Theoretical Models of High-Field Transport and Impact Ionization in Ultra-Wide Band Gap Semiconductors

Theoretical models that attempt to predict high-field carrier transport parameters and the values of the carriers’ ionization coefficients are important since they provide an estimate of the expected values and a first order evaluation of the material performance. The direct measurement of ionization coefficients in wide and ultra-wide band gap semiconductor materials is challenging due to the need to operate at high field strengths and the requirement of specific test structures that enable single carrier injection. More often than not, ionization coefficients are inferred from current multiplication data measured in p-n junctions or transistors structures. Unfortunately, sub-par material quality, processing issues and inappropriate measuring techniques have led to ionization coefficients values that are contradictory and with large variation among different datasets.<br/><br/>Developing theoretical models presents its own set of challenges. The established approach is based on a full electronics structure description of the semiconductor material and a suitable model to quantify the interaction of carriers with phonons, impurities and material imperfections. While this methodology has been successful with conventional elemental and compound semiconductors, and it has been applied to some wide band gap materials such as GaN, 4H-SiC [1,2] and diamond, a number of open issues still exists. The main difficulty is the determination of the carrier-phonon scattering strength at high electric field strengths that cannot be inferred from low-field mobility measurements.<br/><br/>Among all wide band gap semiconductors, 4H-SiC [3] and GaN [4] are the material for which ionization coefficients have been measured by several groups. In the case of GaN, different measured ionization coefficients datasets are available and seems to provide a consistent indication of the expected values. Corresponding theoretical models based on full-band Monte Carlo simulations have been able to predict the correct trends, namely the fact that holes dominate the ionization process, but a quantitative agreement between predicted and measured values has only been achieved recently [5].<br/><br/>This talk will provide an overview of the currently available experimentally measured ionization coefficients for wide band gap semiconductors and compare them to the ones obtained with theoretical models of different complexity. Specifically the development of the theoretical models for high-field transport for 4H-SiC, GaN will be discussed. Three different approaches, one based on empirical carrier-phonon scattering rates, one using the rigid pseudo ion model, and the direct evaluation of the interaction parameters based on a ab-initio DFT approach will be compared, and the outcome for each one of them benchmarked against the measured values. Additionally, the models will be applied to determine the ionization coefficients in ultra-wide band-gap semiconductors including AlGaN alloys, cubic BN [6] and diamond.<br/><br/>[1] E. Bellotti et al., J. Appl. Phys., 87, (8), p.3864, 15 April 2000.<br/>[2] F. Bertazzi et al., J. Appl. Phys., Vol.106, N6, p.063719, 15 September 2009.<br/>[3] A.O. Kostantinov, Appl. Phys. Lett. 71, 90, 1997, T. Hatakeyama, Appl. Phys. Lett. 85, 8, 2004<br/>[4] Cao et al., APL, N.112, 2018, Maeda et al., JAP, N.129, 2021, McClintock et al., APL, N.90, 2007, Ji et al., APL, N115, 2019<br/>[5] E. Bellotti and M. Matsubara, unpublished.<br/>[6] M. Zhu, M. Matsubara, and E. Bellotti, Phys. Rev. App. Under review.