This Java applet simulates the energy bands in semiconductor materials. Silicon (Si) and Germanium (Ge) are used for comparison. In addition to the energy band diagrams there is a plot showing the Fermi-Dirac occupancy probability. Two scrollbars for the Lattice Temperature and Energy Gap (Eg) are provided to see their effect on carrier concentration in the semiconductor material. Two boxes are used to simulate the valence and conduction bands. Gray and Yellow colors are used to represent electron and hole populations.

When uploaded with the browser the applet initially displays the material in the intrinsic form (i.e. Fermi level coincides with that of the intrinsic). The Fermi level is by definition the energy level below which all electron states are occupied at absolute zero (0 K). Thus in intrinsic semiconductors the Fermi Energy coincides with the intrinsic energy level. The position of the Fermi level, above or below the intrinsic level (Ei) implies that the semiconductor is doped (extrinsic). Above the intrinsic level the semiconductors is doped with donors (n-type such as : antimony, arsenic or phosphorous) or acceptors (p-type such as: boron or indium). The donors and acceptor energy levels are represented by by the "+" and "-" signs respectively. By dragging the Fermi level line (red line) with the mouse, electrons (n) and holes (p) carrier density are computed. The neutrality equations:

• e-Err= n-(Nd - nd) = 0;
• h-Err= p-(Na - na) = 0;

Initially the silicon is intrinsic at room temperature. At low temperature the valence band is full of electrons (probability is one). Increasing the temperature in the material the electrons acquire enough energy to migrate to the conduction band. In this intrinsic material the carrier densities of electrons and holes are equal at any temperature.

When the Fermi level is above or below the intrinsic the level the semiconductor is called extrinsic (ie. impurities also called dopant are added to the material). At low temperature the phonons have little or no energy to stimulate the charges (electrons or holes) that leave behind ionized dopant. The semiconductor therefore has low carrier density. At medium and high temperatures, the thermal energy acquired lead to free charges that are responsible for the electrical conduction in the material.

In this applet the Fermi level is constant when scrolling the temperature. For high temperature, the electron-hole density ratio drops while the carrier density increases. In reality the dopant density is constant in the semiconductor and the Fermi level eventually shift toward the intrinsic level when the temperature increases as shown in constant doping applet.

It is worth noting the superior electrical properties of the germanium with respect to those in silicon. However, the abundance of Silicon in nature as well as the capability of making dielectric from silicon and poor handling of high temperature by germanium (see Fermi applet), germanium as single crystal material for microelectronic application was abandoned.