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

Abstract

The frequency- and field-dependent dielectric constant $\epsilon (\omega ,E)$ 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 $\epsilon ({\omega }_p,E)=0\mathrm{}$, 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 $E_{c1\mathrm{}}$ and $E_{c2\mathrm{}}$ defined by ${\sigma }_0\left(E_{c1,2\mathrm{}}\right)=0\mathrm{}$, where ${\sigma }_0$ is the dc differential conductivity, the frequency of one of the plasma modes is purely imaginary and goes to zero as $E\to E_{c1\mathrm{}}$ and $E\to E_{c2\mathrm{}}$, the mode becoming unstable for $E>\mathrm{}{E}_{c1\mathrm{}}$ and $E<\mathrm{}{E}_{c2\mathrm{}}$, respectively. Critical fluctuations associated with the soft modes have been investigated. The density, current, and field fluctuations become temporally long-range as $E\to E_{c1,2\mathrm{}}$. The field (voltage) noise spectrum becomes sharply peaked at $\omega =0\mathrm{}$ 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.