Low-temperature semiconductor band-gap thermal shifts: T4 shifts from ordinary acoustic and T2 from piezoacoustic coupling

Allen, Philip B.; Nery, Jean Paul

doi:10.1103/physrevb.95.035211

Title: Low-temperature semiconductor band-gap thermal shifts: $T^{4}$ shifts from ordinary acoustic and $T^{2}$ from piezoacoustic coupling

Journal Article · Thu Jan 26 00:00:00 EST 2017 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.95.035211· OSTI ID:1535833

Allen, Philip B. ^[1]; Nery, Jean Paul ^[1]

Stony Brook Univ., NY (United States)

At low temperature, the experimental gap of silicon decreases as $E_{g} (T) = E_{g} (0) - A T^{4}$ . The main reason is electron-phonon renormalization. Furthermore, the physics behind the $T^{4}$ -power law is more complex than has been realized. Renormalization at low $T$ by intraband scattering requires a nonadiabatic treatment in order to correctly include acoustic phonons and avoid divergences from piezoacoustic phonon interactions. The result is an unexpected low $T$ term $E_{g} (0) + A^{'} T^{p}$ with positive coefficient $A^{'}$ , and power $p = 4$ for nonpiezoelectric materials, and power $p = 2$ for piezoelectric materials. The acoustic phonons in piezoelectric semiconductors generate a piezoelectric field, modifying the electron-phonon coupling. However, at higher $T$ , thermally excited acoustic phonons of energy $ℏ v_{s} q$ and intraband excitation energies $ε_{q} - ε_{0} = ℏ^{2} q^{2} / 2 m^{*}$ become comparable in size. Above this temperature, the low $q$ and higher $q$ intraband acoustic phonon contributions to $T^{p}$ rapidly cancel, leaving little thermal effect. Then the contribution from interband scattering by acoustic phonons is dominant. This has the power law $T^{4}$ for both nonpiezoelectric and piezoelectric semiconductors. The shift can then have either sign, but usually reduces the size of gaps as $T$ increases. It arises after cancellation of the $T^{2}$ terms that appear separately in Debye-Waller and Fan parts of the acoustic phonon interband renormalization. The cancellation occurs because of the acoustic sum rule.

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Research Organization:: State Univ. of New York (SUNY), Albany, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-08ER46550

OSTI ID:: 1535833

Alternate ID(s):: OSTI ID: 1341284

Journal Information:: Physical Review B, Vol. 95, Issue 3; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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References (36)

Temperature dependent band gap in PbX (X = S, Se, Te) Gibbs, Zachary M.; Kim, Hyoungchul; Wang, Heng Applied Physics Letters, Vol. 103, Issue 26 https://doi.org/10.1063/1.4858195	journal	December 2013
Electron–phonon interaction in tetrahedral semiconductors Cardona, Manuel Solid State Communications, Vol. 133, Issue 1 https://doi.org/10.1016/j.ssc.2004.10.028	journal	January 2005
Temperature Effects in the Band Structure of Topological Insulators Monserrat, Bartomeu; Vanderbilt, David Physical Review Letters, Vol. 117, Issue 22 https://doi.org/10.1103/PhysRevLett.117.226801	journal	November 2016
Polarons in the Degenerate-Band Case Trebin, H. -R.; Rössler, U. physica status solidi (b), Vol. 70, Issue 2 https://doi.org/10.1002/pssb.2220700232	journal	August 1975
Ab initio calculation of spin-dependent electron–phonon coupling in iron and cobalt Verstraete, Matthieu J. Journal of Physics: Condensed Matter, Vol. 25, Issue 13 https://doi.org/10.1088/0953-8984/25/13/136001	journal	March 2013
Theorie des festen Zustandes einatomiger Elemente Grüneisen, E. Annalen der Physik, Vol. 344, Issue 12 https://doi.org/10.1002/andp.19123441202	journal	January 1912
Stochastic Approach to Phonon-Assisted Optical Absorption Zacharias, Marios; Patrick, Christopher E.; Giustino, Feliciano Physical Review Letters, Vol. 115, Issue 17 https://doi.org/10.1103/PhysRevLett.115.177401	journal	October 2015
Temperature Dependence of the Energy Gap of Semiconductors in the Low-Temperature Limit Cardona, Manuel; Meyer, T. A.; Thewalt, M. L. W. Physical Review Letters, Vol. 92, Issue 19 https://doi.org/10.1103/PhysRevLett.92.196403	journal	May 2004
Solids with thermal or static disorder. I. One-electron properties Allen, P. B. Physical Review B, Vol. 18, Issue 10 https://doi.org/10.1103/PhysRevB.18.5217	journal	November 1978
Temperature dependence of the electronic structure of semiconductors and insulators Poncé, S.; Gillet, Y.; Laflamme Janssen, J. The Journal of Chemical Physics, Vol. 143, Issue 10 https://doi.org/10.1063/1.4927081	journal	September 2015
On the theory of temperature shift of the absorption curve in non-polar crystals Antončík, Emil Czechoslovak Journal of Physics, Vol. 5, Issue 4 https://doi.org/10.1007/BF01687209	journal	December 1955
Comparison of zinc-blende and wurtzite GaN semiconductors with spontaneous polarization and piezoelectric field effects Park, Seoung-Hwan; Chuang, Shun-Lien Journal of Applied Physics, Vol. 87, Issue 1 https://doi.org/10.1063/1.371915	journal	January 2000
Verification of first-principles codes: Comparison of total energies, phonon frequencies, electron–phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo Poncé, S.; Antonius, G.; Boulanger, P. Computational Materials Science, Vol. 83 https://doi.org/10.1016/j.commatsci.2013.11.031	journal	February 2014
Cumulant expansion for phonon contributions to the electron spectral function Story, S. M.; Kas, J. J.; Vila, F. D. Physical Review B, Vol. 90, Issue 19 https://doi.org/10.1103/PhysRevB.90.195135	journal	November 2014
Theory of the temperature dependence of electronic band structures Allen, P. B.; Heine, V. Journal of Physics C: Solid State Physics, Vol. 9, Issue 12 https://doi.org/10.1088/0022-3719/9/12/013	journal	June 1976
Deformation Potentials and Mobilities in Non-Polar Crystals Bardeen, J.; Shockley, W. Physical Review, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRev.80.72	journal	October 1950
Influence of Fröhlich polaron coupling on renormalized electron bands in polar semiconductors: Results for zinc-blende GaN Nery, Jean Paul; Allen, Philip B. Physical Review B, Vol. 94, Issue 11 https://doi.org/10.1103/PhysRevB.94.115135	journal	September 2016
Theoretical approaches to the temperature and zero-point motion effects on the electronic band structure Gonze, X.; Boulanger, P.; Côté, M. Annalen der Physik, Vol. 523, Issue 1-2 https://doi.org/10.1002/andp.201000100	journal	November 2010
Temperature dependence of fundamental band gaps in group IV, III–V, and II–VI materials via a two-oscillator model Pässler, R. Journal of Applied Physics, Vol. 89, Issue 11 https://doi.org/10.1063/1.1369407	journal	June 2001
Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation Poncé, S.; Antonius, G.; Gillet, Y. Physical Review B, Vol. 90, Issue 21 https://doi.org/10.1103/PhysRevB.90.214304	journal	December 2014
Die thermische Ausdehnung regulär kristallisierender fester Körper Grüneisen, E. Annalen der Physik, Vol. 360, Issue 5 https://doi.org/10.1002/andp.19183600503	journal	January 1918
ABINIT: First-principles approach to material and nanosystem properties Gonze, X.; Amadon, B.; Anglade, P. -M. Computer Physics Communications, Vol. 180, Issue 12 https://doi.org/10.1016/j.cpc.2009.07.007	journal	December 2009
Extracting semiconductor band gap zero-point corrections from experimental data Monserrat, Bartomeu; Conduit, G. J.; Needs, R. J. Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184302	journal	November 2014
Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN Rinke, Patrick; Winkelnkemper, M.; Qteish, A. Physical Review B, Vol. 77, Issue 7 https://doi.org/10.1103/PhysRevB.77.075202	journal	February 2008
Temperature Dependence of the Energy Gap in Semiconductors Fan, H. Y. Physical Review, Vol. 82, Issue 6 https://doi.org/10.1103/PhysRev.82.900	journal	June 1951
Piezoelectric Scattering and Phonon Drag in ZnO and CdS Hutson, A. R. Journal of Applied Physics, Vol. 32, Issue 10 https://doi.org/10.1063/1.1777061	journal	October 1961
Ab initio phonon coupling and optical response of hot electrons in plasmonic metals Brown, Ana M.; Sundararaman, Ravishankar; Narang, Prineha Physical Review B, Vol. 94, Issue 7 https://doi.org/10.1103/PhysRevB.94.075120	journal	August 2016
Systematic treatment of displacements, strains, and electric fields in density-functional perturbation theory Wu, Xifan; Vanderbilt, David; Hamann, D. R. Physical Review B, Vol. 72, Issue 3 https://doi.org/10.1103/PhysRevB.72.035105	journal	July 2005
Parameter Sets Due to Fittings of the Temperature Dependencies of Fundamental Bandgaps in Semiconductors P�ssler, R. physica status solidi (b), Vol. 216, Issue 2 https://doi.org/10.1002/(SICI)1521-3951(199912)216:2%3C975::AID-PSSB975%3E3.0.CO;2-N	journal	December 1999
Temperature dependence of the energy gap in semiconductors Varshni, Y. P. Physica, Vol. 34, Issue 1 https://doi.org/10.1016/0031-8914(67)90062-6	journal	January 1967
Verification of first-principles codes: comparison of total energies, phonon frequencies, electron-phonon coupling and zero-point motion correction to the gap between ABINIT and QE/Yambo Poncé, S.; Antonius, G.; Boulanger, P. arXiv https://doi.org/10.48550/arxiv.1309.0729	text	January 2013
Temperature dependence of the electronic structure of semiconductors and insulators Poncé, Samuel; Gillet, Yannick; Janssen, Jonathan Laflamme arXiv https://doi.org/10.48550/arxiv.1504.05992	preprint	January 2015
Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: Polar-optical coupling in GaAs Sjakste, J.; Vast, N.; Calandra, M. arXiv https://doi.org/10.48550/arxiv.1508.06172	text	January 2015
Ab initio phonon coupling and optical response of hot electrons in plasmonic metals Brown, Ana M.; Sundararaman, Ravishankar; Narang, Prineha arXiv https://doi.org/10.48550/arxiv.1602.00625	text	January 2016
Temperature effects in the band structure of topological insulators Monserrat, Bartomeu; Vanderbilt, David arXiv https://doi.org/10.48550/arxiv.1608.00584	text	January 2016
Systematic treatment of displacements, strains and electric fields in density-functional perturbation theory Wu, Xifan; Vanderbilt, David; Hamann, D. R. arXiv https://doi.org/10.48550/arxiv.cond-mat/0501548	text	January 2005

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Experimental determination of the bare energy gap of GaAs without the zero-point renormalization Roy, Basabendra; Mukhuti, Kingshuk; Bansal, Bhavtosh Journal of Physics: Condensed Matter, Vol. 32, Issue 10 https://doi.org/10.1088/1361-648x/ab58f8	journal	December 2019
Experimental determination of the bare energy gap of GaAs without the zero-point renormalization Roy, Basabendra; Mukhuti, Kingshuk; Bansal, Bhavtosh arXiv https://doi.org/10.48550/arxiv.1911.10890	text	January 2019

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Title: Low-temperature semiconductor band-gap thermal shifts: T 4 shifts from ordinary acoustic and T 2 from piezoacoustic coupling

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Title: Low-temperature semiconductor band-gap thermal shifts: $T^{4}$ shifts from ordinary acoustic and $T^{2}$ from piezoacoustic coupling