Analysis of Mobility of Intrinsic Germanium and Silicon near Room Temperature

Germanium (Ge) and Silicon (Si) are widely used semiconductors in crystal diodes and transistors. So that study of mobility of intrinsic Ge and Si is an important aspect, in electronics/physics. In the present paper, coupled mass-vibrations of atoms in an intrinsic semiconductor, viz., Germanium or Silicon, are analysed near room temperature . Overall average of resultant mean square amplitudes of an atom in the semiconductor undergoing coupled mass-vibrations is regarded as collision-cross section for conduction electrons or valence holes colliding with the atoms. Here the electrons or the holes are regarded as free and forming a gas with appropriate thermal velocity at the temperature of the semiconductor under consideration. This determines the charge carrier’s collision frequency with the atoms. Whence an expression for mobility of the charge carrier is obtained considering distribution of free paths of the charge-carrier. The expression for mobility for isotropic scattering of the charge-carrier at its collision with an atom given here, is modified by comparing the calculated value of mobility at with the value given in a physical table, for the case of anisotropic scattering. This analysis shows that the mobility of the charge-carrier viz., the electron or the hole, due to the charge carrier’s collisions with atom, varies as where is the temperature of the semiconductor under consideration, a result also confirmed by previous investigators. Present analysis gives fairly well values of mobilities near room temperature for Ge and Si. Purpose of this work is to illustrate in a simple manner, how mobility of the semiconductor comes in picture by anisotropic scattering of the electrons and holes at collisions with atoms in the semiconductor. The electrons undergo reverse anisotropic scattering and holes forward anisotropic scattering in Ge whereas both electrons and holes undergo forward anisotropic scattering at collisions with respective atoms in Si.