References and further reading

Prerequisites. This page consolidates the references cited throughout the quantum-well theory manual.

Estimated reading time. 5 minutes.

The following works are the primary sources for the theory implemented in the OghmaNano quantum-well solvers. Original papers are preferred over secondary summaries, and standard compilations are cited for parameter values. Where a specific convention or equation is used by OghmaNano, the corresponding source is noted on the relevant manual page.

1. k·p theory and multiband Hamiltonians

E. O. Kane, Band structure of indium antimonide. J. Phys. Chem. Solids 1, 249 (1957). doi:10.1016/0022-3697(57)90013-6
J. M. Luttinger and W. Kohn, Motion of electrons and holes in perturbed periodic fields. Phys. Rev. 97, 869 (1955). doi:10.1103/PhysRev.97.869
J. M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: general theory. Phys. Rev. 102, 1030 (1956). doi:10.1103/PhysRev.102.1030
T. B. Bahder, Eight-band k·p model of strained zinc-blende crystals. Phys. Rev. B 41, 11992 (1990). doi:10.1103/PhysRevB.41.11992
R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems. Springer Tracts in Modern Physics 191, Springer (2003).

2. Strain and deformation potentials

G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors. Wiley, New York (1974).
C. G. Van de Walle, Band lineups and deformation potentials in the model-solid theory. Phys. Rev. B 39, 1871 (1989). doi:10.1103/PhysRevB.39.1871
C. Herring and E. Vogt, Transport and deformation-potential theory for many-valley semiconductors with anisotropic scattering. Phys. Rev. 101, 944 (1956). doi:10.1103/PhysRev.101.944

3. Wurtzite k·p

S. L. Chuang and C. S. Chang, k·p method for strained wurtzite semiconductors. Phys. Rev. B 54, 2491 (1996). doi:10.1103/PhysRevB.54.2491

4. Dilute nitrides and band anticrossing

W. Shan, W. Walukiewicz, J. W. Ager III, E. E. Haller, J. F. Geisz, D. J. Friedman, J. M. Olson and S. R. Kurtz, Band anticrossing in GaInNAs alloys. Phys. Rev. Lett. 82, 1221 (1999). doi:10.1103/PhysRevLett.82.1221
J. Wu, W. Shan and W. Walukiewicz, Band anticrossing in highly mismatched III–V semiconductor alloys. Semicond. Sci. Technol. 17, 860 (2002). doi:10.1088/0268-1242/17/8/315

5. Material-parameter compilations

I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys. J. Appl. Phys. 89, 5815 (2001). doi:10.1063/1.1368156
I. Vurgaftman and J. R. Meyer, Band parameters for nitrogen-containing semiconductors. J. Appl. Phys. 94, 3675 (2003).

6. Quantum-well gain and optoelectronic devices

S. L. Chuang, Physics of Optoelectronic Devices. Wiley, New York (1995); 2nd ed. Physics of Photonic Devices (2009).
L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits. 2nd ed., Wiley (2012).
W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals: Physics of the Gain Materials. Springer (1999).

7. Sparse eigenvalue methods

Y. Saad, Numerical Methods for Large Eigenvalue Problems. 2nd ed., SIAM (2011).
T. Ericsson and A. Ruhe, The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems. Math. Comp. 35, 1251 (1980).
T. A. Davis, Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30, 196 (2004). doi:10.1145/992200.992206

Note on conventions. Different sources adopt different sign conventions, energy references and definitions (for example full versus modified Luttinger parameters, or the sign of the Bir–Pikus terms). Where OghmaNano follows a particular convention, it is stated in an implementation note on the relevant page. When comparing OghmaNano output with a published result, check that the two use the same convention before concluding that they disagree.