A Statistical Thermodynamic Model for Studying Energy Band Structure of Semiconductor Heterostructures

Authors: Hilmi ÜNLÜ

Abstract: Advances in the science and technology of device quality semiconductor microstructures opened new directions in the making of heterojunction devices which are much faster than the conventional silicon devices. In order to fully appreciate the potantial electronic and optoelectronic applications of heterostructures there are material issues that must be fully investigated. One of the most important issues is the understanding and determination of the discontinuity in the energy band structure of the heterostructure at its interface and has received world wide interest among the device physicists and engineers over the three decades [1]. These energy band offsets affect various device properties such as the injection efficiency of heterojunction bipolar transistors (HBTs) and the carrier confinement in the recently developed modulation doped field effect transistors (MODFETs)[2]. A statistical thermodynamic model is presented to study the band offsets and temperature and strain induced nonlinearities in the band structure of lattice matched and pseudomorphic heterostructures. The model uses an average internal reference energy level (obtained using the universal tight bonding theory [3]), at which the bonding (valence-like) and antibonding (conduction-like) states are equal, to define the thermodynamic equilibrium for a heterostructure at any temperature and strain. Use of such internal reference level allows one to incorporate the effects of third nearest neighboor interactions on the band offset calculations. The temperature and strain induced nonlinear effects on the band structure is calculated by using two universal statistical thermodynamic postulates [4]: (i) The free electrons and holes are electrically charged weakly interacting quasi-chemical particles; (ii) The electron-hole pairs are generated by the charge transfer from the bonding (antibonding) states toantibonding (bonding) states in tetrahedrally coordinated semiconductors and semimetals. It is shown that there is a good agreement between the model predictions and experimental data for the band offsets and temperature and pressure induced nonlinearities in the energy bandgaps of lattice matched AlGaAs/GaAs and HgCdTe/CdTe heterostructures for over wide range of temperatures and pressures. It is also shown that in the HgTe/CdTe system, the applied pressure moves up the energy of \Gamma_{6c} antibonding states above the energy of the \Gamma_{8v} bonding states and HgTe becomes a diamond type semiconductor above certain pressure with finite bandgap. Above the transition pressure of 25 Kbar, the band alignment at the HgTe/CdTe interface transforms from type III to conventional type I.

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