Impact Ionization and Auger Recombination in Semiconductors: Implementation Within the Flapw Code
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IMPACT IONIZATION AND AUGER RECOMBINATION IN SEMICONDUCTORS: IMPLEMENTATION WITHIN THE FLAPW CODE
S. PICOZZIy , A. CONTINENZAy , R. ASAHIz , W. MANNSTADTx , C. B. GELLER{ and A. J. FREEMAN|
y INFM { Dip. Fisica, Univ. L'Aquila, 67010 Coppito (L'Aquila), Italy z Toyota Central R&D Labs. Inc., Japan x Fachbereich Physik, Philipps-Universitat Marburg, Germany { Bettis Atomic Power Laboratory, West Miin, PA (U.S.A) | Dept. of Phys. and Astron. and Materials Research Center, Northwestern University,
Evanston, IL 60208 (U.S.A.) ABSTRACT
We present a method to calculate impact ionization and Auger recombination rates within density functional theory and a screened{exchange approach and implement it in the all{ electron FLAPW method. We investigate the dependence of the overlap matrix elements as a function of the states involved along the main symmetry lines of the Brillouin zone. Our results for the nal impact ionization rates along X and L directions for GaAs show a strong anisotropy imposed by energy and momentum conservation and related to the use of a realistic and accurate sX-LDA band structure. INTRODUCTION AND FORMALISM The band-to-band impact ionization (I-I), is a carrier-carrier scattering process in which a carrier creates an electron-hole pair, through the excitation of a valence electron in the conduction band. This process is relevant in small high{speed devices, both as a charge multiplication mechanism (see for example avalanche photodiodes) and as a detrimental mechanism (see for example eld e ect transistors) [1]. On the other hand, its reverse e ect, the Auger recombination (AR), is a process in which an electron and a hole recombine, giving energy to a third carrier, either an electron or a hole. Therefore, the AR sets a fundamental limit to the radiative recombination eÆciency in any optoelectronic device. It is therefore particularly important to calculate the AR and I-I rates from rst principles; this allows the complete understanding of the basic mechanisms and physical quantities that a ect the recombination and pair-production processes, in order to nally increase the lifetime of minority carriers (AR case) and/or enhance charge multiplication (I-I case). Due to the complexity of the problem, there are not many accurate theoretical works on the rates; in particular, our approach is the rst fully ab{initio calculation of I-I rates within the screened{exchange local density approximation (sX-LDA) [2] to the density functional theory framework. In fact, most of the theoretical approaches in the literature are based on the k p, empirical pseudopotential [1, 3, 4], Monte-Carlo[5, 6] or tight{binding{like [7] formalisms. In this work, we show some recent results for I-I in direct{gap semiconductors. Let us recall brie y the formalism that has been implemented within the all-electron full potential linearized augmented plane wave (FLAPW) code[8] and consider an electron{ initiated impact ionization process. According to Fermi Golden's rule, the rate r(n1 ; k1) at AA4.17.1
: filled state (electr
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