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Carrier Concentration Temperature Dependence

https://www.fiberoptics4sale.com In this video, we will discuss the carrier concentration’s dependence on ambient temperature. The top figure shows a typical majority-carrier concentration versus temperature relationship in a phosphorus-doped silicon sample, with ND = 1015 /cm3. In order to understand the concentration versus temperature dependence, we must know that the equilibrium number of carriers within a material is affected by two separate mechanisms. The first mechanism is the electrons donated to the conduction band from donor sites. The second mechanism is the valence band electrons excited across the band gap into the conduction band. At temperatures T  0 K the thermal energy available in the system is insufficient to release the weakly bound fifth electron on donor sites and totally insufficient to excite electrons across the band gap. Hence n = 0 at T = 0 K. Slightly increasing the material temperature above T = 0 K frees some of the electrons weakly bound to donor sites. Band-to-band excitation, however, remains extremely unlikely, and therefore the number of observed electrons in the freeze-out temperature region equals the number of ionized donor sites – n = ND+. Continuing to increase the system temperature eventually frees almost all of the weakly bound electrons on donor sites, n approaches ND, and one enters the extrinsic temperature region. In progressing through the extrinsic temperature region, more and more electrons are excited across the band gap, but the number of electrons supplied in this fashion stays comfortably below ND. Ultimately, electrons excited across the band gap equal, then exceed and, as shown on the right-hand side of the graph, finally swamp the fixed number of electrons derived from the donor sites. As a practical note, it should be pointed out that the wider the band gap, the greater the energy required to excite electrons from the valence band into the conduction band, and the higher the temperature at the onset of the intrinsic temperature region. For this reason, silicon devices can operate at higher temperatures than germanium devices, about 200°C at maximum for silicon devices versus about 100°C at maximum for germanium devices. Galium Arsenide devices can operate at even higher temperatures than silicon devices.