MATLAB scripts

1. Excitonic absorption in Ge with and without screening
   % Calculate dielectric function for interband optical transitions in germanium near the direct band gap E_0, following
   % Emminger et al., J. Appl. Phys. 131, 165701 (2022) and Menendez et al., Phys. Rev. B 101, 195204 (2020).
   % Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM. Date: 25 June 2023.
   % Required package: fdigamma.m, to calculate the digamma function with complex arguments.
   % The built-in psi() function only takes real nonnegative arguments.
   Figure 1 Figure 2 Figure 3 Figure 4 Figure 5
2. Nonparabolic 8x8 k.p band structure of alpha-tin
   % Band structure of alpha-tin following Kane (1957) including non-parabolicity
   % corrections, calculated from Vieta's solution to the cubic equation.
   % Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM
   % Date: 22 January 2024
   % Journal article accepted by Journal of Vacuum Science and Technology B on 01/05/2024, published on ...
   Figure 1
3. Intervalence band absorption of alpha-tin
   % Calculate interband optical transitions in alpha-tin, including band filling
   % (Burstein-Moss shift) and screened excitons. The nonparabolicity of the bands is
   % considered with adjusted effective masses. The k-dependence of the optical dipole
   % matrix element has been neglected.
   % The formalism used is similar to Eq. (2) in Carrasco, APL 113, 232104 (2018),
   % but it uses Fermi-Dirac statistics instead of Maxwell-Boltzman statistics.
   % Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM
   % Date: 22 January 2024
   % This script will produce Figure 3 in the JVSTB article by Zollner
   % "Excitonic Effects in the Optical Absorption of Gapless Semiconductor alpha-Tin
   % Near the Direct Band Gap"
   % Accepted by Journal of Vacuum Science and Technology B on 01/05/2024, published on ... ,
   % Required packages: fdigamma.m, to calculate the digamma function with complex arguments.
   % The built-in psi() function only takes real nonnegative arguments.
   % Kramers-Kronig transformation is performed using the add-on kkbook2.
   Figure 1 Figure 2 Figure 3
4. Calculate Fermi level of intrinsic InSb as a function of temperature for parabolic bands
   % Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM.
   % Based on code written by Carlos A. Armenta and Sonam Yadav. Date: 02 October 2023.
   % Required package: Symbolic Math Toolbox Add-On.
   % Reference: Melissa Rivero Arias, Carlos A. Armenta, Carola Emminger, Cesy M. Zamarripa, Nuwanjula S. Samarasingha, Jaden R. Love, Sonam Yadav, and Stefan Zollner, J. Vac. Sci. Technol. B 41, 022203 (2023).
   Figure 1 Figure 2 Figure 3 Figure 4
5. Calculate thermal expansion coefficient of InSb.
   Also calculate redshift of the band gap due to thermal expansion.
   Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM.
   Date: 29 December 2023.
   Figure 1 Figure 2
6. Calculate band structure of InSb for nonparabolic bands in different approximations
   Band structure of InSb following Kane's 8x8 k.p Hamiltonian including non-parabolicity corrections, calculated with different approximations.
   Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM. Date: 18 October 2023.
   Required package: None.
   References:
   E. O. Kane, Band structure of indium antimonide, J. Phys. Chem. Solids 1, 249-261 (1957).
   E. O. Kane, The k.p method, in Semiconductors and Semimetals, edited by Willardson and Beer, vol. 1, 75-100 (1966).
   Stefan Zollner and Jose Menendez, Nonparabolicity and direct gap absorption of InSb (unpublished, 2023).
   Figure 1 Figure 2 Figure 3 Figure 4 Figure 5
7. Calculate Fermi level of intrinsic InSb as a function of temperature for nonparabolic bands
   Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9
8. Calculate Murnaghan's equation of state for Si under hydrostatic pressure
   % Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM.
   % Date: 07 January 2024
   % Required package: None.
   % References:
   % F. D. Murnaghan, The compressibility of media under extreme pressures, Proceedings of the National Academy of Sciences 30, 244 (1944).
   % A. K. Singh and G. C. Kennedy, Compressions of Si, MgO, and ZrSiO4 to 8 GPa as measured with a WC-anvil x-ray apparatus and epoxy pressure medium, J. Appl. Phys. 48, 3362 (1977).
   % S. Anzellini, M. T. Wharmby, F. Miozzi, A. Kleppe, D. Daisenberger, and H. Wilhelm, Quasi-hydrostatic equation of state of silicon up to 1 megabar at ambient temperature, Scientific Reports 9, 15537 (2019).
   Figure 9
9. Calculate electron distribution of GaSb with nonparabolic bands in different conduction band minima
   as a function of electron concentration at different temperatures.
   Prepared by Stefan Zollner, New Mexico State University, Las Cruces, NM.
   Date: 14 June 2024
   Band gap of GaSb as a function of temperature
   Chemical potential of GaSb as a function carrier concentration and temperature
   Relative conduction band valley populations as a function of carrier concentration and temperature
   PDF document as documentation.