Transcription

1

2

3

4

5

6 quantum

7

8

9

10 r rmnh h h E a n = a E b n = b h h h n = 1

11 n = 1 n = h h

12 n h cos sin

13

14

15 1 1

16

17

18

19 N

20 ψ = 1 N! ϕ n1 (x 1 ) ϕ n2 (x 1 ) ϕ nn (x 1 ) ϕ n1 (x 2 ) ϕ n2 (x 2 ) ϕ nn (x 2 ) ϕ n1 (x N ) ϕ n2 (x N ) ϕ nn (x N ) (2.7) ϕ n1 (x 1 ) ϕ n2 (x 1 ) ϕ nn (x 1 ) ψ = 1 ϕ n1 (x 2 ) ϕ n2 (x 2 ) ϕ nn (x 2 ) N! ϕ n1 (x N ) ϕ n2 (x N ) ϕ nn (x N )

21

22

23

24 k k k k

25

26

27

28

29 a

30

31

32 V dd

33

34 N

35 x E

36

37 W 1 W 2 W 3 W K n n MOSFET W 2 W 3 W 4 T = 300 KW 1 W 2 W 3 W 4

38 i i = 1:i = 2:i = 3: i = 4: 0.6 ev r 0.3 r = 0.3 W 4 L--X-U-

39 -X -X X-U -X X L X

40 L X L X L X L X X L L L L L X X X X m l m t

41 III-V MOSFET III-V MOSFET DOS

42

43

44 j H m

45 t k Wigner Transport Equation: WTE u

46 WTE quantum evolution term k k

47 u u

48 R R k p 0 K 1

49 xj

50 R x u u x U x u u u

51 U x u k k j jx n V b

52 L. Shifren M. Nedjalkov

53 D. Querlioz affinity

54

55 n (= 1%)

56 Q Q N L

57 F

58 Γ

59

60 x, y z

61

62

63

64

65 f

66 CDS (Central Differencing Scheme) SDS 2:1 FDS (First-order Differencing Scheme) SDS (Second-order Differencing Scheme) TDS (Third-order Differencing Scheme) FDS SDS

67 TDS

68 [1] PHP 2000 [2] 2015 [3] 2013 [4] 2006 [5] 1969 [6] 1991 [7] 1996 [8] C. Jacoboni and L. Reggiani, The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalentmaterials, Rev. Mod. Phys., vol. 55, no. 3, pp , [9] 2015 [10] H. Tsuchiya and Y. Kamakura, Carrier Transport in Nanoscale MOS Transistors. Wiley, Singapore, [11] H. Tsuchiya, K. Fujii, T. Mori, and T. Miyoshi, A quantum-corrected Monte Carlo study on quasi-ballistic transport in nanoscale MOSFETs, IEEE Trans. Electron Devices, vol. 53, no. 12, pp , [12] E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev., vol. 40, pp , [13] 2007 [14] W. Frensley, Wigner-function model of a resonant-tunneling semiconductor device, Phys. Rev. B, vol. 36, no. 3, pp , [15] N. Kluksdahl, A. Kriman, D. Ferry, and C. Ringhofer, Self-consistent study of the resonant-tunneling diode, Phys. Rev. B, vol. 39, no. 11, pp , [16] S. Koba, Development of Monte Carlo Simulators for Integrated Nanoscale Devices. Doctoral Dissertation of Graduate School of Engineering, Kobe University, [17] H. Tsuchiya and T. Miyoshi, Nonequilibrium Green s function approach to high-temperature quantum transport in nanostructure devices, J. Appl. Phys., vol. 83, no. 5, pp , [18] L. Shifren, C. Ringhofer, and D. K. Ferry, A Wigner function-based quantum ensemble Monte Carlo study of a resonant tunneling diode, IEEE Trans. Electron Devices, vol. 50, no. 3, pp , [19] M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. Ferry, Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices, Phys. Rev. B, vol. 70, , [20] D. Querlioz, P. Dollfus, V.-N. Do, A. Bournel, and V. Nguyen, An improved Wigner Monte-Carlo technique for the self-consistent simulation of RTDs, J. Comput. Electron., vol. 5, no. 4, pp , [21] D. Querlioz, J. Saint-Martin, K. Huet, A. Bournel, V. Aubry-Fortuna, C. Chassat, S. Galdin-Retailleau, and P. Dollfus, On the ability of the particle Monte Carlo technique to include quantum effects in nano-mosfet simulation, IEEE Trans. Electron Devices, vol. 54, no. 9, pp , [22] D. Querlioz and P. Dollfus, The Wigner Monte Carlo Method for Nanoelectronic Devices. Wiley, New York, [23] S. Koba, R. Aoyagi, and H. Tsuchiya, Quantum transport simulation of nanoscale semiconductor devices based on Wigner Monte Carlo approach, J. Appl. Phys., vol. 108, p , [24] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge Univ. Press, [25] C. Auth, C. Allen, A. Blattner, D. Bergstrom, M. Brazier et al., A 22nm high performance and low-power CMOS technology featuring fully-depleted tri-gate transistors, self-aligned contacts and high density MIM capacitors, in Symp. VLSI Tech. Dig., 2012, pp [26] H. Sakaki, T. Noda, K. Hirakawa, M. Tanaka, and T. Matsusue, Interface roughness scattering in GaAs/AlAs

69 quantum wells, Appl. Phys. Lett., vol. 51, no. 23, pp , [27] K. Uchida, H. Watanabe, A. Kinoshita, J. Koga, T. Numata, and S. Takagi, Experimental study on carrier transport mechanism in ultrathin-body SOI n- and p-mosfets with SOI thickness less than 5 nm, in IEDM Tech. Dig., 2002, pp [28] H. Kawaura, T. Sakamoto, and T. Baba, Observation of source-to-drain direct tunneling current in 8 nm gate electrically variable shallow junction metal-oxide-semiconductor field-effect transistors, Appl. Phys. Lett., vol. 76, no, 25, pp , June [29] J. Wang and M. Lundstrom, Does source-to-drain tunneling limit the ultimate scaling of MOSFETs?, in IEDM Tech. Dig., 2002, p [30] H. Wakabayashi, T. Ezaki, M. Hane, T. Ikezawa, T. Sakamoto, H. Kawaura, S. Yamagami, N. Ikarashi, K. Takeuchi, T. Yamamoto, and T. Mogami, Transport properties of sub-10-nm planar-bulk-cmos devices, in IEDM Tech. Dig., 2004, p [31] Y. Yamada, H. Tsuchiya, and M. Ogawa, Quantum transport simulation of silicon-nanowire transistors based on direct solution approach of the Wigner transport equation, IEEE Trans. Electron Devices, vol. 56, no. 7, pp , July [32] 10 nm Si MOSFET, 63, 19a-S223-11, [33] S. Barraud, Dissipative quantum transport in silicon nanowires based on Wigner transport equation, J. Appl. Phys., vol. 110, p , Nov