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Abstract
Binary semiconductors are central to all modern electronic, optoelectronic, and electromechanical systems. Given such practical importance, there is value in finding routes to simplify the determination of physical properties, particularly with respect to nonlinearities. Fortunately, nearly all binary semiconductors crystallize into one of two structures: cubic zinc blende or hexagonal wurtzite. Correspondences between the linear rank 3 piezoelectric and rank 4 elastic tensors of zinc blende and wurtzite polytypes have been addressed. Nonlinear rank 6 elastic tensors have similarly been discussed. Provided herein are the analogous relations for the nonlinear rank 5 tensors that have not previously been treated and which complete this missing transformation gap and enable some nonlinear atomic-level phenomena to be investigated.
Highlights
The technological virtues of binary semiconductors are well documented. Canonical examples such as Group IV–IV (e.g., SiC and SiGe), Group III–IV (e.g., AlN, GaSb, GaAs, GaN, InSb, InN, and InP), and Group II–VI (e.g., ZnS, ZnSe, CdS, CdTe, and ZnO) compounds are ubiquitous in wide-ranging practical applications as LEDs, lasers, photodetectors, solar cells, power electronics, and optoelectronics, to name just a few
The zinc blende [111] direction corresponds to the wurtzite [0001] direction, the [101 ̄] direction in the zinc blende (111) plane is equivalent to the [1120] direction in wurtzite, and [1 ̄010] is parallel to [1 ̄1 ̄2]
Given the abundance of technologically critical binary semiconductors that form into cubic zinc blende or hexagonal wurtzite systems, these results should enable insights into nonlinear atomic-level phenomena from more frequently reported linear behaviors
Summary
The technological virtues of binary semiconductors are well documented. Canonical examples such as Group IV–IV (e.g., SiC and SiGe), Group III–IV (e.g., AlN, GaSb, GaAs, GaN, InSb, InN, and InP), and Group II–VI (e.g., ZnS, ZnSe, CdS, CdTe, and ZnO) compounds are ubiquitous in wide-ranging practical applications as LEDs, lasers, photodetectors, solar cells, power electronics, and optoelectronics, to name just a few.. Hexagonal elastic relations were determined by comparing the nearly identical longitudinal and transverse acoustic velocities along cubic [111] and hexagonal [0001] directions, in conjunction with other invariants.25,30,34,47–49 It was in Robinson’s succinct note that a clear explanation of the correspondences emerged, along with new relations among the linear piezoelectric coefficients of the two phases.. It was in Robinson’s succinct note that a clear explanation of the correspondences emerged, along with new relations among the linear piezoelectric coefficients of the two phases.22 These relations are in addition to those proposed by Kleinman, which stem from symmetry restrictions on the phases taken individually. Given the abundance of technologically critical binary semiconductors that form into cubic zinc blende or hexagonal wurtzite systems, these results should enable insights into nonlinear atomic-level phenomena from more frequently reported linear behaviors
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