Optical Properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Type Indium Arsenide in the Fundamental Absorption Edge Region

Abstract

The optical properties of InAs in the fundamental absorption edge region have been studied experimentally as a function of impurity content over a temperature range extending from 18\ifmmode^\circ\else\textdegree\fi{} to 300\ifmmode^\circ\else\textdegree\fi{}K. The addition of donor impurities moves the absorption edge to higher energies and changes its shape in accordance with the theory of Burstein. For nondegenerate material the energy dependence of absorption coefficients larger than ${10}^{3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ is ${\ensuremath{\alpha}}^{2}=3.0\ifmmode\times\else\texttimes\fi{}{10}^{8} (E\ensuremath{-}0.35)$ ${\mathrm{cm}}^{\ensuremath{-}2}$ at room temperature and is in good agreement with calculations by Stern based on a nonparabolic conduction band. Absorption coefficients below ${10}^{3}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ depend exponentially upon energy down to at least 3 ${\mathrm{cm}}^{\ensuremath{-}1}$, a result which has not yet been explained. The addition of acceptor impurities to the purest material available moves the absorption edge to lower energies by an amount which increases with the acceptor concentration. When 2.4\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ acceptor atoms are added, the absorption edge measured at 100 ${\mathrm{cm}}^{\ensuremath{-}1}$ is shifted by 0.013 ev. The temperature dependence of the forbidden energy gap was found to be linear from 300\ifmmode^\circ\else\textdegree\fi{} to 80\ifmmode^\circ\else\textdegree\fi{}K with a temperature coefficient of -2.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ ev/\ifmmode^\circ\else\textdegree\fi{}K. Below 80\ifmmode^\circ\else\textdegree\fi{}K the change of the energy gap with temperature becomes smaller and nonlinear. It is estimated that lattice dilation accounts for only one-fourth of the total variation of the energy gap with temperature. The radiative lifetime of added carriers in intrinsic material at room temperature was calculated from the optical constants by the method of van Roosbroeck and Shockley and was found to be 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ sec.