MODELING of MOS devices requires a mobility model

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1 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER An Improved Electron and Hole Mobility Model for General Purpose Device Simulation Mohamed N. Darwish, Senior Member, IEEE, Janet L. Lentz, Mark R. Pinto, Senior Member, IEEE, Peter M. Zeitzoff, Member, IEEE, Thomas J. Krutsick, and Hong Ha Vuong, Member, IEEE Abstract A new, comprehensive, physically-based, semiempirical, local model for transverse-field dependent electron and hole mobility in MOS transistors is presented. In order to accurately predict the measured relationship between the effective mobility and effective electric field over a wide range of substrate doping and bias, we account for the dependence of surface roughness limited mobility on the inversion charge density, in addition to including the effect of coulomb screening of impurities by charge carriers in the bulk mobility term. The result is a single mobility model applicable throughout a generalized device structure that gives good agreement with measured mobility data and measured MOS I0V characteristics over a wide range of substrate doping, channel length, transverse electric field, substrate bias, and temperature. I. INTRODUCTION MODELING of MOS devices requires a mobility model which can accurately capture the dependence of inversion layer mobility on doping concentration and bias. But it is also important that the model be based on physical principles so that it is applicable outside the range of known dependence, and that it be easy to implement and efficient to evaluate in a numerical device simulator. Furthermore, a local mobility model suitable for general purpose device simulators, where prior knowledge of device geometry is not required, should have the following features: 1) the evaluation of mobility at each grid point should depend only on the variables (e.g., doping concentration, electric field, etc.) at that node, and 2) a single mobility model should be applicable throughout a generalized device structure. Several recent models reasonably fit the measured dependence of effective mobility on effective transverse field in the inversion layer, but do not meet the above requirements for a general purpose device simulator. Walker and Worlee s [1] model requires calculation of the average distance from the surface of the inversion charge. The model of Huang [2] depends on, which is also a calculated quantity. The MINIMOS [3] mobility model is an empirical model that depends on the the distance from the silicon-oxide Manuscript received September 4, 1996; revised April 10, The review of this paper was arranged by Editor J. R. Hauser. M. N. Darwish is with Siliconix Inc., Santa Clara, CA USA. J. L. Lentz is with AT&T Bell Laboratories, Breinigsville, PA USA. M. R. Pinto and H. H. Vuong are with AT&T Bell Laboratories, Murray Hill, NJ USA. P. M. Zeitzoff is with SEMATECH Inc., Austin, TX USA. T. J. Krutsick is with AT&T Bell Laboratories, Reading, PA USA. Publisher Item Identifier S (97) surface, which is not a local quantity. Similarly, the model proposed by Shin [4] estimates an effective electric field based on an average of its local value at different grid points and is applicable only in the inversion layer of an MOS device, but not in the pinched off region or source and drain regions. These features make such models unsuitable for a general purpose device simulator capable of handling devices with arbitrary geometries. What is needed is a mobility model that depends only on local quantities, and is applicable throughout a general device structure [5], [6]. The model proposed by Lombardi [5] is a commonly used local model which is applicable throughout the device. But the formulation does not account for the screening of ionized impurity scattering sites, and does not accurately model the falloff in mobility at very high perpendicular fields. Fig. 1 shows a comparison between the simulated effective electron mobility in the MOS inversion layer,, versus effective transverse field,, using Lombardi s model [5] and the experimental data of Takagi [7]. is defined as, where and are the depletion and inversion charge density per unit area, respectively. is the average mobility in the inversion layer given by, where and are the device length and width, respectively, and is the drain conductance in the linear region. The values of,, and and were obtained by using a post-processor that performs numerical integration using the nodal values from our device simulator. The measurements show that, except for the region below the threshold voltage of the device, where the carrier concentration is very low, mobilities follow a universal relationship independent of substrate doping. Since carrier screening is not accounted for, simulations using Lombardi s model show a decrease in calculated mobility for doping concentrations higher than about cm. This effect is manifested as lower simulated drain current than measured values in the characteristics. Also, the model does not follow the universal curve at transverse fields higher than V/cm, as can be seen in the Fig. 1. Mujtaba [6] proposed an empirical modification of this model which accounts for carrier screening, but does not accurately capture the dependence of on at very high transverse fields which are common in recent technologies that use higher surface doping concentration and thinner oxides. Shirahata [8] also includes screening, but, because several terms are lumped together, the correct temperature behavior of the mobility in /97$ IEEE

2 1530 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 nature of this model, we will use the variable to designate spatial dependence. The bulk mobility term,, uses the Klaassen model [10], which takes into account coulomb screening effects, separately models majority and minority carrier mobilities, and includes temperature dependence (2) where (3) (4) (5) (6) Fig. 1. Lombardi electron mobility model (lines) overlaid on the measured mobility data of Takagi (points) for several doping values. the bulk and acoustic phonon terms is missing. Neither model accurately calculates mobility as a function of substrate bias, as will be shown later. We propose a global, physically-based, semi-empirical, local model for transverse-field dependent electron and hole mobility. To accurately predict the measured relationship of versus as a function of doping, effective field, and substrate bias [9], we account for the functional dependence of surface roughness limited mobility on the inversion charge density, in addition to accounting for the coulomb screening effect in the bulk limited mobility [10]. This approach is shown to provide a single mobility model that is applicable throughout a general device structure and that is dependent entirely on local quantities. The model is shown to describe accurately MOSFET operation for a wide range of channel impurity concentration ( cm to cm ) and effective transverse (gate) electric field up to 1.2 MV/cm. II. MOBILITY MODEL To evaluate the carrier mobility we use the Mathiessen rule that approximates the local mobility,, at low longitudinal field as the sum of three terms [5] where is the total carrier concentration and. For electrons,, where is the ratio between collision cross sections of repulsive and attractive screened coulomb potentials for electrons, and is a function of the local carrier concentration,. For holes,, where is the ratio between collision cross sections of repulsive and attractive screened coulomb potentials for holes, and also a function of. Other parameters are explained in [10]. In the low transverse field regions of the device, away from the inversion layer, this bulk mobility term dominates the carrier mobility, as given by (1). In the high transverse field inversion layer of an MOS device, this same bulk mobility term is used in (1), along with the other terms that now play a more significant role, therefore yielding a generalized mobility model applicable throughout the device. The second term in (1) is due to surface acoustic phonon scattering, which influences the inversion layer mobility at high transverse fields. This is taken into account here by adopting a similar formulation to that of Lombardi [5], which follows the approximation suggested by Schwarz and Russek [12]. Therefore (7) where is the carrier mobility in the bulk, is the carrier mobility limited by surface acoustic phonon scattering, and is the carrier mobility limited by surface roughness. However, other scattering mechanisms are usually lumped with the surface roughness scattering term, e.g., inter-subband scattering at high inversion charge [11]. To emphasize the local (1) where is the local field component normal to the direction of current flow. The initial values of an are based on physically derived quantities, as explained in [5], [12]. However, it should be pointed out that because of the difficulty in implementing a local formulation of the mobility degradation due to fixed interface charge, we followed the same approach of [5] by allowing to be weakly dependent on the impurity concentration. Therefore, with the

3 DARWISH et al.: IMPROVED ELECTRON AND HOLE MOBILITY MODEL 1531 TABLE I MOBILITY MODEL PARAMETERS Parameter Electrons Holes Units B cm/sec C (cm 2 /Vsec)1(V/cm) 1=3 1cm V/sec A Fig. 3. This hole mobility model (lines) overlaid on the measured hole mobility data of Takagi (points) for several doping values. Fig. 2. This electron mobility model (lines) overlaid on the measured mobility data of Takagi (points) for several doping values. parameters given in [10] could be still used in the interface region. As in the case of [5], it is recognized that this model will not be able to describe mobility degradation due to unusually large fixed interface charge., where is the temperature dependence of the probability of surface phonon scattering, as discussed in [12], and is an empirical parameter fit to measurements [5]. At very high transverse electric field, surface roughness scattering has a significant effect on the inversion layer mobility. In previously published local mobility models [2], [5], [6], [8] the dependence on the transverse field has the form where is a constant that depends on the details of the technology, such as oxide growth conditions. The exponent of the transverse electric field,, has previously been held constant and set to a value between 2.0 and 2.9. However, a careful look at Takagi s data at 77 K, where surface (8) Fig. 4. This electron mobility model (lines) overlaid on the measured electron mobility data of several researchers at various temperatures. roughness scattering dominates, shows that the dependence of on is not constant, but continues to increase with increasing. While the dependence of on is not necessarily the same as the dependence of on, many authors have shown it to be a valid and useful approximation [5], [6], [8]. Earlier experimental investigation [13] of mobility limited by surface roughness scattering at low temperature indicated

4 1532 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 (a) (b) Fig. 5. (a) This electron mobility model at zero and 05 V substrate bias for several doping values. (b) This electron mobility model calculated with a constant value of for several doping values at zero and 05 V substrate bias. that the field exponent remains approximately 2.0, even at high inversion charge and field. Early theoretical calculations of surface roughness scattering [14] showed that the exponent should decrease at high fields because of screening of surface roughness by the increase in surface carriers. But it was later shown that, as the transverse field and inversion charge increase, higher subbands in the quantum well of the inversion layer begin to become occupied, and multi-subband transport between levels separated in energy results in an enhanced decrease in mobility as the transverse field increases [11]. The formulation for surface roughness scattering that is commonly used in the analysis of is the one given by Matsumoto et al. [14], assumes a single subband occupation. Further work is therefore needed to refine this formulation for multisubband transport. These phenomena at very high transverse field can be modeled phenomenologically by an increase in the field exponent of the surface roughness mobility term with increasing carrier concentration. In the present model, we allow the field exponent in (8) to be a function of the local inversion charge. This results in a surface roughness limited mobility that increases with distance from the surface, as physically expected. The following formulation is proposed for : where and are fitting parameters. This formulation accounts for the increase in the rate of falloff of with that is seen in measurements at very high fields, due to the increase in carrier density [7]. It also accounts for the invariability of with substrate bias that is seen experimentally. As the substrate bias increases, the carrier concentration (9) Fig. 6. Normalized electron density and perpendicular field (left axis) versus depth into the substrate. Overlaid is the local electron mobility (right axis) calculated using this model (short dashes) and the Lombardi model (long dashes). in the inversion layer is reduced for the same value of. This results in a decrease in because of the reduction in impurity screening, and hence a dependence of the total mobility on substrate bias. In our model, this reduction in is compensated by an increase in when the carrier concentration reduces. Therefore, the dependence of effective mobility on substrate bias is minimized [9]. The inclusion of a weak dependence on in (9) was found to be necessary for agreement between measured and calculated. This

5 DARWISH et al.: IMPROVED ELECTRON AND HOLE MOBILITY MODEL 1533 (a) Fig. 7. Threshold characteristics: (a) 20-m long NMOS device with a 140 Å gate oxide and a surface concentration of 1: cm 03. Characteristics are shown for 0 V, 02.5 V, and 05 V substrate bias. (b) 10-m long NMOS device with a 90-Å gate oxide and a surface concentration of 2: cm 03. Characteristics are shown for 0 V, V, and 03.3 V substrate bias. Points are measurements, lines are simulations using this mobility model in PADRE. (b) effectively eliminates the weak dependence of on and results in a that is independent of substrate doping. The total mobility is obtained by taking the effect of velocity saturation into account, using the following formula developed by Hänsch [15], and satisfying Thornber s scaling theory [16] (10) where is the electric field parallel to the direction of current flow, and is saturation velocity. The model as formulated calculates local mobility based on the local value of the transverse electric field. But it must replay the measured quantities of as a function of, which are average quantities within a device. Therefore the parameters in the model were determined by comparison to the measurements of Takagi [7]. The local mobility was calculated using equations (1) (10), from which the quantities versus were calculated for devices with substrate dopings as described in [7]. The optimization program, CENTER [17], was then used to select the values of the parameters which gave the best fit to measurements at several doping levels [7] and temperatures [9]. Initial values for the optimization were obtained from [5] and was done stepwise by starting with room temperature, low doping concentration data to optimize most parameters. The higher doping data was included to extract the two doping coefficients, and the high and low temperature data were included to optimize the temperature coefficient,. Finally, a global optimization was done with all data. Parameter values for the bulk mobility term were taken directly from [10]. An optimized set of values for the fitting parameters in the acoustic phonon and surface roughness mobility terms are shown in Table I for both electrons and holes. in (7) (9) is in V/cm, and are in cm, and is in K. The values of and in the table compare favorably to the physically derived values, and to those extracted by Lombardi [5] when normalized for temperature. The parameter in the acoustic phonon scattering term in Lombardi s model has a value of for electrons and for holes. However, because screening of ionized impurities at higher carrier concentration is now taken into account in the bulk mobility term, the value of in this model is greatly reduced to for electrons and for holes. The value of the parameter is 2.58 and 2.18 for electrons and holes, respectively. These are somewhat higher than that theoretically predicted by Matsumoto [14], but consistent with that estimated experimentally by Takagi [7] and within the range of values used in other models to fit the high field region [2], [5], [6], [8]. Over a wide range of doping and perpendicular field, the value of for electrons was found to vary from 2.58 to 2.9, still very consistent with the measurements in [7]. But, because the local electric field is used in this model rather than the effective field, as in the theoretical calculations

6 1534 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 (a) Fig. 8. Output characteristics for (a) a 10-m long NMOS device with a 90 Å gate oxide and a surface concentration of 2: cm 03 and (b) a 0.5-m long NMOS device with a 90-Å gate oxide and a surface concentration of 2: cm 03. Characteristics are shown for gate bias of 1.3 V, 2.3 V, and 3.3 V. Points are measurements, lines are simulation using this mobility model in PADRE. (b) and experimental results, direct comparisons between these parameters and those extracted from the experimental data cannot be made. for holes was found to vary somewhat less, from 2.18 to 2.3. The doping dependence,, in the surface roughness term varies less than a factor of 2 over three orders of magnitude variation in. The coefficient describing the temperature dependence of the probability of surface phonon scattering is 1.7 for electrons. This is consistent with the values of 1.75 [7] and 2.0 [12] which were extracted from different sets of mobility measurements over temperature. III. COMPARISON WITH MOBILITY MEASUREMENTS Figs. 2 and 3 show the calculated effective mobility versus Takagi s data for different substrate doping concentrations for electrons and holes, respectively. The agreement is very good over effective transverse field and as a function of doping. The present model also predicts the roll-off of mobility at low inversion charge, which is a result of the reduction in the screening effect. The roll-off is somewhat more pronounced in the measurements than the simulations because some of the roll-off is a result of the measurement technique, as discussed in [18]. Fig. 4 compares the effective electron mobility versus effective field using this model with the measured data of several researchers [1], [7], [9], [19], [20] at low doping and at several temperatures. The agreement is very good over a wide range of temperature from 200 K to 413 K. Fig. 5(a) shows the mobility calculations using this model for three different doping concentrations at zero substrate bias ( V), and at V. There is very little dependence of the calculated mobility on, consistent Fig. 9. Output characteristics at 400 K for a 10-m long NMOS device with a 90 Å gate oxide and a surface concentration of 2: cm 03. Characteristics are shown for gate bias of 1.0 V, 2.0 V, and 3.3 V. Points are measurements, lines are simulation using this mobility model in PADRE. with the universal relationship shown in [9]. Also shown in Fig. 5(b) are the results using the same model with a constant value of. For clarity, only the calculations with cm and cm are shown. The value of used in Fig. 5(b) has not been optimized, so the calculated is higher than with the proposed model,

7 DARWISH et al.: IMPROVED ELECTRON AND HOLE MOBILITY MODEL 1535 (a) Fig. 10. (a) Threshold characteristics with V bs =0,1:65, and 3:3 V, and (b) output characteristics with V gs = 01:3, 02:3, and 03:3 V for a 5-m long PMOS device with a 90 Å gate oxide. Points are measurements, lines are simulation. (b) but what is important is the large dependence of on for the device with a high substrate doping, which is not seen experimentally. A local model that includes screening and uses a constant value of will have a similar reduction in with substrate bias for devices with substrate doping concentration typical of current technologies. By allowing to depend on, the dependence of the total mobility on is greatly reduced. In order to clarify the model behavior we show in Fig. 6 the normalized electron concentration and normal electric field versus the distance perpendicular to the inversion layer for a device with cm channel doping and a peak transverse field of about V/cm. The electron concentration and field were calculated using classical Fermi-Dirac statistics. It is interesting to note that in comparison with Lombardi s model [5] this model predicts higher mobility further into the the inversion layer and higher mobility degradation at the surface which results in a crossover of the two mobility curves in Fig. 6. This is a result of taking into account, in this model, both the screening of impurities by charge carriers as well as the screening of surface roughness due to the increase in surface carriers, while Lombardi s model does not. The screening of surface roughness results in more mobility degradation close to the surface and when combined with the the screening of impurities by charge carriers a peak results in mobility away from the surface. IV. COMPARISON WITH MEASUREMENTS The model was implemented in the 2-D/3-D device simulation program PADRE [21], and used to characterize devices from submicron CMOS technologies. Devices from three different technologies A, B, and C were compared. Doping profiles used as input into the device simulator were generated with the process simulator BICEPS [22] for technologies A and B with gate length down to 0.5 m. For technology C the gate length goes down to 0.35 m and because of the fabrication process used, Transient Enhanced Diffusion (TED) effects [23] become important. PROPHET process simulator [24] was used so that TED effects could be fully simulated. However, it is important to note that all mobility model parameters were extracted using uniform doping profiles used in [7] and no further parameter adjustment was done in the following comparisons. In the first technology (A) the surface doping concentration of both the NMOS and PMOS devices is about cm, created by a threshold adjust implant before oxidation of the gate. The gate oxide thickness of these devices is 140 Å. The surface doping concentration in the second technology (B) is about cm, and the gate oxide thickness is 90 Å. In technology C, gate oxide thickness is 90 Å and the thermal budget after gate formation was kept small so that the NMOS doping was retrograde, with surface concentration of cm and a peak of cm close to the surface. In all technologies the gate material is n polysilicon. Both long-channel and short-channel devices were created in all technologies. As will be shown, the mobility model adequately describes MOSFET characteristics over a wide region of operation and design parameters using the coefficients as extracted from the mobility measurements described above. The penalty in cpu time to calculate the mobility based on this model is less than 4% as compared to the model proposed by Lombardi [5]. Fig. 7(a) shows a comparison between simulated threshold characteristics and measurements for a 20- m long, NMOS device of technology A. A long-channel device with thin oxide

8 1536 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 (a) (b) (c) Fig. 11. (a) Threshold characteristics with V bs =0,01.65, and 03.3 V, (b) output characteristics with V gs =1:3,2:3, and 3:3 V, (c) subthreshold characteristics with, from left to right, V ds =3:3,2:3,1:3, and 0:1 V, for a 0.35-m long NMOS device with 15-m width, a 90 Å gate oxide, and a surface concentration of 3: cm 03. Points are measurements, lines are simulation using PROPHET and PADRE. and high surface doping is evaluated first to isolate the effects of the transverse field mobility model from the additional velocity saturation and short-channel effects which dominate the characteristics for very short-channel devices. Moreover, any error due to external source and drain resistances that were extracted from measurements and included in the simulations is minimized. Fig. 7(b) shows a comparison of the threshold characteristics for a 10- m long NMOS device of technology B. In both cases the fit is quite good over gate voltage and substrate bias. This illustrates that, while the parameters of the model were determined by comparison with measured mobility data from the literature, the fit of the model to measured characteristics over transverse field, substrate bias, and to devices with varying substrate doping is very good. In Fig. 8(a) and (b), the output characteristics are shown for the 10- m long and 0.5- m long NMOS devices of technology B. The agreement is very good in both the linear and saturation regions of the long-channel and short-channel devices, indicating that the short-channel and velocity saturation effects are also well modeled. Fig. 9 shows the agreement between simulation using this model and measured output characteristics for a 10- m long NMOS device of technology B operating at 400 K. The agreement is still very good at this elevated temperature. Overall, currents are predicted within about 5% of the measured values across all of the important parameters associated with MOS device operation, including doping, channel length, temperature, and drain, gate, and substrate bias. P-channel threshold and output characteristics are shown in Fig. 10(a) and (b), respectively, for a 5- m long device of technology B. Again, the agreement is very good over a wide range of bias conditions. Fig. 11(a) (c) show the comparison for a m NMOS, technology C, device at room temperature. Good agreement was obtained in the linear, saturation, and subthreshold regions. Finally, Fig. 12 shows a comparison of technology C NMOS linear (drain current for V, Fig. 12. Comparison of the linear ion (V gs =3:3V, V ds =0:1V, V bs =0 V) as a function of gate length and temperature for NMOSdevices with 15-m width, a 90 Å gate oxide, and a surface concentration of 3: cm 03. Points are measurements, lines are simulation using PROPHET and PADRE. and V) over gate length and temperature, showing a good agreement. The comparisons for technology C PMOS devices were also good over all the operation range and have been reported elsewhere [25]. V. CONCLUSION A physically-based, semi-empirical, local model for transverse-field dependent electron and hole mobility was

9 DARWISH et al.: IMPROVED ELECTRON AND HOLE MOBILITY MODEL 1537 presented. The model accounts for the functional dependence of surface roughness limited mobility on the inversion charge density, in addition to coulomb screening effects of impurities by charge carriers. It was shown that this approach successfully connects the local model to the global universal relationship of mobility to effective inversion layer field. The model was implemented in the 2-D/3-D device simulation program PADRE and gives very good agreement when compared to measured mobility data and measured MOS characteristics over a wide range of doping ( cm to cm ), effective transverse (gate) electric field up to 1.2 MV/cm, channel length and temperature. REFERENCES [1] A. J. Walker and P. H. Worlee, A mobility model for MOSFET device simulation, in Proc. Europ. Solid-State Dev. Res. Conf. (ESSDERC), 1988, p [2] C.-L. Huang and G. S. Gildenblat, Measurements and modeling of the n-channel MOSFET inversion layer mobility and device characteristics in the temperature range K, IEEE Trans. Electron Devices, vol. 37, p. 1289, May [3] S. Selberherr, W. Hänsch, M. Seavey, and J. Slotboom, The evolution of the MINIMOS mobility model, Solid-State Electron., vol. 33, no. 11, p. 1425, [4] H. Shin, G. M. Yeric, A. F. Tasch, and C. M. Maziar, Physically-based models for effective mobility and local-field mobility of electrons in MOS inversion layers, Solid-State Electron., vol. 34, no. 6, p. 545, [5] C. Lombardi, S. Manzini, A. Saporito, and M. Vanzi, A physicallybasedmobility model for numerical simulation of nonplanar devices, IEEE Trans. Computer-Aided Design, vol. 7, pp , Nov [6] S. A. Mujtaba, R. W. Dutton, and D. L. Scharfetter, Semi-empirical local NMOS mobility model for 2-D device simulation incorporating screened impurity scattering, in Proc. NUPAD V, June [7] S. Takagi, A. Toriumi, M. Iwase, and H. Tango, On the university of inversion-layer mobility in Si MOSFET s Part I: Effects of substrate impurity concentration, IEEE Trans. Electron Devices, vol. 41, pp , Dec [8] M. Shirahata, H. Kusano, N. Kotani, S. Kusanoki, and Y. Akasaka, A mobility model including the screening effect in MOS inversion layer, IEEE Trans. Computer-Aided Design, vol. 11, pp , Sept [9] A. G. Sabnis and J. T. Clemens, Characterization of the electron mobility in the Inverted h100i Si substrate, in IEEE IEDM Tech. Dig., 1979, pp [10] D. B. M. Klaassen, A unified mobility model for device simulation Part I: Model equations and concentration dependence, Solid- State Electron., vol. 35, no. 7, pp , [11] S. Mori and T. Ando, Intersubband scattering effect on the mobility of a Si (100) inversion layer at low temperature, Phys. Rev. B., vol. 19, p. 6433, [12] S. A. Schwarz and S. E. Russek, Semi-empirical equations for electron velocity in silicon Part II: MOS inversion layer, IEEE Trans. Electron Devices, vol. ED-30, pp , Dec [13] A. Hartstein, T. H. Ning and, A. B. Fowler, Electron scattering in silicon inversion layers by oxide and surface roughness, Surf. Sci., vol. 58, p. 178, [14] Y. Matsumoto and Y. Uemura, Scattering mechanism and low temperature mobility of MOS inversion layers, Jpn. J. Appl. Phys., supp. 2. pt. 2, p. 367, [15] W. Haänsch and M. Miura-Mattausch, A new current relation for hot electron transport, INASECODE IV, J. J. H. Miller, Ed. Dublin, Ireland: Boole, 1985, pp [16] K. K. Thornber, Relation of drift velocity to low-field mobility and high-field saturation velocity, J. Appl. Phys., vol. 51, pp , [17] K. Singhal, C. C. McAndrew, S. R. Nassif, and V. Visvanathan, The CENTER design optimization system, AT&T Tech. J., vol. 68, no. 3, p. 77, May/June [18] C.-L. Huang, J. V. Faricelli, and N. D. Arora, A new technique for measuring MOSFET inversion layer mobility, IEEE Trans. Electron Devices, vol. 40, pp , June [19] J. T. Watt and J. D. Plummer, in 1987 Symp. VLSI Technol. Dig. Tech. Papers, 1987, p. 81. [20] V. M. Agostinelli, Jr., unpublished. [21] M. R. Pinto, C. S. Rafferty, R. K. Smith, and J. Bude, ULSI technology development by predictive simulation, in IEDM Tech. Dig., 1993, p [22] B. R. Penumalli, A comprehensive two-dimensional process simulation program, BICEPS, IEEE Trans. Electron Devices, vol. ED-30, Sept [23] M. R. Pinto, D. M. Boulin, C. S. Rafferty, R. K. Smith, W. M. Coughran, I. C. Kizilyalli, and M. J. Thoma, Three-dimensional characterization of bipolar transistors on a submicron BiCMOS technology using integrated process and device simulation, in IEDM 1992, p [24] C. S. Rafferty, H.-H. Vuong, S. A. Eshraghi, M. D. Giles, M. R. Pinto, and S. J. Hillenius, Anomalous short-channel threshold voltage due to transient enhanced diffusion, in IEDM 1993, p [25] H. H. Vuong, C. S. Rafferty, S. A. Eshraghi, J. L. Lentz, P. M. Zeitzoff, M. R. Pinto, and S. J. Hillenius, Effects of oxide interface traps and transient enhanced diffusion on the process modeling of PMOS devices, IEEE Trans. Electron Devices, vol. 43, p. 1144, Mohamed N. Darwish (M 82-SM 89) was born in Cairo, Egypt. He received the Ph.D. degree in electrical engineering in 1981 from the University of Wales, Swansea, U.K. From 1982 to 1984, he was a Postdoctoral Fellow in the Department of Electrical and Electronic Engineering, the University College of Swansea, U.K., where he conducted research on metal-semi-insulator-semiconductor, bulk barrier switching devices and high-voltage DMOS and lateral insulated gate bipolar (LIGBT) transistors. From 1984 to 1993, he was with AT&T Bell Laboratories, Reading/Allentown, PA. where he worked on the technology development and device modeling of Bipolar-CMOS-DMOS (BCDMOS) IC s. Later, he was involved with device physics and modeling related to the m CMOS technology development. In 1993, he joined Siliconix Inc., Santa Clara, CA where he manages submicron BCDMOS technology development and device modeling and characterization for power management, hard disk drives, telecommunications, and automotive applications. Dr. Darwish was a recipient of the AT&T Bell Laboratories Distinguished Member of Technical Staff Award in He has served as the Chairman of the IEEE Lehigh Valley Section and Electron Device Chapter as well as on the Technical Program Committee of IEDM. Janet L. Lentz received the B.S. degree in physics from Thomas More College, Fort Mitchell, KY in 1983, and the M.S. degree in electrical engineering from the University of Cincinnati, Cincinnati, OH, in She joined Bell Laboratories, now part of Lucent Technologies, Breinigsville, PA, in 1985, working in the area of Gallium Arsenide IC process development and device modeling. From 1988 until 1995, she developed silicon process and device simulation software, and aided in the development of advanced submicron silicon CMOS and bipolar devices through simulation. She is currently developing modeling and simulation capability for optoelectronic devices, aiding in the development of high-performance laser designs. Mark R. Pinto (S 84 M 85 SM 96) for a photograph and biography, see this issue, p

10 1538 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 Peter M. Zeitzoff (M 75) received the B.S.E., M.S.E., and Ph.D. degrees in electrical engineering from Princeton University, Princeton, NJ, in 1967, 1972, and 1976, respectively. He is currently on assignment at SEMATECH, Austin, TX, where he is working on defining, optimizing, and characterizing a generic 0.18-m and 0.13-m IC technology, and on performing TCAD validation. From 1985 to 1995, he was at AT&T Bell Laboratories, now part of Lucent Technologies, Allentown, PA, where he worked on IC process and device simulation, and on IC device and technology development, optimization, and characterization. He also assessed the implications for AT&T of both short- and long-range trends in IC technology. From 1975 to 1985, he was at Eastman Kodak Company, Rochester, NY, where he worked on the development and sustaining of bipolar IC processes, and on development of prototype CCD imager technology and devices. Thomas J. Krutsick was born in Stuttgart, West Germany, in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Lehigh University, Bethlehem, PA, in 1981, 1983, and 1988, respectively. In 1988, he joined AT&T Bell Laboratories, now part of Lucent Technologies, Reading, PA, where he is presently a Technologist. He is involved with the development of complementary bipolar device and process design. His research interests include semiconductor device physics, device modeling and design, fabrication technology, and circuit design. Hong Ha Vuong (M 88) was born in Saigon, South Vietnam. She received the B.A. and D.Ph. degrees in physics from Oxford University, U.K. in 1981 and 1985, respectively. From 1985 to 1988, she was an Associate Researcher in the Electrical Engineering Department of Princeton University, Princeton, NJ, where she carried out research on the resonant tunneling characteristics of heterostructures of III V compound semiconductors. Since 1988, she has been a Member of the Technical Staff of AT&T Bell Laboratories, now part of Lucent Technologies, Reading, PA, where she investigated the device physics of GaAs heterostructures and GaAs integrated circuits, worked to reduce process variations, and led the MBE GaAs production team. Since 1991, she has worked in Bell Laboratories, Allentown, PA, and Murray Hill, NJ, in the area of TCAD semiconductor process simulation and TCAD application to advanced silicon technologies, and in the development of ultrashallow junctions. She has authored and coauthored thirty publications, and holds one patent. Dr. Vuong served on the Modeling and Simulation subcommittee at the 1995 and 1996 IEDM.

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