The value of ni at any temperature is a definite number for a given semiconductor and is known for most materials. Thus we can take ni as given in calculating n or p.
With ni and T given, the unknowns in equations (10) and (17) are the carrier concentration and the Fermi level position relative to Ei. One of these quantities must be given if the other is to be found. If the carrier concentration is held at a certain value, as in heavily doped extrinsic material, EF can be obtained from equations (29) & (34). The temperature dependence of electron concentration in a doped semiconductor can be visualized as in Fig. 12. In this example, Si is doped n-type with a donor concentration Nd of 1015 cm-3. At very low temperature (range 1/T) negligible intrinsic electron hole pairs exist and the donor electrons are bound to the donor atoms. As the temperature is raised, these electrons are donated to the conduction band and at about 100 K (1000/T=10) all the donor atoms are ionized. This temperature range is called the ionization region. Once the donors are ionized, the conduction band electron concentration is n = Nd = 1015 cm-3 since one electron is obtained for each donor atom. When every available extrinsic electron has been transferred to the conduction band, n is virtually constant with temperature until the concentration of intrinsic carriers ni becomes comparable to the extrinsic concentration Nd. Finally at higher temperatures ni is much greater than Nd and the intrinsic carriers dominate. In most devices it is desirable to control the carrier concentration by doping rather than by thermal electron hole pair generation. Thus one usually dopes the material such that the extrinsic range extends beyond the highest temperature at which the device is to be used.
Doped n-type with a donor concentration Nd of 1015 cm-3 . At very low temperature (range 1/T) negligible intrinsic electron hole pairs exist and the donor electrons are bound to the donor atoms. As the temperature is raised, these electrons are donated to the conduction band and at about 100 K (1000/T=10) all the donor atoms are ionized. This temperature range is called the ionization region. Once the donors are ionized, the conduction band electron concentration is n = Nd = 1015 cm-3 since one electron is obtained for each donor atom. When every available extrinsic electron has been transferred to the conduction band, n is virtually constant with temperature until the concentration of intrinsic carriers ni becomes comparable to the extrinsic concentration Nd. Finally at higher temperatures ni is much greater than Nd and the intrinsic carriers dominate. In most devices it is desirable to control the carrier concentration by doping rather than by thermal electron hole pair generation. Thus one usually dopes the material such that the extrinsic range extends beyond the highest temperature at which the device is to be used.
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