Electric Susceptibility of Impurity Electrons in Semiconductors

Abstract

It is shown that bound electron around donors make comparable contribution to the electric susceptibility as conduction carriers do when each concentration is comparable. The expression for the susceptibility is derived by calculating the expected value of the current density over the wave function of an impurity electron under an external field. The f -sum rule for an impurity state is derived and is applied to the analysis. The main term of the susceptibility is given by - N I e 2 / m * ω 2 , where N I is the concentration of impurity electrons and m * is the effective mass of the lowest conduction band. And the other contribution from the mixings of the wave functions of the lowest conduction band and the excited bound states is shown to be about a tenth of the above, for \(\hbar\omega\) larger than a few times the impurity activation energy. The contribution of conduction electrons to the susceptibility which arises from the presence of bound states is evaluated and it is shown to be negligible in ord...