Thermal evolution of silicon carbide electronic bands

Abstract

Direct observation of temperature dependence of individual bands of semiconductors for a wide temperature region is not straightforward, in particular, for bands farther from the Fermi-level. However, this fundamental property is a prerequisite in understanding the electron-phonon coupling of semiconductors. Here we apply ab initio many body perturbation theory to the electron-phonon coupling on hexagonal silicon carbide (SiC) crystals and determine the temperature dependence of the bands. We find a significant electron-phonon renormalization of the band gap at 0 K. Both the conduction and valence bands shift at elevated temperatures exhibiting a different behavior. We compare our theoretical results with the observed thermal evolution of SiC band edges, and discuss our findings in the light of high temperature SiC electronics and defect qubits operation.Electron-phonon interaction impacts a large variety of fundamental materials properties [1], from the critical temperature of superconductors to the zero-point renormalization and the temperature dependence of the electronic energy bands, from the electronic band gaps [2][3][4][5][6] to the thermal evolution of the optical spectra and excitonic lifetimes [7][8][9]. In addition the electron-phonon coupling contributes to the optical absorption and emission in indirect gap semiconductors [10][11][12], determines the electronic carrier mobility of semiconductors [13], the carrier relaxation rates [14], the distortion of band structures and phonon dispersion giving rise to kinks and Kohn anomalies in photoemission [15].Direct observation of the temperature evolution of individual bands over a wide region of temperatures is not straightforward. Optical techniques are capable of measuring band gaps, and not the absolute values of the valence band maximum (VBM) and the conduction band minimum (CBM) separately. The interpretation of results from optical techniques is then weakly conclusive. In addition, the indirect band gap nature of some materials prohibits the direct optical transition between VBM and CBM, which turns to be allowed only when phonons assist the optical excitation. Recent attempts used Si 2p core level as a reference to extract the CBM and VBM energy position of Si and hexagonal 6H silicon carbide (SiC) crystals [see Fig. 1(a)] from the onset of soft X-ray absorption spectroscopy (XAS) and soft non-resonant Xray emission spectroscopy (XES), respectively [16,17]. This method assumes temperature independent core exciton binding energy [18], which results in a systematically smaller derived band gap than the observed optical band gap, and it may suffer from the accurate observation of the onset energies at elevated temperatures caused by temperature broadening effects. We stress that none of these methods enables the observation of individual bands other than band edges but observation of the tem-perature dependence of those bands can be an important issue at high temperatures.It is utterly important to apply ab initio many body perturbation theory that ca...

Electron–Phonon Interaction Contribution to the Total Energy of Group IV Semiconductor Polymorphs: Evaluation and Implications

“…In Table 2 , the ZPR of VBM/CBM for SiC-3C (obtained using parameters similar to those used in other studies 55 ) is comparable to reported values. 57 , 58 …”

“…The Allen–Heine theory allows the calculation of EPI correction to any arbitrary eigenstate, Δϵ n k ( T ), including for the valence band maxima (VBM) and the conduction band minima (CBM). For this reason, it is the most widely used ab initio method in EPI studies of band gaps and band structures. − We note that there are other recent methods to obtain the EPI contributions to band gaps and band structures. , …”

“…For this reason, it is the most widely used ab initio method in EPI studies of band gaps and band structures. 47 − 58 We note that there are other recent methods to obtain the EPI contributions to band gaps and band structures. 59 , 60 …”

Phonon-induced renormalization of electron wave functions

“…We note that our expression for the DW self-energy [Eq. (13)] does not require a sum over bands nor solutions of the Sternheimer equations, contrary to the ordinary expressions [S5, S10].…”

“…The Allen-Heine-Cardona (AHC) theory [2][3][4] is one of the current state-of-the-art methods to study the effect of electron-phonon coupling (EPC) on electronic structures from first-principles density functional theory (DFT) and density functional perturbation theory (DFPT). Zero-point renormalization and temperature dependence of the electronic band gap [5][6][7][8][9][10][11][12][13] , optical responses [14][15][16] , and topological properties 17 are being actively investigated with the AHC theory.…”