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A theoretical investigation of optical absorption by donor impurities in silicon Gilliland, John Michael

Abstract

An investigation has been made into the possibility of observing optical transitions (in the 100-micron region) between the ground state of a donor impurity In silicon and the remaining five states of the {1s} set introduced by Kohn and Luttinger. While such transitions are forbidden in the usual effective mass approximation, it is found that application of corrections to the effective-mass wave functions leads to an enhanced transition probability. Under- the assumption of a simple cubic lattice of impurities, the calculated absorption coefficient is of the order of 10 cm[power -1] at an impurity concentration of 1 x 10[power 18] cm[power -3], and falls off exponentially with decreasing impurity concentration. An upper limit is placed on the region in which the transition should be observable by the broadening of the 2s-2p impurity band. It is estimated that for concentrations greater than 5 x 10[power 18] cm[power -3] the transition of interest will be obscured. The calculated values of the absorption coefficient are probably only accurate to within, one, or even two, orders of magnitude, because of the approximations involved. However, there would appear to be no firm theoretical reason why the 1s[superscript (0)] → 1s[superscript (5)] transition should not be observed.

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