ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
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Envelope-Function Equation and Motion of Wave Packet in a Semiconductor Superlattice Structure

  • Published : 1999.03.15
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Abstract

We present a new description of envelope-function equation of the superlattice (SL). The SL wave function and corresponding effective-mass equation are formulated in terms of a linear combination of Bloch states of the constituent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review confirms that the average of SL crystal momentums K = ($k_x,k_y,q$), where ($K_x,k_y$) are bulk inplane wave vectors and q SL wave vector, included in a wave packet satisfies the equation of motion = $_0+Ft/h$; and that the velocity and acceleration theorems provide the same type of group velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been by Altarelli to include the interface-matching condition in the variational calculation for the SL structure in the multi-band envelope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SLs, which agrees in form with the proposed envelope-function formalism. As an illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non-strained $GaAs/Al_{0.32}Ga_{0.68}As$ and strained $In_{0.63}Ga_{0.37}As/In_{0.73}Ga_{0.27}As_{0.58}P_{0.42}SLs$ with well/barrier widths of $60{\AA}/500{\AA}$ and 30${\AA}/30{\AA}$, respectively.

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References

  1. IBM J. Res. Cevelop. v.14 Superlattice and Negative Differential Conductivity in Semiconductors Esaki, L.;Tsu, R.
  2. J. Appl. Phys. v.41 no.6 Electrical Transport Properties in a Superlattice Lebwohl, P.A.;Tsu, R.
  3. Soviet Phys. Semicon. v.6 no.1 Electrical and Electromagnetic Properties of Semiconductors with a Superlattice Kazarinov, R.F.;Suris, R.A.
  4. Phys. Rev. Lett. v.47 no.12 Electronic Properties of Flat-Band Semiconductor Heterostructures White, S.R.;Sham, L.J.
  5. Phys. Rev. B v.24 no.10 Superlattice Band Structure in the Envelope-Function Approximation Bastard, G.
  6. Phys. Rev. B v.25 no.12 Theoretical Investigations of Superlattice Band Structure in the Envelope-Function Approximation Bastard, G.
  7. IEEE Journal of Quantum Electronics v.QE-22 no.9 Electronic States in Semiconductor Heterostructures Bastard, G.;Brum, J.A.
  8. Proceedings Application of High Magnetic Fields in Semiconductor Physics Altarelli, M.;Landwehr, G.(ed.)
  9. Phys. Rev. B v.28 no.2 Electronic Sturcture and Semiconductor-Semimetal Transition in InAs-GaSb Superlattice Altarelli, M.
  10. Phys. Rev. B v.32 no.8 Calculations of Hole Subbands in Semiconductor Quantum Wells and Superlattices Altarelli, M.;Ekenberg, U.
  11. Phys. Rev. B v.31 no.2 Effective Masses of Holes at GaAs-AlGaAs Heterojunctions Broido, D.A.;Sham, L.J.
  12. Phys. Rev. B v.32 no.6 Theoretical Study of Subband Levels in Semiconductor Heterostructures Potz, W.;Porod, W.;Ferry, D.K.
  13. Phys. Rev. B v.33 no.12 k.p Theory of Semiconductor Superlattice Electronic Structure. I. Formal Results Smith, D.L.;Mailhiot, C.
  14. Phys. Rev. B v.33 no.12 k.p Theory of Semiconductor Superlattice Electronic Structure. Ⅱ. Application to $Ga_{1-x}In_{x}As-Al_{1-y}In_yAs$ Mailhiot, C.;Smith, D.L.
  15. Phys. Rev. B v.36 no.11 Hole Subbands in Strained $GaAs-Ga_{1-x}Al_xAs$ Quantum Wells: Exact Solution of the Effective-Mass Equation Andreani, L.C.;Pasquarello, A.;Bassani, F.
  16. Phys. Rev. B v.41 no.6 Electronic and Optical Properties of III-V and II-VI Semiconductor Superlattices Johnson, N.F.;Ehrenreich, H.;Hui, P.M.;Young, P.M.
  17. Phys. Rev. B v.41 Chang, Y.C.;Aspens, D.E.
  18. Phys. Rev. B v.43 no.12 Efficient Band-Structure Calculations of Strained Quantum Wells Chuang, S.L.
  19. Physics of Optoelectronic Devices Chuang, S.L.
  20. J. Appl. Phys. v.77 no.9 Electronic and Intersubband Optical Properties of p-type GaAs/AlGaAs Superlattices for Infrared Photodetectors Kim, B.W.;Majerfeld, A.
  21. J. Appl. Phys. v.81 no.4 Analysis of Optical Properties of p-Type GaAs/AlGaAs Superlattices for Multi-wavelength Normal Incidence Photodetectors Kim, B.W.;Mao, E.;Majerfeld, A.
  22. J. Chem. Phys. v.19 no.11 A Note on the Quantum-Mechanical Perturbation Theory Lowdin, P.O.
  23. ETRI Journal v.20 no.4 Improved Multi-band Transfer Matrix Method for Calculating Eigenvalues and Eigenfunction of Quantum Well and Superlattice Structures Kim, B.W.;Jun, Y.I.;Jung, H.B.
  24. Phys. Rev. v.131 no.6 Composite Wave Variational Method for Solution of the Energy-Band Problem in Solids Schlosser, H.;Marcus, P.M.
  25. Physics of III-V Compounds, Vol. 1 Kane, E.O.;Willardson, R.K.(ed.);Beer, A.C.(ed.)
  26. Phys. Rev. v.102 no.4 Quantum Theory of Cyclotron Resonance in Semiconductros: General Theory Luttinger, J.M.
  27. Quantum Theory of the Solid State Callaway, J.