The Standard Thermodynamic Functions for the Formation of Electrons and Holes in Ge, Si, GaAs , and GaP

The forbidden energy gaps of Ge, Si, , and have been used to obtain the standard Gibbs energy, enthalpy and entropy of formation of electrons and holes for each semiconductor up to the melting points. The forbidden energy gap is the standard Gibbs energy of formation of electrons and holes and the enthalpy and entropy have been obtained from the energy gap as a function of temperature and familiar thermodynamic relationships. Energy gaps as a function of temperature, available in the literature, have been fit to the semiempirical equation of Varshni and used to extrapolate the energy gaps and thereby the three thermodynamic functions to the melting points. It is well known that the energy gaps, i.e., the Gibbs energies, decrease with increasing temperature but it is not well known that the enthalpy of formation increases with temperature and that it is proportional to the slope of the familiar logarithmic plot of the intrinsic carrier concentration over vs. . Examples of the utility of the enthalpy function are given. It is the entropy that leads to the decrease in energy gap with increasing temperature and its magnitude is large near the respective melting points (10–13 cals/deg, i.e.,) arising from the interactions of electrons and holes with the lattice. The intrinsic carrier concentrations were calculated from the forbidden energy gaps and the average effective masses which were estimated for the higher temperatures.