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 \(q_T\).
