On the theory of dielectric breakdown in solids

Abstract

It is shown that the theory of dielectric breakdown in solids previously developed by the author is correct only below a critical temperature T$_{c}$. This temperature is defined in such a way that above T$_{c}$ the density of electrons (in strong fields) is so high that mutual collisions between electrons are more frequent than collisions between electrons and the lattice vibrations. In the presence of strong external fields this leads to an equilibrium distribution of the electrons at an electronic temperature T which is higher than the lattice temperature T$_{0}$. T is determined by the energy balance according to which the rate of energy transfer from the field to the electrons must be equal to the rate of energy transfer from the electrons to the lattice vibrations. It is shown that equilibrium can be obtained only if the field is below a critical field F$^{\ast}$. For stronger fields the electronic temperature T rises steadily until the crystal breaks down. It is found that F$^{\ast}$ decreases exponentially with increasing lattice temperature. The theory now accounts for the rise of dielectric strength with temperature at low temperatures (previous theory) and for its decrease at high temperatures. It also shows why influences which tend to increase the dielectric strength at low temperatures (e.g. admixture of foreign atoms) tend to decrease it in the high-temperature region. The increase of the electronic temperature with the field strength F leads (for F < F$^{\ast}$) to an increase of electronic conductivity with F which is calculated quantitatively.