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.
$$\text{rot}\,\vec H = \vec J + \frac{{\partial \vec D}} {{\partial t}}$$
$$\text{rot}\,\vec E = - \frac{{\partial \vec B}} {{\partial t}}$$
$$\text{div }\vec D = \rho$$
$$\text{div }\vec B = 0$$
\(\vec E\) 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.


Carrier Concentration Boltzmann Equation Bipolar Transistor Impurity Band Electric Field Vector 
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© Springer-Verlag/Wien 1984

Authors and Affiliations

  • Siegfried Selberherr
    • 1
  1. 1.Institut für Allgemeine Elektrotechnik und ElektronikTechnische Universität WienAustria

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