(特邀)宽带隙半导体的冲击电离系数:理论模型和测量数据

Enrico Bellotti, Masahiko Matsubara
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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. 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. 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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 AlGaN alloys, cubic BN and diamond. [1] E. Bellotti et al., J. Appl. Phys., 87, (8), p.3864, 15 April 2000. [2] F. Bertazzi et al., J. Appl. Phys., Vol.106, N6, p.063719, 15 September 2009. [3] A.O. Kostantinov, Appl. Phys. Lett. 71, 90, 1997, T. Hatakeyama, Appl. Phys. Lett. 85, 8, 2004 [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 [5] E. Bellotti and M. 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引用次数: 0

摘要

由于需要在高场强下工作,并且需要能够实现单载流子注入的特定测试结构,因此直接测量宽带隙半导体材料中的电离系数具有挑战性。通常情况下,电离系数是从pn结或晶体管结构中测量的电流倍增数据推断出来的。不幸的是,低于标准的材料质量、加工问题和不适当的测量技术导致电离系数值相互矛盾,并且在不同的数据集之间存在很大差异。因此,试图预测载流子电离系数值的理论模型是重要的,因为它们提供了期望值的估计和材料性能的一阶评估。发展理论模型有其自身的挑战。所建立的方法是基于半导体材料的完整电子结构描述和一个合适的模型来量化载流子与声子、杂质和材料缺陷的相互作用。虽然这种方法已经在传统的元素和化合物半导体中取得了成功,并且已经应用于一些宽带隙材料,如GaN, 4H-SiC[1,2]和金刚石,但仍然存在许多悬而未决的问题。主要的困难是确定载流子-声子在高电场强度下的散射强度,这不能从低场迁移率测量中推断出来。在所有的宽带隙半导体中,4H-SiC[3]和GaN[4]是几个研究小组测量过电离系数的材料。在氮化镓的情况下,不同的测量电离系数数据集是可用的,似乎提供了期望值的一致指示。基于全波段蒙特卡罗模拟的相应理论模型已经能够预测正确的趋势,即空穴主导电离过程,但预测值和实测值之间的定量一致直到最近才实现[5]。本讲座将概述目前可用的实验测量的宽禁带半导体的电离系数,并将其与不同复杂性的理论模型所获得的电离系数进行比较。具体来说,将讨论4H-SiC、GaN的高场输运理论模型的发展。将比较三种不同的方法,一种基于经验载流子-声子散射率,一种使用刚性伪离子模型,以及基于从头算DFT方法直接评估相互作用参数,并将每种方法的结果与测量值进行基准比较。此外,该模型将应用于确定AlGaN合金、立方BN和金刚石中的电离系数。[1]张晓明,李晓明。理论物理。, 87,(8),第3864页,2000年4月15日。[2]张晓明,李晓明。理论物理。, Vol.106, N6, p.063719, 2009年9月15日。[3]李志强,李志强。理论物理。中华人民大学学报,1997,20(1)。理论物理。科学通报,85,8,2004 [4]Cao等,APL, n . 112,2018, Maeda等,JAP, n . 129,2021, McClintock等,APL, n . 90,2007, Ji等,APL, n . 115,2019 [5] E. Bellotti和M. Matsubara,未发表。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
(Invited) A Closer Look at Impact Ionization Coefficients in Wide Band Gap Semiconductors: Theoretical Models and Measured Data
The direct measurement of ionization coefficients in 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. As a result, theoretical models that attempt to predict 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. 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. 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]. 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 AlGaN alloys, cubic BN and diamond. [1] E. Bellotti et al., J. Appl. Phys., 87, (8), p.3864, 15 April 2000. [2] F. Bertazzi et al., J. Appl. Phys., Vol.106, N6, p.063719, 15 September 2009. [3] A.O. Kostantinov, Appl. Phys. Lett. 71, 90, 1997, T. Hatakeyama, Appl. Phys. Lett. 85, 8, 2004 [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 [5] E. Bellotti and M. Matsubara, unpublished.
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