First-principles calculations of charge carrier mobility in semiconductors including charged impurity scattering

Ionized impurities are present in and strongly effect the behaviors of semiconductors in a wide variety of electronic and opto-electronic devices. Ionized impurities generate long-range scattering centers that reduce the electron and hole mobilities. Though a variety of historical models are available to predict carrier mobility as a function of ionized impurity concentration, first-principles calculations offer a way to more accurately describe the physics of ionized impurity scattering in a variety of materials. In this work, we calculate from first principles the electron and hole mobilities and scattering rates limited by both carrier-phonon and carrier-ionized impurity scattering in three prominent semiconductor materials: Si, 3C-SiC, and GaP. We show that the influence of ionized impurity scattering and its balance with phonon scattering are strongly material dependent and influence the expected carrier mobilities as a function of impurity concentration and temperature. Further, we show how the Matthiessen's rule for carrier mobilities limited by different scattering mechanisms breaks down outside of the constant relaxation time approximation. Lastly, we demonstrate the importance of screening and effective mass corrections on calculated carrier mobilities.