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(A Five Minute Tutorial)
- Main Concepts To Learn:
A Quick Step-By-Step:
- Carrier statistics of semiconductor
- Visual, qualitative understanding of
- the energy distribution of electron and hole densities.
- its dependence on the position of Fermi level, Ef.
- our simple color-density model of energy distribution of carrier density.
- Definitions: f(E) = Fermi distribution function, the probability that
an energy state at energy E is occupied by an electron. 1-f(E) = probability
that the state at E is NOT occupied. g(E)dE = number of energy states for
the energy interval E ~ E+dE.
- Total carrier concentration in the band: n = g(E)f(E)dE
over E=Ec to infinity, p = g(E)[1-f(E)]dE
over E= - infinity to Ev.
- At the bottom of applet, click "hide/show f(E)", "hide/show
g(E)", "hide/show Mf(E)" to see respective graphs in the
left-side figure. Here, M=multiplication factor used to make the f(E) visible
in the band.
- Left figure is g(E) for the conduction band (CB) and the valence band
(VB), f(E) for CB and 1-f(E) for VB, and the magnified Fermi function Mf(E)
and M[1-f(E)]. The magnification factor is shown at the top of left-figure.
- Center figure is the plot of f(E)g(E) and [1-f(E)]g(E). These are the
energy distribution of carrier density.
- Right figure is the simple color-density model for the log[f(E)g(E)]
- First click the "Hide EED Model" button at the top of applet.
Use the 'Up/Down' button at the top of applet, or simple mouse drag the
Fermi level Ef, and observe
the variation of the energy distribution.
- Change the temperature by using the scroller at the bottom of applet.
Observe the effects on the Fermi distribution and on the electron/hole
- Click the "Reset" button.
- Click the "Hide DOS,f(E)" and "Show EED Model"
buttons at the top of the applet. Change Ef
and watch the correspondence between the actual f(E)g(E),
the center-figure, and the simple color-density model, the right-figure.
This color-density plot of a logarithm of the carrier density is used throughout