A New Weight Redistribution Technique for Electron ... - IEEE Xplore

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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 51, NO. 9, SEPTEMBER 2004

A New Weight Redistribution Technique for Electron–Electron Scattering in the MC Simulation Jongchol Kim, Hyungsoon Shin, Senior Member, IEEE, Chanho Lee, Member, IEEE, Young June Park, Member, IEEE, and Hong Shick Min

Abstract—A novel technique for the weight redistribution after the electron-electron scattering between weighted electrons in the weighted ensemble Monte Carlo simulation is proposed. By generating an additional electron after each electron–electron collision the conservation of energy, momentum and charge is guaranteed, which has not been possible in the previously reported methods. The proposed technique has been successfully applied to an ideal gas simulation. Based on the new model, the tail carrier behavior due to the electron–electron scattering in the n+ –doped silicon is studied. Index Terms—Electron–electron (e–e) scattering, Monte Carlo (MC) simulation, relaxation time.

I. INTRODUCTION

A

S THE SUPPLIED voltage is scaled to the subbandgap range in the deep submicrometer and nanoscale CMOS technology, the electron-electron scattering (hereafter e–e scattering) plays an increasingly important role in the generation of hot electrons [1]. Since the hot carriers are almost experimently inaccessible, it is desirable to investigate these carriers by means of the physical simulation. The most reliable method is the Monte Carlo (MC) simulation [2]. A disadvantage of the standard MC method is that the statistics of rare events is poor compared to the one of common events, because the sampling frequency of events is proportional to their probability. Hence, the multiplication schemes have been developed in order to enhance the statistics of rare events without increasing the number of common events [3], [4]. The multiplication techniques assign a statistical weight to each particle, and manipulate the weight in order to improve the sampling frequency of rare events. However, it is difficult to conserve the physical quantities such as the total energy and charge after e–e scattering in the weight-manipulating technique. Particularly, the conservation of the total charge has been regarded as the conservation of the total weight in Manuscript received March 2, 2004; revised June 11, 2004. This work was supported in part by the National Research Laboratory project of the Ministry of Science and Technology, and in part the Brain Korea 21 project. The review of this paper was arranged by Editor S. Datta. J. Kim, Y. J. Park, and H. S. Min are with the School of Electrical Engineering and Computer Science and NSI-NCRC, Seoul National University, Seoul 151744, Korea (e-mail: [email protected]). H. Shin is with the Department of Information Electronics Engineering, Ewha Woman’s University, Seoul 120-720, Korea. C. Lee is with the School of Electronics Engineering, Soongsil University, Seoul 156-743, Korea. Digital Object Identifier 10.1109/TED.2004.833969

the multiplication methods [5]. To satisfy the conservation of total energy, each particle should be given a proper weight after every e–e collision. In this work, we propose a novel weight redistribution technique, the detail of which is introduced in Section II. In the present model, a new electron called a “baby electron” is generated after each e–e scattering and given a proper weight to satisfy the conservation in the energy and charge. Hereafter, we name the proposed technique as the baby electron addition technique (BEA). The BEA technique, however, has a disadvantage of increasing the number of particles since one carrier is generated for each e–e scattering event between weighted electrons, which can be solved by more frequent gathering process. The advantage and validity of the BEA technique are verified by an ideal gas simulation where energy exchange is taken place only through the e–e scattering. The simulation results are presented in Section III. Finally, the BEA technique has been applied to the study of tail electron transport where hot electrons are injected into the n doped silicon bar and the transient cooling behavior of the tail electrons in the silicon bar is observed. Tail electrons are the electrons having the energy higher than the critical energy. In this work, the critical energy is defined by 1.0 eV that is close to the silicon energy bandgap. The simulation results are presented in Section III. It will be shown that e–e scattering should be taken into consideration to study the hot carrier transport and the BEA technique gives reasonable results for the transport both in the steady state and transient state. Conclusions will be followed in Section IV. II. MODEL When a multiplication scheme is applied to the MC simulation, each MC particle is assigned a statistical weight [6]. In this case, an MC particle can be considered as a group (or cloud) composed of identical particles. The particles in the MC particle possess identical physical quantity such as momentum and energy. The statistical weight of an MC particle is proportional to the number of particles comprising the MC particle. From this viewpoint, the scattering between two MC particles with different weight can be interpreted as the collision between two groups of particles. Equation (1) describes a collision between two groups of par: group 1 with particles having the ticles during time and group 2 with particles having physical quantity of the physical quantity of . It is assumed for convenience that

0018-9383/04$20.00 © 2004 IEEE

KIM et al.: NEW WEIGHT REDISTRIBUTION TECHNIQUE FOR ELECTRON–ELECTRON SCATTERING IN THE MC SIMULATION

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is larger than . The time interval of is assumed to be sufficiently short so that each particle in a group collides with only one particle in the other group. The collision between the particles in the same group is neglected

(1) where represents the energy or momentum of the -th particle in the group , and is that quantity after collision. If is omitted, the -value represents the energy or momentum represents the avcommon to the particles in the group . particles. erage quantities of the Before the scattering, the particles in a group are all identical. Hence, the left-hand side of (1) has only two -values: for the particles in the group 1 and for the particles in and are defined as the number of particles the group 2. of the group 1 and 2 respectively. particles in the group 1 particles in the group 2 while experience a collision with particles in the group 1 do not experience any collision. All the particles in the group 2, however, will collide with a particles consequently exchange particle in the group 1. 2 collision events. This their momentum and energy during collision events should be handled for the remeans that alization of a collision between two MC particles. In general, the number of particles must be sufficiently large to express the weight of an MC particle exactly. Therefore, a long simulation time is required for the collision process. and can be obtained by two methods in the MC collision simulation. The first method is computing the events between pairs and averaging the energy or momentum particles in each group after collision, which reof the quires excessive computational efforts. The second method is handling the collision between two groups statistically using the acceptance-rejection technique [7], [8]. A random number collision pairs and the selected pair selects a pair from the represents the collision between the two groups. This method is used because less simulation time and memory are required. and are reIf the -th collision pair is selected, and , or simply and . Equation (1) can placed by be written as (2) The difference between (1) and (2) is that particles in each group have same physical quantities after collision in (2). If (2) is divided by a large number on both sides (3) where and are and , respectively. Equation (3) can be interpreted as the equation describing the collision between two weighted particles, the right-hand side of which can be rewritten as

(4)

Fig. 1. Collision between the weighted electrons is described. After the e–e scattering, two electrons with smaller weights (w ) share the energy E and E . The baby electron is given the weight of w w and share the energy of E.

0

DAMOCLES [9] uses (4) for the weight redistribution after each e–e scattering process in the semiconductor device simulation. The weight and momentum redistribution method used in DAMOCLES can be explained in the framework of (4). Assume that a pair of weighted electrons experiences e–e scattering. If the two electrons of the pair have different statistical weights, is scattered, while the other the electron with smaller weight is scattered with probability in particle of weight order to ensure statistically conservation of energy in the ensemble. The disadvantage of the scheme used in DAMOCLES is that neither the total momentum nor the total charge is conserved after each e–e scattering event. Of course, as the number of scattering events increases, the total energy and momentum are expected to be conserved. In this paper, a new scheme is proposed by regarding the three terms in the right-hand side of (4) as the expression of three and . Hence, one electrons with the weight of , electron should be generated to embody the third term in the right-hand side of (3). The generated electron may be named “the baby electron.” In this regard, the weight and momentum redistribution method of this work can be explained with the Fig. 1 as follows. After the e–e scattering, two electrons with share the energy and according smaller weights to the scattering rule. The baby electron is given the weight of and shares the energy of . In this way, both the weight sum and the momentum sum of the three electrons are equal to those of the pair before-scattering. In this way, the exact conservation in the charge and momentum is obtained as seen in (3). The disadvantage of the BEA technique is that a baby electron is generated for every e–e scattering event. The e–e scattering is an electron generating mechanism in the proposed method. When the e–e scattering rate is larger than the other scattering rates, the proposed method may not be adoptable since increasing number of particles may be generated. Those problems can be solved by more frequent gathering process of multiplication [5].

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Fig. 2. Steady-state energy distribution in the ideal gas is shown. Initially, the particles are all given energy of 10 J. The ideal gas particles are simulated based on BEA technique and the resulting energy distribution is compared with the distribution of ideal gas particles obtained without the BEA technique. Both of the distributions are similar to the theoretical one, Maxwell–Boltzmann distribution.

Fig. 3. Average energy during the ideal gas simulation by the BEA method and the method in DAMOCLES are plotted against time. The average energy for DAMOCLES shows the fluctuation. Such an energy fluctuation should not be shown in the ideal gas since the energy exchange happens between particles. The BEA-applied simulation result shows no energy fluctuation.

III. SIMULATION RESULTS In order to study the new model compared with the method used in DAMOCLES [9], two cases have been considered. The first case is for the energy distribution of the ideal gas; the second is for the relaxation of tail electrons in the n silicon region. The ideal gas system has an average kinetic energy that is proportional to the temperature; the kinetic energy will be distributed among the particles according to the Maxwell–Boltzmann distribution through the particle-particle collisions [10]. Since all collisions are elastic, the average energy of ideal gas should maintain the initial value. The validity and advantage of the BEA technique can therefore be verified by the MC simulation of the ideal gas. For the simulation of the ideal gas, 10 000 gas particles are generated in the cubic box with the volume of 0.1 0.1 0.1 m initially. Each particle comprising the ideal gas is allotted a random weight with the mono-energy of 10 [J]. The particles then experience particle-particle collisions and redistribute their weights and energy by two methods; the BEA method and the ideal case as the bench mark where all the particles are given an identical weight without the multiplication. Fig. 2 compares the resulting energy distributions from two methods with the ideal Boltzmann distribution. There exists little difference between the BEA and the ideal case. Fig. 3 shows the transient behavior of the average energy during the simulation. As the elastic collisions between ideal gas particles conserve the total energy, the average energy should be conserved. The method used in DAMOCLES is also shown, where statistical fluctuation in the average energy is found. On the other hand, it can be seen that the average energy maintains the initial value without any statistical fluctuation in the BEA method. Fig. 4 shows the energy distribution obtained at 10 s after the injection of mono-energy particles into the box. The shape of the transient energy distribution is similar to that of the ideal gas. The energy distribution resulting from the BEA technique shows the high energy tail that is formed by collisions between

Fig. 4. Mono-energy of 10 J was given to each particle at 0 s. The energy distribution at t10 s is shown. The transient behavior for MC with BEA is similar to one for MC without multiplication. BEA shows the high energy tail, which is formed by collisions between weighted particles.

weighted particles. From the ideal gas simulation, we conclude that the BEA technique gives reasonable results compared with the benchmark for both the steady and transient states. For the second case, we investigate the influence of e–e scattering on the tail electron behavior in the n silicon. We use SNU-MC [2] as the MC simulator, which uses the multiple refresh method suggested by Jungemann et al. [5] for multiplication and refresh of the particles in the rare event regions. We use the e–e scattering model proposed by Lugli and Ferry [11]. As the e–e scattering is not considered in multiple refresh, the BEA method is applied to the scattering among weighted electrons and weight redistribution after scattering. cm and the size of the The silicon bar is doped with bar is given 0.1 0.1 0.01 m . The hot electrons with the mono-energy of 1.2 eV is located between and m s, so that the cooling behavior of and released from time the hot electrons in the neutral n can be simulated. Fig. 5(a)–(d) shows the spatial distribution of the tail electrons whose energy is above 1.0 eV at different time of


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Fig. 5. (a)Distribution of the electrons of energy over 1.2 eV is plotted. The time is 5.0 10 s after the injection of hot electrons. (b) The distribution of s after the injection of hot electrons. (c) The distribution of the electrons of energy over the electrons of energy over 1.2 eV is plotted. The time is 1.0 10 1.2 eV is plotted. The time is 250 10 s after the injection of hot electrons. (d) The distribution of the electrons of energy over 1.2 eV is plotted. The time is s after the injection of hot electrons. 5.0 10

2

2

2

5.0 , 1.0 , 2.5 and 5.0 s, respectively. In the figures, the same data without considering the e–e scattering are shown so that the effects of the e–e scattering on the cooling process of hot electrons can be observed. It can be seen that the number of tail electrons decreases more slowly when the e–e scattering is taken into consideration. In Fig. 6, the average energy of the silicon bar is plotted against time. Fig. 7 shows the average energy difference between the case with and without e–e scattering normalized to the case with e–e scattering and it can be seen that the average energy is larger when the e–e scattering is taken into account. In order to study the transport property of the tail electrons in the uniform case, 1 % of the total electrons in the n silicon bar were randomly selected and given mono-energy of 1.2 eV at time of 0 s. Notice that the previous case considers the tail electron diffusion from the left area of the n silicon bar. In Fig. 8, the numbers of tail electrons were plotted against time for the case with and without e–e scattering. These results were compared with the previous case where the electrons between 0 m and 0.01 m were given energy of 1.2 eV. It can be seen that both cases the similar curves are obtained.

Ahn et al. derived the moment form of the Boltzmann transport equation for the tail electrons [12]. The derived continuity , the density of the tail electrons can be written equation for as

(5) (5a) (5b) (5c) where is the carrier distribution function and is is the critthe rate of change of due to collision [13], ical energy and defined by 1.0 eV, is the electron charge,

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Fig. 6. Electron average energy of silicon cube is plotted against time. The electron concentration of the silicon cube is 10 [=cm ]. The size of the silicon cube is 0.1 0.1 0.01 [m ]. 20 % of the ensemble electrons were given energy of 1.2 eV initially.

2 2

Fig. 8. Number of the electrons having energy over 1.0 eV is plotted against time. 1 % of the electrons were given mono-energy of 1.2 eV at time 0 s. “EE” is the simulation result that considers electron-electron scattering. And “NO EE” is the result that does not consider electron-electron scattering. The slope of “EE” is deviated from the slope of “NO EE”. Left-end selection means that the electrons in the left end of the silicon bar were selected and given 1.2 eV. Random selection means the hot electrons given 1.2 eV are selected randomly in the silicon bar.

assume that relaxation time approximationis valid forthe description of e–e scattering. If we define by the relaxation time of the e–e scattering, we can rewrite the (6) as

(7)

Fig. 7.

Normalized average energy difference is plotted against time. The is the electron average energy of silicon bar taking electron-electron is the average energy without scattering into consideration and E consideration of electron-electron scattering. The average energy increases when electron-electron scattering is taken into consideration.

E

and is the electric field, is the relaxation time involved is the relaxation time involved in phonon absorption and in phonon emission scattering, is the tail electron density is homogeneous tail electron denand defined by 5(b), and sity obtained from the MC simulation for the uniform field. In becomes equal to [12]. In 5(a), the homogeneous limit, is defined as the current density at the energy and is defined in (5c) as the current surface of density in the wave vector space. As the field is negligible in the n region in our case and the divergence term can be neglected in the uniform case, the (5) becomes (6) The constant slope of the “NO EE” curve in Fig. 8 shows that the (6) is applicable. From the curve, the phonon scattering relaxation time for the tail carriers (carriers with the energy higher than 1.0 eV)maybederived.Theconsiderationofe–escatteringvariesonly the slope of the curve. From the shape of the curve in Fig. 8, we can

In Fig. 9(a), the data for simulation when 1 % of the total electrons were given 1.2eVand when 10 % were given 1.2 eV arecompared. The relaxation time and obtained from Fig. 9(a) are plotted against time in Fig. 9(b). The relaxation time is in the s and is in the neighborhood of neighborhood of 1.7 1.3 s when the e–e scattering is included. It is interesting to see that the relaxation time is similar for both the 1% and 10% s. cases. The value derived from and is around 5.5 Simulations with the conditions where 10% of electrons are given mono-energy of 1.2 eV and the condition of 1.8 eV are compared. As shown in Fig. 9(c) and (d), the relaxation times are similar to the values found in the previous case, implying that the relaxation time values are insensitive to the initial energy of the hot electrons given at time of 0 s. The simulation results show that e–e scattering affects the cooling process of the electrons of silicon; the e–e scattering tends to slow down the cooling rate of hot electrons in heavily doped silicon. IV. DISCUSSIONS In Section III, the influence of e–e scattering on the tail electron behavior in the n silicon has been studied. Other than the e–e scattering, which is short-range electron-electron interaction, there exists long-range electron-electron interaction, which is the plasmon-electron scattering, associated with the collective plasma excitations [14]. It has been reported that the long-range plasmon-electron scattering acts as an additional energy relaxation mechanism, while the short-range electron-electron


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Fig. 9. (a) Number of high energy electrons is plotted against time. “EE” is the simulation result that considers electron-electron scattering. and “NOT EE” is the result that does not consider electron-electron scattering. “1%” means that 1% of the electrons were given mono-energy of 1.2 eV. “10%” means 10% of electrons were given 1.2 eV. (b) The cooling rate was plotted against time. the cooling rate value on average is in the neighborhood of 3 10 [s ] with electron-electron scattering and 4 10 [s ] without electron-electron scattering. (c) The number of high energy electrons is plotted against time. “energy 1.2 eV” means that 10% of electrons are given mono-energy of 1.2 eV; “energy 1:2 1:8 eV” means the energy is randomly given between 1.2 and 1.8 eV and “energy 1.8 eV” the energy of 1.8 eV. The slope of “EE” energy 1.2, 1:2 1:8, and 1.8 eV are similar, and the slope of “NOT EE” energy 1.2, 1:2 1:8; and 1.8 eV are similar. The difference between the slope of “EE” and “NOT EE” means the difference of the cooling rate. (d) The cooling of high energy electrons is plotted against time. The figure shows that the cooling rate is not affected by the initial energy of the electrons.

2

2

scattering yields an increase of the high energy tail [15]. In this paper, we included only the short-range e–e scattering to demonstrate the algorithmic improvement in treating the e–e scattering. In Bthe EA technique, the baby electrons are generated after each e–e scattering and they are eliminated only in the gathering process. In a gathering process, random numbers select the electrons that will remain in the gathering region. If the weight of a baby electron is larger compared with other electrons in the gathering region, the baby electron will be eliminated with relatively low probability. In the DAMOCLES technique, the electron corresponding to a baby electron should be eliminated after each scattering of weighted electrons. The probability of elimination is not determined by the weight ratio of the baby electron to the total electrons in the gathering region as in BEA technique, but by the weight ratio of the baby electron to the scattering pair. Consequently, the latter is expected to cause more statistical fluctuations than the former.

V. CONCLUSION A weight redistribution technique (BEA) was proposed. The proposed technique can explain the other weight redistribution techniques proposed by researchers. An ideal gas simulation verifies the validity and advantage of the BEA. The BEA is used to study the influence of electron-electron scattering on the cooling process of hot electrons. The BEA shows that an addition of a baby electron can satisfy the exact conservation of total charge, total momentum and total energy of an electron pair. The SNU-MC simulation results show that the electron- electron scattering is one of the hot electron generating or maintaining mechanism. It is shown that the relaxation time of silicon has a different value when electron-electron scattering is taken into consideration. The value of the compensated relaxation time is calculated from the simulation results.

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REFERENCES [1] K. G. Anil, S. Mahapatra, and I. Eisele, “Role of inversion layer quantization on sub-bandgap impact ionization in deep-sub-micron n-channel MOSFETs,” in IEDM Tech. Dig., 2000, pp. 994–994. [2] S. -J. Hong, J. -J. Kim, Y. J. Park, and H. S. Min, “Analysis of the spurious negative resistance of PN junction avalanche breakdown,” IEEE Trans. Electron Devices, vol. 46, Jan. 1999. [3] A. Phillips and P. J. Price, “Monte Carlo calculations on hot electron energy tails,” Appl. Phys. Lett., vol. 30, pp. 528–530, 1977. [4] E. Sangiorgi, B. Ricco, and F. Venturi, “MOS: An efficient Monte Carlo simulation for MOS devices,” IEEE Trans. Computer-Aided Design, vol. 7, pp. 259–271, Feb. 1988. [5] C. Jungemann, S. Decker, B. Thoma, W. L. Engl, and H. Goto, “Phase space multiple refresh: A general purpose statistical enhancement technique for Monte Carlo device simulation,” J. Tech. Computer-Aided Design, Jan. 1997. [6] A. Pacelli and U. Ravaioli, “Analysis of variance reduction schemes for ensemble Monte Carlo simulation of semiconductor devices,” Solid State Electron., vol. 41, pp. 599–605, 1997. [7] P. J. Price, “Monte Carlo calculation of electron transport in solids,” Semicond. Semimetals, vol. 14, pp. 249–309, 1979. [8] C. Jacoboni and L. Reggiani, “The Monte Carlo method for the solution of charge transport in semiconductors with application to covalent materials,” Rev. Mod. Phys., vol. 55, pp. 645–705, 1983. [9] M. V. Fischetti and S. E. Laux, Damocles Theoretical Manual: IBM, 1994. [10] C. Kittel and H. Kroemer, Thermal Physics, 2nd ed. San Francisco, CA: Freeman, 1980. [11] P. Lugli and D. K. Ferry, “Electron-electron interaction and high field transport in Si,” Appl. Phys. Lett., vol. 46, pp. 594–596, 1985. [12] J. -G. Ahn, C. -S. Yao, Y. J. Park, H. S. Min, and R. W. Dutton, “Impact ionization model using simulation of high energy tail distribution,” IEEE Electron Device Lett., vol. 15, pp. 348–350, Sept. 1994. [13] R. W. Hockeny and J. W. Eastwood, Computer Simulation Using Particles. New York: McGraw-Hill, 1981. [14] M. V. Fischetti and S. E. Laux, “Understanding hot-electron transport in silicon devices: Is there a shortcut?,” J. Appl. Phys., vol. 78, no. 2, pp. 1058–1058, July 1995. [15] N. Sano, K. Matsuzawa, M. Mukai, and N. Nakayama, “Role of longrange and short-range Coulomb potentials in threshold characteristics under discrete dopants in sub-0.1 m MOSFETs,” in IEDM Tech. Dig., 2000, pp. 275–275. Jongchol Kim received the B.S. and M.S. degrees in electronic engineering from Seoul National University, Seoul, Korea, in 1999 and 2001, respectively. He is currently pursuing the Ph.D. degree at Seoul National University. His research focuses on device physics and simulation.

Hyungsoon Shin (M’91–SM’01) was born in Seoul, Korea, in 1959. He received B.S. in electronics engineering from the Seoul National University in 1982, M.S. and Ph.D. in electrical engineering from the University of Texas at Austin in 1984 and 1990, respectively. From 1990 to 1994, he was with LG Semicon Company, Ltd., in Korea, where he worked on the development of 64M DRAM, 256M DRAM, 4M SRAM, and 4M Flash memory. Since 1995, he has been a faculty member of the department of information electronics engineering at Ewha Woman’s University, Seoul, Korea. His present research areas include new processes, devices, and circuit developments and modeling based on Si, both for high density memory and RF IC. He has published numerous journal articles on implant profile models, mobility models, deep-submicrometer MOSFET structure analysis, current crowding effect in diagonal MOSFET, hot-carrier degradation, alpha-particle-induced soft error and MRAM. Dr. Shin is a senior member of the Institute of Electrical and Electronics Engineers and the Institute of Electronics Engineers of Korea. He received the Technical Excellence Award from the Semiconductor Research Corporation (SRC) in 1991.

Chanho Lee (S’86–M’95) received the B.S. and M.S. degrees in electronics engineering from Seoul National University, Seoul, Korea, in 1987 and 1989, respectively, and the Ph.D. degree from the University of California at Los Angeles in 1994. In 1994, he joined the semiconductor R&D center of Samsung Electronics, Kiheung, Korea. Since 1995, he has been a faculty member of the School of Electronics Engineering, Soongsil University, Seoul, Korea, and he is currently an Associate Professor. His research interest is quantum devices using SiGe and -doping, and modeling of deep-submicrometer MOSFETs. He is also working on the design of channel codec and security processor, low power design, and SoC on-chip bus.

Young June Park (S’77-M’83) received the B.S. and M.S. degrees from Seoul National University, Seoul, Korea in 1975 and 1977, respectively, and the Ph.D. degree from the University of Massachusetts, Amherst, in 1983. From 1983 to 1985, he worked for the Device Physics and Technology Department, IBM, East Fishkill, NY. In 1985, he joined Gold Star Semiconductor Company, Anyang, Kyungki, (currently Hynix Semiconductor Inc.) to work in the area of the CMOS technology. In 1993, he spent his sabbatical year at Stanford University, Stanford, CA, and performed research on advance semiconductor transport model. Since 1988, he has been with Seoul National University (SNU), where he is a Professor in the School of Electrical Engineering and Computer Science. From 1996 to 2001, he served the Inter-University Semiconductor Research Center (ISRC), SNU, as a Director. In 2001, he was on a leave of absence to work for Hynix Semiconductor Inc. as a Director of the Memory Research and Development Division. His areas of interest are the advanced device structures, device/noise and reliability modeling, and low-power circuit technology. Since 2003, he serves the director of the Nano System Institute under the NCRC (Nano Core Research Center) program supported by KOSEF, Korea. His current area of interest is the Nano MOSFET modeling and MOSFET applications to Biosystems.

Hong Shick Min received the B.S. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1966, and M.S. and Ph.D. degrees in electrical engineering from the University of Minnesota, Minneapolis, in 1969 and 1971, respectively. From 1971 to 1972, he was a Postdoctoral Fellow at the University of Minnesota. In 1973, he joined the Department of Electronics Engineering at Korea University, Seoul, as an Assistant Professor. Since 1976, he has been with the School of Electrical Engineering, Seoul National University, where he is currently a Professor. His main research interests include noise in semiconductors and semiconductor devices.