Journal of IKEEE (전기전자학회논문지)

Institute of Korean Electrical and Electronics Engineers (한국전기전자학회)
권호 표지
DOI QR코드

DOI QR Code

Qantum Transition properties of Si in Electron Deformation Potential Phonon Interacting Qusi Two Dimensional System

준 2차원 시스템에서 전자 변위 포텐셜 상호 작용에 의한 Si의 양자 전이 특성

  • Joo, Seok-Min (Dept. of Electronical Engineering, Masan University) ;
  • Cho, Hyun-Chul (Dept. of Avionics & Aviation Maintenance Kyungbuk college) ;
  • Lee, Su-Ho (Dept. of Electronical Engineering, Donga University)
  • Received : 2019.06.07
  • Accepted : 2019.06.20
  • Published : 2019.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We investigated theoretically the quantum optical transition properties of qusi 2-Dinensinal Landau splitting system, in Si. We apply the Quantum Transport theory (QTR) to the system in the confinement of electrons by square well confinement potential. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS). In order to analyze the quantum transition, we compare the temperature and the magnetic field dependencies of the QTLW and the QTLS on two transition processes, namely, the phonon emission transition process and the phonon absorption transition process. Through the analysis of this work, we found the increasing properties of QTLW and QTLS of Si with the temperature and the magnetic fields. We also found the dominant scattering processes are the phonon emission transition process.

우리는 준 2차원 Landau 분할 시스템의 양자 광학 전이 특성을 실리콘(Si)에서 이론적으로 고찰하였다. Squre wall 구속 포텐셜에 의한 전자 구속 시스템에 양자 수송 이론(QTR)을 적용하였습니다. 평형 평균 투영 계획(Equilibrium Average Projection Scheme : EAPS)으로 계획된 Liouville 방정식 방법을 사용하였으며, 양자 전이를 분석하기 위해 포톤 방출 전이과정과 포논 흡수 전이 과정의 두 전이 과정에서 QTLW와 QTLS의 온도와 자기장 의존성을 비교하였습니다. 이 연구를 통해 Si의 QTLW와 QTLS의 온도와 자기장의 증가하는 특성을 발견하였으며, 또한 우세한 산란 과정이 포논 방출 전이 과정이라는 것을 발견했다.

Keywords

JGGJB@_2019_v23n2_502_f0001.png 이미지

Fig. 1. Temperature dependence of QTLW γ(T) of Si, with λ=220, 394, 513, 550 and 720 μm (from the top line to the bottom line). 그림 1. 파장 λ=220, 394, 513, 550 and 720 μm에서 Si의 온도에 따른 QTLW의 값(γ(T))

JGGJB@_2019_v23n2_502_f0002.png 이미지

Fig. 2. Magnetic field dependence of QTLW γ(B) of Si, with λ=220, 394, 513, 550 and 720 μm(from the top line) 그림 2. 파장 λ=220, 394, 513, 550 and 720 μm에서 Si의 자기장에 따른 QTLW의 값(γ(B))

JGGJB@_2019_v23n2_502_f0003.png 이미지

Fig. 3. Comparisons of the temperature dependence of QTLW of Si, γ(T)total, γ(T)emandγ(T)ab with λ=394μm. 그림 3. 파장 λ=394μm에 있어 Si의 QTLW의 값 γ(T)total, γ(T)em 및 γ(T)ab의 온도의존성

JGGJB@_2019_v23n2_502_f0004.png 이미지

Fig. 4. Comparisons of the magnetic field dependence of QTLW of Si, γ(B)total, γ(B)em and γ(B)ab at T=50K. 그림 4. 온도 T=50K에서 Si의 QTLW의 값, γ(B)ab 및 γ(B)total, γ(B)em의 자기장 의존성

JGGJB@_2019_v23n2_502_f0005.png 이미지

Fig. 5. The Magnetic Field dependence of normalized P(B) (QTLS) of Si with λ=394 μm the at T=50,70,90,120 and 210K. (from the bottom line to top) 그림 5. 온도 T=50, 70, 90, 120 및 210K에서 파장 λ=393μm에대한 Si의 QTLS의 흡수력 P(B)의 자기장 의존성

JGGJB@_2019_v23n2_502_f0006.png 이미지

Fig. 6. The relativity frequency dependence of (QTLS) P(Δω) of Si and the magnetic field dependence of the absorption power, P(B) (QTLS) with λ=220, 394, 513, 550 and 550 μm at T=50K. 그림 6. 최대 흡수 전력의 자기장 의존성과 온도 T=50K에서 λ=220, 394, 513, 550 및 720μm 인 Si의 흡수력(QTLS) P(Δω)의 상대 주파수 의존성

Table 1. Material constant of Si. 표 1. Si의 물질 상수

JGGJB@_2019_v23n2_502_t0001.png 이미지

References

  1. C. S. Ting, S. C. Ying and J. J. Quinn, "Theory of cyclotron resonance of interacting electrons in a semiconducting surface inversion layer," Physical Review B, vol.16, no.12, pp. 5394-5404, 1977. DOI: 10.1103/PhysRevB.16.5394
  2. Wu Xiaoguang, F. M. Peeters and J. T. Devreese, "Theory of the cyclotron resonance spectrum of a polaron in two dimensions," Physical Review B, vol.34, no.12, pp.8800-8809, 1986. DOI: 10.1103/PhysRevB.34.8800
  3. P. Grigoglini and G. P. Parravidini, "Phonon thermal baths: A treatment in terms of reduced models," Physical Review B, vol.25, no.8, pp.5180-5187, 1982. DOI: 10.1103/PhysRevB.25.5180
  4. J. R. Barker, "Quantum transport theory of high-field conduction in semiconductors," Journal of Physics C: Solid State Physics, vol.6, no.17, pp.2633-2684, 1973. DOI: 10.1088/0022-3719 /6/17/009
  5. R. Kubo, "Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems," Journal of the Physical Society of Japan, vol.12, no.6, pp.570-586, 1957. DOI: 10.1143/ JPSJ.12.570
  6. H. Mori, "Transport, Collective Motion, and Brownian Motion," Progress of Theoretical Physics, vol.33, no.3, pp.423-455, 1965. DOI: 10.1143/PTP.33.423
  7. K. Nagano, T. Karasudani and H. Okamoto, "Reduced Equations of Motion for Generalized Fluxes and Forces in the Continued-Fraction Expansion," Progress of Theoretical Physics, vol.63, no.6, pp.1904-1916, 1980. DOI: 10.1143/ PTP.63.1904
  8. R. Zwanzig, "Theoretical basis for the Rouse-Zimm model in polymer solution dynamics," The Journal of Chemical Physics, vol.60, no.7, pp.2717-2720, 1960. DOI: 10.1063/1.1681433
  9. V. M. Kenkre, "Integrodifferential Equation for Response Theory," PHYSICAL REVIEW A, vol.4, no.6, pp.2327-2330, 1971. DOI: 10.1103/Phys.,Rev,A.4.2327
  10. S. G. Jo, N. L. Kang, Y. J. Cho, S. D. Choi. "Modeling of the Cyclotron Transition Theory for Quasi-2-Dimensional Electron-Systems by the Isolation-Projection Technique," J. Korea Phys. Soc. 30, pp.103-110, 1997.
  11. J. Y. Sug and S. D. Choi. "Quantum transport theory based on the equilibrium density projection technique," PHYSICAL REVIEW E, vol.55, no.1, pp.314-321. 1997. DOI: 10.1103/PhysRevE.55.314
  12. J. Y. Sug and S. D. Choi. "Quantum transition processes in deformation potential interacting systems using the equilibrium density projection technique," PHYSICAL REVIEW B, vol.64, no.23, pp.235210, 2001. DOI: 10.1103/PhysRevB.64.235210
  13. H. Kobori, T. Ohyama, and E. Otsuka, "Line-Width of Quantum Limit Cyclotron Resonance. I. Phonon Scatterings in Ge, Si, CdS and InSb," Journal fo the Physical Society of Japan, vol.59, no.6, pp.2141-2163, 1989. DOI: 10.1143/JPSJ.59.2141
  14. J. Y. Sug, S. H. Lee, J. J. Kim, "The magnetic field dependence of the deformation potential materials in the square well confinement potential," Central European Journal of Physics, vol.6, no.4, pp.812-824, 2008. DOI: 10. 2478/s11534-008-0114-1 https://doi.org/10.2478/s11534-008-0114-1
  15. J. Y. Sug, S. H. Lee, J. Y. Choi, G. Sa-Gong. and J. J. Kim, "Magnetic Properties of Optical Quantum Transition Line Shapes and Line Widths of Electron-Piezoelectric Potential Phonon Interacting Materials under Circularly Oscillating Fields," Japanese Journal of Applied Physics, vol.47, no.9, pp.7757-7763, 2008. DOI: 10.1143/JJAP.47.7757
  16. J. Y. Sug, S. H. Lee and J. Y. Choi, "The temperature dependence of quantum optical transition properties of GaN and GaAs in a infinite square well potential system," Journal of the Korean Physical Society, vol.54, no.4, pp. 1015-1019, 2009. DOI: 10.3938/jkps.57.1015
  17. C. M. Wolfe and G. E. Stillman Processes, Physical Properties of Semiconductors, Prentice-Hall, 1989.
  18. D. K. Ferry Process, "Semiconductors," Macmillan, New York, 1991.