Theory of Luminescent Efficiency of Ternary Semiconductors

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Abstract
The luminescent efficiency is calculated for a ternary semiconductor, wherein the total electron concentration is divided between the direct and indirect conduction‐band minima. In each valley, the rate equations are determined by radiative, nonradiative, and intervalley transfer times. Although such intervalley transfer times are unimportant at 300°K for efficient material, they are found to be important at 300°K when the internal radiative efficiencies are less than 1%. Furthermore, since phonon cooperation is mandatory for transitions between the direct and indirect valleys, the intervalley transfer times become quite long (>10−9 sec in GaAsP) at lattice temperatures below 77°K. In order to compare the analytical expressions of luminescent efficiency with experiment, it was necessary to derive expressions for the external quantum efficiency of a p‐n junction in a direct band‐gap material. The external electroluminescent efficiency is derived in terms of the junction depth, diffusion length, and absorption coefficient. For the particular case of radiative transitions between free electrons and holes, the predicted ternary electroluminescent efficiencies are in agreement with published experimental results on GaAsP. Furthermore, application of the efficiency expressions to the case of deep impurity emission associated with Si in GaAlAs leads to good agreement with published experimental data on this system. Finally, it is shown that the nonradiative transitions associated with the alloying process are unimportant for most direct band‐gap ternaries, as well as inefficent indirect band‐gap compositions.