms of spectral densities. The spectral density of the open-circuit voltage fluctuations measured at the terminals is given by [16] L SAV = I f L K(x')IVZ(x',f)12dx'dydz (4.11) zy0 .. where K(x') is the spectral density of the current fluctuations in volume dx'dydz, and the integration is carried out over the entire volume of the device. Using eq. (4.11), the spectral density of 1/f noise, generation-recombination (g-r) noise, and velocity-fluctuation noise can be calculated if the proper source term K(x) is inserted. In this chapter the focus is on velocity-fluctuation noise only. It has been shown in Chapter I that the spectral density of velocity fluctuations is directly related to the diffusion coefficient D(E), which may be field dependent. Taking this effect into account, Nougier shows that the spectral density of the voltage fluctuations due to velocity fluctuations in a one-dimensional treatment becomes [441 L2 SAV = f A(x')4q 2D[E(x')]n(x')IVZ(x',f)12dx' (4.12) 0 where A(x') is the cross-sectional area, n(x') is the carrier density and -q is the electron charge. The equivalent current-noise spectral density SAI can be calculated from SA S = )AV 2 (4.13) AI JZ(L) 12 4.1.2. Application of the impedance field method to the MODFET In the following a one-dimensional, collision-dominated transport model is used to obtain simple analytical expressions for the impedance and noise of the device. The advantage of this approach is that it provides physical insight into the ac and noise behavior of the channel. Clearly this treatment breaks down for very short submicron devices (L < .5 um) since in that case the usual concept of mobility and diffusion needs to be generalized (see Constant [45]). Assuming no leakage .. current through the gate and neglecting both diffusion and displacement currents, the charge transport equation is given by I = qwn s[V(x)]v[E(x)], (4.14) where w is the gate width and v[E(x)] is the field-dependent carrier velocity. The sign convention is as follows. The source is chosen at x = 0, the drain at x = L > 0, q > 0, V(x) > 0, E(x) < 0, v[E(x)] > 0, and I > 0. The two-dimensional sheet carrier concentration n s[V(x)] is assumed to be only a function of the local electrical potential under the gate. Velocity saturation will cause accumulation and/or depletion of the sheet carrier concentration in the high-field region under the gate, making eq. (4.14) invalid. For this reason the model we employ only describes the linear and triode regimes of the current-voltage characteristic. At T = 300 K the velocity-field characteristic of the two-dimensional electron gas is assumed to be identical to the one of bulk GaAs [46]. Consequently, -P0E v(E) = 1 E/E (4.15) where U0 is the low-field mobility taken to be 8000 cm2/V sec at room temperature, and the critical field Ec is chosen to be 11.4 kV/cm. When the electric field exceeds 3.5 kV/cm, the model [eq. (4.14)] no longer holds due to the saturation effects mentioned above. The large critical field Ec is chosen to provide the proper curvature of the velocity characteristic at low electric fields. Using the bulk GaAs velocityfield characteristic as a first attempt is justified since in the highfield region under the gate the reduced sheet carrier concentration .. |

Full Text |

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n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n FRQGXFWRU KHWHURMXQFWLRQ LQWHUIDFHV $Q ,QWHUHVW LQ WKH KRWHOHFWURQ EHKDYLRU RI HOHFWURQ WUDQVSRUW SDUDOOHO WR WKH LQWHUIDFH KDV DULVHQ ,Q WKLV GLVVHUWDWLRQ WKH FKDUJHWUDQVSRUW QRLVH LQ WKH GLUHFWLRQ SDUDOOHO ZLWK WKH *D$V$O*D$V LQWHUIDFH LV VWXGLHG 0RQWH &DUOR FDOFXn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n FRQGXFWRU KHWHURMXQFWLRQ ,QWHUIDFHV 'XH WR LQFUHDVHG SURFHVVLQJ FDSDn ELOLWLHV QRYHO VHPLFRQGXFWRU KHWHURMXQFWLRQV RI YDULRXV PDWHULDO FRPSRn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f >@ DQG WKH PRGXODWLRQ GRSHG ILHOGHIIHFW WUDQVLVWRU 02')(7f >@ DUH GLVFXVVHG %DQG 6WUXFWXUH RI $O*D$V*D$V 7KH DOOR\ V\VWHP $O[*DMB[$V*D$V LV RI JUHDW LPSRUWDQFH LQ KLJKn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f [ [ f Df J ( [f [ [ [ f Ef J DQG WKH XQLWV DUH LQ H9 )RU PROH IUDFWLRQV OHVV WKDQ DSSUR[LPDWHO\ WKH $O*D$V KDV D GLUHFW EDQGJDS )RU ODUJHU PROH IUDFWLRQV WKH PAGE 8 DOOR\ EDQGJDS LV LQGLUHFW ZLWK WKH ;YDOOH\ KDYLQJ WKH ORZHVW HQHUJ\ 7KH /YDOOH\ OLHV EHWZHHQ WKH U DQG ;YDOOH\V IRU PROH IUDFWLRQV ODUJHU WKDQ 7KH VXP RI WKH YDOHQFH DQG FRQGXFWLRQEDQG GLVFRQWLQXLWLHV PXVW HTXDO WKH HQHUJ\ EDQGJDS GLIIHUHQFH EHWZHHQ WKH *D$V DQG $O*D$V 2ULJLQDOO\ LW ZDV EHOLHYHG WKDW WKH FRQGXFWLRQEDQG GLVFRQWLQXLW\ ZDV ( [f >@ +RZHYHU PRUH UHFHQW PHDVXUHPHQWV >@ KDYH VKRZQ WKDW 2 VL[W\ILYH SHUFHQW RI WKH EDQGJDS GLIIHUHQFH OLHV LQ WKH FRQGXFWLRQ EDQG IRU [ 7KHQ WKH FRQGXFWLRQEDQG GLVFRQWLQXLW\ IROORZV IURP $( O[ H9f IRU [ f F )URP PHDVXUHPHQWV RI WKH YDOHQFHEDQG GLVFRQWLQXLW\ DV D IXQFWLRQ RI PROH IUDFWLRQ LW ZDV GHWHUPLQHG WKDW WKH PD[LPXP FRQGXFWLRQEDQG GLVFRQWLQXLW\ OLHV LQ WKH YLFLQLW\ RI [ >@ $ IXUWKHU LQFUHDVH RI WKH PROH IUDFWLRQ UHVXOWV LQ D GHFUHDVH LQ WKH FRQGXFWLRQEDQG GLVn FRQWLQXLW\ ZLWK D FRUUHVSRQGLQJ ODUJHU LQFUHDVH LQ WKH YDOHQFHEDQG GLVFRQWLQXLW\ 2I VSHFLDO LQWHUHVW LQ WKH $O*D$V*D$V V\VWHP LV WKH PHWKRG RI PRGXODWLRQ GRSLQJ ,Q WKLV GRSLQJ SURFHVV WKH *D$V OD\HU LV XQGRSHG DQG WKH GRSDQW DWRPV XVXDOO\ VLOLFRQ DWRPV IRU QW\SHf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n WULF ILHOG ,V ODUJH HQRXJK WKH ZLGWK RI WKH WULDQJXODU SRWHQWLDO ZHOO PD\ EH VPDOOHU WKDQ WKH FDUULHU GH%URJOLH ZDYH OHQJWK 7KH PRPHQWXP YHFWRU SHUSHQGLFXODU WR WKH ,QWHUIDFH WKHQ EHFRPHV TXDQWL]HG 6KRZQ LQ )LJXUH LV DQ H[DPSOH RI D KHWHURMXQFWLRQ ZKHUH WKH $O*D$V LV GRSHG QW\SH DQG WKH *D$V LV VOLJKWO\ SW\SH 7KH PRGXODWLRQGRSLQJ SURFHVV ZDV GHYHORSHG WR ,QFUHDVH WKH ORZ ILHOG PRELOLW\ RI HOHFWURQV LQ WKH GLUHFWLRQ SDUDOOHO WR WKH LQWHUIDFH $W URRP WHPSHUDWXUH .f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n QLILFDQWO\ EH\RQG WKH WKHUPDO HTXLOLEULXP YDOXH 7KLV LQFUHDVH LQ HQHUJ\ OHDGV WR QRQOLQHDU FKDUJH WUDQVSRUW LH GHYLDWLRQV IURP 2KPnV /DZf DOVR NQRZQ DV KRWHOHFWURQ WUDQVSRUW 7R LPSURYH WKH PRGHOLQJ DQG SHUIRUPDQFH RI HOHFWURQ GHYLFHV KLJKILHOG WUDQVSRUW SURSHUWLHV QHHG D PRUH WKRURXJK XQGHUVWDQGLQJ $Q LQWHUHVWLQJ KRWHOHFWURQ HIIHFW LV WKH RFFXUUHQFH RI D QHJDWLYH GLIIHUHQWLDO PRELOLW\ UHJLPH LQ EXON *D$V 7KLV SKHQRPHQRQ FRPPRQO\ PAGE 10 )LJ $O*D$V*D$V KHWHURMXQFWLRQ DW HTXLOLEULXP PAGE 11 NQRZQ DV WKH *XQQ HIIHFW >@ LV GXH WR WKH WUDQVIHU RI HOHFWURQV IURP WKH KLJKPRELOLW\ FHQWUDO UYDOOH\ WR WKH ORZPRELOLW\ VDWHOOLWH / DQG ; YDOOH\V $W ORZ ILHOGV WKH HOHFWURQ YHORFLW\ LQFUHDVHV LQ SURSRUWLRQ WR WKH HOHFWULF ILHOG $W KLJKHU ILHOG VWUHQJWKV WKH HOHFWURQV SDUWLDOO\ RFFXS\ WKH ORZPRELOLW\ VDWHOOLWH YDOOH\V DQG WKH DYHUDJH YHORFLW\ LV ORZHUHG 7KLV QHW GHFUHDVH LQ YHORFLW\ ZLWK LQFUHDVLQJ ILHOG JLYHV ULVH WR WKH QHJDWLYH GLIIHUHQWLDO PRELOLW\ LQ *D$V )URP WKH PHDVXUHPHQWV E\ 5XFK DQG .LQR >@ RQ EXON *D$V LW ZDV IRXQG WKDW WKH GLIIXVLRQ FRHIILFLHQW VKRZV D VKDUS LQFUHDVH LQ WKH VDPH ILHOG UDQJH DV WKH RQVHW RI WUDQVIHU RI HOHFWURQV WR WKH VDWHOOLWH YDOOH\V 6LQFH WKH GLIIXVLRQ FRHIILFLHQW LV FORVHO\ UHODWHG WR WKH YHORFLW\ IOXFWXDWLRQV FDXVHG E\ UDQGRP VFDWWHULQJ LQIRUPDWLRQ DERXW WKH VFDWWHULQJ SURFHVV FDQ EH REWDLQHG 7KH LQFUHDVH LQ GLIIXVLRQ LV YHU\ VHQVLWLYH WR WKH LQWHUYDOOH\ FRXSOLQJ FRQVWDQW 7KXV DFFXUDWH /L PHDVXUHPHQWV RI WKH ILHOG GHSHQGHQFH RI WKH GLIIXVLRQ FRHIILFLHQW FDQ SURYLGH D PRUH DFFXUDWH YDOXH IRU WKLV FRQVWDQW 6LQFH WKH / YDOOH\ LV ORFDWHG H9 DERYH WKH FRQGXFWLRQEDQG PLQLPXP LW WDNHV WLPH IRU PRVW HOHFWURQV WR JDLQ VXIILFLHQW HQHUJ\ XQGHU DQ DSSOLHG ILHOG WR XQGHUJR LQWHUYDOOH\ WUDQVIHU ,I WKH GHYLFH OHQJWK LV VKRUW IHZ HOHFWURQV ZLOO WUDQVIHU WR WKH VDWHOOLWH YDOOH\V EHIRUH EHLQJ FROOHFWHG E\ WKH FRQWDFW 7KH ODUJH FKDQJHV LQ YHORFLW\ DVVRFLDWHG ZLWK LQWHUYDOOH\ WUDQVIHU ZLOO QRW RFFXU DQG OHVV QRLVH ZLOO EH SURGXFHG LQ WKH H[WHUQDO FLUFXLW $ GHVFULSWLRQ RI D 0RQWH &DUOR H[SHULPHQW WR REVHUYH WKLV HIIHFW LV RXWOLQHG LQ &KDSWHU ,, ,Q WKH $O*D$V*D$V LQWHUIDFH WKHUH DUH WZR PHFKDQLVPV WKDW FDQ SURGXFH QHJDWLYH GLIIHUHQWLDO PRELOLW\ DW KLJK HOHFWULF ILHOGV 7KH ILUVW LV WKH *XQQ HIIHFW MXVW RXWOLQHG IRU EXON *D$V 7KH VHFRQG PAGE 12 PHFKDQLVP LV FDOOHG UHDOVSDFHFKDUJH WUDQVIHU ZKLFK VWDQGV IRU WKH IROORZLQJ SK\VLFDO SURFHVV (OHFWURQV LQ WKH KLJKPRELOLW\ *D$V JDLQ HQHUJ\ DV WKH\ GULIW XQGHU DQ DSSOLHG HOHFWULF ILHOG SDUDOOHO WR WKH LQWHUIDFH :KHQ WKH HQHUJ\ EHFRPHV FRPSDUDEOH WR WKH FRQGXFWLRQEDQG GLIIHUHQFH WKHUH LV WKH SRVVLELOLW\ RI WUDQVIHUULQJ WR WKH $O*D$V %HFDXVH RI WKH KLJK GRSLQJ FRQFHQWUDWLRQ ZKLFK LQWURGXFHV D VLJQLILFDQW DPRXQW RI LRQL]HG LPSXULW\ VFDWWHULQJ LQ WKH $O*D$V OD\HU WKH HOHFWURQ PRELOLW\ LQ WKLV OD\HU LV ORZHU WKDQ LQ WKH *D$V OD\HU 7KH LQFUHDVLQJ SHUFHQWDJH RI HOHFWURQV WUDQVIHUULQJ WR WKH $O*D$V OD\HU ZLWK LQFUHDVLQJ ILHOG FDXVHV WKH GULIW YHORFLW\ WR GHFUHDVH VLPLODU WR WKH *XQQ HIIHFW ([SHULPHQWDOO\ UHDOVSDFHFKDUJH WUDQVIHU KDV EHHQ VKRZQ WR EH WKH FDXVH RI QHJDWLYH GLIIHUHQWLDO GHYLFH FRQGXFWDQFH RI VSHFLDOO\ PDGH KHWHURVWUXFWXUHV >@ +RZHYHU DFFXUDWH PRGHOLQJ RI WKH SURFHVVHV LQYROYHG LV GLIILFXOW DQG HYHQ JHWWLQJ H[SHULPHQWDO YHULILFDWLRQ RI QHJDWLYH FRQGXFWDQFH LV UDWKHU LQYROYHG 7KH OHQJWK RI WKH KHWHURn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f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n FROOLVLRQ WLPH RI WKH FDUULHUV LQ KLJKPRELOLW\ VHPLFRQGXFWRUV LV YHU\ VPDOO WKH YHORFLW\IOXFWXDWLRQ VSHFWUXP H[WHQGV WR YHU\ KLJK IUHTXHQn FLHV 7KH HPSKDVLV LQ WKLV GLVVHUWDWLRQ LV SODFHG RQ WKH KRWHOHFWURQ HIIHFWV WKDW DUH DVVRFLDWHG ZLWK WKH YDULRXV VFDWWHULQJ PHFKDQLVPV 7KHUHIRUH YHORFLW\ IOXFWXDWLRQ QRLVH DOVR NQRZQ DV WKHUPDO RU GLIIXn VLRQ QRLVH LV XVHG DV D WRRO IRU SURELQJ WKHVH HIIHFWV &RQVLGHU D RQHSRUW QHWZRUN ELDVHG E\ DQ DUELWUDU\ GF YROWDJH 9T ZLWK D GF FXUUHQW ,T IORZLQJ WKURXJK LW 7KH VPDOOVLJQDO 7KHYHQLQ DQG 1RUWRQ HTXLYDOHQW FLUFXLWV HYDOXDWHG DURXQG WKH ELDV SRLQW DUH GHSLFWHG LQ )LJXUH ,Q JHQHUDO WKH VPDOOVLJQDO LPSHGDQFH =9JIf DQG DGPLWWDQFH <9JIf DUH IXQFWLRQV RI ELDV DQG IUHTXHQF\ 7KH YROWDJH DQG FXUUHQW QRLVH JHQHUDWRUV UHSUHVHQW WKH QRLVH PHFKDQLVPV LQ WKH QHW ZRUN 7KH PHDQ VTXDUH YROWDJH IOXFWXDWLRQV $9 FDQ EH H[SUHVVHG LQ WHUPV RI WKH YROWDJH VSHFWUDO GHQVLW\ E\ $9 6$99IfGI f ZKHUH I GHQRWHV IUHTXHQF\ N VLPLODU UHODWLRQ V09I!GI Â‘ f PAGE 14 = )LJ 7KHYHQLQ DQG 1RUWRQ VPDOOVLJQDO HTXLYDOHQW FLUFXLWV PAGE 15 KROGV IRU PHDQ VTXDUH FXUUHQW IOXFWXDWLRQV LQ WHUPV RI FXUUHQW QRLVH VSHFWUDO GHQVLW\ 2QH FDQ QRZ GHILQH WKH FRQFHSW RI DQ DF QRLVH WHPSHUDWXUH 7Q9JIf RI WKH QHWZRUN LQ DQDORJ\ ZLWK WKH 1\TXLVW UHODWLRQ LQ WKH IROORZLQJ ZD\ :If N%7Q9fIf5HL=9fIf` Gf 6$,9fIf N%7Q9If5H^<9If` rf ZKHUH NJ LV %ROW]PDQQnV FRQVWDQW DQG 5H ^ ` VWDQGV IRU WKH UHDO SDUW RI ,W VKRXOG EH QRWHG WKDW WKH QRLVH WHPSHUDWXUH LV DQ HOHFWULFDO SDUDPHWHU RI WKH QHWZRUN DQG KDV QRWKLQJ WR GR ZLWK WKH HOHFWURQ WHPn SHUDWXUH %\ FRQQHFWLQJ D FRQMXJDWHO\ PDWFKHG ORDG WR WKH QHWZRUN WKH PD[LPXP DYDLODEOH SRZHU LV GHOLYHUHG WR WKH ORDG 7KLV PD[LPXP DYDLOn DEOH SRZHU KDV WKH YDOXH 3 DY 9f9If0 f ZKHUH $I LV WKH EDQGZLGWK RI WKH PHDVXULQJ V\VWHP 7KHUHIRUH 7U KDV SK\VLFDO PHDQLQJ DQG FDQ EH PHDVXUHG $W KLJK IUHTXHQFLHV I 0+]f V PHDVXUHPHQWV RI 7T DUH SUHIHUUHG EHFDXVH LW LV PXFK HDVLHU WR PHDVXUH SRZHU IORZ WKDQ WHUPLQDO YROWDJHV DQG FXUUHQWV 7KH DERYH GHILQLWLRQV DUH YDOLG IRU HYHU\ RQHSRUW QHWZRUN ZKHWKHU LW LV OLQHDU RU QRQOLQHDU 7KH IROORZLQJ GLVFXVVLRQ LV UHVWULFWHG WR KRPRJHQHRXV VHPLFRQGXFWRU VDPSOHV IRU ZKLFK D RQHGLPHQVLRQDO WUHDWPHQW LV ZDUUDQWHG 7KH OLQN EHWZHHQ GLIIXVLRQ FRHIILFLHQW DQG YHORFLW\ IOXFn WXDWLRQV LV RXWOLQHG ,W VKRXOG EH QRWHG WKDW WKH TXDQWXP FRUUHFWLRQ IDFWRU IRU WKHUPDO QRLVH LV QHJOHFWHG >@ PAGE 16 /HW WKH LQVWDQWDQHRXV YHORFLW\ RI D FDUULHU L DW WLPH W EH YÂWf YA(f $YAWf f ZKHUH YA(f LV WKH DYHUDJH GULIW YHORFLW\ DQG ( LV WKH HOHFWULF ILHOG 7KH WHUP $YAWf UHSUHVHQWV WKH IOXFWXDWLRQV LQ WKH YHORFLW\ DERXW YA(f ZLWK WKH DYHUDJH $YAWf %\ GHILQLWLRQ >@ WKH GLIIXVLRQ FRHIILFLHQW LV UHODWHG WR WKH VSHFWUXP RI YHORFLW\ IOXFWXDWLRQV E\ 6 (If '(If fÂ§A ]I I $YWf$YW[f H A A 7G[ f fÂ§ ZKHUH WKH WHUP $YWf$YWWf LV WKH DXWRFRUUHODWLRQ IXQFWLRQ RI WKH YHORFLW\ IOXFWXDWLRQV $W ORZ IUHTXHQFLHV HT f UHGXFHV WR WKH ZHOONQRZQ (LQVWHLQ IRUPXOD IRU GLIIXVLRQ $[ 'W f IRU VXIILFLHQWO\ ORQJ W &RQVLGHU D VHPLFRQGXFWRU VDPSOH RI OHQJWK / DQG FURVVVHFWLRQDO DUHD $ ZLWK RKPLF FRQWDFWV $Q HOHFWURQ ZLWK YHORFLW\ $YAWf JLYHV ULVH WR D FXUUHQW $LAWf LQ WKH H[WHUQDO FLUFXLW VXFK WKDW T$Y Wf $LLWf Â f DQG WKH FRUUHVSRQGLQJ VSHFWUXP RI FXUUHQW IOXFWXDWLRQV LV 6$LIf A 6$YIf b rIf f ff / /L ,I WKH HOHFWURQ JDV LQ QRQGHJHQHUDWH DQG WKHUH DUH Q$/ HOHFWURQV LQ WKH PAGE 17 VDPSOH WKHQ WKH WRWDO QRLVH FXUUHQW VSHFWUDO GHQVLW\ EHFRPHV 2 WL $ 6$,If Q$/ 6$If T A 'If f 8VLQJ HT f RQH REWDLQV f 5HFRJQL]LQJ WKDW 5H PAGE 18 6$,If T $ 'IfN%7OLe-/f f 7KH H[SUHVVLRQ IRU GLIIXVLRQ LQ WHUUDV RI PRELOLW\ IRU GHJHQHUDWH VHPLn FRQGXFWRUV WKHQ EHFRPHV T'If Qf 5HSn f f 2QFH WKH VRXUFHV RI QRLVH LQ VHPLFRQGXFWRUV KDYH EHHQ GHWHUPLQHG LW LV SRVVLEOH WR FKDUDFWHUL]H WKH QRLVH DW WKH WHUPLQDOV RI VROLGVWDWH GHYLFHV 7KUHH PHWKRGV DUH XVHG LQ KRWHOHFWURQ SUREOHPV WKH /DQJHYLQ WKH LPSHGDQFH ILHOG DQG WKH WUDQVIHU LPSHGDQFH )LUVW LQ DOO WKUHH PHWKRGV WKH HTXDWLRQV GHVFULELQJ WKH GHYLFH EHKDYLRU DUH IRUPXODWHG 7KHQ HDFK YDULDEOH LQYROYHG LV VHW HTXDO WR 4 4T $4 H[SMXLWf 7KH ]HURRUGHU WHUPV JLYH WKH GF FKDUDFWHULVWLFV 7KH ILUVWRUGHU WHUPV JLYH WKH DF HTXDWLRQV ,Q WKH /DQJHYLQ PHWKRG >@ WKH DSSURSULDWH ZKLWH QRLVH VRXUFH LV DGGHG WR HDFK DF HTXDWLRQ $X[LOLDU\ YDULDEOHV DUH WKHQ HOLPLQDWHG WR JHW D UHODWLRQVKLS EHWZHHQ WKH DF FXUUHQW $, DQG WKH DF ILHOG $( :ULWLQJ WKH VROXWLRQ RI $( LQ WHUPV RI WKH RWKHU YDULDEOHV DQG LQWHJUDWn LQJ RYHU WKH GHYLFH OHQJWK RQH JHWV WKH DF YROWDJH DFURVV WKH WHUPLn QDOV %\ VHWWLQJ WKH QRLVH VRXUFHV WR ]HUR WKH GHYLFH LPSHGDQFH LV REWDLQHG &RQYHUVHO\ ZKHQ $, PXOWLSO\LQJ E\ WKH FRPSOH[ FRQMX r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n WHU ,9 :KHQ WKH YDULDEOHV XVHG WR GHVFULEH WKH DF SURSHUWLHV RI D GHYLFH DUH ZULWWHQ LQ WHUPV RI FXUUHQW $O DQG HOHFWULF ILHOG $( WKH PRVW JHQHUDO WHFKQLTXH IRU FDOFXODWLQJ WKH LPSHGHQFH DQG QRLVH SURSHUWLHV LV WKH WUDQVIHU ,PSHGDQFH PHWKRG 9DQ 9OLHW HW DO >@ GHYHORSHG WKLV PHWKRG WR GHVFULEH WKH QRLVH EHKDYLRU LQ VSDFHFKDUJH OLPLWHGFXUUHQW 6&/&f VROLGVWDWH GLRGHV ,W ZDV IRXQG WKDW WKH WUDQVIHU LPSHGDQFH PHWKRG LV TXLWH JHQHUDO DQG HQFRPSDVVHV WKH LPSHGDQFHILHOG WHFKQLTXH ,WV DELOLW\ ZDV UHFHQWO\ XWLOL]HG E\ 7HKUDQL HW DO >@ LQ 6&/& VLOLFRQ FDUELGH GHYLFHV $V GHYLFH GLPHQVLRQV FRQWLQXH WR VKULQN WUDGLWLRQDO DQDO\WLFDO PHWKRGV RI FKDUDFWHUL]LQJ VROLGVWDWH GHYLFHV EHFRPH TXHVWLRQDEOH 7UDQVLHQW WUDQVSRUW HIIHFWV DQG ERXQGDU\ FRQGLWLRQV ZLOO EHFRPH LQFUHDVn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n WLRQ EHFRPHV QHJOLJLEOH 7KHQ WKH HPLWWHU HIILFLHQF\ FDXVHG E\ EDFN LQMHFWLRQ RI FDUULHUV IURP WKH EDVH WR WKH HPLWWHU GRPLQDWHV WKH FXUn UHQW JDLQ ,Q KRPRMXQFWLRQ WHFKQRORJ\ WKH HPLWWHU LV KHDYLO\ GRSHG ZLWK D OLJKWO\ GRSHG EDVH UHJLRQ WR GHFUHDVH WKH EDFN LQMHFWLRQ +RZn HYHU WKH KLJK UHVLVWDQFH RI WKH OLJKWO\ GRSHG EDVH VHYHUHO\ OLPLWV WKH KLJK IUHTXHQF\ DQG QRLVH SHUIRUPDQFH RI ELSRODU GHYLFHV 'RSLQJ WKH EDVH PRUH KHDYLO\ ZRXOG ORZHU WKH UHVLVWDQFH EXW GHJUDGH HPLWWHU HIILn FLHQF\ 7R FLUFXPYHQW WKHVH HIIHFWV LW ZDV SURSRVHG E\ .URHPHU >@ WKDW D KHWHURMXQFWLRQ DW WKH HPLWWHUEDVH MXQFWLRQ EH XVHG 8VLQJ D ZLGH EDQGJDS HPLWWHU ZRXOG DOORZ WKH EDVH UHJLRQ WR EH KHDYLO\ GRSHG WKXV ORZHULQJ WKH EDVH UHVLVWDQFH ZKLOH PDLQWDLQLQJ KLJK HPLWWHU HIILFLHQF\ 7KLV LV WKH EDVLF SUHPLVH RI WKH KHWHURMXQFWLRQ ELSRODU WUDQVLVWRU +%7f 0XFK UHVHDUFK LV FXUUHQWO\ EHLQJ SXUVXHG RQ WKLV LQWHUHVWLQJ GHYLFH WRSLF $OWKRXJK WKH WHFKQRORJ\ LV DYDLODEOH WR PDNH KHWHURn MXQFWLRQ ELSRODU WUDQVLVWRUV WRGD\ WKH SURFHVVLQJ RI LQWHJUDWHG FLUn FXLWV LV GLIILFXOW GXH WR OD\RXW DQG LQWHUFRQQHFWLRQ SUREOHPV +HWHURMXQFWLRQV KDYH DOVR LPSURYHG ILHOGHIIHFW WUDQVLVWRU WHFKn QRORJ\ 7KH 6L6LOA LQWHUIDFH KDV EHHQ XVHG WR PDNH 026)(7V IRU \HDUV +RZHYHU WKH LQWHUIDFH LV RIWHQ GHJUDGHG GXH WR VXUIDFH URXJKn QHVV DQG ,QWHUIDFH VWDWHV 7KH $O*D$V*D$V KHWHURMXQFWLRQ GRHV QRW KDYH PAGE 21 WKHVH SUREOHPV LI SURSHUO\ JURZQ 7KH PRGXODWLRQGRSHG ILHOGHIIHFW WUDQVLVWRU 02')(7f DOVR NQRZQ DV WKH KLJK HOHFWURQ PRELOLW\ WUDQVLVWRU +(07f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n LVWLFV DW KLJK IUHTXHQFLHV DQG ZLOO SUREDEO\ H[FHHG FRQYHQWLRQDO 0(6)(7 FDSDELOLWLHV LQWR WKH PLOOLPHWHUZDYH UHJLRQ ,Q &KDSWHU ,9 WKH GF DF DQG QRLVH SURSHUWLHV RI WKH 02')(7 FKDQQHO DUH GHULYHG DQG H[SHULn PHQWDOO\ YHULILHG PAGE 22 $,*D$V *D$V 8QGRSHG )LJ 02')(7 FRQGXFWLRQ EDQG GLDJUDP PAGE 23 &+$37(5 ,, 0217( &$5/2 02'(/,1* 2) +27 (/(&7521 75$163257 7KH VHPLFODVVLFDO %ROW]PDQQ WUDQVSRUW HTXDWLRQ %7(f GHVFULEHV WKH HYROXWLRQ RI WKH GLVWULEXWLRQ IXQFWLRQ LQ SKDVH VSDFH 2QFH WKH GLVWULn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n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n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f DQG SWI!f DUH WKH UHVSHFWLYH SUREDELOLW\ GHQVLn WLHV ZKHUH U LV DVVRFLDWHG ZLWK WKH SVHXGRUDQGRP FRPSXWHU GLVWULEXWLRQ DQG Mf LV WKH SK\VLFDO TXDQWLW\ WR EH REWDLQHG IURP WKH PDSSLQJ (TXDWLQJ WKH FXPXODWLYH GLVWULEXWLRQV PAGE 25 `! U S I! r fGW! r SUnfGUn f DQG XVLQJ D XQLIRUP GLVWULEXWLRQ IRU SUf U S!n fGWM!n f (YDOXDWLQJ WKH LQWHJUDO RI HT RQH REWDLQV M! LQ WHUPV RI U ,Q WKH IROORZLQJ 0RQWH &DUOR SURJUDP WKLV PHWKRG RI REWDLQLQJ UDQGRP YDULDEOHV LV XVHG WR JHQHUDWH IUHHIOLJKW WLPHV FKRRVH EHWZHHQ VFDWWHULQJ PHFKDQn LVPV DQG VHOHFW WKH ILQDO LFVSDFH SRVLWLRQ DIWHU VFDWWHULQJ ,Q DGGLWLRQ WKH HQHUJ\ RI WKH HOHFWURQV ,QMHFWHG LQWR WKH DFWLYH GHYLFH UHJLRQ LV FDOFXODWHG XVLQJ UDQGRP QXPEHUV 7KH SURJUDP WR EH GHVFULEHG LV EXLOW XSRQ WKH )RUWUDQ YHUVLRQ RXWOLQHG E\ %RDUGPDQ >@ 7KH RULJLQDO %RDUGPDQ SURJUDP RQO\ DOORZHG IRU D FHQWUDO YDOOH\ DQG RQH W\SH RI VDWHOOLWH YDOOH\ LQ WKH HQHUJ\ ZDYHYHFWRU GLVSHUVLRQ UHODWLRQ (Nf IRU HOHFWURQV LQ WKH FRQGXFWLRQ EDQG 2ULJLQDOO\ LW ZDV EHOLHYHG WKDW WKH RUGHULQJ LQ HQHUJ\ RI WKH FRQGXFWLRQEDQG YDOOH\V ZDV 7 ; / IRU *D$V LQ LQFUHDVLQJ RUGHU RI HOHFWURQ HQHUJ\ )RU WKLV UHDVRQ WKH RULJLQDO YHUVLRQ LQFOXGHG RQO\ WKH 7 DQG ; YDOOH\V VLQFH WKH / YDOOH\ SRSXODWLRQ LQ WKLV PRGHO FRXOG EH QHJOHFWHG 0RUH UHFHQWO\ LW ZDV GLVFRYHUHG WKDW WKH RUGHULQJ RI WKH YDOOH\V LV 7 / ; >@ 7KH SURJUDP ZDV UHZULWWHQ WR LQFOXGH DOO WKUHH YDOOH\V LQ WKH DSSURSULDWH RUGHU 7KH YDOXHV IRU LQWHUYDOOH\n VFDWWHULQJ FRXSOLQJ FRQVWDQWV DQG HQHUJ\ RIIVHWV EHWZHHQ YDOOH\V ZHUH WDNHQ IURP 3R]KHOD DQG 5HNODLWLV >@ )LJXUH VKRZV WKH HQHUJ\ ZDYHYHFWRU UHODWLRQVKLS IRU WKH *D$V FRQGXFWLRQ EDQG (DFK YDOOH\ LV WDNHQ WR EH SDUDEROLF PAGE 26 )LJ (QHUJ\ZDYHYHFWRU UHODWLRQ IRU *D$V PAGE 27 (OHFWURQ PRWLRQ ,V PRVW HDVLO\ GHVFULEHG LQ N VSDFH ,Q VLPSOH VHPLFRQGXFWRUV WKH HOHFWURQV DUH UHJDUGHG DV IUHH SDUWLFOHV ZLWK DQ HIIHFWLYH PDVV P RI WKH DSSURSULDWH YDOOH\ 7KH HOHFWURQ HQHUJ\ LV WKHQ JLYHQ E\ r (LWf f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f f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f SRODU RSWLFDO SKRQRQ ,QWUDYDOOH\f PAGE 28 0 N S HOHF ILHOG ( r!Â‘ )LJ (OHFWURQ PRWLRQ LQ N VSDFH PAGE 29 HTXLYDOHQW ,QWHUYDOOH\ / } / RU ; } ;f DQG QRQHTXLYDOHQW LQWHUYDOOH\ / ; HWFfr ,QWUDYDOOH\ VFDWWHULQJ PHDQV WKDW WKH LQLWLDO DQG ILQDO VWDWHV EHIRUH DQG DIWHU VFDWWHULQJ DUH LQ WKH VDPH YDOOH\ DQG LQWHUn YDOOH\ VFDWWHULQJ PHDQV WKDW WKH WZR VWDWHV DUH LQ GLIIHUHQW YDOOH\V %RWK W\SHV RI LQWHUYDOOH\ VFDWWHULQJ DUH YLD RSWLFDO SKRQRQV VLQFH DFRXVWLF DQG SRODU RSWLFDO SKRQRQ VFDWWHULQJ GRHV QRW DOORZ IRU ODUJH FKDQJHV LQ WKH ZDYHYHFWRU )RU DOO LQWUDYDOOH\ VFDWWHULQJ SURFHVVHV LQYROYLQJ RSWLFDO SKRQRQ ILHOGV WKH HQHUJ\ VWDWH DIWHU VFDWWHULQJ PXVW VDWLVI\ WKH UHODWLRQ (Nnf (LFf s @X f ZKHUH Z LV WKH UDGLDQ IUHTXHQF\ RI WKH ODWWLFH YLEUDWLRQ WKH SOXV VLJQ LQGLFDWHV DEVRUSWLRQ DQG WKH PLQXV VLJQ HPLVVLRQ RI DQ RSWLFDO SKRQRQ $FRXVWLF SKRQRQ VFDWWHULQJ KRZHYHU LV WUHDWHG DV DQ HODVWLF SURFHVV DQG WKHUHIRUH (Nnf (Nf 7KH HQHUJ\ RI WKH HOHFWURQ LV PHDVXUHG ZLWK UHVSHFW WR WKH PLQLPXP RI WKH YDOOH\ LW RFFXSLHV 7KHUHIRUH ZKHQ D QRQHTXLYDOHQW LQWHUYDOOH\ WUDQVLWLRQ RFFXUV WKH HQHUJ\ GLIIHUHQFH EHWZHHQ YDOOH\V PXVW EH DFFRXQWHG IRU :KHQ WKH WUDQVLWLRQ LV VXFK WKDW WKH ILQDO VWDWH LV LQ D YDOOH\ ZLWK D PLQLPXP KLJKHU LQ HQHUJ\ WKDQ WKH LQLWLDO YDOOH\ WKH HQHUJ\ RI WKH HOHFWURQ EHFRPHV (Nnf (Nf s +X $ f ZKHUH $ LV WKH HQHUJ\ GLIIHUHQFH EHWZHHQ WKH YDOOH\ PLQLPD DQG -LP LV WKH RSWLFDO SKRQRQ HQHUJ\ ,I WKH WUDQVLWLRQ LV WR D YDOOH\ ZLWK D ORZHU PLQLPD WKHQ WKH HQHUJ\ GLIIHUHQFH LV DGGHG WR WKH ILQDO HQHUJ\ PAGE 30 (DFK SURFHVV WKDW FDQ VFDWWHU DQ HOHFWURQ DW WKH HQG RI D FROOLn VLRQ IUHH IOLJKW LV FKDUDFWHUL]HG E\ D WUDQVLWLRQ UDWH 6QNNnf ZKLFK LV HTXDO WR WKH SUREDELOLW\ SHU XQLW WLPH WKDW DQ HOHFWURQ LV VFDWWHUHG IURP WKH VWDWH N WR D VWDWH Nn 7KH VXEVFULSW Q GHQRWHV D SDUWLFXODU VFDWWHULQJ SURFHVV 7KH VFDWWHULQJ UDWH ; Nf IURP VWDWH N WR DQ\ Q A Wr OO VWDWH Nn GXH WR WKH QWQ SURFHVV LV IRXQG E\ LQWHJUDWLQJ RYHU DOO SRVVLn EOH ILQDO VWDWHV Nn +HQFH ; Nf 6 NNnfGNn f Q Q 7KH WRWDO VFDWWHULQJ UDWH LV WKHQ IRXQG IURP D VXPPDWLRQ RYHU DOO SURFHVVHV 1 ;Nf $QNf f Q O 7KH VFDWWHULQJ UDWHV IRU HDFK SURFHVV DUH OLVWHG LQ 7DEOH ZKHUH WKH UDWHV DUH SUHVHQWHG LQ WHUPV RI HQHUJ\ UDWKHU WKDQ LQ WHUPV RI ZDYH YHFWRU 7KH YDOXHV RI WKH SK\VLFDO FRQVWDQWV XVHG WR ILW H[SHULPHQWDO GDWD DUH OLVWHG LQ 7DEOH 7KH VFDWWHULQJ UDWHV IRU WKH FHQWUDO 7f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n OLWH YDOOH\V LQWHUYDOOH\ WUDQVIHU SOD\V D UROH LQ WKH WRWDO VFDWWHULQJ UDWHV $V VHHQ LQ )LJ SRODU RSWLFDO SKRQRQV VWLOO GRPLQDWH XS WR PAGE 31 7$%/( 6FDWWHULQJ 5DWHV 0HFKDQLVP 6FDWWHULQJ 5DWHV $(f $FRXVWLF SKRQRQ LQWUDYDOOH\f r[ f B B P f NB7 ( D D LUSV _$ 3RODU RSWLFDO SKRQRQ LQWUDYDOOH\f PAGE 32 7$%/( 3K\VLFDO &RQVWDQWV 0DWHULDO GHQVLW\ JFQAf 6RXQG YHORFLW\ AFPVf +LJKIUHTXHQF\ GLHOHFWULF FRQVWDQW /RZIUHTXHQF\ GLHOHFWULF FRQVWDQW 2SWLFDO SKRQRQ IUHTXHQF\ UDGVHFf ,QWHUYDOOH\ SKRQRQ IUHTXHQF\ AUDGVHFf $FRXVWLF GHIRUPDWLRQ SRWHQWLDO H9f ,QWHUYDOOH\ FRXSOLQJ FRQVWDQWV AH9FPf 7 / U [ OR / ; / / ; ; (QHUJ\ VHSDUDWLRQ EHWZHHQ YDOOH\V H9f 7 / U ; (IIHFWLYH PDVV PrPJf 7 / ; PAGE 33 )LJ 6FDWWHULQJ UDWHV IRU 7 YDOOH\ PAGE 34 DERXW H9 $ERYH H9 WKH U WR ;YDOOH\ WUDQVLWLRQV GRPLQDWH 7KH VFDWWHULQJ UDWHV LQ WKH / DQG ; YDOOH\V DUH VKRZQ LQ )LJV DQG UHVSHFWLYHO\ $V PHQWLRQHG SUHYLRXVO\ RQH PXVW JHQHUDWH FROOLVLRQ IUHHIOLJKW WLPHV IURP WKH VFDWWHULQJ UDWHV ,I SWf LV WKH SUREDELOLW\ SHU XQLW WLPH WKDW DQ HOHFWURQ KDV D IOLJKW RI GXUDWLRQ W DQG VXEVHTXHQWO\ VFDWWHUV WKHQ WKH IOLJKW WLPH W LV IRXQG IURP W U SWnfGW r f ZKHUH U LV WKH XQLIRUPO\ GLVWULEXWHG UDQGRP QXPEHU $V VKRZQ LQ %RDUGPDQ >@ HT f FDQ EH ZULWWHQ DV W U H[S^ $NfGWn` f 7KH LQWHJUDO FDQQRW EH HYDOXDWHG DQDO\WLFDOO\ DQG WKXV UHTXLUHV QXPHULn FDO HYDOXDWLRQ 7KLV LQYROYHV D VLJQLILFDQW DPRXQW RI FRPSXWHU &38 WLPH IRU HDFK IOLJKW 7R FLUFXPYHQW WKLV SUREOHP %RDUGPDQ HW DO >@ GHYHORSHG WKH FRQFHSW RI YLUWXDO VFDWWHULQJV ,Q D YLUWXDO VFDWWHULQJ HYHQW WKH VWDWH RI WKH HOHFWURQ GRHV QRW FKDQJH 7KH VFDWWHULQJ UDWH IRU WKH HOHFWURQ LQFOXGLQJ YLUWXDO VFDWWHULQJ EHFRPHV HTXDO WR *$00$ ;7Nf $Nf $\2Ff f ZKHUH *$00$ LV WKH QRPHQFODWXUH XVHG E\ %RDUGPDQ DQG $A LV WKH YLUWXDO VFDWWHULQJ UDWH 6LQFH *$00$ LV D FRQVWDQW WKH LQWHJUDO LQ HT f FDQ EH HDVLO\ HYDOXDWHG DQG RQH ILQGV IRU W W ORJUf*$00$ f 7KH YDOXH RI *$00$ LV XVXDOO\ WDNHQ WR EH HTXDO WR WKH PD[LPXP HOHFWURQ UHDO VFDWWHULQJ UDWH HYDOXDWHG RYHU WKH SRVVLEOH HOHFWURQ HQHUJ\ UDQJH PAGE 35 (QHUJ\ H9f )LJr 6FDWWHULQJ UDWHV IRU / YDOOH\ PAGE 36 (QHUJ\ HYf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n JHQFH WKH TXDQWLWLHV RI LQWHUHVW VXFK DV WKH PHDQ YHORFLW\ WKH GLIIXn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n HWHUV DUH WKH LQWHUYDOOH\ VFDWWHULQJ FRXSOLQJ FRQVWDQWV ZKLFK UHSUHVHQW WKH VWUHQJWK RI WKH HOHFWURQ WUDQVIHU PHFKDQLVP UHVXOWLQJ LQ LQWHUYDOOH\ WUDQVLWLRQV YLD D GHIRUPDWLRQ SRWHQWLDO $FFRUGLQJ WR UHFHQW OLWHUDWXUH 2 $ >@ WKHVH FRQVWDQWV KDYH YDOXHV WKDW UDQJH IURP WR H9FP IRU *D$V PAGE 38 $W ORZ HOHFWULF ILHOGV WKH ,QWHUYDOOH\ WUDQVLWLRQV SOD\ D PLQRU UROH LQ WUDQVSRUW VLQFH PRVW RI WKH HOHFWURQV VWD\ LQ WKH FHQWUDO Uf YDOOH\ :LWK ODUJHU ILHOGV SUHVHQW WKH HOHFWURQV PRYH WR KLJKHU HQHUn JLHV LQ WKH FRQGXFWLRQ EDQG WKXV HQDEOLQJ WKH LQWHUYDOOH\ WUDQVIHU IURP 7 WR / YDOOH\V 7KLV LQWHUYDOOH\ WUDQVIHU WR WKH ORZPRELOLW\ VDWHOOLWH YDOOH\V LV WKH FDXVH RI WKH QHJDWLYH GLIIHUHQWLDO PRELOLW\ UHJLPH LQ EXON *D$V 6KRZQ LQ )LJ LV WKH YDULDWLRQ RI WKH YHORFLW\ILHOG FKDUDFn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f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n WURQV KHDW XS IDVW ,Q DGGLWLRQ WKH SURFHVV EHFRPHV OHVV HIILFLHQW ZLWK LQFUHDVLQJ HOHFWURQ HQHUJ\ &RQVHTXHQWO\ IDVW HOHFWURQV PRYH HYHQ IDVWHU 7KLV FDXVHV WKH YHORFLW\ GLVWULEXWLRQ WR ZLGHQ FRUUHVSRQGLQJ WR DQ ,QFUHDVH LQ $Y $VVXPLQJ WKDW WKH FRUUHODWLRQ WLPH RI YHORFLW\ IOXFWXDWLRQV LV QRW VLJQLILFDQWO\ DOWHUHG LQ WKLV SURFHVV WKH ORZ IUHTXHQF\ GLIIXVLRQ FRHIILFLHQW SODWHDX YDOXHf ZLOO LQFUHDVH ZLWK HOHFn WULF ILHOG VHH HT f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f ZKLOH WKH WLPH GHSHQGHQFH RI WKH PAGE 42 )LJ $YHUDJH / DQG ; YDOOH\ SRSXODWLRQ RI EXON *D$V YV 7/ LQWHUYDOOH\ FRXSOLQJ FRQVWDQW PAGE 43 )LJ 'LIIXVLRQ VSHFWUD YV HOHFWULF ILHOG IRU HOHFWURQV LQ U YDOOH\ SRODU UXQDZD\f PAGE 44 YHORFLW\ DXWRFRUUHODWLRQ IXQFWLRQ H[SHULHQFHV OLWWOH FKDQJH 6HFn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n DZD\ DUH QRW DV FOHDU $V D UHVXOW RI WKH GHFUHDVHG FRXSOLQJ VWUHQJWK RQFH WKH HOHFWURQ VFDWWHUV WR WKH / YDOOH\ WKHUH LV D VPDOO SUREDELOLW\ RI UHWXUQLQJ WR WKH FHQWUDO YDOOH\ 7KLV LV WKH FDXVH RI WKH DYHUDJH / YDOOH\ SRSXODWLRQ LQFUHDVH 0RQWH &DUOR 6SHFWUDO $QDO\VLV RI 9HORFLW\ )OXFWXDWLRQV 6LQFH WKH GLIIXVLRQ FRHIILFLHQW LV D IUHTXHQF\GHSHQGHQW SDUDPHWHU DV VKRZQ E\ HT f LW LV LQWHUHVWLQJ WR LQYHVWLJDWH WKH YHORFLW\ IOXFWXDWLRQ VSHFWUXP WR JDLQ LQVLJKW LQWR WUDQVSRUW SURFHVVHV ,Q WKLV VHFWLRQ WKH SURFHVV RI KRZ WR JHQHUDWH WKH YHORFLW\ WLPH VHULHV LQ WKH 0RQWH &DUOR SURJUDP LV GHVFULEHG LQFOXGLQJ WKH VHOHFWLRQ RI VDPSOLQJ UDWH 7KH GHILQLWLRQ RI VSHFWUDO GHQVLW\ LV UHYLHZHG DQG WKH FDOFXODn WLRQ RI WKH VSHFWUXP IURP GLVFUHWHO\ VDPSOHG VLJQDOV LV H[SODLQHG 5HVXOWV IRU EXON *D$V DUH SUHVHQWHG DQG WKH\ LQGLFDWH WKH HIIHFWV RI D GRPLQDQW VFDWWHULQJ SURFHVV RQ WKH VSHFWUXP PAGE 45 7KH 1\TXLVW VDPSOLQJ WKHRUHP VWDWHV WKDW WKH VDPSOLQJ UDWH I $W PXVW EH DW OHDVW WZLFH WKH KLJKHVW IUHTXHQF\ FRPSRQHQW RI WKH V ZDYHIRUP EHLQJ VDPSOHG +HUH $W LV WKH OHQJWK RI WLPH EHWZHHQ VDPSOHV ,I WKH VDPSOLQJ UDWH LV OHVV WKDQ WZLFH WKH KLJKHVW IUHTXHQF\ SUHVHQW WKHQ DOLDVLQJ ZLOO RFFXU ,Q RWKHU ZRUGV WKH VDPSOLQJ WLPH $W XVHG LQ WKH 0RQWH &DUOR SURJUDP PXVW EH PXFK VPDOOHU WKDQ WKH LQWHUFROOLVLRQ WLPH $IWHU FRQVLGHULQJ WKH VFDWWHULQJ UDWHV LQ *D$V VHH )LJV f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ef 9] f IW N ] f 7KHVH VXEIOLJKWV FRQWLQXH XQWLO WKH HQG RI WKH IUHH IOLJKW RU WKH WLPH ZLQGRZ OHQJWK 7 1$Wf KDV EHHQ UHDFKHG V PAGE 46 7KH DFWXDO DOJRULWKP RI WKH SURFHVV LV GHVFULEHG EHORZ DQG RXWn OLQHG LQ WKH IORZ FKDUW RI $SSHQGL[ % 6LQFH VFDWWHULQJ HYHQWV RFFXU LQ JHQHUDO EHWZHHQ WKH VDPSOLQJ WLPHV WKH FRPSXWHU PXVW NHHS WUDFN RI ZKHQ LW ODVW WRRN D VDPSOH 7KH SURJUDP ODEHOV WKH WLPH SDVVHG VLQFH WKH ODVW VDPSOH ZDV WDNHQ DV 7,0(; :KHQ WKH IUHHIOLJKW WLPH EHWZHHQ VFDWWHULQJ HYHQWV 7,0(f LV JHQHUDWHG WKH DOJRULWKP ILUVW GHWHUPLQHV ZKHWKHU WKH JHQHUDWHG WLPH 7,0(f SOXV WKH WLPH UHPDLQLQJ VLQFH WKH ODVW VDPSOH 7,0(;f LV ORQJ HQRXJK WR UHDFK WKH QH[W VDPSOLQJ WLPH ,I LW LV QRW WKH IOLJKW WLPH LV DGGHG WR 7,0(; WR EHFRPH WKH QHZ 7,0(; DQG WKH SURJUDP SURFHHGV WR WKH QH[W VFDWWHULQJ VHOHFWLRQ ZLWKRXW WDNLQJ D VDPSOH RI WKH YHORFLW\ :KHQ WKH JHQHUDWHG IUHHIOLJKW WLPH SOXV 7,0(; LV JUHDWHU WKDQ WKH VDPSOLQJ WLPH $W WKH SURJUDP DGYDQFHV WR WKH QH[W VDPSOLQJ WLPH E\ WKH WLPH ODEHOHG 7,0(9 $W 7,0(; 7KH YHORFLW\ RI WKH HOHFWURQ LV WKHQ FDOFXODWHG XVLQJ HT f DQG VWRUHG LQ WKH WLPH VHULHV )LJXUH SLFWRULDOO\ UHSUHVHQWV WKH UHODWLRQVKLS RI WKH WLPHV LQ WKH VDPSOLQJ SURFHVV 7KH QXPEHU RI VDPSOHV LQ WKH WLPH VHULHV WKDW FDQ EH WDNHQ LQ WKH UHPDLQLQJ IUHHIOLJKW WLPH LV GHVLJQDWHG E\ 11 7KH YDOXH RI 11 LV DQ LQWHJHU QXPEHU DQG LV GHWHUPLQHG E\ GLYLGLQJ WKH UHPDLQLQJ IOLJKW WLPH E\ $W DQG WUXQFDWLQJ DQ\ IUDFWLRQDO TXDQWLW\ :KHQ 11 LV HTXDO WR ]HUR WKH UHPDLQLQJ WLPH LV QRW ORQJ HQRXJK WR UHDFK WKH QH[W VDPSOLQJ WLPH VR WKH UHPDLQLQJ WLPH EHFRPHV 7,0(; 7KH SURJUDP WKHQ JRHV WR WKH QH[W VFDWWHULQJ VHOHFWLRQ )RU 11 JUHDWHU WKDQ ]HUR WKH DOJRULWKP ORRSV WKURXJK 11 VXEIOLJKWV JHQHUDWLQJ DGGLWLRQDO WLPHVHULHV GDWD $W WKH HQG RI WKH 11 ORRS WKH QHZ YDOXH RI 7,0(; LV XSGDWHG E\ WKH UHPDLQLQJ WLPH EHIRUH WKH ORRS PLQXV WKH ORRS WLPH 7KH SURJUDP WKHQ SURFHHGV WR WKH QH[W VFDWWHULQJ VHOHFWLRQ PAGE 47 7,0(; ,rfÂ§$W 7,0(9 11[$W W r VFDWWHULQJ HYHQW M 7,0(; W VFDWWHULQJ HYHQW )LJ 5HSUHVHQWDWLRQ RI WLPHV XVHG WR JHQHUDWH YHORFLW\ WLPH VHULHV PAGE 48 7KH QXPEHU RI VDPSOHV 1 LQ WKH WLPH VHULHV LV PRQLWRUHG DW HDFK VDPSOLQJ WLPH :KHQ WKH QXPEHU UHDFKHV 7 $W WKH SURJUDP VWRSV V VDPSOLQJ DQG SURFHHGV WR WKH ))7 DOJRULWKP 7KH PHWKRGV RI FDOFXODWLQJ WKH YHORFLW\IOXFWXDWLRQ VSHFWUDO GHQVLW\ IURP WKH WLPH VHULHV ZLOO QRZ EH UHYLHZHG +HUH ZH IROORZ WKH RXWOLQH JLYHQ E\ 7HKUDQ >@ /HW D UDQGRP VLJQDO [Wf LQ WKH LQWHUYDO W 7J EH GHILQHG LQ WHUPV RI D )RXULHU VHULHV MLUI W [Wf O D H f RW ZKHUH I fÂ§ s s f DQG DA LV WKH )RXULHU FRHIILFLHQW RI V [Wf DW I^e 7KH GLVFUHWH )RXULHU FRHIILFLHQWV DA DUH GHILQHG DV 1O 9 $B? U.$IQ$W Y D. Â“ÂƒW $ $W [nQ$Wn H f Q ZKHUH [Q$Wf LV WKH VDPSOHG WLPH GDWD $I LV WKH IUHTXHQF\ VSDFLQJ WU GHILQHG DV $I 1$W DQG GHQRWHV WKH IUHTXHQF\ FRPSRQHQW I fÂ§ N 1$W .$I )RXULHU FRPSRQHQW RI [Wf KDYLQJ D IUHTXHQF\ IMM LV JLYHQ E\ MXI W MLUI W ;5 D5H DB.H f 7KH HQVHPEOH DYHUDJH RI ;. LV IRXQG WR EH 9N f VLQFH WKH )RXULHU FRHIILFLHQWV KDYH DQ DUELWUDU\ SKDVH UHVXOWLQJ LQ PAGE 49 Df D f DQG VLQFH IRU D UHDO VLJQDO [Wf fÂ§. DBA D. f :ULWLQJ WKH HQVHPEOH DYHUDJH LQ WHUPV RI WKH GLVFUHWH )RXULHU WUDQVIRUP UHVXOWV ,Q r ;. D.D. 1O 1O OO $Wf [Qf[Pf H[SM 7LI.PQf $Wf 1$Wf Q P f )RU D VWDWLRQDU\ SURFHVV DQG VHWWLQJ V PQ WKH WZR VXPPDWLRQV FDQ EH GHFRXSOHG DV VKRZQ LQ >@ UHVXOWLQJ ,Q $W [Qf[QVf H[SMLUI V$Wf f 1$W V 0 6LQFH [Qf[QVf IRU V!0 DQG ,I 1}0 WKH OLPLWV RI VXPPDWLRQ FKDQJH VXFK WKDW ;U :W A $W [AQA[4Vf H[SMPI.V$Wf f J 6fÂ§ 7KH VSHFWUDO GHQVLW\ RI [Wf FDQ EH GHILQHG E\ WKH GLVFUHWL]HG :LHQHU .KLQWFKLQH WKHRUHP 6 I f ? $W [Qf[QVf H[SMLUI V$Wf f ; . 6 fÂ§ ZKLFK LV HVVHQWLDOO\ WKH )RXULHU WUDQVIRUP RI WKH GLVFUHWL]HG DXWRn FRUUHODWLRQ IXQFWLRQ [Qf[QVf RI WKH SURFHVV [Wf 6LQFH $I LV WKH IUHTXHQF\ LQWHUYDO EHWZHHQ DGMDFHQW IAnV WKH VSHFWUDO GHQVLW\ FDQ EH ZULWWHQ DV PAGE 50 6 [ f $I r D.D. $I f (TXDWLRQV f DQG f VKRZ WKDW WKHUH DUH WZR URXWHV WKDW FDQ EH WDNHQ WR FDOFXODWH WKH VSHFWUDO GHQVLW\ RI D VLJQDO 2QH FDQ HLWKHU JHQHUDWH WKH GLVFUHWL]HG DXWRFRUUHODWLRQ IXQFWLRQ IURP WKH WLPH VHULHV DQG WKHQ FRPSXWH WKH )RXULHU WUDQVIRUP RU RQH FDQ FDOFXODWH WKH )RXULHU FRHIILFLHQWV DA GLUHFWO\ E\ IDVW )RXULHU WUDQVIRUP ))7f DQG DYHUDJH HDFK VSHFWUXP 7KH ODWWHU PHWKRG ZDV SUHIHUUHG LQ WKLV FDVH VLQFH LW LQYROYHV FDOOLQJ RQO\ RQH RI WKH VWDQGDUG OLEUDU\ VXEURXWLQHV DYDLODEOH RQ WKH +DUULV FRPSXWHU V\VWHP &RPSXWLQJ WKH VSHFWUXP IURP WKH DXWRFRUUHODWLRQ IXQFWLRQ ZRXOG UHTXLUH FDOOLQJ WZR VXEURXWLQHV RQH WR FRPSXWH WKH DXWRFRUUHODWLRQ IXQFWLRQ DQG DQRWKHU WR WDNH WKH )RXULHU WUDQVIRUP 7KLV PHWKRG ZRXOG EH PRUH WLPH FRQVXPLQJ 7KH +DUULV VXEURXWLQH XVHG LV QDPHG ))75& 7KLV VXEURXWLQH FRPn SXWHV WKH IDVW )RXULHU WUDQVIRUP RI D UHDO YDOXHG VHTXHQFH 7LPHVHULHV OHQJWKV XS WR 6 KDYH EHHQ WUDQVIRUPHG E\ WKH VXEURXWLQH YHU\ TXLFNO\ DQG ZLWKRXW DQ\ SUREOHPV $OO YDULDEOHV WUDQVIHUUHG WR WKH VXEn URXWLQH PXVW EH GHILQHG LQ VLQJOH SUHFLVLRQ 6LQFH PDQ\ RI WKH YDULDn EOHV XVHG LQ WKH 0RQWH &DUOR SURJUDP DUH LPSOHPHQWHG LQ GRXEOH SUHFLVLRQ IRU DFFXUDF\ WKH GDWD WR EH SDVVHG RQ DUH VWRUHG LQ VLQJOHSUHFLVLRQ YDULDEOHV EHIRUH FDOOLQJ WKH VXEURXWLQH 7KH FRPSXWHU SURJUDP SURFHHGV DV IROORZV )LUVW WKH SURJUDP FRP L SXWHV WKH DYHUDJH YDOXH RI WKH YHORFLW\ WLPH VHULHV DQG VXEWUDFWV LW IURP WKH GDWD 7KLV QHZ WLPH VHULHV LV WKHQ VWRUHG LQ WKH VLQJOHn SUHFLVLRQ UHDO YHFWRU $*f $ UXQQLQJ DYHUDJH RI WKH DYHUDJH YHORFLW\ LV PDGH IRU HDFK WLPH VHULHV 7KH YHFWRU $*f LV WKH GDWD WR EH WUDQVn IRUPHG E\ WKH ))7 7KH RXWSXW LV H[SUHVVHG LQ WKH FRPSOH[ YHFWRU ;*f PAGE 51 7KH ))7 DOJRULWKP FRPSXWHV WKH IROORZLQJ VXPPDWLRQ f e 7KHUHIRUH WKH VSHFWUDO GHQVLW\ DW IUHTXHQF\ RI WKH WLPH VHULHV LV IRXQG E\ PXOWLSO\LQJ [AfÂ§f E\ LWV FRPSOH[ FRQMXJDWH ; WKHQ PXOWL R SO\LQJ WKH UHVXOW E\ 761 DQG DYHUDJLQJ RYHU PDQ\ WLPH VHULHV 7KH YHORFLW\IOXFWXDWLRQ VSHFWUDO GHQVLW\ LV WKHQ FDOFXODWHG IURP f ,Q RUGHU WR REWDLQ WKH GLIIXVLRQ FRHIILFLHQW RQH VLPSO\ GLYLGHV WKH YHORFLW\IOXFWXDWLRQ VSHFWUDO GHQVLW\ E\ DV LQGLFDWHG LQ HT f 7KH DYHUDJH GLIIXVLRQ VSHFWUXP LV VWRUHG LQ WKH YHFWRU $9*f R 7KH FRQVWDQW 7J1 LV OXPSHG LQWR D VLQJOH QXPEHU WR ,PSURYH FRPSXWDn WLRQ WLPH $OWKRXJK WKH ILUVW 1 FRHIILFLHQWV RI WKH )RXULHU WUDQVIRUP DUH DYDLODEOH RQO\ WKH ILUVW IUHTXHQFLHV ZHUH RXWSXWHG IRU RXU SXUSRVHV 7KH WLPH ZLQGRZ 7J ZDV FKRVHQ WR EH SV JLYLQJ D IUHTXHQF\ UHVROXWLRQ $I 7 f RI *+] V :H DUH QRZ LQ D SRVLWLRQ WR FDOFXODWH WKH YHORFLW\IOXFWXDWLRQ VSHFWUDO GHQVLW\ RI EXON *D$V DW URRP WHPSHUDWXUH .f &DOFXODWLRQV RI WKH ORZIUHTXHQF\ GLIIXVLRQ FRHIILFLHQW '(f DV D IXQFWLRQ RI HOHFn WULF ILHOG XVLQJ WKH WLPHRIIOLJKW DQG VSHFWUDOGHQVLW\ PHWKRGV VKRZ JRRG DJUHHPHQW $W HDFK ILHOG VWUHQJWK WKH VSHFWUD KDYH EHHQ QRUPDOL]HG WR WKHLU ORZIUHTXHQF\ SODWHDX OHYHO VR WKDW WKH UHODWLYH VSHFWUDO VKDSHV FDQ EH FRPSDUHG DV VKRZQ ,Q )LJV DQG )RU WKH ORZILHOG UDQJH PAGE 52 )LJ 1RUPDOL]HG GLIIXVLRQ FRHIILFLHQW VSHFWUDO GHQVLW\ IRU DQG N9FP PAGE 53 )LJ 1RUPDOL]HG GLIIXVLRQ FRHIILFLHQW VSHFWUDO GHQVLW\ IRU DQG N9FP PAGE 54 EHWZHHQ DQG N9FP WKH VSHFWUXP KDV D /RUHQW]LDQ VKDSH ZLWK D KDOIn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f YHORFLW\ ZDYHIRUP Ef VSHFWUDO FKDUDFWHULVWLFV PAGE 57 ZDV UHZULWWHQ WR PRQLWRU WKH HOHFWURQ SRVLWLRQ LQ UHDO VSDFH (OHFWURQV FDQ EH LQMHFWHG IURP D FDWKRGH DW VRPH ZHOOGHILQHG SRVLWLRQ ] f DQG UHPRYHG DW WKH DQRGH DIWHU GULIWLQJ VRPH IL[HG OHQJWK / 7KH LQMHFWHG HOHFWURQ HQHUJ\ DW WKH FDWKRGH FDQ EH WDLORUHG WR DQ\ SUREDELOLW\ GLVn WULEXWLRQ GHVLUHG 7KH SURJUDP VWLOO FRQWDLQV WKH YHORFLW\ WLPHVHULHV FDSDELOLW\ VR WKDW WKH YHORFLW\ VSHFWUDO GHQVLW\ LQIRUPDWLRQ RI VKRUWFKDQQHO GHYLFHV LV REWDLQHG 7KLV PHWKRG LV SK\VLFDOO\ VDWLVI\LQJ LQ WKDW LW LV DQDORn JRXV WR WKH PHDVXUHPHQW RI QRLVH LQ DFWXDO GHYLFHV 7KH SURJUDP GRHV QRW KRZHYHU DFFRXQW IRU QRLVH DVVRFLDWHG ZLWK WKH LQMHFWLRQ SURFHVV $OVR WKH HIIHFWV RI VSDFH FKDUJH DUH QHJOHFWHG E\ DVVXPLQJ D XQLIRUP HOHFWULF ILHOG WKURXJKRXW WKH DFWLYH GHYLFH UHJLRQ $Q RXWOLQH RI WKH DOJRULWKP WR PRQLWRU WKH SRVLWLRQ RI WKH HOHFn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f ] 8 DQG SRVLWLRQ ] =T 9JW DWA f ZKHUH W LV WLPH 9T LV WKH LQLWLDO YHORFLW\ ]J LV WKH LQLWLDO SRVLWLRQ A f9 DQG WKH DFFHOHUDWLRQ D LV JLYHQ E\ T_(_P $W WKH EHJLQQLQJ RI WKH VLPXODWLRQ DQ HOHFWURQ LV LQMHFWHG ZLWK VRPH SRVLWLYH LQLWLDO YHORFLW\ GHULYHG IURP WKH PRGLILHG 0D[ZHOOLDQ YHORFLW\ GLVWULEXWLRQ DW WKH SRVLn WLRQ ] 7KH 0RQWH &DUOR SURJUDP WKHQ JHQHUDWHV WKH FROOLVLRQ IUHH IOLJKW WLPH DFFRUGLQJ WR WKH VWDQGDUG SURFHGXUH DV RXWOLQHG LQ VHFn WLRQ 7KH ILUVW WKLQJ WKDW KDV WR EH GHWHUPLQHG DW WKH EHJLQQLQJ RI HDFK FROOLVLRQ IUHH IOLJKW LV ZKHWKHU DW DQ\ WLPH GXULQJ WKH IOLJKW WKH HOHFn WURQ HYHU JRHV EDFN LQWR WKH FDWKRGH ,Q RWKHU ZRUGV D FKHFN LV PDGH WR VHH LI WKH HOHFWURQ SRVLWLRQ EHFRPHV QHJDWLYH ] f 7KH SRVLWLRQ RI WKH HOHFWURQ REH\V D TXDGUDWLF HTXDWLRQ f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f $ FKHFN LV PDGH WR GHWHUPLQH ZKHWKHU WKH IOLJKW WLPH 7,0(f LV OHVV WKDQ 70,1 ,I LW LV OHVV WKDQ 70,1 WKH PLQLPXP SRVLWLRQ LV GHWHUPLQHG E\ WKH IOLJKW WLPH 7KH PLQLPXP SRVLWLRQ =0,1 GXULQJ WKH HOHFWURQ IOLJKW LV QRZ FDOFXODWHG IURP f XVLQJ 70,1 RU 7,0( ZKLFKHYHU LV VPDOOHU :KHQ =0,1 LV OHVV WKDQ ]HUR =0,1 f WKH SURJUDP FDOFXODWHV DW ZKDW WLPH GXULQJ WKH IOLJKW =0,1 6ROYLQJ f IRU WKH WLPH ZKHQ ] RQH REWDLQV W Y ,YJ D]4@, f VLQFH WKH VPDOOHU RI WKH WZR URRWV RI WKH TXDGUDWLF HTXDWLRQ FRUUHVSRQGV WR WKH ILUVW WLPH WKH HOHFWURQ FURVVHV WKH ERXQGDU\ 7KLV QHZ FDOFXn ODWHG WLPH f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f XVLQJ WKH IUHHIOLJKW WLPH 7KLV ILQDO SRVLWLRQ LV FRPSDUHG WR GHYLFH OHQJWK / WR VHH LI WKH HOHFWURQ ZDV FROOHFWHG E\ WKH DQRGH :KHQ ] / WKH WLPH VHULHV LV XSGDWHG GXULQJ WKH IUHH IOLJKW DQG WKHQ SURFHHGV WR WKH QH[W VFDWWHULQJ VHOHFWLRQ ,I WKH ILQDO SRVLWLRQ LV JUHDWHU WKDQ / WKH H[DFW WLPH WKDW WKH HOHFWURQ SDVVHG WKH DQRGH ERXQGDU\ PXVW EH FDOFXODWHG 7KLV QHZ IOLJKW WLPH LV W Y WY D]4/f@ f DQG LV XVHG LQ XSGDWLQJ WKH WLPH VHULHV $V EHIRUH WKH IODJ LV VHW ZKHQ WKH HOHFWURQ UHDFKHV WKH DQRGH LQGLFDWLQJ LQMHFWLRQ RI DQRWKHU HOHFWURQ IURP WKH FDWKRGH 7KLV WLPH WKRXJK WKH IODJ YDOXH LV HTXDO WR VR DV QRW WR LQWHUIHUH ZLWK NHHSLQJ WUDFN RI WKH QXPEHU RI EDFN VFDWWHULQJ $ EORFN GLDJUDP RI WKH SRVLWLRQPRQLWRULQJ DOJRULWKP LV JLYHQ LQ $SSHQGL[ & 'XULQJ WKH SURFHVV RI HYDOXDWLQJ WKH YHORFLW\ WLPH VHULHV WKH FRXQWHU 1 LV PRQLWRUHG :KHQ WKH DSSURSULDWH WLPH ZLQGRZ OHQJWK 7 Â‘ 1$Wf LV UHDFKHG WKH SURJUDP SURFHHGV ZLWK WKH VSHFWUDO GHQVLW\ V FDOFXODWLRQV DV RXWOLQHG LQ VHFWLRQ (YHU\ WLPH WKH HOHFWURQ DUULYHV DW WKH DQRGH RU VFDWWHUV EDFN WR WKH FDWKRGH D QHZ FHQWUDOYDOOH\ HOHFWURQ LV LQMHFWHG LQWR WKH DFWLYH UHJLRQ WR PDLQWDLQ FRQVWDQW VSDFH FKDUJH 7KH HOHFWURQV LQMHFWHG LQ WKH ] GLUHFWLRQ REH\ D PRGLILHG 0D[ZHOOLDQ GLVWULEXWLRQ >@ 7KH SUREDn ELOLW\ WKDW DQ HOHFWURQ ,V HPLWWHG ZLWK D YHORFLW\ EHWZHHQ YB DQG YB ] ] $Y LV ] PAGE 61 fÂ§ PY fÂ§ PY $3Y f H[S ] f ZKHUH 7 LV WKH ODWWLFH WHPSHUDWXUH 7KH PRGLILHG 0D[ZHOOLDQ GLVWULEXn WLRQ FDQ EH JHQHUDWHG IURP D XQLIRUP GLVWULEXWLRQ ZLWK WKH WHFKQLTXHV RI VHFWLRQ +HUH WKH YDULDEOH (= DVVRFLDWHG ZLWK WKH HQHUJ\ GXH WR WKH YB FRPSRQHQW LV UDQGRPO\ JHQHUDWHG IURP U XVLQJ ] (= NIL7 ORJUf f 7KH DYHUDJH YDOXH RI WKLV GLVWULEXWLRQ LV NJ7 7KH ZDYHYHFWRU RU YHORFLW\f FRPSRQHQW LV IRXQG GLUHFWO\ IURP (= E\ f 2QO\ WKH SRVLWLYH URRW QHHG EH WDNHQ VLQFH QHJDWLYH YDOXHV VLJQLI\ HOHFn WURQ PRWLRQ EDFN LQWR WKH FDWKRGH 7KH HPLWWHG HOHFWURQV DOVR KDYH YHORFLW\ FRPSRQHQWV SHUSHQGLFXODU WR WKH ILHOG GLUHFWLRQ 7KHVH HOHFWURQV REH\ D 0D[ZHOOLDQ GLVWULEXWLRQ LQ HDFK GLUHFWLRQ 7KH HQHUJ\ GLVWULEXWLRQ DVVRFLDWHG ZLWK WKH SHUSHQn GLFXODU YHORFLW\ FRPSRQHQWV FDQ EH H[SUHVVHG LQ D IRUP VLPLODU WR f VR WKH ZDYHYHFWRU FRPSRQHQW NS LV GHWHUPLQHG LQ PXFK WKH VDPH ZD\ XVLQJ f DQG f 7KH DFWXDO PDJQLWXGHV RI WKH WZR SHUSHQn GLFXODU FRPSRQHQWV N[ DQG N\ DUH QRW QHHGHG VLQFH WKH SURJUDP VLPXODWLRQ FRQVLGHUV WKH [\ GLPHQVLRQV WR EH LQILQLWH +RZHYHU WKH WZR FRPSRn QHQWV FDQ EH GHWHUPLQHG E\ JHQHUDWLQJ D UDQGRP SKDVH DQJOH EHWZHHQ DQG LU RQFH WKH PDJQLWXGH RI WKH NS ZDYHYHFWRU LV NQRZQ 7KLV ZRXOG QHHG WR EH GRQH WR JDLQ LQIRUPDWLRQ RQ WKH WUDQVYHUVH GLIIXVLRQ FRHIILFLHQW PAGE 62 %RWK SHUSHQGLFXODU FRPSRQHQWV KDYH DQ DYHUDJH HQHUJ\ HTXDO WR NJ7 7KHUHIRUH WKH WRWDO DYHUDJH HQHUJ\ RI LQMHFWHG HOHFWURQV LQWR WKH DFWLYH UHJLRQ LV NA7 >@ $Q LQWHJHU YDULDEOH QDPHG ,,1LV XVHG WR NHHS WUDFN RI KRZ PDQ\ HOHFWURQV DUH LQMHFWHG IURP WKH FDWKRGH 7KH GLIIHUHQFH EHWZHHQ ,,1DQG WKH QXPEHU RI HOHFWURQV UHWXUQLQJ WR WKH FDWKRGH ,/72 JLYHV WKH QXPEHU RI HOHFWURQV WUDYHUVLQJ WKH HQWLUH OHQJWK RI WKH DFWLYH UHJLRQ WR WKH DQRGH $ FRS\ RI WKH HQWLUH SURJUDP LV OLVWHG LQ $SSHQGL[ 6LPXODWLRQ UHVXOWV 7KH SURJUDP ZDV UXQ IRU *D$V DW URRP WHPSHUDWXUH .f ZLWK WKH VDPH LQWHUYDOOH\ FRXSOLQJ SDUDPHWHUV XVHG WR ILW WKH EXON H[SHULPHQWV LQ VHFWLRQ 7KH OHQJWK RI WKH DFWLYH UHJLRQ ZDV YDULHG IURP WR SP DQG WKH YDOXHV DW WKH HOHFWULF ILHOG ZHUH FKRVHQ EHWZHHQ DQG N9FP $ QXPEHU RI LQWHUHVWLQJ HIIHFWV RQ WUDQVSRUW EHKDYLRU YHUVXV GHYLFH OHQJWK FDQ EH REVHUYHG LQ WKH UHVXOWV SUHVHQWHG LQ 7DEOH )LUVW ZKHQ WKH HOHFWURQV DUH LQMHFWHG LQWR WKH DFWLYH UHJLRQ WKH\ DUH UDSLGO\ DFFHOHUDWHG E\ WKH HOHFWULF ILHOG WR YHU\ KLJK YHORFLn WLHV ,I WKH GHYLFH OHQJWK LV VKRUW WKH HOHFWURQ YHORFLW\ KDV LQVXIILn FLHQW WLPH WR UHOD[ WR WKH VWHDG\VWDWH EXON YHORFLW\ EHIRUH EHLQJ FROOHFWHG E\ WKH DQRGH 7KLV WUDQVLHQW YHORFLW\ SKHQRPHQRQ LV WHUPHG YHORFLW\ RYHUVKRRW >@ $V VKRZQ LQ 7DEOH IRU D JLYHQ ILHOG YDOXH DV WKH GHYLFH OHQJWK LV UHGXFHG WKH DYHUDJH YHORFLW\ WKURXJKRXW WKH DFWLYH UHJLRQ LQFUHDVHV 7KLV LQFUHDVH LQ DYHUDJH YHORFLW\ VLJQLILHV WKH RFFXUUHQFH RI YHORFLW\ RYHUVKRRW QHDU WKH FDWKRGH 6HFRQG WKH DPRXQW RI LQWHUYDOOH\ WUDQVIHU IURP 7 WR / YDOOH\V LV UHGXFHG LQ VKRUW GHYLFHV ,Q )LJ WKH DYHUDJH IUDFWLRQ RI WLPH VSHQW LQ WKH / YDOOH\ GXULQJ WKH VLPXODWLRQ RI N9FP DV D IXQFWLRQ RI PAGE 63 7$%/( 6LPXODWLRQ 5HVXOWV IRU 6KRUW/HQJWK *D$V /HQJWK (OHFWULF )LHOG 9 V$Yf \UDf N9FPf FPVf FPAVf %XON PAGE 64 DFWLYH UHJLRQ OHQJWK LV SUHVHQWHG DQG FRPSDUHG WR WKH EXON *D$V YDOXH ,QMHFWHG HOHFWURQV ZLWK KLJK HQHUJLHV QHDU WKH 7/ HQHUJ\ RIIVHW RI H9 FDQ XQGHUJR LQWHUYDOOH\ WUDQVIHU DIWHU WUDYHOLQJ RYHU VKRUW GLVWDQFHV +RZHYHU VLQFH PRVW RI WKH LQMHFWHG HOHFWURQV KDYH ORZ LQLWLDO HQHUJ\ (DY NJ7f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n WLYH LQFUHDVH LQ WKH QRLVH FKDUDFWHULVWLFV YHUVXV ILHOG VWUHQJWK IRU YDULRXV GHYLFH OHQJWKV DV ZHOO DV IRU D EXON GHYLFH $OVR LQFOXGHG LQ WKH ILJXUH DUH WKH QRUPDOL]HG GLIIXVLRQ FRHIILFLHQW PHDVXUHPHQWV RI D QQQ *D$V PHVD VWUXFWXUH SHUIRUPHG E\ $QGULDQ >@ 7KH GRQRU FRQn FHQWUDWLRQ LQ WKH \P DFWLYH QOD\HU ZDV A FPA 7KH 0RQWH &DUOR GDWD VXSSRUW WKH PHDVXUHPHQWV VKRZLQJ WKDW WKH UHODWLYH LQFUHDVH LQ WKH FXUUHQWQRLVH VSHFWUDO GHQVLW\ PHDVXUHG LQ VKRUW *D$V UHJLRQV LV QRW DV ODUJH DV IRU EXON *D$V PAGE 65 2 nfÂ§RfÂ§4 /fMPf )LJ )UDFWLRQ RI WLPH HOHFWURQV VSHQW LQ / YDOOH\V DW N9FP DV D IXQFWLRQ RI DFWLYH UHJLRQ OHQJWK PAGE 66 6Y 6YR (N9FPf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n IHUHQW FKDUDFWHULVWLFV VXFK DV OHQJWK IUDFWLRQ RI DOXPLQXP FRQWHQW VKHHWFDUULHU FRQFHQWUDWLRQ HWF DUH XVHG LQ WKH H[SHULPHQWV ,Q WKLV GLVVHUWDWLRQ WKH HPSKDVLV LV RQ QRLVH FKDUDFWHUL]DWLRQ VR ILUVW D UHYLHZ RI WKH PHWKRGV RI PHDVXULQJ WKH GHYLFH DF QRLVH WHPSHUDn WXUH 7Q LV JLYHQ :LWK WKH XVH RI QRLVH WHPSHUDWXUH GDWD WKH GLIIXVLRQ FRHIILFLHQW FDQ EH GHWHUPLQHG DV D IXQFWLRQ RI HOHFWULF ILHOG IRU WUDQVn SRUW SDUDOOHO WR WKH $O*D$V*D$V LQWHUIDFH 7KH GLIIHUHQFHV LQ WKH H[SHULPHQWDO UHVXOWV EHWZHHQ WKH WZR LQWHUIDFHV DUH H[DPLQHG DQG FRPn SDUHG WR EXON *D$V EHKDYLRU 'HVFULSWLRQ RI 'HYLFH 6WUXFWXUHV 7KH GHYLFHV XVHG LQ WKH H[SHULPHQWV ZHUH PRGXODWLRQGRSHG ILHOG HIIHFW WUDQVLVWRU VWUXFWXUHV ZLWKRXW WKH JDWH PHWDOL]DWLRQ 7KH DGYDQn WDJH RI WKHVH VWUXFWXUHV ZDV WKDW WKH\ ZHUH UHDGLO\ VXLWDEOH IRU KLJK IUHTXHQF\ PHDVXUHPHQWV DQG GHYLFHPRXQWLQJ SURFHGXUHV $ GLDJUDP RI WKH JDWHOHVV 02')(7 GHYLFH VWUXFWXUH LV SUHVHQWHG LQ )LJ 7KHVH 02')(7 VWUXFWXUHV ZHUH IDEULFDWHG E\ 'U 0RUNRF RI WKH 8QLYHUVLW\ RI ,OOLQRLV 7KH GHYLFHV DUH JURZQ RQ D VHPLLQVXODWLQJ 6,f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n IHUHQFH GHWHUPLQH WKH TXDVLWZRGLPHQVLRQDO HOHFWURQ VKHHW FDUULHU FRQn FHQWUDWLRQ QJ DW WKH LQWHUIDFH $ WKLQ KLJKO\ GRSHG Q FDS OD\HU RI *D$V LV JURZQ WR IDFLOLWDWH RKPLF FRQWDFW IRUPDWLRQ 6RXUFH DQG GUDLQ UHJLRQV DUH GHILQHG E\ SKRWROLWKRJUDSK\ DQG JROG LV GHSRVLWHG IRU FRQn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n FLHV KLJK HQRXJK WR DYRLG WKH JU DQG I QRLVH FRQWULEXWLRQV $W KLJK IUHTXHQFLHV LW EHFRPHV GLIILFXOW WR PHDVXUH WKH DFWXDO WHUPLQDO YROWDJHV DQGRU FXUUHQWV VR LW LV HDVLHU WR PHDVXUH WKH DYDLODEOH SRZHU IURP WKH QHWZRUN 7KLV DYDLODEOH QRLVH SRZHU LV UHODWHG WR WKH QRLVH WHPSHUDWXUH 7Q DV GHVFULEHG LQ &KDSWHU , PAGE 71 7$%/( 'HYLFH 6WUXFWXUH 3DUDPHWHUV &DS OD\HU WKLFNQHVV $f &DS OD\HU GRSLQJ OHYHO FP r [ 'RSHG $O*D$V WKLFNQHVV $f $O*D$V GRSLQJ OHYHO FPf [O [ $OXPLQXP PROH IUDFWLRQ [ 8QGRSHG VSDFHU WKLFNQHVV $f *D$V EXIIHU WKLFNQHVV SPf &RQWDFW UHVLVWDQFH 5F f :LGWK Z SPf /HQJWK / SPf PAGE 72 7KH WHFKQLTXH XVHG WR PHDVXUH WKH QRLVH WHPSHUDWXUH RI WKH GHYLFH XQGHU WHVW '87f LV VLPLODU WR WKH PHWKRG GHYHORSHG E\ *DVTXHW HW DO >@ 7KH PDLQ DGYDQWDJH RI WKLV SDUWLFXODU VFKHPH LV WKDW LW DOORZV PHDVXUHPHQW RI WKH QRLVH WHPSHUDWXUH ZLWKRXW WKH QHHG WR PDWFK WKH '87 WR WKH FKDUDFWHULVWLF LPSHGDQFH IOf DW HDFK ELDV DQG IUHn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f ZKLFK LV FDSDEOH RI UHFHLYLQJ LQSXW IUHTXHQFLHV IURP 0+] WR *+] 7KH QRLVH VRXUFH +3%f LV DOVR EURDGEDQG FRYHULQJ 0+] WR *+] ZLWK DQ HIIHFWLYH QRLVH UDWLR RI G% 7 .f $PSOLILFDWLRQ DQG SRZHU GHWHFWLRQ DUH SHUIRUPHG DW WKH LQWHUPHGLDWH IUHTXHQF\ 0+]f RI WKH VSHFWUXP DQDO\]HU 7KH H[SHULPHQWDO SURFHGXUH FRQVLVWV RI IRXU PHDVXUHPHQWV WR GHWHUn PLQH WKH QRLVH WHPSHUDWXUH 7A RI WKH '87 7KHVH PHDVXUHPHQWV DOVR PDNH DYDLODEOH WKH SRZHU UHIOHFWLRQ FRHIILFLHQW _U_ DW SRUW RI WKH FLUFXn ODWRU WKH QRLVH WHPSHUDWXUH 7J RI WKH PHDVXULQJ V\VWHP DQG WKH JDLQ EDQGZLGWK SURGXFW *% RI WKH V\VWHP 7KH ILUVW PHDVXUHPHQW 0O FRQVLVWV RI D UHIHUHQFH WHPSHUDWXUH VLJn QDO 7F IORZLQJ IURP SRUW LQ WKH SUHIHUUHG GLUHFWLRQ WR SRUW ZKHUH D VKRUWFLUFXLW WHUPLQDWLRQ LV SODFHG 7KH UHIHUHQFH VLJQDO LV WRWDOO\ PAGE 73 )LJ 1RLVH WHPSHUDWXUH PHDVXUHPHQW VHWXS PAGE 74 UHIOHFWHG E\ WKLV VKRUW FLUFXLW DQG SURFHHGV WR WKH DPSOLILHU VWDJHV DW SRUW 7KH DPSOLILHU V\VWHP SURYLGHV SURSHU LPSHGDQFH WHUPLQDWLRQ DW SRUW 7KH PHDVXUHG SRZHU LV WKHQ SURSRUWLRQDO WR 0O N *%7 7 f f % D F ZKHUH N% LV WKH %ROW]PDQQ FRQVWDQW 7KH VHFRQG PHDVXUHPHQW 0 LV HVVHQn WLDOO\ WKH VDPH H[FHSW WKDW WKH UHIHUHQFH WHPSHUDWXUH LV QRZ 7A ZKHUH 7K 7F! JLYLQJ 0 N4*%7D 7IDf f 1RZ WKH VKRUW FLUFXLW DW SRUW LV UHSODFHG E\ WKH '87 ZKLFK LV ELDVHG WR WKH GF YROWDJH RI LQWHUHVW 7KH UHIOHFWLRQ FRHIILFLHQW EHWZHHQ WKH '87 DQG FLUFXODWRU LV GHILQHG LQ WHUPV RI WKH '87 LPSHGDQFH =SX7 DQG WKH FKDUDFWHULVWLF LPSHGDQFH =TT E\ WKH UHODWLRQ ='87 a = ='87 = f 6LQFH WKH '87 KDV LQ JHQHUDO DQ LPSHGDQFH GLIIHUHQW IURP WKH FKDUDFn WHULVWLF LPSHGDQFH RI WKH FLUFXODWRU WKH DYDLODEOH QRLVH SRZHU IURP WKH '87 LV UHGXFHG E\ WKH IDFWRU _U_ f 7KLV SURSHUW\ LV H[SORLWHG LQ WKH QH[W WZR PHDVXUHPHQWV 7KH QRLVH VRXUFH WHPSHUDWXUH LV DJDLQ VHW WR 7F IRU WKH WKLUG PHDVXUHPHQW 6LQFH WKH ORZQRLVH DPSOLILHU VHHV D FRQVWDQW LPSHGDQFH ORRNLQJ LQWR SRUW UHJDUGOHVV RI WKH LPSHGDQFH FKDQJH DW SRUW WKH V\VWHP QRLVH WHPSHUDWXUH 7J UHPDLQV WKH VDPH $OVR WKH UHIHUHQFH WHPn SHUDWXUH LV SDUWLDOO\ UHIOHFWHG DW SRUW EHFDXVH RI WKH PLVPDWFK VR WKH PHDVXUHG SRZHU LV SURSRUWLRQDO WR PAGE 75 0 N%*7D 7QO _U_f 7F_U_f f $ ILQDO UHDGLQJ LV GRQH ZLWK WKH UHIHUHQFH WHPSHUDWXUH DW SURYLGLQJ 0 N%*%7D 7QO _U_f 7K_U_f f 0DQLSXODWLQJ WKHVH IRXU PHDVXUHPHQWV RQH REWDLQV WKH XQNQRZQ GHYLFH QRLVH WHPSHUDWXUH 7 0 0Of 7 0 0f UUL B BK F Q 0 0O 0 0 f DQG WKH SRZHU UHIOHFWLRQ FRHIILFLHQW DV 0 0 0 0 0O f ,W VKRXOG EH SRLQWHG RXW WKDW WKH SDUDPHWHUV GHWHUPLQHG E\ f DQG f DUH DVVRFLDWHG ZLWK WKH QHWZRUN FRQQHFWHG DW WKH UHIHUHQFH SODQH RI SRUW RI WKH FLUFXODWRU ,I WKHUH DUH QR UHVLVWLYH RU UDGLDWLYH ORVVHV EHWZHHQ WKH DFWXDO '87 DQG WKH FLUFXODWRU SRUW WKHQ LV WKH DFWXDO GHYLFH QRLVH WHPSHUDWXUH $Q\ NQRZQ ORVVHV EHWZHHQ WKH '87 DQG FLUFXODWRU FDQ EH HDVLO\ FRUUHFWHG $OVR WKH ORVV EHWZHHQ SRUWV DQG RQO\ DIIHFW WKH YDOXHV RI WKH UHIHUHQFH WHPSHUDWXUHV 7e DQG 7A &RUn UHVSRQGLQJO\ WKH ORVV EHWZHHQ SRUWV DQG DIIHFW RQO\ WKH V\VWHP QRLVH WHPSHUDWXUH 7J 7KH V\VWHP QRLVH WHPSHUDWXUH FDQ EH GHWHUPLQHG IURP 0,7 07 K F 7D 0 0O f DQG WKH JDLQ EDQGZLGWK RI WKH V\VWHP LV JLYHQ E\ PAGE 76 f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Â PLFURVWULS WUDQVPLVVLRQ OLQH WHVW IL[WXUH 7KH PLFURVWULS OLQH ZDV PDGH IURP D PLOWKLFN DOXPLQD VXEVWUDWH DQG DWWDFKHG WR 60$ FRD[LDO FRQQHFWRUV $OO PHDVXUHPHQWV ZHUH PDGH ZLWK D FRYHUHG PRXQW WR NHHS WKH GHYLFH LQ WKH GDUN 7KH ILUVW GHYLFH WR EH PHDVXUHG ZDV ZDIHU 0HDVXUHPHQWV ZHUH GRQH ZLWK D SXOVH ELDV WLPH RI PV DQG D b GXW\ F\FOH DW URRP WHPSHUDWXUH .f 7KH GF FXUUHQWYROWDJH FKDUDFWHULVWLF IRU WKLV SP KHWHURVWUXFWXUH LV GHSLFWHG LQ )LJXUH 7KH ORZILHOG HTXLOLEULXP UHVLVWDQFH LV IRXQG WR EH RKPV $V FDQ EH VHHQ LQ WKH ILJXUH WKH ,9 FKDUDFWHULVWLF EHJLQV WR GHYLDWH IURP 2KPnV ODZ DURXQG P9 7KLV QRQOLQHDU EHKDYLRU LV DQ LQGLFDWLRQ RI KRWHOHFWURQ HIIHFWV LQ WKH FKDQQHO &KDQJLQJ WKH SRODULW\ RI WKH YROWDJH KDG QR PAGE 77 , W 7 $f Fr R A 2 2 R f Z M L n L L L M L L nnnnn 99f )LJ &XUUHQWYROWDJH FKDUDFWHULVWLF RI PAGE 78 HIIHFW RQ WKH ,9 UHODWLRQVKLS LQGLFDWLQJ WKDW WKH FRQWDFWV ZHUH LQGHHG RKPLF DQG KDG QR UHFWLI\LQJ SURSHUWLHV )URP WKH ,9 FKDUDFWHULVWLF RQH FDQ REWDLQ WKH GF PRELOLW\ DV D IXQFWLRQ RI HOHFWULF ILHOG 7KH HOHFWULF ILHOG LQ WKH FKDQQHO LV DVVXPHG WR EH XQLIRUP DQG IRXQG E\ WDNLQJ WKH YROWDJH GURS DFURVV WKH DFWLYH UHJLRQ DQG GLYLGLQJ LW E\ WKH OHQJWK 7KH GHILQLWLRQ RI GF PRELOLW\ LV JLYHQ E\ \(f ;LOO f )LJXUH VKRZV WKH GF PRELOLW\ DV D IXQFWLRQ RI HOHFWULF ILHOG QRUn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n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n WLRQ RI HOHFWULF ILHOG &LUFOHV LQGLFDWH XQJDWHG 02')(7 VTXDUHV LQGLFDWH 5XFK DQG .LQR >@ LQYHUWHG WULDQJOHV LQGLFDWH *DVTXHW HW DO >@ DQG WKH ULJKW VLGHXS WULDQJOHV LQGLFDWH %DUHLNLV HW DO >@ PAGE 83 QRUPDOL]HG GLIIXVLRQ FRHIILFLHQW PHDVXUHPHQWV RI EXON *D$V >@ ,W FDQ EH VHHQ WKDW WKH GLIIXVLRQ FRHIILFLHQW RI WKH KHWHURVWUXFWXUH GRHV QRW LQFUHDVH DV VLJQLILFDQWO\ DV WKH EXON *D$V UHVXOWV 'HYLFH VWUXFWXUH ZDV PHDVXUHG QH[W 2QH RI WKH PDLQ DGYDQn WDJHV RI WKLV VWUXFWXUH ZDV WKDW RQ WKH VDPH ZDIHU GLIIHUHQWOHQJWK GHYLFHV ZHUH DYDLODEOH IRU PHDVXUHPHQW ,Q WKLV ZD\ WKH FRQWDFW UHVLVn WDQFH FRXOG EH GHWHUPLQHG PRUH DFFXUDWHO\ 7KH ORZILHOG RKPLF UHVLVn WDQFH DV D IXQFWLRQ RI GHYLFH OHQJWK LV SORWWHG LQ )LJ 7KH FLUFOHV LQGLFDWH WKH GDWD REWDLQHG E\ XVLQJ WKH ZDIHU SUREH VWDWLRQ DQG WKH WULDQJOHV LQGLFDWH WKH DFWXDO ZLUH ERQGHG YDOXHV 7KH GLVFUHSDQF\ EHWZHHQ WKH WZR GLIIHUHQW PHDVXUHPHQWV LV DWWULEXWHG WR WKH FRQWDFWLQJ SUREOHPV DVVRFLDWHG ZLWK WKH ZDIHU SUREHV +RZHYHU ERWK VHWV RI GDWD H[WUDSRODWH WR WKH VDPH YDOXH DW WKH RULJLQ / f JLYLQJ D FRQWDFW UHVLVWDQFH RI OLIW 7KH FXUUHQWYROWDJH FKDUDFWHULVWLFV RI IRU OHQJWKV RI DQG SP DUH VKRZQ LQ )LJV DQG UHVSHFWLYHO\ %RWK GHYLFHV VKRZHG KRWHOHFWURQ HIIHFWV DW KLJK ELDV +DYLQJ WKH ,9 FKDUDFWHULVWLFV DQG WKH FRQWDFW UHVLVWDQFH LW LV DJDLQ SRVVLEOH WR ILQG WKH GF PRELOLW\ YHUVXV HOHFWULF ILHOG 7KH QRUn PDOL]HG GF PRELOLW\ RI LV JLYHQ LQ )LJXUH 7KHUH ZDV QR GLIIHUHQFH IRXQG LQ WKH GF PRELOLW\ IRU WKH WZR OHQJWKV PHDVXUHG $OVR WKH GF PRELOLW\ EHKDYLRU RI LV YHU\ VLPLODU WR WKDW RI 2EWDLQLQJ WKH 5H PAGE 84 )LJ 5HVLVWDQFH YV OHQJWK IRU WR GHWHUPLQH FRQWDFW UHVLVWDQFH &LUFOHV LQGLFDWH ZDIHU SUREHG YDOXHV ZKHUHDV WULDQJOHV LQGLFDWH ZLUH ERQG YDOXHV PAGE 85 )LJ &XUUHQWYROWDJH FKDUDFWHULVWLF RI / SPf PAGE 86 G $f LG U MMP fÂ§ 7 fÂ§ fÂ§ ? ? ?? R fÂ§ ZR fÂ§ Q r Rn Sn R S BO // ,nOO n ,, UO r 99f )LJ &XUUHQWYROWDJH FKDUDFWHULVWLF RI / \Pf PAGE 87 )LJ 1RUPDOL]HG GF PRELOLW\ YV HOHFWULF ILHOG IRU PAGE 88 ERQGLQJ ZLUHV PDGH LW GLIILFXOW WR REWDLQ D JRRG KLJKIUHTXHQF\ JURXQG DQG WKH ODUJH ZDIHU PD\ LQWURGXFH RWKHU XQDFFRXQWHG IRU SDUDVLWLFV $V D UHVXOW WKH 5H PAGE 89 Â‘ 2r 7Q.f n n fÂ§ 7 SP 9 P9 0OOO_ R R R rr ,, 0LOO R WR I +]f ,n )LJ 1RLVH WHPSHUDWXUH YV IUHTXHQF\ IRU PAGE 90 )LJ 1RLVH WHPSHUDWXUH YV HOHFWULF ILHOG IRU PAGE 91 f , (9FPf )LJ 1RUPDOL]HG GLIIXVLRQ FRHIILFLHQW YV HOHFWULF ILHOG IRU 6TXDUHV DQG FLUFOHV LQGLFDWH DQG \P GDWD UHVSHFWLYHO\ PAGE 92 PRELOLW\ RI ERWK DQG GHFUHDVHV ZLWK LQFUHDVLQJ ILHOG VWUHQJWK LQ WKH KRWHOHFWURQ UHJLPH ZKLFK DOVR DJUHHV ZLWK WKH SUHYLRXVO\ SXEOLVKHG UHVXOWV +RZHYHU WKHUH GRHV VHHP WR EH GLIIHUHQFHV LQ WKH QRLVH EHKDYLRU EHWZHHQ GLIIHUHQW KHWHURLQWHUIDFH FRPSRVLWLRQV )RU GHYLFH WKH GLIIXVLRQ FRHIILFLHQW RU YHORFLW\ IOXFWXDWLRQ VSHFWUDO GHQVLW\f UHPDLQV QHDUO\ FRQVWDQW ZLWK LQFUHDVLQJ ILHOG ZKHUHDV VKRZV D VOLJKW GHFUHDVH LQ WKH KRWHOHFWURQ UHJLPH 7KLV GLIIHUHQFH LQ GLIIXVLRQ FRHIILFLHQWV UHVXOWV PDLQO\ IURP WKH ORZHU QRLVH WHPSHUDWXUH PHDVXUHG LQ %RWK KHWHURMXQFWLRQ LQWHUIDFH VWUXFWXUHV VKRZ D FOHDUO\ GLIIHUHQW QRLVH EHKDYLRU WKDQ EXON *D$V ,Q EXON WKH LQFUHDVH LQ WKH GLIIXVLRQ FRHIILFLHQW ZLWK ILHOG ZDV DWWULEXWHG WR SRODU UXQDZD\ DQG LQWHUYDOOH\ WUDQVIHU VHF f $ GHFUHDVH LQ WKH LPSRUWDQFH RI RQH RU ERWK RI WKHVH PHFKDQLVPV LQ WKH KHWHURLQWHUIDFHV PLJKW EH UHVSRQVLEOH IRU WKH REVHUYHG '(f GHSHQGHQFH 'LIIHUHQFHV GXH WR GHYLFH OHQJWK DUH QRW VXVSHFWHG VLQFH QR QRWLFHDEOH OHQJWK GHSHQGHQFH RI '(f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n FXOW WR PRGHO RU RWKHUZLVH HYDOXDWH KRWHOHFWURQ SURSHUWLHV LQ WKLV UHJLRQ RU ,WV HIIHFW RQ UHDOVSDFHFKDUJH WUDQVIHU 7KH RQO\ DQDO\WLFDO VXSSRUW IRU WKH GLIIXVLRQ FRHIILFLHQW EHKDYLRU LQ WKH KHWHURLQWHUIDFHV LV IURP WKH 0RQWH &DUOR PRGHO RI YDQ 5KHHQHQ DQG %RVPDQ >@ ,Q WKHLU PRGHO WKH\ XVH DQ LQILQLWHO\ KLJK VTXDUH SRWHQn WLDO ZHOO WR VLPXODWH WKH WZRGLPHQVLRQDO WUDQVSRUW EHKDYLRU RI D WZR YDOOH\ *D$V FKDQQHO 7KH GLIIXVLRQ FRHIILFLHQW LQ WKLV VLPXODWLRQ VKRZV D GHFUHDVH ZLWK LQFUHDVLQJ HOHFWULF ILHOG DV RSSRVHG WR WKH LQFUHDVH LQ GLIIXVLRQ REVHUYHG LQ WKHLU EXON VLPXODWLRQ 7KHUHIRUH WKH GHFUHDVH LQ WKH GLIIXVLRQ FRHIILFLHQW ZLWK LQFUHDVLQJ ILHOG LQ WKH KHWHURVWUXFWXUHV LV SRVVLEO\ OLQNHG WR WKH WZRGLPHQVLRQDOLW\ RI WKH HOHFWURQ JDV PAGE 94 &+$37(5 ,9 7+( '& $& $1' 12,6( &+$5$&7(5,=$7,21 2) 7+( $/*$$6*$$6 02')(7 &+$11(/ ,Q UHFHQW \HDUV PXFK DWWHQWLRQ KDV EHHQ SDLG WR $O*D$V*D$V PRGXODWLRQGRSHG ILHOGHIIHFW WUDQVLVWRUV 02')(7Vf IRU SRWHQWLDO XVH LQ KLJKVSHHG ORJLF FLUFXLWV 7KH YHU\ KLJK WUDQVFRQGXFWDQFH JP DQG KLJK FXWRII IUHTXHQFLHV IA DOVR PDNH WKHP RI LQWHUHVW IRU ORZQRLVH PLFUR ZDYH DPSOLILFDWLRQ ([FHOOHQW DUWLFOHV E\ 6RORPRQ DQG 0RUNRF >@ DQG 'UXPPRQG HW DO >@ KDYH EHHQ ZULWWHQ UHYLHZLQJ WKH FKDUDFWHULVWLFV RI WKHVH QHZ WUDQVLVWRUV 6LQFH WKH ILUVW UHSRUW RI WKH QRLVH ILJXUH RI WKHVH GHYLFHV LQ WKH PLFURZDYH IUHTXHQF\ UDQJH DQ LQWHUHVW LQ WKH QRLVH EHKDYLRU KDV GHYHOn RSHG 7KH QRLVH ILJXUHV RI YDULRXV 02')(7V KDYH EHHQ UHSRUWHG UHFHQWO\ DQG VKRZ LPSURYHPHQWV RYHU FRQYHQWLRQDO *D$V 0(6)(7V RI FRPSDUDEOH JDWH OHQJWKV 8S WR QRZ RQO\ QRLVHILJXUH PHDVXUHPHQWV KDYH EHHQ UHSRUWHG LQ WKH PLFURZDYH IUHTXHQF\ UDQJH ,Q WKLV FKDSWHU ZH ZLOO QRW IRFXV RQ WKH QRLVH ILJXUH EXW LQVWHDG UHSRUW RQ WKH QRLVH FKDUDFWHULVWLFV RI WKH )(7 FKDQQHO $W LQWHUPHGLDWH IUHTXHQFLHV I *+]f WKH FKDQQHO QRLVH ,V GXH WR IOXFWXDWLRQV RI WKH IUHHFDUULHU YHORFLW\ DQG LV WKH PDMRU FRQWULEXWRU WR WKH RYHUDOO GHYLFH QRLVH 0HDVXUHPHQWV RI WKH WKHUPDO QRLVH LH YHORFLW\ IOXFWXDWLRQ QRLVHf DV D IXQFWLRQ RI ELDV DUH GLVFXVVHG LQ WKLV FKDSWHU ,Q VHFWLRQ ZH ZLOO RXWOLQH WKH WKHRU\ RI WKH LPSHGDQFH ILHOG PHWKRG ZKLFK LV XVHG WR REWDLQ WKH DF DQG QRLVH SURSHUWLHV RI WKH 02')(7 FKDQQHO 6HFWLRQ H[SODLQV WKH PHWKRGV RI REWDLQLQJ WKH FKDUJHYROWDJH UHODWLRQVKLS IRU WKH GHYLFHV XVHG ,Q RXU H[SHULPHQWV 6RPH RI WKH PHWKRGV RI REWDLQLQJ WKH FKDUJHYROWDJH UHODWLRQVKLS LQYROYH PAGE 95 RQO\ ORZELDV GDWD ZKLOH RWKHU PHWKRGV LQYROYH KLJKELDV GDWD &RPSDUn LQJ WKH UHVXOWV RI WKH GLIIHUHQW PHWKRGV FDQ KHOS GHWHUPLQH WKH SUHVHQFH RU DEVHQFH RI UHDOVSDFHFKDUJH WUDQVIHU 6HFWLRQ GHVFULEHV WKH 02')(7 VWUXFWXUHV WR EH FRQVLGHUHG 0HDVXUHPHQW SURFHGXUHV DUH GLVn FXVVHG LQ VHFWLRQ 7KH H[SHULPHQWDO UHVXOWV ZLOO WKHQ EH SUHVHQWHG DQG GLVFXVVHG LQ VHFWLRQ IROORZHG E\ FRQFOXVLRQV LQ VHFWLRQ ,PSHGDQFH )LHOG 0RGHOLQJ ,Q WKLV VHFWLRQ WKH SURFHGXUH IRU REWDLQLQJ WKH SRVLWLRQGHSHQGHQW DF FKDQQHO YROWDJH LQ WHUPV RI WKH *UHHQnV IXQFWLRQ IRU D 02')(7 FKDQQHO LV GLVFXVVHG ,W ZLOO EH VKRZQ KRZ WKH *UHHQnV IXQFWLRQ LV UHODWHG WR WKH LPSHGDQFH ILHOG >@ 2QFH WKH LPSHGDQFH ILHOG LV REWDLQHG WKH DF DQG QRLVH SURSHUWLHV FDQ EH HDVLO\ FDOFXODWHG 9DQ 9OLHW >@ DQG 1RXJLHU >@ KDYH RXWOLQHG WKLV PHWKRG IRU WKH FDVH RI WKH MXQFWLRQ ILHOGHIIHFW WUDQVLVWRU -)(7f ,Q WKLV FKDSWHU WKH LPSHGDQFH ILHOG IRU D 02')(7 LV FDOFXODWHG XVLQJ WKH SURSHU WUDQVSRUW HTXDWLRQV DQG WKH DF DQG QRLVH SURSHUWLHV RI WKH 02')(7 DUH GHULYHG 5HYLHZ RI LPSHGDQFH ILHOG PHWKRG 7KH SURFHGXUH EHJLQV E\ FRQVLGHULQJ WKH GHYLFH WUDQVSRUW HTXDn WLRQV 6PDOOVLJQDO YDULDWLRQV DURXQG WKH VWHDG\VWDWH YDOXHV RI DOO RI WKH YDULDEOHV DUH LQWURGXFHG +DYLQJ GRQH WKLV DQG QHJOHFWLQJ VHFRQG RUGHU DQG KLJKHU WHUPV WKH DF DQG GF HTXDWLRQV FDQ EH VHSDUDWHG 7KH GF HTXDWLRQ FDQ EH XVHG WR REWDLQ WKH VWHDG\VWDWH FXUUHQWYROWDJH FKDUDFWHULVWLF RI WKH GHYLFH 7KH DF HTXDWLRQ KDV VRPH LQWHUHVWLQJ SURSHUWLHV *HQHUDOO\ WKH DF HTXDWLRQ LQYROYHV WKH SRVLWLRQGHSHQGHQW VWHDG\VWDWH SDUDPHWHUV 7KLV HTXDWLRQ FDQ EH ZULWWHQ DV IROORZV +$9[f $,[f f PAGE 96 ZKHUH + ,V D OLQHDU RSHUDWRU DQG $9 DQG $, DUH WKH VPDOOVLJQDO DF FKDQQHO YROWDJH DQG FXUUHQW UHVSHFWLYHO\ %\ OHWWLQJ ][[nIf EH WKH $ *UHHQnV IXQFWLRQ RI + LH $ +][[nIf [[nf f ZKHUH 6[[nf LV WKH 'LUDF GHOWD IXQFWLRQ DQG I GHQRWHV IUHTXHQF\ WKH WRWDO DF YROWDJH DW SRVLWLRQ [ FDQ EH FDOFXODWHG IURP / $9 [f ][[nIf$,[nfG[n f 7KH LQWHJUDWLRQ LV WDNHQ RYHU WKH HQWLUH OHQJWK RI WKH GHYLFH 7KH WRWDO DF YROWDJH DW [ JLYHQ E\ HT f LV VLPSO\ WKH VXPPDWLRQ RYHU DOO RI WKH VPDOOVLJQDO FXUUHQW VRXUFHV SURSHUO\ ZHLJKWHG E\ WKH WHUPV ][[nIf}G[n 'HSHQGLQJ RQ WKH FKDUJH WUDQVSRUW PHFKDQLVPV LQYROYHG VRPH RI WKH WHUPV ][[nIf PLJKW EH ]HUR 7KLV SRLQW ZLOO EH LOOXVWUDWHG ZKHQ WKH HTXDWLRQV DUH GHYHORSHG IRU WKH 02')(7 2I FRXUVH RQH LV PDLQO\ LQWHUHVWHG LQ WKH YDOXHV RI WKH VPDOOVLJQDO TXDQWLWLHV DW WKH GHYLFH WHUPLQDOV VLQFH WKHVH FDQ EH PHDVXUHG 7KH WRWDO VPDOO VLJQDO YROWDJH DW WKH GHYLFH WHUPLQDO [ /f LV / $9 /f ]/[nIf$,[nfG[n f 7KH RQHGLPHQVLRQDO GHYLFH VKRZQ LQ )LJ LV JURXQGHG DW [ DQG KDV DQ DUELWUDU\ VWHDG\VWDWH GF ELDV DSSOLHG DW [ / 6XSSRVH D FXUUHQW RI YDOXH $,[f LV LQWURGXFHG DW SRVLWLRQ [ $[ DQG H[WUDFWHG DW [ $,[f ZLOO SURGXFH DQ RSHQFLUFXLW YROWDJH UHVSRQVH $9/f DW WKH WHUPLQDO [ /f ,I WKH DF LPSHGDQFH EHWZHHQ SRVLWLRQ [ DQG JURXQG [ f LV JLYHQ E\ =[f WKHQ WKH YROWDJH UHVSRQVH DW / FDQ EH H[n SUHVVHG DV PAGE 97 $O[f )LJ $ VPDOO VLJQDO FXUUHQW $,[f SURGXFHV D YROWDJH UHVSRQVH $9/f DW WKH WHUPLQDO [ / 6WHDG\ GF FXUUHQW ,T DQG YROWDJH 94 DUH LQGLFDWHG PAGE 98 $9/f >=[$[If =[If@$,[f f )RU VPDOO $[ =[$[If =[If $[ } f DQG RQH REWDLQV $9/f 9=[If$,[f$[ f 7KH WHUP 9=[If LV NQRZQ DV WKH LPSHGDQFH ILHOG DQG ZDV ILUVW LQWURn GXFHG E\ 6KRFNOH\ HW DO >@ 7KH LPSHGDQFH ILHOG UHODWHV WKH DF FXUUHQW LQVLGH WKH GHYLFH WR WKH YROWDJH UHVSRQVH DW WKH WHUPLQDOV ,Q WKH OLPLW $[ !f G[ WKH WRWDO DF YROWDJH DW / LV JLYHQ E\ / $9 /f 9=[nIf$,[nfG[n f &RPSDULQJ HTV f DQG f RQH VHHV WKDW 9=[nIf ]/[nIf f 7R ILQG WKH WRWDO GHYLFH LPSHGDQFH DW WKH WHUPLQDOV RQH PDNHV XVH RI WKH IDFW WKDW WKH DF FXUUHQW LV FRQVHUYHG 7KHQ $O[f $, DQG FRQn VHTXHQWO\ $9 /f / / =/f Us 9=[nIfG[n ]/[nIfG[n f 8VLQJ WKH LPSHGDQFH ILHOG RQH FDQ H[SUHVV WKH QRLVH LQ WHUPV RI VSHFWUDO GHQVLWLHV 7KH VSHFWUDO GHQVLW\ RI WKH RSHQFLUFXLW YROWDJH IOXFWXDWLRQV PHDVXUHG DW WKH WHUPLQDOV LV JLYHQ E\ >@ / 6$9 .[nf_9=[nIf_ D[nG\G] ] \ f PAGE 99 ZKHUH .[nf LV WKH VSHFWUDO GHQVLW\ RI WKH FXUUHQW IOXFWXDWLRQV LQ YROXPH G[nG\G] DQG WKH LQWHJUDWLRQ LV FDUULHG RXW RYHU WKH HQWLUH YROXPH RI WKH GHYLFH 8VLQJ HT f WKH VSHFWUDO GHQVLW\ RI I QRLVH JHQHUDWLRQUHFRPELQDWLRQ JUf QRLVH DQG YHORFLW\IOXFWXDWLRQ QRLVH FDQ EH FDOFXODWHG LI WKH SURSHU VRXUFH WHUP .[f LV LQVHUWHG ,Q WKLV FKDSWHU WKH IRFXV LV RQ YHORFLW\IOXFWXDWLRQ QRLVH RQO\ ,W KDV EHHQ VKRZQ LQ &KDSWHU WKDW WKH VSHFWUDO GHQVLW\ RI YHORFLW\ IOXFWXDWLRQV LV GLUHFWO\ UHODWHG WR WKH GLIIXVLRQ FRHIILFLHQW '(f ZKLFK PD\ EH ILHOG GHSHQGHQW 7DNLQJ WKLV HIIHFW LQWR DFFRXQW 1RXJLHU VKRZV WKDW WKH VSHFWUDO GHQVLW\ RI WKH YROWDJH IOXFWXDWLRQV GXH WR YHORFLW\ IOXFWXDWLRQV LQ D RQHGLPHQVLRQDO WUHDWPHQW EHFRPHV >@ / 6$9 $[ffT '>([ff@Q[nf_9=[nIf_ FO[n f ZKHUH $[nf LV WKH FURVVVHFWLRQDO DUHD Q[nf LV WKH FDUULHU GHQVLW\ DQG T LV WKH HOHFWURQ FKDUJH 7KH HTXLYDOHQW FXUUHQWQRLVH VSHFWUDO GHQVLW\ FDQ EH FDOFXODWHG IURP 6 /, f $SSOLFDWLRQ RI WKH LPSHGDQFH ILHOG PHWKRG WR WKH 02')(7 ,Q WKH IROORZLQJ D RQHGLPHQVLRQDO FROOLVLRQGRPLQDWHG WUDQVSRUW PRGHO LV XVHG WR REWDLQ VLPSOH DQDO\WLFDO H[SUHVVLRQV IRU WKH LPSHGDQFH DQG QRLVH RI WKH GHYLFH 7KH DGYDQWDJH RI WKLV DSSURDFK LV WKDW LW SURn YLGHV SK\VLFDO LQVLJKW LQWR WKH DF DQG QRLVH EHKDYLRU RI WKH FKDQQHO &OHDUO\ WKLV WUHDWPHQW EUHDNV GRZQ IRU YHU\ VKRUW VXEPLFURQ GHYLFHV / SPf VLQFH LQ WKDW FDVH WKH XVXDO FRQFHSW RI PRELOLW\ DQG GLIIXn VLRQ QHHGV WR EH JHQHUDOL]HG VHH &RQVWDQW >@f $VVXPLQJ QR OHDNDJH PAGE 100 FXUUHQW WKURXJK WKH JDWH DQG QHJOHFWLQJ ERWK GLIIXVLRQ DQG GLVSODFHPHQW FXUUHQWV WKH FKDUJH WUDQVSRUW HTXDWLRQ LV JLYHQ E\ TZQ >9[f@Y>([f@ f V ZKHUH Z LV WKH JDWH ZLGWK DQG Y>([f@ LV WKH ILHOGGHSHQGHQW FDUULHU YHORFLW\ 7KH VLJQ FRQYHQWLRQ LV DV IROORZV 7KH VRXUFH LV FKRVHQ DW [ WKH GUDLQ DW [ / T 9[f ([f Y>([f@ DQG 7KH WZRGLPHQVLRQDO VKHHW FDUULHU FRQFHQWUDWLRQ Q >9[f@ LV V DVVXPHG WR EH RQO\ D IXQFWLRQ RI WKH ORFDO HOHFWULFDO SRWHQWLDO XQGHU WKH JDWH 9HORFLW\ VDWXUDWLRQ ZLOO FDXVH DFFXPXODWLRQ DQGRU GHSOHWLRQ RI WKH VKHHW FDUULHU FRQFHQWUDWLRQ LQ WKH KLJKILHOG UHJLRQ XQGHU WKH JDWH PDNLQJ HT f LQYDOLG )RU WKLV UHDVRQ WKH PRGHO ZH HPSOR\ RQO\ GHVFULEHV WKH OLQHDU DQG WULRGH UHJLPHV RI WKH FXUUHQWYROWDJH FKDUDFWHULVWLF $W 7 WKH YHORFLW\ILHOG FKDUDFWHULVWLF RI WKH WZRGLPHQVLRQDO HOHFWURQ JDV LV DVVXPHG WR EH LGHQWLFDO WR WKH RQH RI EXON *D$V >@ &RQVHTXHQWO\ Y(f 9 (( f R ZKHUH LV WKH ORZILHOG PRELOLW\ WDNHQ WR EH FP 9 VHF DW URRP WHPSHUDWXUH DQG WKH FULWLFDO ILHOG (e LV FKRVHQ WR EH N9FP :KHQ WKH HOHFWULF ILHOG H[FHHGV N9FP WKH PRGHO >HT f@ QR ORQJHU KROGV GXH WR WKH VDWXUDWLRQ HIIHFWV PHQWLRQHG DERYH 7KH ODUJH FULWLFDO ILHOG (e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f LQ WKH IROORZLQJ ZD\ ,QWURGXFLQJ VPDOOVLJQDO YDULDWLRQV DURXQG WKH VWHDG\VWDWH TXDQWLWLHV RQH REWDLQV , $, GQ QV9f QV9f AfT$9 f f Y(f Y(Tf $( r f 6XEVWLWXWLQJ f f DQG f LQWR f WKH H[SUHVVLRQ IRU WKH GF FXUUHQW EHFRPHV ,4 TZQJ>9[f@X([fO ([f(Ff f DQG IRU WKH DF FXUUHQW DIWHU QHJOHFWLQJ VHFRQGRUGHU WHUPV DQG XVLQJ $( G$9G[ RQH ILQGV $,[f TZQV>94[f@ Jf TZ Af Y(4f$9[f f (TXDWLRQ f UHODWHV WKH DF FXUUHQW DQG YROWDJH DW SRVLWLRQ [ E\ D ILUVWRUGHU GLIIHUHQWLDO HTXDWLRQ $Q DQDO\WLFDO VROXWLRQ LV HDVLO\ REWDLQHG E\ UHDUUDQJLQJ HT f WR WKH IRUP PAGE 102 G\ G[ 3[f\ 4[f f ZKLFK KDV WKH VROXWLRQ \ H[S 3[fG[ U 3[fG[ >H[S4[fG[ F@ f 6LQFH WKH VRXUFH HQG RI WKH 02')(7 LV JURXQGHG $9f DQG WKH LQWHn JUDWLRQ FRQVWDQW YDQLVK &RQVHTXHQWO\ RQH REWDLQV (Q[nf +[[nf f$,[n f L9[!n Lf:9[nf_& 9(F GQ r f}QR(Rnf H[S OÂ‘ mffR:f 9(F f ZKHUH +[[nf LV WKH XQLW VWHS IXQFWLRQ 8SRQ LQWHJUDWLRQ RI WKH H[SRn QHQWLDO WHUP HT f VLPSOLILHV WR ][[nIf 9rnf +[[nf f F TZ8RQV>\R;f@ ,(F f 7KH XQLW VWHS IXQFWLRQ KDV WKH SK\VLFDO VLJQLILFDQFH WKDW WKH DF YROWDJH DW SRVLWLRQ [ RQO\ GHSHQGV RQ WKH DF FXUUHQW YDULDWLRQV LQWURn GXFHG EHWZHHQ WKH VRXUFH [ f DQG SRVLWLRQ [ +HQFH DF FXUUHQW YDULn DWLRQV RQO\ SURSDJDWH D YROWDJH UHVSRQVH WRZDUG WKH GUDLQ HQG RI WKH GHYLFH 7KLV DULVHV EHFDXVH WKH FRQGXFWLRQ LQ D 02')(7 LV GRPLQDWHG E\ GULIW ,I GLIIXVLRQ KDG D VLJQLILFDQW HIIHFW RQ FXUUHQW IORZ DQG KDG WR EH LQFOXGHG WKH DF WUDQVSRUW HTXDWLRQ ZRXOG EHFRPH VHFRQG RUGHU 7KHQ WKH YROWDJH UHVSRQVH RI $,[f ZRXOG SURSDJDWH WR WKH GUDLQ DV ZHOO DV WR WKH VRXUFH WHUPLQDO RI WKH GHYLFH 7KLV HIIHFW ZDV IRXQG LQ VKRUW VSDFHFKDUJHOLPLWHG GLRGHV E\ 7HKUDQ HW DO >@ PAGE 103 7R REWDLQ WKH LPSHGDQFH ILHOG IURP f RQH VXEVWLWXWHV [ / DQG ILQGV f 7KHQ ZLWK WKH KHOS RI HT f RQH GHULYHV IRU WKH GHYLFH LPSHGDQFH f ZKHUH 9/f LV WKH GF YROWDJH DW / +DYLQJ REWDLQHG WKH LPSHGDQFH ILHOG DQG GHYLFH LPSHGDQFH IRU WKH 02')(7 WKH H[SUHVVLRQV IRU WKH QRLVH FDQ EH FDOFXODWHG 7KH VSHFWUDO GHQVLW\ RI WKH RSHQFLUFXLWYROWDJH QRLVH XVLQJ f DQG f EHFRPHV f 7KH VSHFWUDO GHQVLW\ RI WKH FXUUHQW QRLVH FDQ HDVLO\ EH IRXQG IURP HTV f DQG f 2IWHQ WKH H[SUHVVLRQV IRU WKH QRLVH RI D GHYLFH DUH JLYHQ LQ WHUPV RI DQ DF QRLVH WHPSHUDWXUH 7Q(f :LWK WKH KHOS RI WKH JHQHUDOL]HG (LQVWHLQ UHODWLRQ f ZKHUH NJ LV %ROW]PDQQnV FRQVWDQW Xn(f LV WKH GLIIHUHQWLDO PRELOLW\ LH WKH GHULYDWLYH RI WKH YHORFLW\ILHOG FKDUDFWHULVWLF DW D JLYHQ PAGE 104 ILHOG RQH JHWV (Q/f / 6$9 T8ZN% A 7QW([nf@QV>9[nf@G[f f DQG TXQZN5 / 6 Â‘-/-Â M 7 >([ff@Q >9Q[nf@G[n f &O_ILLf9 r F IRU WKH VSHFWUDO GHQVLWLHV RI WKH YROWDJH DQG FXUUHQW QRLVH UHVSHFn WLYHO\ &KDUJH9ROWDJH 'HSHQGHQFH 7R VXFFHVVIXOO\ XVH WKH H[SUHVVLRQV IRU WKH LPSHGDQFH DQG QRLVH LQ WKH FDVH RI D 02')(7 WKH SURSHU UHODWLRQVKLS EHWZHHQ WKH VKHHW FDUULHU FRQFHQWUDWLRQ DQG WKH HOHFWULFDO SRWHQWLDO LQ WKH FKDQQHO KDV WR EH NQRZQ 6HYHUDO DXWKRUV >@ XVHG DQ HIIHFWLYH FDSDFLWDQFH DQG WKUHVKROG YROWDJH WR FDOFXODWH QB9f DV LV XVXDOO\ GRQH LQ D 026)(7 ,Q V DGGLWLRQ WKH\ DVVXPHG D FRQVWDQW PRELOLW\ XS WR VDWXUDWLRQ *RRG DJUHHn PHQW EHWZHHQ H[SHULPHQWDO DQG WKHRUHWLFDO ,9 FKDUDFWHULVWLFV YDV IRXQG IRU VRPH HQKDQFHPHQWPRGH GHYLFHV $OVR WKH WKHUPDO QRLVH ZDV FDOFXODWHG XVLQJ WKHVH PRGHOV >@ +RZHYHU RXU H[SHULPHQWDO ILQGLQJV FRXOG QRW EH H[SODLQHG XVLQJ WKHVH PRGHOV 6ROYLQJ WKH 3RLVVRQ DQG 6FKURGLQJHU HTXDWLRQV VHOIFRQVLVWHQWO\ 9LQWHU >@ VKRZV WKDW IRU WKH 02')(7 VWUXFWXUHV KH FRQVLGHUV WKDW WKH JDWH FDSDFLWDQFH GHSHQGV VWURQJO\ RQ JDWH ELDV 7KLV JDWH ELDV GHSHQn GHQFH RI WKH FDSDFLWDQFH FDQ EH REVHUYHG H[SHULPHQWDOO\ LQ WKH WUDQVFRQn GXFWDQFH PHDVXUHPHQWV RI *XSWD HW DO >@ 7KHUH DUH VHYHUDO H[SHULPHQWDO PHWKRGV IRU REWDLQLQJ WKH FRUUHFW FKDUJHYROWDJH GHSHQGHQFH ,Q WKH ILUVW PHWKRG WKH VPDOOVLJQDO JDWH PAGE 105 WRFKDQQHO FDSDFLWDQFH LV PHDVXUHG DV D IXQFWLRQ RI JDWH ELDV 7KLV FDSDFLWDQFH LV SURSRUWLRQDO WR WKH GHULYDWLYH RI WKH FKDUJHYROWDJH UHODWLRQVKLS ,Q DGGLWLRQ D PHDVXUHPHQW RI WKH ORZ GUDLQ ELDV 9'6 m P9f WRWDO FKDQQHO UHVLVWDQFH DV D IXQFWLRQ RI 9T LV UHTXLUHG 7KLV UHVLVWDQFH LV JLYHQ E\ 5B9Bf 5 5 + MWfÂ§U '6 VV GG TZSQQ 9 f 86 X f ZKHUH 5JJ DQG 5A DUH WKH VRXUFH DQG GUDLQ DFFHVV UHVLVWDQFHV UHVSHFn WLYHO\ DQG / LV WKH JDWH OHQJWK 7KH ODVW WHUP LQ f DFFRXQWV IRU WKH UHVLVWDQFH RI WKH FKDQQHO UHJLRQ XQGHU WKH JDWH 7DNLQJ WKH GHULYDn WLYH RI f ZLWK UHVSHFW WR 9T RQH REWDLQV GQ U e AG9 G5'6A9*A GY TAQV9*f f ,W LV FOHDU IURP HT f DQG WKH FDSDFLWDQFH PHDVXUHPHQWV WKDW RQH KDV HQRXJK LQIRUPDWLRQ WR REWDLQ WKH FKDUJHYROWDJH UHODWLRQVKLS ZLWKRXW WKH NQRZOHGJH RI WKH DFFHVV UHVLVWDQFHV 5JJ DQG 5A 'LUHFW PHDVXUHPHQWV RI WKH JDWH FDSDFLWDQFH RQ VPDOO JHRPHWU\ 02')(7V / SPf PD\ SURYH WR EH GLIILFXOW DQGRU LQDFFXUDWH EHFDXVH RI SDUDVLWLF HIIHFWV ,I RQH KDV ODUJH DUHD GHYLFHV IDEULFDWHG RQ WKH VDPH ZDIHU PHDVXUHPHQWV RI WKLV VRUW FRXOG EH GRQH $ VHFRQG DSSUR[LPDWH PHWKRG LV WR XVH HT f DQG HVWLPDWH WKH YDOXH RI 5JJ 5A 7KH FKDUJHYROWDJH UHODWLRQVKLS LV WKHQ GLUHFWO\ REWDLQDEOH ZLWKRXW NQRZOHGJH RI WKH FDSDFLWDQFH (VWLPDWHV RI WKH YDOXH RI 5JV 5AM FDQ EH PDGH ZLWK WKH KHOS RI FDOFXODWLRQV IRU KHWHURMXQF WORQ OLQHXS LQ HTXLOLEULXP >@ DQG WKH TXDVLWULDQJXODU SRWHQWLDOZHOO DSSUR[LPDWLRQ 7KHVH FDOFXODWLRQV DUH H[SHFWHG WR JLYH VKHHW FDUULHU PAGE 106 FRQFHQWUDWLRQV RI UHDVRQDEOH HQRXJK DFFXUDF\ WR REWDLQ WKH HQG UHVLVn WDQFHV )LQDOO\ D WKLUG PHWKRG LV LQWURGXFHG WR REWDLQ WKH FKDUJHYROWDJH UHODWLRQVKLS ,W LQYROYHV WKH VPDOOVLJQDO LPSHGDQFH RI WKH FKDQQHO IRU DQ\ YDOXH RI GUDLQ ELDV IRU ZKLFK WKH LPSHGDQFH ILHOG PRGHO RXWOLQHG HDUOLHU KROGV 3RVLWLRQ /M VHH )LJ f LV WKH SRLQW WDNHQ WR EH WKH GUDLQVLGH HGJH XQGHU WKH JDWH $W WKLV SRLQW WKH PD[LPXP HOHFWULF ILHOG LQ WKH FKDQQHO LV SURGXFHG ,WV YDOXH LV QRW DOORZHG WR H[FHHG WKH SHDN ILHOG YDOXH RI N9FP LQ RXU LPSHGDQFH ILHOG PRGHO 7KH FKDUJH DW LV FRQWUROOHG E\ WKH JDWH YROWDJH 7KH LPSHGDQFH DW LV JLYHQ E\ >FI HT f@ =/;f ( / f/ 9/ f /L L /f 7 -" 7 ( / F f :LWK UHDVRQDEOH NQRZOHGJH RI WKH GUDLQ UHVLVWDQFH 5MA WKHQ WKLV LPSHn GDQFH LV m9 =/f 5GG DQG WKH GF YROWDJH DW LV f 99 9'6 9GG f 7KHQ IURP HT f D YDOXH IRU (J/Af FDQ EH FDOFXODWHG XVLQJ WKH PHDVXUHG FXUUHQW DQG LPSHGDQFHYROWDJH FKDUDFWHULVWLFV DQG WKH VKHHW FDUULHU FRQFHQWUDWLRQ DW /M IROORZV IURP HT f ,Q WKLV ZD\ WKH FKDUJHYR,WDJH UHODWLRQVKLS LV REWDLQHG LQ WKH SUHVHQFH RI KLJK HOHFWULF ILHOGV XQGHU WKH JDWH ,I WKLV PHWKRG JLYHV UHVXOWV IRU Q 9f VLPLODU V PAGE 107 * n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n WULQVLF $O*D$V VSDFHU OD\HU ZLWK DQ DOXPLQXP PROH IUDFWLRQ [ ZDV JURZQ RQ WRS IROORZHG E\ D $ OD\HU RI $O*D$V GRSHG WR D OHYHO RI fÂ§ [ FP 7KH VHFRQG GHYLFH f PHDVXUHG KDG D \PWKLFN *D$V EXIIHU OD\HU $ VSDFHU OD\HU ZLWK DOXPLQXP PROH IUDFWLRQ [ fa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n WHULVWLF RI HDFK GHYLFH ZDV PHDVXUHG IURP WKH OLQHDU UHJLRQ XS LQWR VDWXUDWLRQ XVLQJ D GLJLWDO RVFLOORVFRSH 7KH QRLVH PHDVXUHPHQW VFKHPH LV VKRZQ LQ )LJ DQG LV D PRGLn ILHG YHUVLRQ RI WKH VHWXS GHVFULEHG LQ &KDSWHU ,,, )URP D VHULHV RI IRXU PHDVXUHPHQWV DW HDFK ELDV VHWWLQJ WKH QRLVH WHPSHUDWXUH 7U RI WKH GHYLFH XQGHU WHVW '87f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n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f RI WKH V\VWHP 7KH QRLVH JHQHUDWRU LV XVHG DV D FDOLEUDWLRQ QRLVH VRXUFH DV ZHOO DV IRU WKH SXUSRVH RI PDWFKLQJ WKH '87 $ FLUFXODWRU LV XVHG WR FRXSOH ERWK WKH GHYLFH QRLVH DQG WKH FDOLEUDWLRQ QRLVH JHQHUDWRU WR WKH DPSOLILHU VWDJHV 7KH FRQWULEXWLRQ IURP WKH QRLVH JHQHUDWRU VHHQ E\ WKH DPSOLn ILHU VWDJHV GHSHQGV RQ WKH UHIOHFWLRQ FRHIILFLHQW VHHQ DW SRUW RI WKH FLUFXODWRU 6LQFH WKH LPSHGDQFH OHYHOV RI WKH 02')(7 FKDQQHO IURP WKH OLQHDU WR VDWXUDWLRQ UHJLPHV GR QRW FDXVH ODUJH PLVPDWFKHV IURP WKH FKDUDFWHULVWLF LPSHGDQFH WKH WXQHU LV QRW DOZD\V QHHGHG 0HDVXUHPHQWV RI 7IO REWDLQHG ZLWK DQG ZLWKRXW WKH WXQHU DJUHHG ZHOO ZLWKLQ WKH H[SHULn PHQWDO HUURU ,I WKH WXQHU LV RPLWWHG WKH FKDQQHO UHIOHFWLRQ FRHIILn FLHQW DQG WKH QRLVH FDQ EH PHDVXUHG VLPXOWDQHRXVO\ 8VLQJ EURDGEDQG FLUFXODWRUV DQG DPSOLILHUV D IUHTXHQF\ UDQJH IURP 0+] WR *+] FRXOG EH FRYHUHG $ UDQJH RI IUHTXHQFLHV QHHGV WR EH PHDVXUHG WR GHWHUPLQH ZKHWKHU WKH QRLVH VSHFWUXP LV LQGHHG ZKLWH )UHn TXHQF\ VHOHFWLRQ LV REWDLQHG IURP WKH VSHFWUXP DQDO\]HU ZKLFK VKLIWV WKH KLJKIUHTXHQF\ QRLVH VLJQDO WR DQ LQWHUPHGLDWH IUHTXHQF\ ,)f RI 0+] $W WKLV IUHTXHQF\ IXUWKHU DPSOLILFDWLRQ DQG SRZHU GHWHFWLRQ DUH SHUIRUPHG 7KLV V\VWHP KDV WKH DGYDQWDJH WKDW WKH QRLVH RI WKH '87 FDQ EH PHDVXUHG XQGHU FRQWLQXRXV RU SXOVH ELDV ,I WKH PHDVXUHPHQW LV GRQH XQGHU SXOVH ELDV WKH 5) VZLWFK DQG WKH SXOVH ELDV JHQHUDWRU DUH PAGE 112 V\QFKURQL]HG VR WKDW RQO\ QRLVH JHQHUDWHG GXULQJ WKH ELDV SXOVH LV PHDVXUHG 2QFH WKH DF QRLVH WHPSHUDWXUH LV NQRZQ WKH '87 HTXLYDOHQW FXUUHQWQRLVH VSHFWUDO GHQVLW\ LV REWDLQHG IURP 6BIf N 7 5H PAGE 113 >P$@ 9 9GV&9@ )LJ &XUUHQWYROWDJH FKDUDFWHULVWLF RI DW 94 9 7KH EODFN GRWV SUHVHQW WKH H[SHULPHQWDO GDWD 7KH VROLG OLQH LQGLFDWHV WKH UHVXOWV RI RXU PRGHO DQG WKH GDVKHG OLQH LQGLFDWHV WKH UHVXOWV RI WKH FRQVWDQW FDSDFLWDQFH DQG PRELOLW\ PRGHO PAGE 114 6Y>9 9+]@ 1, ? A Z )LJ 9ROWDJH DQG FXUUHQW QRLVH VSHFWUDO GHQVLWLHV DV D IXQFn WLRQ RI GF FXUUHQW ,T 7KH VROLG OLQH LQGLFDWHV WKH UHVXOWV RI WKH LPSHGDQFH ILHOG PRGHO RXWOLQHG LQ WKH WH[W XVLQJ '(f 'T 7KH GDVKHG OLQH LQGLFDWHV WKH UHVXOWV RI WKH FRQVWDQW FDSDFLWDQFH DQG PRELOLW\ PRGHO PAGE 115 QR PHWKRG ,,,f $ GUDLQ UHVLVWDQFH 5A RKPV ZDV XVHG 7KLV YDOXH UHVXOWV IURP HTXLOLEULXP FDOFXODWLRQV IRU KHWHURMXQFWLRQ OLQHXS $OWKRXJK FDOFXODWLRQV DQG PHDVXUHPHQWV >@ VKRZ WKDW WKH GLIn IXVLRQ FRHIILFLHQW EHJLQV WR LQFUHDVH QHDU N9FP IRU EXON *D$V ZH DVVXPH WKDW '(f 'T $OVR PHDVXUHPHQWV RI WKH GLIIXVLRQ FRHIILFLHQW RQ JDWHOHVV 02')(7 VWUXFWXUHV VKRZQ LQ &KDSWHU ,,, GR QRW LQFUHDVH ZLWK ILHOG DV LQ EXON IXUWKHU MXVWLI\LQJ RXU DVVXPSWLRQ 7KH GDVKHG OLQHV LQ )LJV DQG DUH WKH SUHGLFWHG SHUIRUn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f FORVH WR WKH 02')(7 WR HPSW\ WKHVH WUDSV +RZHYHU WKLV PHWKRG LV QRW VXLWDEOH LQ QRLVH PHDVXUHPHQWV VLQFH WKH /(' PD\ FDXVH FKDQJHV LQ WKH QRLVH WHPSHUDWXUH RI WKH HOHFWURQ JDV $IWHU UHWXUQLQJ WKH GHYLFH WR URRP WHPSHUDWXUH WKH VWDWLF ,9 FKDUDFWHULVWLF KDG FKDQJHG JLYLQJ D ORZHU VDWXUDWLRQ FXUUHQW DQG KLJKHU UHVLVWDQFH LQ WKH OLQHDU UHJLPH 6LQFH WKH GHYLFH KDG QRW EHHQ KHUPHWLn FDOO\ VHDOHG ZKHQ ORZHUHG LQWR WKH OLTXLGQLWURJHQ EDWK WKH QXPEHU RI PAGE 116 ,OO VXUIDFH VWDWHV ,Q UHJLRQV DQG ,,, PLJKW KDYH EHHQ FKDQJHG PRGXODWLQJ WKH ZLGWK RI WKH VXUIDFH DQG $O*D$V*D$V LQWHUIDFH GHSOHWLRQ UHJLRQV DQG KHQFH 5JJ DQG 5A 7KLV ZRXOG UHVXOW LQ DQ LQFUHDVH LQ WKH DFFHVV UHVLVWDQFHV DQG DFFRXQW IRU WKH ORZHU VDWXUDWLRQ FXUUHQW ,W LV DVVXPHG WKDW WKH JDWH PHWDOOL]DWLRQ SURWHFWHG WKH VXUIDFH LQ UHJLRQ ,, 7KLV VHHPV WR EH MXVWLILHG E\ WKH PHDVXUHPHQWV RI WKH WUDQVFRQGXFWDQFH DQG FKDUJHYROWDJH UHODWLRQVKLS ERWK EHIRUH DQG DIWHU FRROLQJ 7KH ,9 FKDUDFWHULVWLF DQG QRLVH DW 7 DIWHU D FRROLQJ F\FOH DUH VKRZQ LQ )LJV DQG UHVSHFWLYHO\ 7KHUH LV OLWWOH FKDQJH LQ WKH EHKDYLRU RI WKH QRLVH FKDUDFWHULVWLFV 6LQFH WKH WRWDO FKDQQHO UHVLVWDQFH KDV FKDQJHG WKH OHYHOV RI WKH QRLVH DUH VOLJKWO\ GLIIHUHQW 2XU PRGHO DJDLQ VKRZV JRRG DJUHHPHQW ZLWK H[SHULPHQW 6KRZQ LQ )LJ DUH WKH UHVXOWV IRU WKH FKDUJHYROWDJH UHODWLRQn VKLS REWDLQHG XVLQJ WZR GLIIHUHQW PHWKRGV 7KH WULDQJOHV LQGLFDWH WKH UHVXOWV IRU QJ9Jf FDOFXODWHG XVLQJ PHWKRG ,,, ZLWK DQ LQFUHDVHG GUDLQ UHVLVWDQFH RI RKPV DIWHU FRROLQJ 7KH FLUFOHV UHSUHVHQW WKH YDOXHV GHWHUPLQHG ZLWK WKH KHOS RI PHWKRG ,, ZLWK 5JJ 5A [ RKPV 7KH FKDUJHYROWDJH GHSHQGHQFH FKRRVLQJ VOLJKWO\ GLIIHUHQW WRWDO DFFHVV UHVLVWDQFHV HTXDO WR RKPV LV LQGLFDWHG E\ WKH VTXDUHV 1RWH WKDW PHWKRG ,,, LQYROYHV KLJKILHOG UHJLRQV XQGHU WKH JDWH ZKLOH PHWKRG ,, DVVXPHV D ORZILHOG RKPLF UHJLPH XQGHU WKH JDWH )URP WKH IDFW WKDW ERWK PHWKRGV JLYH LGHQWLFDO UHVXOWV IRU Q ZH FRQFOXGH WKDW V WKH YHORFLW\ILHOG FXUYH XVHG LQ RXU PRGHO FRUUHFWO\ GHVFULEHV WKH FKDUJH WUDQVSRUW XQGHU WKH JDWH DQG VHFRQGO\ WKDW UHDOVSDFHFKDUJH WUDQVIHU LQ WKH JDWH UHJLRQ RI D 02')(7 LV DEVHQW 0HDVXUHPHQWV RI WKH ,9 FKDUDFWHULVWLF DQG WKH VSHFWUDO GHQVLW\ RI WKH FXUUHQW QRLVH LQ GHYLFH DUH VKRZQ LQ )LJV DQG PAGE 117 )LJ &XUUHQWYROWDJH FKDUDFWHULVWLF RI DW 9T 9 DQG 7 DIWHU FRROLQJ F\FOH PAGE 118 ORPDf )LJ 9ROWDJH DQG FXUUHQW QRLVH VSHFWUDO GHQVLWLHV DV D IXQFWLRQ RI GF FXUUHQW ,T IRU DW 9T 9 DQG 7 DIWHU FRROLQJ F\FOH PAGE 119 r 7 QV [,2 Â’ FPf R DD R R$r R r $T$ 4 Â’ $ Â’ $ 4 D D 7 O L L O 2 9J9f )OJ &KDUJHYROWDJH UHODWLRQVKLS RI GHYLFH 7KH FLUn FOHV DQG VTXDUHV LQGLFDWH GDWD REWDLQHG ZLWK PHWKRG ,, ORZ ILHOGf XVLQJ 5VJ DQG RKPV UHVSHFn WLYHO\ 7ULDQJOHV LQGLFDWH PHWKRG ,,, KLJK ILHOGf ZLWK 5MA RKPV PAGE 120 UHVSHFWLYHO\ DQG ZHUH GRQH DW WKH JDWH ELDV RI PD[LPXP WUDQVFRQGXFWDQFH 9T 9 1RWH WKH ODFN RI VWURQJ FXUUHQW VDWXUDWLRQ DW KLJKHU ELDV 0HDVXUHPHQWV RI WKH UHIOHFWLRQ FRHIILFLHQW 7 DQG 6SDUDPHWHU GDWD LQGLn FDWH WKDW WKH UHDO SDUW RI WKH RXWSXW DGPLWWDQFH YDULHV VWURQJO\ ZLWK IUHTXHQF\ 7KH PHDVXUHG VSHFWUDO GHQVLW\ RI WKH FXUUHQW QRLVH RI GHYLFH VKRZV D IUHTXHQF\GHSHQGHQW EHKDYLRU LQGLFDWLQJ WKDW JHQHUDWLRQ UHFRPELQDWLRQ JUf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n GDQFH ILHOG 7KH LPSHGDQFH ILHOG ZDV WKHQ GHULYHG IRU WKH 02')(7 FKDQn QHO &DOFXODWLRQV XVLQJ WKH LPSHGDQFH ILHOG PRGHO VKRZ H[FHOOHQW DJUHHn PHQW ZLWK PHDVXUHPHQWV 0HWKRGV RI REWDLQLQJ WKH FRUUHFW FKDUJHYROWDJH UHODWLRQVKLS XQGHU WKH JDWH UHJLRQ DUH H[DPLQHG 7KH FKDUJHYROWDJH UHODWLRQVKLS REWDLQHG ZLWK ORZ DQG KLJK ILHOGV LQ WKH FKDQQHO VKRZ H[FHOOHQW DJUHHPHQW LQGLFDWLQJ WKDW UHDOVSDFHFKDUJH WUDQVIHU LV QRW SUHVHQW LQ WKH ELDV UDQJH XS WR VDWXUDWLRQ $OVR LW ZDV VKRZQ WKDW SRRU LQWHUIDFH JURZWK VWURQJO\ DIIHFWV WKH QRLVH LQ WKH FKDQQHO RI 02')(7V PAGE 121 PDf 7 / 9G9f )LJ &XUUHQWYROWDJH FKDUDFWHULVWLFV RI GHYLFH DW JDWH ELDV 9* 9 DQG 7 PAGE 122 R 6DL $+]f 7 DR'DRF[UD Â’ R R R Â’ R Â’ R % L r ORPDf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n GLQDO FKDUDFWHULVWLFV :LWK WKH DGGLWLRQ RI PRQLWRULQJ WKH WUDQVYHUVH YHORFLW\ FRPSRn QHQWV RQH FRXOG REWDLQ WKH HOHFWURQ SRVLWLRQ LQ WKH SODQH SHUSHQGLFXn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n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f LQ ZKLFK HOHFWURQ WUDQVSRUW RFFXUV 02')(7 &KDUDFWHUL]DWLRQ &KDSWHU ,9 KLJKOLJKWHG WKH LPSHGDQFH ILHOG WHFKQLTXH DQG KRZ WR DSSO\ WKH PHWKRG WR WKH PRGHOLQJ RI WKH PRGXODWLRQGRSHG ILHOGHIIHFW WUDQVLVWRU 02')(7f 7KH PRGHO ZDV EDVHG RQ D FROOLVLRQGRPLQDWHG PDFURVFRSLF WUHDWPHQW RI WKH WUDQVSRUW SDUDPHWHUV LQ WKH DFWLYH FKDQQHO UHJLRQ *RRG UHVXOWV EHWZHHQ WKH WKHRUHWLFDO DQG H[SHULPHQWDO GF DF DQG QRLVH SURSHUWLHV ZHUH REWDLQHG ([WHQVLRQV FDQ EH PDGH H[SHULPHQWDOO\ LQ WKH GHWHUPLQDWLRQ DQG FKDUDFWHUL]DWLRQ RI WKH FXUUHQW QRLVH REVHUYHG DW WKH JDWH WHUPLQDO ZKLFK SURIRXQGO\ DIIHFWV WKH KLJKIUHTXHQF\ QRLVH ILJXUH $OVR FRPn SDUDWLYH VWXGLHV RI WKH QRLVH SURSHUWLHV EHWZHHQ GLIIHUHQW 02')(7 LQWHUIDFH FRPSRVLWLRQV DQG FRQYHQWLRQDO 0(6)(7V PLJKW SURYLGH LQVLJKW LQWR WKH SK\VLFDO PHFKDQLVPV UHVSRQVLEOH IRU WKH LPSURYHPHQW LQ WKH QRLVH ILJXUH REVHUYHG LQ 02')(7V ZKLFK DUH SUHVHQWO\ XQNQRZQ )RU WKH DUHD RI PRGHOLQJ LPSURYHPHQWV FDQ EH PDGH LQ WKH FDVH RI YHU\ VKRUW JDWHOHQJWK GHYLFHV +HUH WKH FROOLVLRQGRPLQDWHG PRGHOV XVHG LQ &KDSWHU ,9 EUHDN GRZQ DQG D PRUH PLFURVFRSLF DSSURDFK PD\ EH QHFHVVDU\ 7KH DVVXPSWLRQ WKDW WKH YHORFLW\ IOXFWXDWLRQV DUH XQFRUUHn ODWHG LQ VSDFH ZKHQ WKH DFWLYH GHYLFH OHQJWK EHFRPHV FRPSDUDEOH WR WKH PHDQ IUHH SDWK UHTXLUHV IXUWKHU FRQVLGHUDWLRQ PAGE 126 $33(1',; $ 0217( &$5/2 (/(&7521 75$163257 $/*25,7+0 PAGE 127 $33(1',; % 9(/2&,7< 7,0( 6(5,(6 $/*25,7+0 PAGE 128 $33(1',; & 326,7,21021,725,1* $/*25,7+0 PAGE 129 $33(1',; 0217( &$5/2 &20387(5 352*5$0 PAGE 130 & &20387(5 6,08/$7,21 2) 7+( ',))86,21 &2()),&,(17 & $1' 9(/2&,7< )/8&78$7,21 63(&7580 2) & (/(&75216 ,1 6+257 /(1*7+ *$$6 '(9,&(6 & U '28%/( 35(&,6,21} .% .5+2.=) .=,.7 0 121(1,.=7279$9*9$9*9$9*9$9*',) ',) )7 7) 9, 7727 7,0 7,0 7,0 0$;( 7,0(97,0;;7,0(;'7.=,9.=)972797 %==,170,1=0,1/*7+$&&(/ '28%/( 35(&,6,1r )f*$00$f()f6&$77Of '.f/f ,17(*(5} 1):957796566.*0$;1',)0$;11 &20021 $f9=f; &203/(; ;f 5($/ )5(4f:.f$9f ,17(*(5 ,:.f1,,1-,/72,)/$* & )81'$0(17$/ &2167$176 + ( & O_ .% 0 & '$7$ 21 0$7(5,$/ *$$6 r :5,7(f )250$72;n0$7(5$/ '(16,7<*0&0f nf 5($'f5+( :5,7(f )250$7;n9(/2&,7< 2) 6281'r}&06fnf 5($'f6 :5,7(f )250$72;n+,*+ )5(48(1&< ',(/(&75,& &2167$17nf 5($'f5 :5,7(f )250$72;n/2: )5(48(1&< ',(/(&75,& &2167$17ff 5($'f5 :5,7(f )250$72;n237,&$/ 3+2121 )5(48(1&<}r5$'6fnf 5($'f:2 :5,7(f )250$72;r(48 ,17(59$//(< 3+2121 )5(4nf 5($'f:( :5,7(f )250$7;n121(48,9 ,17(59$//(< 3+2121 )5(48(1& PAGE 131 :5,7(f )250$7;n (48 ,17(5 &283/,1* &2167 //}f 5($'f7+(// :5,7(f7+(// :5,7(f )250$72;n(48 ,17(5 &283/,1* &2167 ;;rf 5($'f7+(;; :5,7(f7+(;; :5,7(f :5,7(f )250$722; n121 (48 ,17(5 &283/,1* */rf 5($'f7+,*/ :5,7(f7+,*/ :5,7(f7+,*/ :5,7(f )250$72;n 121 (48 ,17(5 &283/,1* *;rf 5($'f7+,*; :5,7(f7+,*; :5,7( f )250$72;r121 (48 ,17(5 &283/,1* /;nf 5($' f7+,/; :5,7(f7+,/; :5,7(f )250$7;n*/ 9$//(< 6(3$5$7,21nf 5($'f' :5,7(f' :5,7(f )250$72;n*; 9$//(< 6(3$5$7,21nf 5($'f' :5,7(f' :5,7(f )250$72;n&(175$/*f 9$//(< ())(&7,9( 0$66nf 5($'f(0 :5,7(f(0 :5,7(f )250$72;n/ 9$//(< ())0$66nf 5($'f(0 :5,7(f(0 :5,7(f )250$722;n; 9$//(< ())0$66ff 5($'f(0 :5,7(f(0 )250$722;(8f )250$7(f & ),1$/ '$7$ ,1387 :5,7(f )250$72;n7(03(5$785(.(/9,1fnf 5($'f 7 )250$7(f :5,7(f )250$722; n0$;,080 (1(5*<(9f ff 5($'f (0$; PAGE 132 )50$7(f :5,7(f )250$72;n180%(5 2)$9(5$*(6rf 5($'f 1',) )250$7f & ,)7+,1(22f *2 72 ,)1',)/(f *2 72 :5,7(f )250$72;n0$;,080 &2//,6,216 ,1 21( 9$//(< nf *2 72 ,)1',)/(f *2 72 :5,7(f )250$72 2; n0$;,080 &2//,6,216 ,1 7:2 9$//(<6 nf *2 72 :5,7(f )250$72 2;n180%(5 2) (/(&75,& ),(/'6nf 5($'f 1) )250$7f '2 1) :5,7(f )250$72 2;n),(/'r f 5($'f ),f )250$7(f &217,18( :5,7(f )250$7;n9$//(< )25 ',675,%87,21 )81&7,21 nf 5($'f : )250$7f :5,7(f )250$72 2;f',67$1&( )520 .= $;,6 2) ',675,%87,21 72 nf 5($'f 95 )250$7f & & &$/&8/$7( 3+2121 )5(48(1&,(6 $1' 2&&83$7,21 5$7,26 & +:2 +r:2(rf +:, +:,(rf +:( +r:((rf ,) :2 1(f *2 72 1 *2 72 12 (;3:2}f7ff 1, (;3:,rf7ff 1( (;3:(}f7ff & & &2167$176 )25 6&$77(5,1* 5$7(6 & 32/$5 237,&$/ ($ & 2(m&m&r64570f}:2m55ff12fr+m6457(ff & &m11f & $&2867,& %27+ ($f & (rr0frrr.%}7r7+$r7+$r(r(6457(frm5+( r6r6r+r+r+r+f & (48,9$/(17 ,17(59$//(< PAGE 133 & // ($ & 2( r0mr r7+(// r7+(// r( r( r 1( fr6457(f r f r5+(r:(r+r+r+f & &r1(+(f & ;; ($ & (r0rrr7+(;;r7+(;;r(r(r1( fr6457(f rr5+(r:(r+r+r+f & &r1(1(f & & 121(48,9$/(17 ,17(59$//(< & */; ($ & 2(r(0r0frrr(r(r1,fr6457(f rr5+(r:,r+r+r+f & 2(r(0r0frrr(r(r1,fr6457(f rr5+(r:,r+r+r+f & 2(r(0r0frrr(r(r1,fr6457(f rr5+(r:,r+r+r+f & &r1,1,f & &r1, 1,f & &}1,1,f & &$/&8/$7( 63$&( 0(6+ (/(0(17 )25 $// 9$//(<6 & U '.f (r6457r(0r0r(0$;r(f+rf '.f (r6457r(0r0r(0$;r(f+rf '.f (r6457r(0r0r(0$;r(f+rf & &$/&8/$7( 9$/8(6 2) .= $7 &(175( 2) ($&+ 0(6+ (/(0(17 & ,1 &+26(1 9$//(< $1' :5,7( 72 ),/( .=, '.:fr '2 // :5,7(f .=, )250$7(f .=, .=,'.:f &217,18( & 6(7 3$5$0(7(56 )25 &(175$/ 9$//(<7+(1 &$/&8/$7( 7+( & 727$/ 6&$77(5,1* 5$7( )25 5($/ 352&(66(65f )25 $ 180%(5 & 2) (1(5*,(6 83 72 7+( 0(6+ 6,=(6725( 0$;,080 9$/8( 2) 5 & ,1 *$00$&f 72 &$/&8/$7( 36(8'2 6(/)f 6&$77(5,1* 5$7( & 77 (1$%/(6 352*5$0 72 5(7851 72 /$%(/ 77 (0 (0 9 *$00$9f (, (, (,(0$;4 *2 72 5 '2 5 5/,f PAGE 134 &217,18( ,)5*7 *$00$9ff *$00$9f 5 ,)-1(f *2 72 & & 6(7 3$5$0(7(56 )25 6$7(//,7( 9$//(<6 $1' 5(3($7 352&(66 & 72 2%7$,1 *$00$f $1' *$00$f & ,)9(4f *2 72 ,)9(4f *2 72 (0 (0 9 *2 72 (0 (0 9 *2 72 :5,7(f *$00$f*$00$f*$00$f :5,7(Mf *$00$f*$00$f*$00$f )250$7;*$00$f n(A*$00$f (n*$00$f (f :5,7(f 71',)(0$; :5,7(f 71',)(0$; )250$7;n7(03 n(;n 180 )/,*7 n;n0$;(1(5*< r (f :5,7(f :5,7(f )250$7n),(/' 9$9 ,,1,/72 1 *0$; ,',)nf & & 6(7 0(6+ 5(*,67(56 72 =(52 $1' 3/$&( (/(&7521 $7 & 67$57,1* 32,17 ,1 0(6+77 )25 ,7(5$7,9( 352&(66 & 77 777 9$9 9$9* 9$9* ',) 9$9* 9$9* ',) &+(&. 7) ( )7 7) '7 ( ,',) (727 .=77 7,0 7,0 7,0 0$;( 0$; 1 11 PAGE 135 7,0(9 7,0(; 7,0;; 65 66 *0$; /*7+ ( :5,7( f /*7+ :5,7( f /*7+ )250$7 ; }'(9,&( /(1*7+ f (}f ,,1,/7 ,)/$* 135,17 & ,1-(&7 1(: (/(&7521 $7 = 86,1* & 02',),(' 0$;:(//,$1 ',675,%87,21 ,1 (1(5*< & 9 (0 (0 ,),)/$*(4 f ,/7 ,/7 ,)/$* ,,1,,15 5$18f ,)5(422f 5 ( (= (r7r$/2*O5f .=) 2(fr6457$%6r(0r0r(=r(ff+ 5 5$18f ,)5(422f 5 ( (5+2 (m7r$/2*5f .5+2 (fr6457$%6r(0r0r(5+r(ff+ =,1 = & &$// 5$1'20 180%(517 f $1' &$/&8/$7( 7,0( 2) & )/,*+7 81'(5 (/(&75,& ),(/' $1' 1(: 326,7,21 2) & (/(&7521 63$&( & 5 5$18f ,)5(422f 5 ( 7,0( $/2*5f*$00$9f .=, .=)7,0(r(r)-fm2(f+ .7 6457.5+2r.5+2.=,r.=,f (, +r+r.7r.7r2((}r(0}0f & &+(&. )25 5281',1* (55256 /($',1* 72 1(*$7,9( (1(5*< 9$/8(6 & ,) 7+,6 2&&856 3/$&( (/(&7521 $7 67$57,1* 326,7,21 ,)(,*722f *2 72 .5+2 .=) 2( (0 (0 9 *2 72 PAGE 136 & ,) (/(&7521 /($9(6 0(6+ 3/$&( ,7 21 ('*( 2) 0(6+ $1' & 5(*,67(5 2&&855(1&( ,1 &2817(5 *0$; ,)(,*70$;(f 0$;( (, ,)(,/((0$;f *2 72 *0$; *0$; (, (0$; .7 (r6457}(0r0m(0$;}(f+ ,).=,*722f *2 72 .=, 6457$%6.7r.7.5+2r.5+2ff *2 72 .=, 6457$%6.7r.7.5+2r.5+2ff & &+(&. ,) ,1,7,$/ 9(/2&,7< $)7(5 &2//,6,21 ,6 /(66 7+$1 =(52 & ,) <(6 &+(&. 72 6(( ,) (/(&7521 326,7,21 *2(6 /(66 7+$1 =(52 & '85,1* 7+( )/,*+7 & U L $&&(/ (m)-f0r(0f}( 9,1 r.=)(0 ,)9,1*722f *2 72 & &$/&8/$7( 0,1,080 326,7,21 =0,1 70,1 9,1$&&(/ ,)70,1*77,0(f *2 72 =0,1 =,19,1r70,1r$&&(/r70,1rr ,)=0,1*722f *2 72 *2 72 = =,19,1r7,0( r$&&(/r7,0( r ,)=*722f *2 72 ,)/$* % 64579,1rrr$&&(/r=,1f 7,0( 9,1%f$&&(/ *2 72 & &+(&. )25 = /*7+ = =,19,1}7,0(r$&&(/m7,0(rr & :5,7(f=9,,1-,/72 & :5,7(f=9,,1-M,/72 & )250$7;(O ;;;f ,)=/7/*7+f *2 72 ,)/$* % 64579,1rrr$&&(/r=,1/*7+ff 7,0( 9,1%f$&&(/ & /223 72 *(1(5$7( 9(/2&,7< 7,0( 6(5,(6 & & &+(&. 72 6(( ,) )/,*+7 /21* (128*+ & ,) 127 *2 72 1(;7 6&$77(5,1* (9(17 & $)7(5 83'$7,1* 7,0(; =,1 = PAGE 137 ,)7,0(*7f *2 72 :5,7(f :5,7(f )250$7;n(5525 1(*$7,9( 7,0( *(1(5$7('nf *2 72 ,)9(4f 7,0 7,07,0( ,)9(4f 7,0 7,07,0( ,)9(4f 7,0 7,07,0( 7,0;; 7,0(;7,0( ,)7,0;;*7'7f *2 72 7,0(; 7,0(;7,0( ,),)/$*(42f *2 72 *2 72 & $'9$1&( 72 1(;7 '7 $1' &$/&8/$7( .=)9 .=) 7,0(9 '77,0(; 1 1 .=,9 .=)97,0(9r(r)-fm2(f+ 9=1f r.=,9(0 .=)9 .=,9 ,)1(4f *2 72 & $'-867 7,0( 2) )/,*+7 5(0$,1,1* $1' &$/& /223 & ,) 11 83'$7( 7,0(; $1' *2 6&$77(5 & U 7,0( 7,0('77,0(;f 11 7,0('7 ,)111(2f *2 72 7,0(; 7,0( ,),)/$*(42f *2 72 *2 72 '2 11 1 1I 7,0(9 '7 .=,9 .=)97,0(9r(})-fm(f+ 9=1f m.=,9(0 .=)9 .=,9 ,)1(4f *2 72 &217,18( 7,0(; 7,0(11r'7 ,),)/$*(42f *2 72 *2 72 & &$/&8/$7( ),1$/ (1(5*< 9$/8( )25 ($&+ 6&$77(5,1* 352&(66 R R ,, ,, ,, 32/$5 237,&$/ ($ ()f (,+:2 ()f (,+:2 F $&2867,&$/ ($ ()f (, ()f (, & (48,9$/(17 ,17(59$//(< ($ PAGE 138 ()f (,+:( () f (,+:( & 121(48,9$/(17 ,17(59$//(< & / ($ ()f (,+:,' ()f (,+:,' & ; ($ ()f (,+:,' ()f (,+:,' & / ($ ()f (,+:,' ()f (,+:,' & / ; ($ ()f (,+:,' 'f ()f (,+:,''f & ; ($ ()f (,+:,' ()f (,+:,' & ; / ($ ()f (,+:,'' ()f (,+:,'' & 6&$77(5,1* 5$7(6 )25 5($/ 352&(66(6 & U & (0,66,21 2) 237,&$/ 3+2121 & ,)()2f*722f *2 72 /f *2 72 /f &r6457(0fr$/*$%66457(,f6457()fff6457(Of 6457()fffff6457(Of & & $%62537,21 2) 237,&$/ 3+2121 & ,)()f*722f *2 72 /f *2 72 /f &m6457(0fr$/2*$%66457(Of6457()fff6457(Of 6457()fffff6457(Of & & (0,66,21 2) $&2867,& 3+2121 & ,)()f*722f *2 72 /f *2 72 QR /f &r(0mrr6457()ff & & $%62537,21 2) $&2867,& 3+2121 & QR ,)()f*722f *2 72 /f *2 72 /f /f PAGE 139 & (48,9$/(17 ,17(59$//(< / 25 ; & (0,66,21 2) 3+2121 & ,)()f/7f *2 72 ,)9 (4 f *2 72 ,)9 (4 f *2 72 & / 9$//(< /f &m(0rrr6457()ff *2 72 & ; 9$//(< /f &m(0r}r6457()ff *2 72 /f & & (48,9$/(17 ,17(59$//(< / 25 ; & $%62537,21 2) 3+2121 ,)()f/7f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 & / 9$//(< /f &r(0rrr6457()ff *2 72 & ; 9$//(< /f &r(0rrr6457()ff *2 72 /f & & 121(48,9$/(17 ,17(59$//(< & / (0,66,21 2) 3+2121 ,)()f/7f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 /f &r6457()ffr7+,*/r7+,*/ *2 72 /f & & / $%62537,21 2) 3+2121 ,)()f/7f *2 72 ,)9(4f *2 72 ,)9 (4f *2 72 /f &r6457()ffr7+,*/r7+,*/ *2 72 /f & & ; (0,66,21 2) 3+2121 ,)() f/7f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 /f &r6457()ffr7+,*;r7+,*; *2 72 / f & PAGE 140 & ; $%62537,21 2) 3+2121 ,)()f/722f *2 72 ,)9 (4 f *2 72 ,)9(4f *2 72 /f & m6457()ff}7+,*;m7+,*; *2 72 /f & & / (0,66,21 2) 3+2121 ,)()f/722f *2 72 ,)9(4 f *2 72 ,)9(4f *2 72 /f &r6457()ffr7+,*/r7+,*/ *2 72 /f & & / $%62537,21 2) 3+2121 ,)()f/722f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 /f &m6457()ffr7+,*/m7+,*/ *2 72 /f & & / ; (0,66,21 2) 3+2121 ,)()f/722f *2 72 ,)&9(4f *2 72 ,)9(4f *2 72 /f &m6457()ffm7+,/;m7+,/; *2 72 /f & & / ; $%62537,21 2) 3+2121 ,)()f/722f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 / f &r6457 ()ff }7+,/;m7+,/; *2 72 /f & & ; (0,66,21 2) 3+2121 ,)()f/722f *2 72 ,)9(4f *2 72 ,)9(4f *2 72 /f &r6457()ffm7+,*;m7+,*; *2 72 /f & & ; $%62537,21 2) 3+2121 ,)()f/722f *2 72 ,)9 (4 f *2 72 ,)Â9(4f *2 72 /f &m6457()ffr7+,*;r7+,*; *2 72 PAGE 141 & & & & & & & & & & & /f ; / (0,66,21 2) 3+2121 ,)()f/7f *2 72 ,)&9(4f *2 72 ,)9(4f *2 72 /f & r6457()ffr7+,/;r7+,/; *2 72 / f ; / $%62537,21 2) 3+2121 ,)()f/7f *2 72 ,)9(4 f *2 72 ,)Â9(4f *2 72 /f &m6457()ff}7+,/;m7+,/; *2 72 /f ,)77(4f *2 72 &$/&8/$7( 680 2) 5($/ 352&(66 6&$77(5,1* 5$7(6 6&$77f /f*$00$9f '2 6&$77.f 6&$77.f/.f*$00$9f &217,18( ,)6&$77f/7f 7+(1 :5,7( f :5,7(f )250$7n 1(*$7,9( 6(/)6&$77(5,1* 5$7(nf 0$; 0$; ,)0$;(4f *2 72 (1' ,) &$// 5$1'20 180%(56(/(&7 6&$77(5,1* &+$11(/ 5 5$18f ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$7722ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff ,)5/76&$77ff *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 *2 72 PAGE 142 ,)5/76&$77 ff *2 72 *2 72 & 6(7 (1(5*< $)7(5 6&$77(5,1* 352&(66 & (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 () f *2 72 (),1 () f *2 72 (),1 () f *2 72 (),1 () f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 ()f *2 72 (),1 () f *2 72 (),1 () f *2 72 (),1 (, *2 72 & 5(*,67(5 5($/ &2//,6,21&$/&8/$7( 63$&( 326,7,21 $)7(5 & $&2867,&,17(59$//(< 25 (48,9$/(17 ,17(59$//(< 3+2121 6&$77(5,1* 65 65 5 5$18f .7 (r6457r(0r0r(),1r(f+ .=) .7rr5f .5+2 .7r6457r5r5ff *2 72 PAGE 143 & 5(*,67(5 5($/ &2//,6,21&$/&8/$7( 63$&( 326,7,21 $)7(5 & 237,&$/ 3+2121 6&$77(5,1* 65U65 5 5$18f 8 5$18f 3+, rr5 (; r6457(),1r(,f6457(Of6457(),1ffrrf %(7$ (;0 m(;frm8f(;f 5+2 %(7$r.=,.76457$%6%(7$r%(7$ffr.5+2.7r&263+,ff .7 2( r6457r(0r0r(),1r(f+ .=) .7r5+2 .5+2 .7r6457$%65+r5+ff *2 72 + & U & &+$1*( 9$//(< 3$5$0(7(56 )25 ,17(59$//(< 352&(66(6 & 9 (0 (0 *2 72 9 (0 (0 *2 72 9 (0 (0 *2 72 & n 5(*,67(5 6(/) 6&$77(5,1* 352&(66. 63$&( 326,7,21 81&+$1*(' 66 66 .=) .=, .7 6457.=)r.=).5+2r.5+2f (),1 +r+r.7r.7r2((mr(0m0f & &+(&. ,) (/(&7521 ,6 6&$77(5(' 287 2) 0(6+,) 625(*,67(5 & 352&(66 21 &2817(5 *0$;$1' 3/$&( (/(&7521 21 ('*( 2) 0(6+ & /$%(/ 5(3($76 ,7(5$7,9( 352&(66 67$57,1* :,7+ )5(( & (/(&7521 )/,*+7 81'(5 (/(&75,& ),(/' ,)(),1/((0$;f *2 72 *0$; *0$; .7 ( r6457r(0r0r(0$;r(f+ ,).5+2*7.7f .5+2 .7 .=) 6457$%6.7r.7.5+2r.5+2ff *2 72 & ),1$/ &$/&8/$7,216 2) 7,0( 6(5,(6 $)7(5 1 32,176 +$9( & %((1 *(1(5$7(' ,',) ,',) 135,17 135,17 9$ '2 1 9$ 9$9=*f PAGE 144 &217,18( 9$ 9$1 9$9 9$9r,',)f9$f,',) & 5(029( $9(5$*( 9(/2&,7<387 ,1 9(&725 $ & U U U U '2 1 $*f 9=*f9$ &217,18( :5,7(f)-f9$9,,1-,/721*0$;,',) :5,7(f)-f9$9,,1-,/721*0$;,',) )250$7(;f;,;,;,;,;,f ,),',)/71',)f *2 72 :5,7( f :5,7(f & L & &$/&8/$7( 9$//(< 3238/$7,21 5$7,26 & UU U )250$7;n3238/$7,21 *$0 / ;nf 72797 7,07,07,0 7,0 7,072797 7,0 7,072797 7,0 7,072797 :5,7(f7,07,07,0 :5,7( f7,07,07,0 )50$7;(;ff & & &$// ))75& 72 &$/&8/$7( ))7 2) 7,0( 6(5,(6 &217,18( &$// ))75& $1;,:.:.f :5,7(f & :5,7(f )250$7 ;n)5(48(1& PAGE 145 ,)-1(1)f *2 72 6723 (1' PAGE 146 5()(5(1&(6 + .URHPHU 3URFHHGLQJV ,((( f f 3 6RORPRQ DQG + 0RUNRF ,((( 7UDQV (OHF 'HY (' f f 6 $GDFKL $SSO 3K\V A f 5 f +& &DVH\ -U DQG 0% 3DQLVK +HWHURVWUXFWXUH /DVHUV 3DUW $ )XQGDPHQWDO 3ULQFLSOHV $FDGHPLF 3UHVV 1HZ PAGE 147 6 7HKUDQO / +HQFK &0 9DQ 9OOHW DQG %RVUDDQ $SSO 3K\V f f + .URHPHU 3URF ,5( f f $' %RDUGPDQ ,Q 3K\VLFV 3URJUDPV -RKQ :LOH\ t 6RQV 1HZ PAGE 148 . 7VXEDNL $ /LYLQJVWRQH 0 .DZDVKLUDD + 2NDPRWR DQG .XPDEH 6ROLG 6WDWH &RPPXQ f : 0DVVHOLQN : .RSS 7 +HQGHUVRQ DQG + 0RUNRF ,((( (OHFWURQ 'HYLFH /HWW ('/ f 5 YDQ :HO]HQLV + :LMVKRII DQG 3ORRJ 3K\VLFD % & f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xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0008229300001datestamp 2009-02-24setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Hot-electron noise in gallium arsenide/aluminum gallium arsenide heterojunction interfacesdc:creator Whiteside, Christopher Francisdc:publisher Christopher Francis Whitesidedc:date 1987dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00082293&v=0000116865103 (oclc)000947009 (alephbibnum)dc:source University of Floridadc:language English |