Question

What is the probability that a donor atom at energy ED is ionized ?

Answer 1

Answer on Question #46476, Physics, Atomic Physics

Problem.

What is the probability that a donor atom at energy ED is ionized?

Solution:

There are three possible states of the system that consist of a single donor atom:

- one ionized state with no electron;

- two unionized states (either spin-up or spin-down).

If $I$ is the ionization energy, then the Gibbs factors of these states are

- ionized state $\exp(0) = 1$ ($\varepsilon = 0$, $n = 0$);

- unionized state $\exp\left(-\frac{-I - \mu}{kT}\right) = \exp\left(\frac{I + \mu}{kT}\right)$.

Hence the probability equals $\frac{1}{1 + 2\exp\left(\frac{I + \mu}{kT}\right)}$.

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