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2420 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 12, DECEMBER 2000 Modeling of High Current Density Trench Gate MOSFET K. G. Pani Dharmawardana and Gehan A. J. Amaratunga, Member, IEEE Abstract—This paper presents a semianalytical model devel) of trench gate MOSFETs. It oped for the ON state ( incorporates a more realistic model for the inversion channel region, taking the effects of doping variation, transverse, and longitudinal electric fields including the surface scattering, into consideration. Accurate modeling of the inversion channel region is of paramount importance, especially in the case of low voltage power devices where the inversion channel resistance is a significant portion of the overall resistance. The carrier velocity saturation at high longitudinal electric fields is also taken into account in the formulation of the model. The proposed model is supported by both numerical simulation results using MEDICI and experimental results, which are in good agreement with the results of the model. This can be a useful tool in the design of optimum devices. Index Terms—Inversion channel, mobility, modeling, MOSFET, trench gate. I. INTRODUCTION T HE TRENCH GATE MOSFET (TMOSFET) is considered to be one of the most promising devices for power switching at voltages up to 100 V [1]–[3]. The basic reason for its attractiveness is that, in a multicell geometry, it allows for maximization of the gate perimeter to cell area ratio by virtue of having the inversion and accumulation channel regions placed at right angles to the surface plane. Specific on resistances below 1 m cm for 50 V n-channel [4] and 30–40 V p-channel [5] devices have been reported, and with the application of ULSI technology to make submicrometer-wide trench gates, further reductions in specific on resistances are expected. In addition to the geometrical advantages of the TMOSFET structure, there are device phenomena related effects which also give it some advantages. These are mainly associated with the lack of a “JFET” region. Traditionally in a DMOSFET the diffused p-body regions in the n-drift region, through which the main channel current has to flow, has been viewed as giving rise to depletion pinch off of this region as in a classical JFET. Detailed studies however, show that at very high current densities the depletion region in the n-drift side of the p-body/n-drift region junction can be retarded due to enhanced carrier flow from accumulation channel formed in the gate-drain overlap region [6], [7]. In a TMOSFET this accumulation region is used very effectively as it is placed within the n-drift region. The ul- timate limit to the reduction of the specific on resistance of a TMOSFET is not due to any pinch-off type saturation, but rather velocity saturation of electrons in the n-drift region [8], [9]. Interestingly, it was noted by Darwish [6] in one of the original analyses of DMOSFET operation that velocity saturation can also be the limiting mechanism in the planar structure. Analytical models for the power DMOSFET have been developed by several researchers [10], [11]. These models have been adequate for modeling the larger cell geometry devices. However, there has been no analytical treatment to date of the ultrahigh current density TMOSFET where there are several differences in the way in which current enters the drift region from the inversion channel compared to the large cell geometry DMOSFET. Of fundamental importance for both DMOSFET and TMOSFET models is the accurate modeling of the inversion channel voltage drop. This is a nontrivial task in power MOSFETs due to the fact that the inversion channel is formed in a substrate (p-body) region in which the concentration is continuously varying, from a peak value at the source end to a minimum (equal to the drain concentration) at the drain end. We have analyzed the channel region with a much more realistic model and report here the success of the approach. It is also applicable to DMOSFETs and LDMOSFETs, where to date the channel region has been approximated to be a constant electric field region [10]. In addition, special attention is paid to the current transfer from the accumulation region into the n-drift region in the TMOSFET. The model presented, and validated against experimental devices can be a useful design aid to initial device optimization and the determination of how different physical parameters interact to limit performance. II. MODEL A semianalytical model for the ON state of a typical trench gate MOS (TMOS) transistor is derived using charge control analysis of the channel and drain drift regions. The doping distribution and the dependence of low field mobility on doping concentration, transverse and parallel field within the channel region are taken into account in deriving this model. The TMOS structure shown in Fig. 1 is used for the purpose of modeling. A. Channel Region Manuscript received December 20, 1999; revised April 17, 2000. This work was supported by Fuji Electric Research and Development Ltd, Japan. The review of this paper was arranged by Editor G. Baccarani. The authors are with the Department of Engineering, University of Cambridge, Cambridge CB2 1PZ U.K. (e-mail: [email protected]). Publisher Item Identifier S 0018-9383(00)10409-5. Gradual channel approximation is assumed to be valid in modeling the channel region so that the channel and depletion layer widths are governed only by the perpendicular fields. The doping profile of the channel region is taken to be a one sided 0018–9383/00$10.00 © 2000 IEEE DHARMAWARDANA AND AMARATUNGA: TRENCH GATE MOSFET Fig. 1. 2421 Structure of the trench MOS. gaussian distribution with the peak at the source end of the channel region and is given by (1) peak doping concentration in atoms/cm and standard deviation of the doping distribution. In order to take a proper account of the doping distribution in the channel region, it is divided into a number of subregions of equal length as shown in Fig. 2(a) and doping concentration in each region is set to be constant as shown in Fig. 2(b). The analysis is performed for a single subregion at a time and extended for the entire channel region by matching of current boundary conditions at each region boundary. An incremental length along a sub region sustains a voltage [see Fig. 2(c)] that can be expressed as a product of the drop and the incremental resistance . drain current where where Fig. 2. (a) Subdivision of the channel region. (b) Doping profile. (c) Subregion analysis. fine the longitudinal field dependence of low field mobility, various empirical expressions for the electron drift velocity have been proposed. Equation (4) describes the piecewise-continuous electron velocity model which is used in [10], [11]. voltage drop across the element ; drain current; width of the device (in the direction); electron mobility; inversion layer charge densit. for for Hence (2) where subregion length and Equations (5) and (6) show the famous Caughey–Thomas expression for electron velocity [12], is given by (3) where Flatband voltage (4) with and respectively. (5) oxide capacitance per unit area; ; metal, semiconductor work function potential difference; Si/oxide interface charge; The integration of (2) requires an expression for which is dependent on longitudinal and transverse electric fields. To de- (6) Fig. 3 shows the velocity curves for these models. The saturation effect of the electron velocity is observed to be a built 2422 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 12, DECEMBER 2000 Fig. 4. Variation of low field mobility with doping concentration. Fig. 3. Velocity curves for the three different models. in feature in model (5). Further, the saturation electric field described by this model agrees well with the experimental satuV/cm [13]. ration electric field in Si which is around Hence, model (5) is used here to obtain an expression for the . mobility given by (7) is the effective mobility. where The simplified Takagi mobility model [14], which is in good agreement with the experimental results for surface scattering effects, is used to account for the transverse field dependence of the mobility. is given Electron mobility limited by phonon scattering, by Integration of (2) is performed taking a linear variation of the voltage within the subregion thus giving a constant longitudinal given by and assuming an average electric field inside the inversion layer. transverse electric field strength The transverse electric field within the channel is calculated by taking the depletion charge (relating only to the vertical doping profile) and the inversion charge into account. At present, the variation of the doping profile in the direction is not taken into consideration. This has not been built into the calculation due to the difficulty in obtaining experimental two-dimensional (2-D) doping profiles. It can be easily included if such data is available. For calculating conduction in the inversion channel, which is the average of the perpendicular trapea quantity is taken zoidal electric field within the channel is defined. to be constant in each of the subregions of the channel in the direction, but changes from subregion to subregion. This gives rise to a constant mobility within each subregion. within a subregion is described by Hence the drain current (8) and K where Surface roughness limited mobility, is given by (9) where The effective mobility, is obtained by Matthiessen’s rule, (11) (10) is the doping concentration dependent low field mowhere bility. The combination of (7) and (10) describes a composite model for mobility , which takes the effects of doping variation, longitudinal and transverse electric fields including surface scattering into account. is obtained for each subregion by The low field mobility means of the graph shown in Fig. 4 [15] in order to account for the doping concentration dependence of the low field mobility. is given by equation (10) and the transverse electric where field averaged inside the inversion layer is (12) The derivation of (12) is given in the Appendix. DHARMAWARDANA AND AMARATUNGA: TRENCH GATE MOSFET 2423 field is becomes , the current at the end of the th subregion (15) Fig. 5. Current flow path. The threshold voltage for the gate at which source end is given by at the (13) For a particular drain current, which should be continuous throughout the channel, the voltage in each subregion can be calculated sequentially starting from the first sub region at the source end with a source voltage of 0 V. This is analogous to having nMOSFETs in series where the nodal potentials need to be calculated. The Newton–Raphson iterative method is used to solve (11) in each subregion to get the nodal potentials in that sub region. The Matlab software suite was used to perform all the necessary computation. B. Drift Region The drift region is partitioned into two based on the current flow path as shown in Fig. 5. In region 1 a portion of the current is confined to the accumulation layer at the trench wall, whereas in region 2 current flows throughout the total area. The same model that was derived for the inversion channel region is used for the current flow in region 1 with the inversion layer charge density being replaced by the accumulation layer charge density. However, a current decrease after each subregion must be included in the model to take into account the continuous injection of accumulation channel charge into the drift region. The injection of accumulation charge into the drift region in TMOS devices has been studied in detail by Evans and Amaratunga [9]. Variation in channel current in each accumulation sub region is calculated in the following manner. being replaced by the accumulation charge Using (2) with , with we obtain density The surface potential in the accumulation layer, and is given by (10). Voltage in each subregion is calculated sequentially using equations (14) and (15) assuming no accumulation injection and voltage in the from the first subregion last subregion in the inversion channel. Current is assumed to be uniformly distributed throughout ) in Fig. 5. the total available area in region 2 which is ( Therefore, in the drift layer below the trench bottom, the voltage varies only in the vertical ( ) direction and is constant in the in this region. lateral ( ) direction. Hence, Equation (18), a combination of (16) and (17), is solved numerically using second/third-order Runge–Kutta method to obtain the voltage in region 2 in Fig. 5. (16) and where the cross sectional area, by equations (7) and (10) with the assumption that region 2. is given in (17) (18) can be Therefore, for a given current , drain voltage calculated using the channel and drift region analysis and is given by (19) where channel voltage drop; voltage drop in region 1; voltage drop in region 2. by only It should be noted that it is adequate to obtain considering the accumulation channel voltage drop because the accumulation channel region is in effect a parallel path to that in which carriers injected from the accumulation channel region flow in region 1. (14) III. RESULTS AND DISCUSSION Using the fact that the accumulation charge at the end of the th and the electric subregion is The semianalytical model was evaluated first by comparing the results predicted with those obtained from direct numerical 2424 Fig. 6. IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 12, DECEMBER 2000 I–V characteristic at V = 10 V. Fig. 7. Electron velocity in the channel region at V simulation of the semiconductor equations using the MEDICI program and secondly by comparing with experimental results. Both semianalytical and numerical simulation was performed for a TMOS having the following channel region parameters. atoms/cm 0.3 m where the doping profile is given by equation (1). F/cm Oxide layer 1000 Å giving thickness C/cm 1 m and 25 subregions giving m in the inversion channel region. The trench depth in the drift region was taken as 1.7 m and the accumulation region was divided into 25 subregions. For is the above mentioned parameter values, threshold voltage approximately 4 V. The other parameter values of this device are atoms/cm , m, m and m (See Fig. 5 for definition of parameters). The nominal off-state break down voltage for the trial device is 400 V. Fig. 6 shows the current–voltage (I–V) characteristic for this device obtained using the proposed model. The physics based device simulator, MEDICI which uses a numerical method to solve the basic semiconductor equations (20) and (21) was used to obtain the “correct” TMOSFET characteristics for comparison with the semianalytical model. (20) (21) In MEDICI simulations, the p-body concentration was made very close to that in the semianalytical model, Fig. 2(b) and the other structure parameters were kept the same as for the model. The Lombardi mobility model was used in place of the Takagi model with adjusted parameter values so that it becomes closely equivalent to the Takagi model. In Fig. 6, I–V characteristics obtained from modeling and MEDICI numerical simulation are compared. The agreement = 50 V. Fig. 8. I versus V at V = 5, 7:5 and 10 V (Dashed lines show the curves obtained using the model in [10], [11]). over a large range of values is very good. This agreement between the model and the numerical simulation is remarkably good in the linear region. We believe that this is because of the accurate semianalytical model that we have developed for the inversion channel region taking into account the doping variation in the p-body and a detailed mobility model. The deviation from the numerically simulated curve is most noticeable in the quasisaturation region where velocity saturation of carriers commences in the n-drift region of the device [6]. The assumption regarding the current path in the model is perhaps most inaccurate in this regime of operation. Nevertheless, the model only gives a 5% error even in this regime where velocity saturation of carriers in the drift region prevails. value of 50 V considered, the channel At the maximum cm/s in the velocity is seen to have a maximum value of velocity plot in Fig. 7. This is well below the saturation velocity cm/s). Therefore the saturation of electrons in of electrons ( the n-drift region is the main cause for current saturation in the trench gate MOSFET as previously proposed [9]. This is further DHARMAWARDANA AND AMARATUNGA: TRENCH GATE MOSFET 2425 (a) (a) (b) Fig. 9. (a) Channel voltage versus distance (b) electric field magnitude distribution at V 10 V and I 0.06 mA/m. = = confirmed by the fact that the saturation velocity for electrons value of the in the channel region is only reached when the TMOSFET has a much higher value of 190 V. For the 400 V trial device, the specific on resistance at V in the linear region is 30 m cm whereas a classical DMOS would have a specific on resistance of about 70 m cm . This confirms the significant reduction in on-state loss which can be obtained from the TMOS structure even for devices rated at high voltage. Fig. 8 shows the calculated drain current ( )–channel ) characteristic using the proposed model and voltage ( the same characteristic obtained using the DMOSFET channel models used previously [10], [11], which do not take the effects of doping distribution, concentration dependence of the low field mobility, and scattering effects on the voltage variation along the channel into account. Comparison of the results of both models in Fig. 8 shows that value is significantly reduced the channel current at a given (b) Fig. 10. (a) Electric field magnitude variation. (b) Carrier velocity plot in the inversion channel region at V 10 V. (i) I 0:04 mA/m, (ii) I = 0:06 mA/m, (iii) I = 0:08 mA/m, (iv) I = 0:10 mA/m. = = by the use of more accurate channel mobility model. This is because of the degradation of electron mobility due to the longitudinal and transverse electric fields, with the major contribution being from the transverse field. This is discussed below with respect to Fig. 11. Fig. 9(a) is a plot of the channel voltage from the source end (0 m) to the drift layer (1 m) and Fig. 9(b) shows the corresponding electric field magnitude distribution for a drain current of 0.06 mA/ m. It is apparent that for this drain current, electric field gradually decreases with a maximum near the source end of the channel. In Fig. 10, we present electric field and carrier velocity plots through the inversion channel for a series of drain currents (drain voltages). It is interesting to note that the maximum electric field position in the channel moves from the source end to the . This is a conmiddle of the channel with increasing sequence of the varying p-body doping concentration leading 2426 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 12, DECEMBER 2000 (a) Fig. 12. (b) Fig. 11. (a) Electric field magnitude distribution in the inversion channel region at V 10 V and I 0:1 mA/m. (b) I–V characteristics for the inversion channel region at V = 10 V (i) not considering the effects of both doping variation and gate electric field on mobility, (ii) considering only the effect of doping variation on mobility, (iii) considering only the effect of gate electric field on mobility, and (iv) considering the effect of both doping variation and gate electric field on mobility. = = to the initial high field region occurring close to the source at values. As increases, voltage along the channel low becomes more comparable with the gate voltage and voltage increase and the doping variation along the channel have opposite effects on the inversion layer charge. This leads to a maximum electric field point at the middle of the inversion channel region. Fig. 11(a) shows the relative impact of the different mobility models on the channel electric field distribution. The more complete mobility model leads to a shift in the maximum electric field position away from the source end into the middle of the channel region. The effect of the doping profile and the gate electric field is therefore to shift the point of maximum electric field in the channel away from the source end. Fig. 11(b) shows the channel I–V characteristics for the inversion channel region with and without the effects of doping variation and gate electric field on mobility being considered. It can be clearly seen that the doping variation and gate electric field, with the latter Impact of number of subregions. playsing the major role, causes a reduction in the value of at . higher values of The impact of the subdivision of the channel region into discrete elements with constant electric field was also evaluated. values for a of 0.1 mA/ m for a Fig. 12 is a plot of series of values. It is evident that the results converge to almost identical values when the number of subregions is greater than 25. Hence, division of the channel region into 25 subregions gives an acceptable accuracy for this model with parameters used for gate oxide thickness, channel doping and length. Fig. 13 shows the current flow lines in the device to a depth values obtained from MEDICI. of 3.2 m for two different It should be pointed out that the current flow assumed in region 1 for the model, Fig. 5, is similar to the one produced by MEDICI. In Fig. 13, the separation between each current flow contour represents 2% of the total current. It is interesting to note that approximately 2% of the drain current ( ) in the trench MOSFET at the bias points shown, is a punch through current through the depletion region under the MOS inversion channel. The broken contour represents the edge of the depletion region in the n-drift region. The carrier concentration due to the current in the depletion region in the n-drift region at the p-body/n-drift junction close to the trench gate is higher than the depletion car. This in turn leads to the rier concentration, i.e. “drowning” out of the n-drift depletion region and the consequent onset of quasi saturation. The junction however stays reverse biased with the built in potential being maintained by the growth of the depletion region on the p-body side of the junction. A TMOSFET rated at a lower break down voltage of 100 V was also studied. The differences in the 100 V device structure atoms/cm are that drift region doping is increased to and length reduced to 7.2 m. The p-body region was adjusted to have the same peak doping concentration ( atoms/cm ) at the source end and the channel length (1 m) as for the 400 V device. The trench depth and width were characteristics 3 m and 0.5 m. The predicted values obtained from the for the 100 V device for three model and MEDICI are shown in Fig. 14. Again the agreement DHARMAWARDANA AND AMARATUNGA: TRENCH GATE MOSFET 2427 Fig. 14. I–V characteristics of the 100 V device at V Fig. 15. Experimental and modeled results for a 60 V device. = 5 V, 10 V, and 15 V. (a) (b) = Current flow lines in a portion of the device at (a) V 10 V, = 10 V, V = 10 V (the broken lines show the edges of the depletion regions). Fig. 13. V = 1 V (b) V between the numerical simulation and the model is excellent. The fact that the quasisaturation, as opposed saturation in the channel region, is the main phenomenon responsible for current saturation in TMOSFETs leads to almost identical characteristic curves for values of 10 V and 15 V. The experimental results for a 60 V TMOSFET were also compared with the results predicted by the model. The model was modified to read the experimental doping profile instead of the Gaussian profile given in 1. This device has an oxide thickness of 500 Å, a channel length of 1.4 m, and the trench depth in the drift region is 0.6 m. The other parameter values atoms/cm , m, for this device are m and m (see Fig. 5 for definition of parameters). The interface charge, at the Si/Oxide interface C/cm to obtain the experimental was taken to be threshold voltage which is 1.5 V. The resistance of the 0.007 cm, 300 m substrate was also included in the model. The predicted results from the model are in excellent agreement with the experimental results. The value of the parameter in the Caughey–Thomas expression for electron velocity was taken as 1.9. An value of 1.9, as opposed to 2, in (5) was also found to be appropriate for modeling power MOSFETs in previous work [13]. All other parameters were as specified previously. Fig. 15 shows the experimental results and the results predicted by the model. The model is capable of reproducing the experimental results extremely well. IV. CONCLUSION A compact semianalytical model for a trench gate MOSFET that is useful in the design of optimum high current density devices is presented here. The formulation is based on the regional 2428 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 12, DECEMBER 2000 analysis of carrier transport in channel and drift regions. The effects of doping concentration, and transverse and longitudinal electric fields on electron mobility are taken into account. This model also considers the effect of carrier velocity saturation at high longitudinal electric fields. The channel region modeling methodology is also applicable to conventional VDMOS and LDMOS transistors. The methodology can also be used in circuit simulation where a subcircuit model for a power TMOSFET can be defined in terms of a number of series connected low voltage MOSFETs. A key feature of the model is the accurate incorporation of the voltage drop in the accumulation channel region as it loses current into the n region. Results of the proposed model are in good agreement with the MEDICI simulation results. The current voltage characteristic is accurate to the extent of greater than 95.5% with the least 50 V for the 400 V device. This can accuracy of 95.5% at be clearly seen in Fig. 6. The agreement is very good for a series of Gate voltages for the 100 V device as well. The predicted IV characteristics of the model are in excellent agreement with experimental results for a 60 V device as shown in Fig. 15. APPENDIX DERIVATION OF AVERAGE PERPENDICULAR ELECTRIC FIELD INSIDE THE INVERSION LAYER The electric field at the surface can be related to the total charge per unit area using Gauss’ Law of electrostatics. (A1) and are the depletion and inversion charge per where unit area, respectively. The electric field just below the inversion layer can be determined by assuming a very thin inversion layer so that the total . charge per unit area below the inversion layer is (A2) Thus the average electric field inside the inversion layer is REFERENCES [1] D. Ueda, H. Takagi, and G. Kano, “A new vertical power MOSFET structure with extremely low on resistance,” IEEE Trans. Electron Devices, vol. ED-32, p. 2, Jan. 1985. [2] K. Shenai, “Optimized trench MOSFET technologies for power devices,” IEEE Trans. Electron Devices, vol. 39, p. 1435, June 1992. [3] C. Bulucea and R. Rossen, “Trench DMOS transistor technology for high current (100 A range) switching,” Solid-State Electron., vol. 34, no. 5, p. 493, 1991. [4] K. Shenai, “A 55 V, 0.2 m cm vertical power trench MOSFET,” IEEE Electron Device Lett., vol. 12, p. 108, Mar. 1991. [5] R. K. Williams et al., “A 30 V p-channel trench gate DMOSFET with 900 cm specific on resistance at 2.7 V,” in Proc. ISPSD, Yokohama, Japan, 1995, p. 53. [6] M. N. Darwish, “Study of quasisaturation effect in VDMOS transistors,” IEEE Trans. Electron Devices, vol. ED-33, Nov 1986. [7] K. H. Lou, C. M. Liu, and J. B. Kuo, “An analytical quasisaturation model for vertical DMOS power transistors,” IEEE Trans. Electron Devices, vol. 40, p. 676, Mar. 1993. [8] J. L. Evans and G. A. J. Amaratunga, “The behavior of very high current density power MOSFETs,” in Proc. ISPSD, Hawaii, 1996, p. 161. [9] J. Evans and G. Amaratunga, “The behavior of very high current density power MOSFETs,” IEEE Trans. Electron Devices, vol. 44, p. 1148, July 1997. [10] Y.-S. Kim and J. G. Fossum, “Physical DMOST modeling for highvoltage IC CAD,” IEEE Trans. Electron Devices, vol. 37, Mar. 1990. [11] Y.-S. Kim, J. G. Fossum, and R. K. Williams, “New physical insights and models for high voltage LDMOS IC CAD,” IEEE Trans. Electron Devices, vol. 38, July 1991. [12] D. M. Caughey and R. E. Thomas, “Carrier mobilities in silicon empirically related to doping and field,” Proc. IEEE, pp. 2192–2193, Dec. 1967. [13] D. A. Grant and J. Gowar, Power MOSFETs: Theory and Applications: Wiley, 1989. [14] S. Takagi et al., “On the universality of inversion layer mobility in Si MOSFETS: Part II—Effects of surface orientation,” IEEE Trans. Electron Devices, vol. 41, Dec. 1994. [15] Avant! Inc., MEDICI Two Dimensional Device Simulation Program. K. G. Pani Dharmawardana was born in Colombo, Sri Lanka, in 1966. He received the B.Sc. degree in electronic and telecommunication engineering (first class honor) from the University of Moratuwa, Sri Lanka. He is currently pursuing the Ph.D degree in the area of high performance power MOSFETs at Cambridge University, U.K. He was with the academic staff of the Department of Electronic and Telecommunication Engineering, University of Moratuwa. His research interests include low power and high power semiconductor devices, optical communication and electromagnetic waves. (A3) where and ACKNOWLEDGMENT The authors are grateful to R. Grover and R. Hyndman of Philips Semiconductors, Stockport, U.K., for providing experimental data and collaborating on model validation. The constructive comments of the referees for enhancing the paper were much appreciated. Gehan Amaratunga (M’85) received the B.Sc. degree from the University of Wales, Cardiff, and the Ph.D. degree from the University of Cambridge, U.K. He was a Lecturer in the Department of Electronics and Computer Science, University of Southhampton, U.K., prior to joining the faculty of the University of Cambridge in 1986. From 1995 to 1998 he was Professor and Chair in Electrical Engineering at the University of Liverpool, U.K., and returned to Cambridge to take up his present position in 1998. He is currently Professor of electrical engineering and Head of Electrical Power and Energy Conversion, Department of Engineering, Cambridge University. His current research interests are in the areas of power semiconductor devices and ICs, carbon for electronic applications and vacuum electronic devices. He has also recently initiated a research program at Cambridge on very low-cost solar cell technologies and power ICs for grid connection of solar modules. He has published over 250 journal and refereed conference papers in these and other topics in electrical engineering, physics, and materials science.