Part 2 : Nanostuctures Module 1 : Introduction
Lecture 9 : Statistics for donors and acceptors
 

More accurate Joyce-Dixon formula would give

Note that

which shows that as the carrier injection is increased, the separation (μe − μh)  increases.
References:
  • Semiconductor Devices, Basic Principles, by Jasprit Singh, John Wiley & Sons Inc. 2001
  • Semiconductor Physics and Devices, by D. A. Neaumen, Tata McGrawHill, Third Edition, 2003
  • The Physics of Semiconductors, An Introduction including Nanophysics and Application by M. Grundmann, Second Edition, Springer-Verlag 2010.