Phase-shift calculation of electron mobility in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-type silicon at low temperatures

Abstract

The mobility of electrons in $n$-type silicon has been calculated and compared with the available experimental data for temperatures between 5 and 80 K. Ionized impurity scattering is treated using the partial-wave phase-shift formalism. It is found that since the Born approximation is invalid at low temperatures, use of Brooks-Herring theory introduces serious error in that regime. For relatively pure samples excellent agreement between theory and experiment is observed, while the agreement is not as good for more highly doped samples. Possible reasons for this disagreement are discussed.