What is the difference between density of states of free electrons and effective

Question

What is the difference between density of states of free electrons and effective density of states of electrons and holes in a crystalline semiconductor? Show that electrons at the bottom of the conduction band and holes at the top of the valence band of a semiconductor behave like free particles. What is the effective mass of an electron/hole? Why do electrons at the top of a band have negative effective mass? f) Show that electrical conductivity, mu is given by: nemu,where n is the carrier concentration, e is the electronic charge and mu, the mobility.

Explanation / Answer

For electrons or electron holes in a solid, the effective mass is usually stated in units of thetrue mass of an electron, me (9.11×1031 kg). In these units it is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. As it simplifies the more general band theory, the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit.

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