(Carrier Concentration vs. Fermi Level)

The concentration of electrons, in a
lightly-to-moderately
doped semiconductor, with donor impurities for example, can be found
using
this simple formula if the Fermi level Ef is known: n = Nc exp[
-(Ec-Ef)/kT
], where Nc is a constant of material (density of states of conduction
band), and Ec-Ef is the energy separation of the Conduction Band edge
(Ec)
from the Fermi level (Ef) and kT is the thermal energy (0.0259 eV at
300K).
This simple formula, however, does not work if the semiconductor is *heavily
*doped (a simple rule of thumb is **n > 0.1 Nc** for n-type
or
**p > 0.1 Nv** for p-type).

A heavily doped semiconductor material is found in the device regions such as:

- the Emitter region of bipolar junction transistor
[in
Si BJT, emitter doping is typically 10
^{19}cm^{-3}], - the Base region of AlGaAs/GaAs HBT where the
AlGaAs Emitter
is dopped to 5x10
^{17}impurities/cm^{3}, and GaAs Base is doped to 5x10^{18}impurities/cm^{3}, - both the p- and n-type regions of a pn-junction
GaAs
laser diode with both p and n at 10
^{18}cm^{-3}, - the active region of a AlGaAs/GaAs
heteronjunction laser
diode where the injection level into the active region approaches 10
^{18}cm^{-3}, - the impurity-doped region of a AlGaAs/GaAs MODFET
where
the Al
_{0.3}Ga_{0.7}As layer is doped to N_{d}= 1.5x10^{18}cm^{-3}, - the Source and Drain regions of Si MOSFET where doping level is very high.

The simple exponential concentration formula in the *lightly*-or-*moderately
*doped semiconductor is called ** Maxwell-Boltzman** (MB)
approximation;
where as the accurate experssion [required in a

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Copyright (c) C.R.Wie 1999-2000