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12 "poisson" - charge and potential distributions in the pn-junction and MIS diodes

"poisson" calculates and displays one-dimensional numerical solutions for the band bending and carrier concentrations in inhomogeneous semiconductors. It simulates both the pn-junction and the sub-gate region of the MISFET for a wide range of material parameters under both equilibrium and biased conditions.

"poisson" was programmed by Russ Thompson.


"poisson" displays both the carrier densities and the band energy diagram for the two types of diodes. In the figures below you see plotted the carrier densities and band energy diagram for a reverse biased pn-junction. (Which side of the junction is more heavily doped, the n-side or the p-side?)

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The second example shows an MIS diode with the gate on the left and semiconductor on the right. The origin is at the insulator/semiconductor interface. A positive bias on the gate has brought the p-type semiconductor into inversion.
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Table of contents for Chapter 12 of Simulations for Solid State Physics
  1. Introduction
  2. pn-junction
    1. Equilibrium
    2. Debye screening*
    3. Einstein relation*
    4. Applied voltage
    5. Diode characteristic
  3. Metal-insulator-semiconductor (MIS) diode
    1. Accumulation and depletion
    2. Inversion
    3. Interface states*
  4. Contact potential and work functions**
    1. Clean surface**
    2. Dirty surface**
  5. Summary
  6. Appendix: "poisson" -- the program
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