Theory Of Hot Carriers And Carrier Heating In A Semiconductor

  Subhajit Sarkar [1,2]  ,  Ieng-Wai Un [2]  ,  Yonatan Sivan [2]  ,  Yonatan Dubi [1]  
[1] Department of Chemistry, Ben Gurion University of the Negev, Beer Sheva, Israel.
[2] School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel.

The dynamics of the optically generated hot carriers in semiconductors are critically important in estimating the performance of electronic and optoelectronic devices. The interplay of optically generated carriers, their thermalization, and subsequent recombination leads to the formation of non-equilibrium distributions of hot carriers, and heating of carriers and phonons. Surprisingly, a theoretical framework, incorporating the non-equilibrium nature of the carriers, and the carrier and lattice heating effects are lacking to date. Here, we present a semi-quantum coupled Boltzmann-heat equation formalism for calculating the non-equilibrium steady-state electron and hole distributions, and temperatures of both carriers and lattice. The formalism correctly accounts for energy and particle number conservation required for a physically consistent solution of the Boltzmann equations. We first identify various parameter regimes, originating from the interplay between carrier-carrier interactions, carrier-phonon dissipation, and carrier recombination. We show how the illumination energy splits between the different energy dissipation channels, discuss the various ways the electron and hole temperatures are determined experimentally, characterize the non-equilibrium as a function of the illumination intensity, and discuss implications to the heating and even cooling. Beyond the elucidation of all these fundamental aspects, our work is the first step towards a full theory of hot-carrier generation and transport in solar cells and of the efficiency of many other optoelectronic devices.