SOFT MODES CRITICAL FLUCTUATIONS AND OPTICAL PROPERTIES FOR A TWO-VALLEY MODEL OF GUNN-INSTABILITY SEMICONDUCTORS

The frequency- and field-dependent dielectric constant ε(ω,E) has been calculated for the uniform-field state of a two-valley model of Gunn-instability semiconductors, using a phenomenological approach based on momentum balance and particle conservation. In this model, four plasma modes are obtained as solutions of ε(ωp,E)=0, and the dependence of all four modes on the electric field has been determined. We show that in the neighborhood of each of the critical fields Ec1 and Ec2 defined by σ0(Ec1,2)=0, where σ0 is the dc differential conductivity, the frequency of one of the plasma modes is purely imaginary and goes to zero as E→Ec1 and E→Ec2, the mode becoming unstable for E>Ec1 and E<Ec2, respectively. Critical fluctuations associated with the soft modes have been investigated. The density, current, and field fluctuations become temporally long-range as E→Ec1,2. The field (voltage) noise spectrum becomes sharply peaked at ω=0 in these limits. We have also calculated the field dependence of the optical properties for frequencies in the neighborhood of the zero-field plasma frequency and in the low-frequency region. At the critical fields the medium becomes nonabsorptive in the zero-frequency limit. © 1969 The American Physical Society.