QuickNote
(A Five Minute Tutorial)

1. Main Concepts To Learn:
• 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.
2. A Quick Step-By-Step:
1. 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.
2. 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.
3. 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.
4. 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.
5. Center figure is the plot of f(E)g(E) and [1-f(E)]g(E). These are the energy distribution of carrier density.
6. Right figure is the simple color-density model for the log[f(E)g(E)] and log[g(E)(1-f(E))].
7. 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.
8. Change the temperature by using the scroller at the bottom of applet. Observe the effects on the Fermi distribution and on the electron/hole energy distribution.
9. Click the "Reset" button.
10. 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 this website.