An Oldie: Cryogenic Electron Emission

Why does the electron emission in the absence of light increase as the temperature of a photomultiplier is decreased?

A spinning temperature particle exert a positive electric field around it.  This field contributes to the total force that holds the electrons in the solid.

For a solid of $N$ molecules,

$V_{q_T}=n_{T}\cfrac{Nq_{T}}{4\pi\varepsilon_o r_{q_{T}}}$

$E_{q_T}=n_{T}\cfrac{Nq_{T}}{4\pi\varepsilon_o r^2_{q_{T}}}$

where $q_{T}$ is the partial charge associated with each spinning positive temperature particle.  In the case of a solid it is expected that,

$q_{T}\propto \psi$

$\psi$ being the energy density around the temperature particle that decreases with decreasing temperature.

$T\downarrow\implies\psi\downarrow\implies q_{T}\downarrow\implies E_{q_T}\downarrow$

As such the positive electric field that holds the electron back is weaken with decreasing temperature, and electrons emission increases with decreasing temperature.

Note:

Lower particle spin also decreases $q_T$.