Soft Modes, Critical Fluctuations, and Optical Properties for a Two-Valley Model of Gunn-Instability Semiconductors

Abstract

The frequency- and field-dependent dielectric constant $\ensuremath{\epsilon}(\ensuremath{\omega},E)$ 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 $\ensuremath{\epsilon}({\ensuremath{\omega}}_{p},E)=0$, 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 ${E}_{c1}$ and ${E}_{c2}$ defined by ${\ensuremath{\sigma}}_{0}({E}_{c1,2})=0$, where ${\ensuremath{\sigma}}_{0}$ is the dc differential conductivity, the frequency of one of the plasma modes is purely imaginary and goes to zero as $E\ensuremath{\rightarrow}{E}_{c1}$ and $E\ensuremath{\rightarrow}{E}_{c2}$, the mode becoming unstable for $Eg{E}_{c1}$ and $El{E}_{c2}$, respectively. Critical fluctuations associated with the soft modes have been investigated. The density, current, and field fluctuations become temporally long-range as $E\ensuremath{\rightarrow}{E}_{c1,2}$. The field (voltage) noise spectrum becomes sharply peaked at $\ensuremath{\omega}=0$ 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.