Temperature dependence of carrier ionization rates and saturated velocities in silicon

The temperature dependencies of the carrier ionization rates and saturated drift velocities in silicon have been extracted from microwave admittance and breakdown voltage data of avalanche diodes. The avalanche voltage and broadband (2–8 GHz) microwave small-signal admittance were measured for junction temperatures in the range 280 to 590 K. An accurate model of the diode was used to calculate the admittance characteristic and voltage for each junction temperature. Subsequently, the values of ionization coefficients and saturated velocities were determined at each temperature by a numerical minimization routine to obtain the best fit between the calculated values and measured data. The resulting ionization rates are well fitted by the temperature dependent model developed by Crowell and Sze from the Baraff ionization-rate theory. The carrier scattering mean free path lengths, average energy loss per collision, and relative ionization cross section are obtained from the best fit agreement between the scattering model and experimental data. The parameter values determined here relevent for use with the above theory are the following:Parameter Holes Electrons ε_r(eV) 0.063 0.063 ε_i(eV) 1.6 1.6 λ_oo(Å) 81.2 77.4 σ 0.391 0.593 The values and temperature dependence of the saturated carrier velocities determined are in good agreement with other published results. At 300 K the low field (E?10⁴ V/cm) saturated velocity for electrons and holes is 10.4 and 7.4×10₆ cm/sec, respectively. The results obtained in this study are of general use for the modeling of effects related to avalanche breakdown and high-field carrier transport in silicon.