How is the number of charge carriers related to the conductivity in semiconductors?

Conductometric gas sensors based on metal oxides (such as this one) use the variation of electrical resistance as an indicator of the concentration of the detected gas. In the aforementioned article, $$\mathrm{ZnO}$$ (an n-type semiconductor) is deposited on interdigitated electrodes to detect the gas $$\mathrm{CO_2}$$. When there is no $$\mathrm{CO_2}$$ in the atmosphere, $$\mathrm{O_2}$$ molecules chemisorb on the surface of the $$\mathrm{ZnO}$$, and each oxygen molecule extracts an electron from the conduction band of the semiconductor, thus decreasing the conductivity of the $$\mathrm{ZnO}$$ film. However, in the presence of a reducing gas such as $$\mathrm{CO_2}$$, the chemisorbed oxygen combines with this gas and releases the electron captured by the oxygen, increasing the conductivity of the $$\mathrm{ZnO}$$.

If we could relate the measured variation in the conductivity of $$\mathrm{ZnO}$$ to the number of charge carriers, then we could easily assess the concentration of the sensed gas.

So, is there any way to relate the number of charge carriers and the conductivity in a semiconductor?

• Do you mean something like Drude conductivity? May 23, 2023 at 9:11

As Roger in the comments suggested, the Drude model might be what you are looking for. In short it assumes an electron gas, that is treated classically and the resistance comes from scatter events of the electrons. The conductivity in this model is given as $$\sigma = e n \mu$$ with the electron charge $$e$$, the charge carrier density $$n$$ and the charge carrier mobility $$\mu = \frac{e\tau}{m^*}$$ ($$m^*$$ is the effective electron mass in the electrongas and $$\tau$$ is the mean time between scattering events for an electron).