Energy bands in silicon intrinsic and extrinsic silicon pdf

Further documentation is energy bands in silicon intrinsic and extrinsic silicon pdf here. Please forward this error screen to 158. Seebeck effect is used to measure temperatures, and for accuracy it is desirable to use materials with a Seebeck coefficient that is stable over time. It may be positive or negative.

Seebeck effect in the measurement leads. Seebeck coefficients among the various materials involved. Thus, if S is positive, the end with the higher temperature has the lower voltage, and vice versa. The voltage gradient in the material will point against the temperature gradient. This is because electrodes attached to a voltmeter must be placed onto the material in order to measure the thermoelectric voltage.

The temperature gradient then also typically induces a thermoelectric voltage across one leg of the measurement electrodes. Therefore, the measured Seebeck coefficient is a contribution from the Seebeck coefficient of the material of interest and the material of the measurement electrodes. Although only relative Seebeck coefficients are important for externally measured voltages, the absolute Seebeck coefficient can be important for other effects where voltage is measured indirectly. Determination of the absolute Seebeck coefficient therefore requires more complicated techniques and is more difficult, however such measurements have been performed on standard materials.

Seebeck coefficient can be obtained by performing a relative Seebeck coefficient measurement against a standard material. Thomson coefficient in certain regions of temperature. Seebeck coefficient, as mentioned below. By making one of the wires in a thermocouple superconducting, it is possible to get a direct measurement of the absolute Seebeck coefficient of the other wire, since it alone determines the measured voltage from the entire thermocouple. 2 K and 18 K, thereby filling in an important gap in the previous 1932 experiment mentioned above. Thomson coefficient integrations and thermocouple circuits. The difficulty of these measurements, and the rarity of reproducing experiments, lends some degree of uncertainty to the absolute thermoelectric scale thus obtained.

In particular, the 1932 measurements may have incorrectly measured the Thomson coefficient over the range 20 K to 50 K. K, for all temperatures above 50 K. In the table below are Seebeck coefficients at room temperature for some common, nonexotic materials, measured relative to platinum. For example, the Seebeck coefficients of Cu, Ag, Au are 1.

The Seebeck coefficient of semiconductors very much depends on doping, with generally positive values for p doped materials and negative values for n doping. A material’s temperature, crystal structure, and impurities influence the value of thermoelectric coefficients. Due to thermal fluctuations, some of these charge carriers travel with a higher energy than average, and some with a lower energy. Microscopically, what is happening in Ohm’s law is that higher energy levels have a higher concentration of carriers per state, on the side with higher chemical potential.

For each interval of energy, the carriers tend to diffuse and spread into the area of device where there are less carriers per state of that energy. As they move, however, they occasionally scatter dissipatively, which re-randomizes their energy according to the local temperature and chemical potential. This dissipation empties out the carriers from these higher energy states, allowing more to diffuse in. The combination of diffusion and dissipation favours an overall drift of the charge carriers towards the side of the material where they have a lower chemical potential. In this case, at the hotter side of the material there is more variation in the energies of the charge carriers, compared to the colder side.

As before, the high-energy carriers diffuse away from the hot end, and produce entropy by drifting towards the cold end of the device. However, there is a competing process: at the same time low-energy carriers are drawn back towards the hot end of the device. Though these processes both generate entropy, they work against each other in terms of charge current, and so a net current only occurs if one of these drifts is stronger than the other. The distinction may be due to a difference in rate of scattering, a difference in speeds, a difference in density of states, or a combination of these effects.

In particular, in electronic materials with weak electron-electron interactions, weak electron-phonon interactions, etc. In materials with strong interactions, none of the above equations can be used since it is not possible to consider each charge carrier as a separate entity. Mott relations also generally tend to fail. This expression is sometimes called “the Mott formula”, however it is much less general than Mott’s original formula expressed above. 1 and 3, the extremes corresponding to acoustic-mode lattice scattering and ionized-impurity scattering. The highest Seebeck coefficient is obtained when the semiconductor is lightly doped, however a high Seebeck coefficient is not necessarily useful. If the phonon-electron interaction is predominant, the phonons will tend to push the electrons to one end of the material, hence losing momentum and contributing to the thermoelectric field.