Streaming motion and population inversion of hot electrons in silver halides at crossed electric and magnetic fields

Galvanomagnetic measurements on photocarriers in pure AgCl and AgBr have been extended to an intense electric field ($E_x\sim 5$ kV/cm) and high magnetic field ($H_z\sim 58$ kOe) at 4.2 K by using a fast-pulse technique. improved arrangements of blocking electrodes were adopted in order to detect simultaneously the three components of the transient photocurrent, $Q_x$, $Q_y$, and $Q_z$. Substantial roles of the LO-phonon emission in hot-electron kinetics have been revealed and clear pictures of the hot-electron phenomena in silver halides were obtained, for the first time, by a quantitative analysis of the results: (1) At $H_z=0\mathrm{}$, the momentum distribution of electrons (or holes) forms a line connecting the two points $\overrightarrow{\mathrm{v}}=0\mathrm{}$ and $\overrightarrow{\mathrm{v}}=(-V_{\mathrm{LO}},0,0)$, where $\left(\frac{1}{2}\right)m^{*}{V}_{\mathrm{LO}}^2\equiv \hslash {\omega }_{\mathrm{LO}}$, and the electrons are ideally streaming on the trajectory repeatingly emitting LO phonons. Hence, the electron drift velocity at high $E_x$ at $H_z=0\mathrm{}$ is saturated to $\left(\frac{1}{2}\right)V_{\mathrm{LO}}$. (2) An anomalous distribution of hot electrons involving population inversion predicted by Maeda and Kurosawa, is realized by applying a moderately high $H_z$ such that $1<\mathrm{}\zeta <2\mathrm{}$, where $\zeta \Xi {\left(\frac{2\hslash {\omega }_{\mathrm{LO}}}{m^{*}}\right)}^{\frac{1}{2}}{\left(\frac{c{E}_x}{H_z}\right)}^{-1\mathrm{}}$. The distribution consists of two groups of electrons; the first group of electrons are streaming and the second group are accumulated within a high-energy area $K$ in momentum space. Depending on the electron accumulation in the area $K$, the tangent of the Hall angle, $tan\theta \equiv \frac{Q_y}{Q_x}$ and also $Q_z$ increase abruptly with $H_z$. (3) It was found that the electron trapping lifetime varies with $E_x$ and $H_z$. The streaming motion is responsible for the variation in lifetime. The experimental results here afford, for the first time, a set of conclusive evidence for the streaming motion, the anomalous distribution, and the advent of population inversion of the polarons in momentum space.