# Some Fundamental Properties

• Siegfried Selberherr
Chapter

## Abstract

To accurately analyze an arbitrary semiconductor structure which is intended as a seif contained device under various operating conditions, a mathematieal model has to be given. The equations which form this mathematieal model are commonly called the basic semiconductor equations. They can be derived from Maxwell’s equations (2-1), (2-2), (2-3) and (2-4), several relations obtained from solid-state physics knowledge about semiconductors and various — sometimes overly simplistic — assumptions.
$$\text{rot}\,\vec H = \vec J + \frac{{\partial \vec D}} {{\partial t}}$$
(2-1)
$$\text{rot}\,\vec E = - \frac{{\partial \vec B}} {{\partial t}}$$
(2.2)
$$\text{div }\vec D = \rho$$
(2.3)
$$\text{div }\vec B = 0$$
(2.4)
$$\vec E$$ and $$\vec D$$are the electric field and displacement vector; $$\vec H$$and $$\vec B$$are the magnetic field and induction vector, respectively. $$\vec J$$denotes the conduction current density, and ρ is the electric charge density.

## Keywords

Carrier Concentration Boltzmann Equation Bipolar Transistor Impurity Band Electric Field Vector

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