A Computationally Efficient Physics-Based Compact Bipolar Transistor ...

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 2, FEBRUARY 2006

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A Computationally Efficient Physics-Based Compact Bipolar Transistor Model for Circuit Design—Part I: Model Formulation Michael Schroter, Member, IEEE, Steffen Lehmann, Sébastien Frégonèse, and Thomas Zimmer

Abstract—A compact bipolar transistor model is presented that combines the simplicity of the SPICE Gummel–Poon model (SGPM) with some major features of HICUM. The new model, called HICUM/L0, is more physics-based and accurate than the SGPM and at the same time, from a computational point of view, suitable for simulating large circuits. The new model has been implemented in Verilog-A and, as compiled code, in various commercial circuit simulators. In Part I, the fundamental model formulation is presented along with a derivation of the most important equations. Experimental results are shown in Part II. Index Terms—Analog high-frequency circuit design, bipolar transistors, compact transistor modeling, HICUM.

I. INTRODUCTION

R

ELIABLE design and optimization of analog high-frequency (HF) circuits, fabricated in advanced Si/SiGe bipolar and BiCMOS as well as in III-V HBT technologies, have become seriously affected by the deficiencies of the more than 25-year-old SPICE Gummel–Poon model (SGPM). The formulation of charge storage effects, of the transfer current and resulting transconductance, and of the internal base resistance as well as the missing self-heating and base–collector (BC) avalanche effect are the most important deficiencies of the SGPM. Advanced compact models such as HICUM/L(evel)2 [1], MEXTRAM [2], and VBIC [3] eliminate many of the above issues. However, these advanced models are also more complicated than the SGPM with respect to equivalent circuit (EC), model equations, parameter extraction and computational effort. Thus, the availability of a less complicated model can have certain advantages such as: • During the conceptual circuit design phase, it is usually advantageous to start with a simple transistor model that is easily understandable for designers, but contains the essential transistor features. This facilitates a quick evaluation of the basic circuit functionality, before spending Manuscript received July 14, 2005; revised November 8, 2005. This work was supported in part by Atmel Germany, in part by Jazz Semiconductor, in part by STMicroelectronics, and in part by the German Ministry for Research under Grant SFB 358. The review of this paper was arranged by Editor J. Burghartz. M. Schroter is with the Department of Electrical Engineering and Information Technology, Dresden University of Technology, Dresden 01062, Germany, and also with the Department of Electronic and Computer Engineering, University of California San Diego, La Jolla, CA 92093 USA. S. Lehmann is with the Department of Electrical Engineering and Information Technology Dresden University of Technology, Dresden 01062, Germany. S. Frégonèse and T. Zimmer are with the IXL, UMR 5818 CNRS, University Bordeaux, Bordeaux, France. Digital Object Identifier 10.1109/TED.2005.862241

time on longer optimization cycles, using a more accurate model. Also, being able to start with a simple model and then gradually move to a sophisticated model provides a better feeling for the impact of certain effects on circuit characteristics. • In larger circuits often only a few (very) critical transistors need to be represented by a very sophisticated model that takes into account all relevant physical effects; the other transistors can be represented by simpler models. • While integrated circuit design and optimization generally requires geometry scalable models, sometimes discrete devices have to be dealt with. Model parameter determination from such a “single geometry transistor” naturally is quite difficult for sophisticated models, unless they are simplified with respect to, e.g., geometry effects. • Another example is variable capacitors (varactors) that are often realized as transistors. They require an accurate description of the bias dependent capacitance, series resistance and leakage and are best described by a simple transistor model. To address the above issues, a simplified compact bipolar transistor model, called HICUM/Level0 or just HICUM/L0, has been developed on the basis of the full version, HICUM/L2, that is described in [1]. HICUM/L0 combines the simplicity of the SGPM in terms of equivalent circuit and some of its model equations with several important features of HICUM/L2. As a result, HICUM/L0 is a more physics-based and accurate model than the SGPM, but also reduces parameter extraction efforts, especially for single transistor sizes, compared to HICUM/L2 and the SGPM. Part I presents the fundamental formulation of the new model in terms of its equivalent circuit and model equations. Only those model equations and their derivation that are different from HICUM/L2 and the SGPM will be presented. An experimental verification for a variety of advanced processes is presented in Part II [4]. II. MODEL FORMULATION OVERVIEW Fig. 1 shows the large-signal EC of the simplified model. Compared to HICUM/L2, the following simplifications have been made in the EC topology. • The perimeter base node (B ) has been eliminated by properly merging the respective internal and external , base recomponent of the BE depletion capacitance across the BE junction, and sistance , base current

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Fig. 1.


Large-signal equivalent circuit of HICUM/L0.

of the BC depletion capacitance . The partitioning of the latter will be discussed later in more detail. • The BE tunnelling current, the substrate coupling network, the parasitic substrate transistor, and the capacitance for modeling ac emitter current crowding have been omitted. The resulting isothermal EC is the same as for the SGPM, except for the representing the BC (weak) avalanche effect, • current and , that • parasitic capacitance elements, result from fringing fields in isolation regions, and • self-heating network, consisting of the generated power as well as the thermal resistance and capacitance . In addition, compared to the SGPM, various physical effects are taken into account or are formulated in an improved form, and are reflected in the model equations for the various elements. The small-signal model is obtained from the large-signal model by linearization. Noise sources are added for each dissipative element in the usual way, enabling low-frequency and HF noise simulation. The formulation of the BC depletion capacitance requires more explanation. For transistors with selectively implanted collectors, which is a standard option in modern high-speed proand , as cesses, the (original) physical components they are used in HICUM/L2, differ in their bias dependence, particularly in terms of punch-through behavior. An accurate bias is important for modeling dependent description of the total HF applications, such as power transfer and in some cases disis required for accurately modeling tortion. Furthermore, the bias dependent Early effect, low-current transit time, and avalanche current. Therefore, a separate set of model parameand . The goal is to forters has to be maintained for mulate and implement a flexible scheme that also allows to meet the following criteria. • It should be possible to extract the separate sets of model parameters from single transistors, i.e., without the knowledge of geometry specific data. • The formulation should, on the other hand, also allow calculating the parameters from a geometry scalable methodology used for generating HICUM/L2 parameters. • The partitioning of the capacitances should be as simple as possible, with a minimum number of model parameters.

Fig. 2. Implementation of a flexible partitioning scheme for the various BC junction capacitance components. (a) Small-signal equivalent circuit. (b) Code example (for preprocessing).

The implementation chosen in HICUM/Level0 is shown in Fig. 2(a), which represents a more detailed view of the small-signal EC between the B and C node. In the illustrated is split across , using a case, the zero-bias value of which is similar partitioning parameter in the SGPM. At the node B’ this leads to the parameter to two separate elements and with the desired different voltage dependence, and which together contain the in Fig. 1. charge However, in practice sometimes the internal and external component cannot be separated although their voltage dependence is different. This can occur if the extraction is performed on a single geometry transistor. In this case, it is still desirable to partition the total capacitance and also to make sure there is an internal component. This can be done by defining , which is fully compatible with the SGPM. Note that the total capacitance will only be correct exactly at and . zero-bias due to the possibly different values The proposed code implementation that covers both cases discussed above in a flexible way, is shown in Fig. 2(b), in which , , and represent model parameters the variables and the underscored variables are local. III. ISOTHERMAL CASE A main feature of HICUM/L0 is the decoupling of dc and a.c. behavior which makes parameter extraction easier but also reduces the validity range of the model and makes its parameters less physical. Below, the charge equations of the internal transistor are described first, followed by a derivation of the transfer current. Then, the equations of the various other elements of the equivalent circuit are discussed. A. Charge Formulation of the Internal Transistor All depletion charges and capacitances are described with the same equations as in HICUM/L2v2.2 [1]. Thus, collector punch-through as well as a smooth limitation at high forward bias are included also in HICUM/L0. is The formulation of the forward minority charge strongly based on HICUM’s accurate description of the transit

SCHROTER et al.: COMPUTATIONALLY EFFICIENT PHYSICS-BASED MODEL FOR CIRCUIT DESIGN – PART I

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time . This is a main improvement over the SGPM. As in HICUM/L2, the bias dependence of is modeled as (1) , the high-current compowith the low-current component nent , and as the forward transfer current (cf. [12]). is the same as in HICUM/L2 (e.g., [5]) The formulation for and, hence, includes as the only existing model the impact of both the Early effect and the delay through the BC SCR. This peak with inis visualized in Fig. 3. Thus, a decrease of , which often occurs in power transistors (and creasing III-V HBTs) can be described well with this model. is partially simplified comThe current dependence of pared to [1], [5] by neglecting the bias dependent portion of the collector current spreading formulation, which allows merging into a single expresthe base and collector component of sion, and after adding a possible emitter contribution is given by

(2) Here,

is the normalized injection width in the collector [5]

(3) , , The model parameters in the above expression are , , plus those for the critical current that determines the onset of high-current effects [1], [5], [6]. used for dynamic transistor operaThe minority charge tion is then obtained analytically by integrating over (4) with the high-current contribution (5) corresponds to the HICUM/L2 expression with i.e., no collector current spreading. In order to maintain an accurate physics-based description of the shift of the , temperature, doping and getransit time increase with ometry, the bias independent collector current spreading factor is included in according to [1] and [5]. Together with properly, the impact of possible adjusting the parameter can still be described quite well (up current spreading on to the validity limit of HICUM/L0) [1]. with the The reverse minority charge is simply reverse transit time as model parameter.

Fig. 3. Voltage dependence of the low-current transit time for different dominating effects.

with the transport related hole charge (index “ ”) (7) and are weighting factors for HBTs that take where into account mostly bandgap and mobility variations within the and are the depletion charges of transistor structure; and are equal to and for the internal transistor; BJTs, but can include weighted charge components for HBTs. Note that (6) and (7) are very accurate up to high current densities (e.g., [7] and [8]), but result in a nonlinear implicit equation for any realistic current dependence of the charge comfor ponents at medium and high current densities. at zero-bias As a first simplification step, the hole charge is replaced by a hole charge at a different reference point [9], that , ) is defined at an arbitrary operating point ( at low forward bias, at which the minority charge is negligible. As a result, the new reference charge reads (8) as the internal BE depletion charge at the new with reference bias point. The main reason for this step is that in HICUM/L0—like in the SGPM and any other model with the simple EC in Fig. 1—the true internal BE depletion charge is not available anymore, but only the total BE depletion charge. However, using the latter would make (6) inaccurate. gives Normalizing the charge terms in (7) to (9)

where

B. Transfer Current HICUM/L0 contains a simplified transfer current equation the derivation of which starts with the generalized integral charge-control relation (GICCR) [7] in HICUM/L2 (6)

with (10) Since

, one can separate the term containing and write the approximation

(11) For the same reason, the first term can be considered as series expansion of an exponential function, yielding instead of (6) (12) which now contains the nonideality coefficient (13)

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and a modified saturation current

sulting in the simplifying assumption for the normalized charge terms of (12) (14)

(17)

The denominator in (12) is often referred to as normalized base charge in texts on the SGPM. However, the above derivation clearly shows the actual meaning of the denominator and the , which has been expressed in (13) nonideality coefficient by physical quantities. A simplified form of this coefficient was given many years ago in [10]. The above formulation removes the ambiguity in the parameter extraction if—like in the SGPM—a nonideality coefficient ( ) and a reverse Early ) are available to model the same effect in BJTs. voltage ( The next goal is to replace the normalized BC depletion charge by a somewhat simpler expression and to eliminate the . First of all, note that due to , the variable used in HICUM/L0 (cf. Fig. 1 and subsequent charge comments) in general is not equal to the physically correct of the internal transistor that needs to be inserted charge instead into the GICCR. As a consequence, just inserting into (12) would lead to an incorrect modeling of the of forward Early effect. This problem can be solved by introducing an artificial Early voltage parameter as shown below. The expression “artificial” is used since the parameter does not correspond to an actual Early voltage in the commonly used sense and its value is often confusing for circuit designers. Normalization of the original expression leads to

This decouples the calculation of the dc model currents from the a.c. model characteristics, but comes at the expense of accuracy at medium and high current densities. Unfortunately, any other approximation than that of a current independent transit time in leads to either an iterative or an inconsistent solution. Defining the critical (or knee) currents of the forward and reverse transfer curve as

(15)

(20)

(18) permits elimination of

in the charge ratios of (12) (19)

where and need to be introduced as additional model parameters for adjusting the characteristics and for compensating obviously errors introduced by the model simplification. , but is now corresponds directly to the SGPM parameter clearly defined (at V). The possible voltage depen(via ) in HICUM/L2 has been neglected dence of in favor of the high-current correction introduced later. Physiand represent base conductivity cally, the two currents modulation, if would represent just the base transit time. Inserting (15) and (19) into (12) gives the normalized charge

by which the artificial Early voltage is defined as which has the same form as in the SGPM with (16)

(21)

Basically, is a derived or composite parameter, that contains different basic physical variables. (A similar discussion holds for a “reverse” Early voltage if one would keep the corresponding charge in the denominator of .) The definition of an Early voltage leads to a reduced coupling of the modeling of the dc behavior from that of the a.c. behavior, since only the voltage dependence of the depletion charge is used, while the magnitude of its impact on the transfer current can be adjusted separately . Note, that the expression (15) is used in VBIC [3], with and that (16) clarifies the physical meaning of the Early voltage parameter. The accurate and physically correct modeling of (and ) in the high-current region requires a description of the (modin (12). Unfortunately, at medium ified) minority charge is a strongly nonlinear funcand high current densities tion of current and, hence, can only be calculated iteratively in HICUM/L2. With the goal of simplicity and, particularly, reduction of computation time in mind here, the internal iteration can be avoided by assuming a current independent transit time. The corresponding charge then depends only linearly on current re-

In order to indicate the fact that the above description is only valid for sufficiently low current densities, in (20), rather than and the currents (22) are used, with the ideal current components defined as (23) The quadratic equation (20) can be easily solved yielding (24) From the above derivation of , it is obvious that the formulation will definitely become quite inaccurate at high current densities, but possibly already at medium current densities when the current dependence of the transit time becomes significant. The main reason for the inaccuracy at high current densities is assumption (17). Fig. 4 illustrates the impact of the approxima-


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higher current densities, which is (physically) determined by . The resulting normalized charge is then the critical current (29)

Fig. 4. Illustration of the impact of the various approximations on the (normalized) forward collector current at high current densities.

tion (17) on the forward collector current at medium to high current densities for a one-dimensional transistor structure. Comwill show a certain reduction at pared to the ideal current, values, but will still have a significant deviation larger compared to the actual current. Note, that compared to Si BJTs, SiGe HBTs exhibit a much larger current reduction at high current densities due to the BC barrier. Also, the inaccuracy of the current will be reflected directly in the transconductance. All the above applies to the SGPM, too. An approximation with improved accuracy at high current densities is described next. For this, the normalized charge in the original formulation (12) is expressed as

(25) where the last term contains the additional charge (compared ) caused by high-current effects. The desired to and need to be unknown transfer current components eliminated from (25). The charge term is up to medium current densities and negligible compared to at high current densities. then also compared to is negligible for the intended apSimilarly, plication and validity range. The remaining term, , strongly determines the dc behavior at high current densities since it increases much more rapidly than linear with the current. In order to keep the physics-based bias dependence of with its the well-proven critical current and to avoid an itis approximated by erative solution,

since , which reflects the funNote that damental physical meaning of the two currents; i.e., onset of collector induced high-current effects versus base conductivity modulation. The above “high-current” approximation circumvents the originally (and aforementioned) implicit formulation for the transfer current components and yields the following explicit and final formulation for the HICUM/L0 transfer current components: (30) The total transfer current in HICUM/L0 is then given by (31) The term in the denominator of (30) can be viewed as a correction of the current given by the solution of the quadratic equation, or as a second correction of the ideal current. Basically, the high-current behavior of the transfer current is described by employing the fundamental bias dependence of the minority charge increase, but in a quite simplified form. The additional model and , which still have a physical meaning, parameters and using from (29) separately adjust the impact of the nonlinear charge (increase) at high current densities on the dc transfer current, in order to decouple the model calculations and parameter extraction for dc and ac operation as much as possible. by leads to a too large Fundamentally, replacing charge, which has to be compensated for by properly adjusting and , but this can still lead the new model parameters characteristic at to a significant deviation of the very high current densities and also in the output characteristics toward very low voltages. and in the origFor SiGe HBTs, the weighting factors [1], [7] can still be incorporated, since inal expression for the charge components are in principle still separately available for the E, B, and C region.

(26) from (5) is evaluated for rather than for . in which To further decouple the dc from the a.c. model characteristics, is “normalized” to its major time the absolute value of , yielding constant

C. Junction Related Current Components The components resulting from 1) back injection into the emitter across the perimeter and bottom BE junction and 2) recombination within the BE SCR are merged into a single expression

(27) Setting parameters

for simplification and introducing the model

(28) further decouples the a.c. and dc model description, except for the voltage dependence of the characteristic at

(32) The saturation currents and ideality coefficients are model parameters, that allow to model the base current independently of the collector current. Thus, in contrast to the SGPM, the current gain – although a useful parameter for circuit designers – has been eliminated as model parameter in favor of a more flexible physics-based and accurate formulation.

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The currents across the internal and external collector–base as well as the collector–substrate junction are described by a re, lation like the first term in (32), but written with , and as model parameters. Usually, the latter currents are negligible. However, they not only provide a dc path between the respective nodes, which sometimes aids convergence, but also are useful as flag for circuit designers in case the transistor enters an undesired operating region outside the model’s validity range. D. Avalanche Effect The weak avalanche effect is modeled by the current (33) with the normalized capacitance the model parameters

, and

At low current densities, the internal base sheet resistance is only voltage dependent via the depletion charges. Normalizing the latter to their respective zero-bias capacitance, i.e., defining , the charge ratio is approximated by (37) and are model parameters, which are defined similarly to the artificial Early voltages . Note, that the bias dependence of usually difused for fers from that of ; also the weighting factors, that were in related charge expression (9), do not enter relation (36). the and need to Therefore, separate model parameters be introduced. For homojunction transistors, usually so that holds. In analogy to the simplification of the current dependent charge ratios for the GICCR, the ratio containing the minority charges in (36) can be simplified by introducing “critical” and currents

(34) (38) and are the (temperature dependent) ionization coHere, efficients, and is the area specific internal zero-bias BC depletion capacitance. Relation (33) can be derived from the one used in HICUM/L2 [1], [11] by merging parameters and using only the bias dependent expression of the internal BC depletion capacitance rather than the absolute capacitance values. Thus, the two model parameters can be calculated from HICUM/L2 parameters, if available.

and . Since 1) the value with of is somewhere in between and , 2) HICUM/L0 becomes less accurate at high current densities in any way, and decreases at high current densities com3) the importance of , the number of model parameters is further reduced pared to by setting and . The internal base resistance that results from conductivity modulation only is then given by

E. Series Resistances

(39)

In Fig. 1, represents the series resistance caused by the collector contact and sinker as well as by the buried layer. Note that the effect of the bias dependent internal collector resistance is already being taken into account by the GICCR and the simplified transfer current formulation as well as in . In the series resistance , the contributions from the bulk emitter regions, the interfaces and the metal are included. The element

with as a model parameter, that is a function of zero-bias , emitter size and configuration (i.e., sheet resistance number of emitter and base fingers) [13]. The effect of emitter current crowding can be quite well approximated for all emitter geometries by the function [13] (40)

(35) represents the total base resistance, with as the bias independent external portion. The bias dependent internal base is described in a simplified form compared to resistance HICUM/L2, but still contains significant improvements compared to the physically incorrect formulation in the SGPM. The starting point for deriving a simplified formulation is the HICUM/L2 description of the dc internal base sheet resistance (36) with as zero-bias sheet resistance and as modified “zero-bias” charge due to mobility changes with bias [12]. Since the actual values of the internal depletion charges are not separately available in HICUM/L0, the corresponding charge ratios are replaced by available quantities as shown below.

with the current crowding factor (41) Due to the previous simplifications the internal base current is not available in the model, it has to be calculated from the total current across the BE junction. This is done by modifying the in HICUM/L2 according to the ratio geometry factor of the perimeter to area specific base current (at low current densities) to yield (42) with and as emitter window area and perimeter length. does not depend on bias and can be directly deterSince mined for a given (transistor) geometry, it is defined as a model parameter.


The final equation for the internal base resistance then reads (43)

IV. TEMPERATURE DEPENDENCE Self-heating is included to overcome one of the most significant deficiencies of the SGPM for advanced processes, including III-V HBTs. The single-pole network consisting of the and thermal capacitance as shown thermal resistance in Fig. 1 is sufficient for most applications that fall in the validity range of HICUM/L0. In addition, access to the thermal allows modeling any type of higher order and disnode tributed temperature effects. The dissipated power in the device is approximated by (44) in order to keep the model simple. Compared to the first version [14], wherever applicable the dependence of all relevant elements on temperature is taken into account similarly as in HICUM/L2v2.2 [1]. V. MODEL IMPLEMENTATION AND DEPLOYMENT HICUM/L0 has been implemented in a variety of commercial simulators, such as ADS, AnalogOffice, APLAC, ELDO, HSPICE, SPECTRE (as compiled model) as well as in Verilog-A. The latter allows an immediate evaluation of the model’s suitability for existing process technologies (cf. [4]). This implementation also has the advantage of a much more rapid integration in commercial circuit simulators, using newly available model compilers [15], [16], as compared to the conventional hand coding which has been causing a significant and unacceptable burden for model developers. For instance, with these compilers successful compilations into ADS and SPECTRE have already been performed. Simulation speed of an optimized HICUM/L0 implementation without self-heating is expected to be in between SGPM and VBIC.

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• Self-heating network with externally accessible node. Like the SGPM, all equations are formulated explicitly, leading to fast execution times. As a consequence of the above, the model: • is computationally efficient, allowing the simulation of large circuits; • is easy to understand for circuit designers; • is sufficiently accurate for many applications; and • allows fast parameter extraction, especially for single geometry transistors. The model parameters have a clear (physical) meaning and are related to HICUM/L2 parameters. Hence, as an additional benefit, the geometry scaling features of HICUM/L2 can be employed to (automatically) generate geometry scalable HICUM/L0 parameters using the TRADICA program [17]. Obviously, simplifications generally lead to limitations of the validity range. Therefore, if an accurate description of the transfer current characteristics, including transconductance and output conductance at high current densities and/or low voltages is required, it is recommended to use HICUM/L2. However, elements for modeling parasitic effects such as substrate coupling and the parasitic substrate transistor can always be added in a subcircuit, enabling a compact model hierarchy with variable complexity anywhere between a simple model, such as HICUM/L0, and a sophisticated model, such as HICUM/L2. Model availability in Verilog-A together with an adequate model compiler will allow a fast and consistent model implementation across platforms and simulators, while the Verilog-A code itself can serve as reference for testing the compiled version. In conclusion, HICUM/L0 offers a convenient migration from a conventional, single-transistor- and SGPM based modeling methodology to a process-based geometry scalable parameter extraction and model usage in order to meet todays requirements for advanced integrated analog HF circuit design. For a complete description of the model the reader is referred to [18].

VI. CONCLUSION

ACKNOWLEDGMENT

A simplified compact bipolar transistor model, called HICUM/L(evel)0 is described, that combines the simplicity of the SGPM equivalent circuit with various important improvements from HICUM/L(evel)2. Thus, the new model has the following important advantages over the SGPM. • Significantly improved charge storage model for both depletion and minority charge, allowing an accurate description of the bias dependence of the transit frequency. • Improved description of the transfer current with respect to the Early effect and toward high current densities. • Improved internal base resistance model, removing the incorrect formulations of the SGPM. • Separate description of base and collector current, enabling a flexible approximation of the current gain. • Collector–base breakdown model accounting for the weak avalanche effect.

The authors would like to thank G. Coram, Analog Devices (USA), C. McAndrew, Freescale (USA), F. Sischka, Agilent (Germany), M. Mierzwinski, Tiburon (USA), M. Yakupov, Cadence (USA), and J.C. Perraud, CAEN University (France) for their support and discussions regarding the Verilog-A implementation and compiler usage, and Agilent (Santa Rosa, USA), Applied Wave Research (El Segundo, USA), and Cadence (Munich, Germany), for software donations. REFERENCES [1] M. Schroter. (2005) “HICUM, a scalable physics-based compact bipolar transistor model,” User’s Manual HICUM/Level2. [Online]. Available: www.iee.et.tu-dresden.de/iee/eb/eb_homee.html [2] J. Paaschens and W. Kloosterman, “The MEXTRAM bipolar transistor model, level 504,” Nat. Lab., Unclassified report NL-UR2000/811, 2001. [3] C. McAndrew et al., “BJT Modeling with VBIC, basics and V1.3 updates,” in Proc. Nanotech 2003, vol. 2, 2003, pp. 278–281.

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Sébastien Frégonèse was born in Bordeaux, France in 1979. He received the M.Sc. and Ph.D. degrees in electronics from the University of Bordeaux, in 2002 and 2005, respectively. During his Ph.D. work, he investigated bulk and thin SOI SiGe HBTs, with emphasis on compact modeling. He has recently joined the Technical University of Delft, Delft, The Netherlands, where his research activities deal with FET emerging devices, focusing on process and device simulation.

Michael Schroter received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering and the “venia legendi” on semiconductor devices in 1982, 1988, and 1994, respectively, from the Ruhr-University Bochum (RUB), Bochum, Germany. From 1993 to 1996, he was with Nortel and Bell Northern Research, Ottawa ON, Canada, first as Senior Member of Scientific Staff and later as Team Leader and Advisor, continuing the bipolar transistor modeling and parameter extraction activities. During 1994 to 1996, he was also Adjunct Professor at Carleton University, Ottawa. In 1996, he joined Rockwell Semiconductor Systems, Newport Beach, CA, as a Group Leader, where he established the RF Device Modeling Group and was responsible for modeling (Si, SiGe, AlGaAs) bipolar transistors, MOS transistors and integrated passive devices with emphasis on high-frequency process technologies and applications. In 1999, he was appointed Full Professor as the Chair for Electron Devices and Integrated Circuits at Dresden University of Technology, Dreseden, Germany. In 2003, he was also appointed Research Professor (part-time) at the University of California at San Diego. He has published several book chapters and is the author or coauthor of more than 80 technical publications. He also has given numerous lectures and invited tutorials on compact device modeling at international conferences and industrial sites, and is a regular reviewer for internationally renowned scientific journals. He is the author of the compact bipolar transistor model HICUM which has become an industry-wide standard. He is a cofounder of XMOD Technologies, Talence, France, a start-up company specializing in high-frequency semiconductor device modeling services for foundries and design houses. He is also on the Technical Advisory Board of RFMagic, a communications circuit design company in San Diego, CA. Dr. Schroter was a member of the BCTM CAD/Modeling subcommittee from 1994 to 2001, which he chaired from 1998 to 2000.

Thomas Zimmer was born in Wollbach, Germany. He received the M.Sc. degree in physics from the University of Würzburg, Würzburg, Germany, in 1989 and the Ph.D. degree in electronics from the University of Bordeaux, France, in 1992. Since 2003, he has been a Professor at the University of Bordeaux, Bordeaux, France. His research focuses on characterization and modeling of high-frequency devices, in particular Si/SiGe heterojunction bipolar transistors. He is co-founder of the company XMOD Technologies and he has published about 100 technical papers related to his research.

Steffen Lehmann was born in Hoyerswerda, Germany, in 1974. He received the M.S. degree in electrical engineering from the Technical University Dresden, Dresden, Germany, in 2004, working on parameter extraction for the HICUM bipolar compact model and high frequency on-wafer measurements. He is currently pursuing the Ph.D. degree at the same university, investigating advanced SiGe processes, focusing on device simulation and compact model development.