Effect of the Thermal Population of the (000) and (100) Conduction Bands on the Elastic Constants of Heavily Doped n-Type Germanium

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Abstract
The effect of the thermal population of the (000) and (100) conduction bands on the elastic constants of heavily doped n‐type Ge is investigated. The theory predicts changes with doping (relative to pure Ge) in all three elastic constants: c44, C′=(1/2) (c11−c12), and B=(1/3) (c11+2c12). The changes in the shear elastic constant C′ and bulk modulus B gradually disappear when the temperature becomes low enough to allow the depopulation of the higher lying bands while the change in c44 becomes identical with that predicted theoretically and verified experimentally by others. The magnitude of C′ as a function of temperature is estimated and found to be within the range of sensitivity of present day ultrasonic techniques. From measurements of the changes in C′ at different temperatures it is possible to determine the effective mass and the magnitude of the shear deformation potential constant associated with the six (100) minima. Measurements of the changes in B at different temperatures lead to two sets of dilatational‐compressional deformation potential constants associated with the (000) and (100) minima depending on what sign is assumed for the shear deformation potential constant of the (100) band.