Effect of Temperature on Photoelectric Emission

Abstract

A survey of the existing theories of photoelectric emission near the threshold shows that for $\ensuremath{\nu}\ensuremath{\ll}{\ensuremath{\nu}}_{0}$, $I=\mathrm{const} {T}^{n}{e}^{\frac{h(\ensuremath{\nu}\ensuremath{-}{\ensuremath{\nu}}_{0})}{\mathrm{kT}}}$ and for $\ensuremath{\nu}={\ensuremath{\nu}}_{0}$, $I=\mathrm{const} {T}^{n}$. Different theories demand values of $n$ from 1/2 to 5/2. The usual method of comparing theory with experiment, by making logarithmic plots of the current, fails to give any information as to the effect of the $T$ term and hence fails to provide a test of the theories. If, however, data are taken at the threshold for different temperatures, the equation above should yield the correct value of $n$. This is a situation unlike that in the Richardson equation for thermionic emission where the effect of the $T$ term is small compared to that of the exponential term. An analysis of the existing photoelectric data shows that $n$ lies between about 0.7 and 1.7 for the different elements. The apparent departure from a ${T}^{2}$ law can be adequately explained if it is assumed that the work function increases with temperature. Values of the temperature coefficient between 4 and 10\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ ev/deg. are required for the different data. A new method for determining temperature coefficients is suggested which depends on data taken at the threshold. These values predict an intersection of spectral sensitivity curves for different temperatures in agreement with experiment. This suggests an alternative method for determining temperature coefficients using data at the point of intersection. The two methods are in agreement. The value of the constant $A$ in Richardson's thermionic equation is computed on the hypothesis that for a clean metal the departure from the theoretical value of 120 amp./${\mathrm{cm}}^{2}$ ${\mathrm{deg}.}^{2}$ is due to a temperature coefficient of the work function. The computed values are in excellent agreement with those experimentally determined from thermionic measurements on the same specimens.