# Statistical Physics of Carriers in Heavily Doped Semiconductors

• Victor I. Fistul’
Part of the Monographs in Semiconductor Physics book series (MOSEPH, volume 1)

## Abstract

Distribution — Function Concept. In a system of N particles there are some whose coordinates lie within the intervals
$$x = x \pm \Delta x,\,\,\,\,\,y = y \pm \Delta y,\,\,\,\,\,z = z \pm \Delta z$$
(2.2.1)
and whose momentum components are, respectively,
$$p_x = p_x \pm \Delta p_x ,\,\,\,\,\,p_y = p_y \pm \Delta p_y ,\,\,\,\,\,p_z = p_z \pm \Delta p_z .$$
(2.1.2)
If the number of such particles is ΔN, they represent a fraction ΔN/N of the total number of particles. The fraction of such particles will increase or decrease proportionally to the variation of the intervals Δx, Δy, Δz, and Δpx, Δpy, Δpz. The coefficient of proportionality may be a function of coordinates and momenta, as well as of the time t :
$$\frac{{\Delta N}}{N} = f\left( {x,y,z,p_x ,p_y ,p_z ,t} \right)\Delta x\,\Delta y\,\Delta z\,\Delta p_x \,\Delta p_y \,\Delta p_z .$$
(2.1.3)
Since ΔxΔyΔz = ΔV is an element of volume in the coordinate space, ΔpxΔpyΔpz = Δω is an element of volume in the momentum space, and ΔVΔω = Δγ is an element of volume in the phase space, it follows that
$$\frac{{\Delta N}}{N} = f\Delta \gamma .$$

## Keywords

Fermi Level Dirac Distribution Neutrality Equation Neutrality Equa Universal Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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