Carrier concentrations

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

Fig. 15. Excess carrier concentration in HgCdTe in a saturated Hg vapor as a function of temperature where the dashed line represents Hg vacancies. The extrinsic impurity concentration can be adjusted in the growth process from low 10 up to mid-10. Low temperature annealing reduces Hg vacancy...

Material Cubic lattice constant, pm Band gap, eV Inttinsic carrier concentration, cm Relative dielectric constant, S Mobihty, Electrons cm"/(Vs) Holes... 

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

The carrier concentrations in doped or extrinsic semiconductors to which donor or acceptor atoms have been added can be deterrnined by considering the chemical kinetics or mass action of reactions between electrons and donor ions or between holes and acceptor ions. The condition for electrical neutraHty is given by equation 6. When the predominant dopants are donors, the semiconductor is... 

As the temperature increases, the intrinsic carrier concentration rises exponentially so that at some point n ... 

Lp = D r ) is the minority carrier diffusion length for electrons in the -region, (0) is the minority carrier concentration at the boundary between the depletion layer and the neutral region. The sign of this equation indicates that electron injection into the -region results in a positive current flow from p to n a.s shown in Figure 7. 

More precise coefficients are available (33). At room temperature, cii 1.12 eV and cii 1.4 x 10 ° /cm. Both hole and electron mobilities decrease as the number of carriers increase, but near room temperature and for concentrations less than about 10 there is Htde change, and the values are ca 1400cm /(V-s) for electrons and ca 475cm /(V-s) for holes. These numbers give a calculated electrical resistivity, the reciprocal of conductivity, for pure sihcon of ca 230, 000 Hem. As can be seen from equation 6, the carrier concentration increases exponentially with temperature, and at 700°C the resistivity has dropped to ca 0.1 Hem. 

For insulators, Z is very small because p is very high, ie, there is Htde electrical conduction for metals, Z is very small because S is very low. Z peaks for semiconductors at - 10 cm charge carrier concentration, which is about three orders of magnitude less than for free electrons in metals. Thus for electrical power production or heat pump operation the optimum materials are heavily doped semiconductors. 

As indicated in Figure 4, the basic thermoelectric parameters are all functions of carrier concentration. Thus adjusting the dopant level to increase the output voltage generally also increases the electrical resistance. In addition, it affects the electronic component of the thermal conductivity. However, there are limitations on what can be accompHshed by simply varying the carrier concentration in any given material. 

Fig. 4. Dependence of thermoelectric parameters on carrier concentration, where (—) is the Seebek coefficient (5) the figure of merit Z) (-),...

The relatively high mobilities of conducting electrons and electron holes contribute appreciably to electrical conductivity. In some cases, metallic levels of conductivity result ia others, the electronic contribution is extremely small. In all cases the electrical conductivity can be iaterpreted ia terms of carrier concentration and carrier mobiUties. Including all modes of conduction, the electronic and ionic conductivity is given by the general equation ... 

As mentioned above, the interpretation of CL cannot be unified under a simple law, and one of the fundamental difficulties involved in luminescence analysis is the lack of information on the competing nonradiative processes present in the material. In addition, the influence of defects, the surface, and various external perturbations (such as temperature, electric field, and stress) have to be taken into account in quantitative CL analysis. All these make the quantification of CL intensities difficult. Correlations between dopant concentrations and such band-shape parameters as the peak energy and the half-width of the CL emission currently are more reliable as means for the quantitative analysis of the carrier concentration. 

A method for quantification of the CL, the so-called MAS corrections, in analogy with the ZAP correction method for X rays (see the article on EPMA), has been proposed to account for the effects of the excess carrier concentration, absorption and surface recombination. In addition, a total internal reflection correction should also be included in the analysis, which leads to the MARS set of corrections. This method can be used for further quantification efforts that also should involve Monte Carlo calculations of the generation of excess carriers. 

The [111] orientation samples were found to be n-type with impurity carrier concentrations of from 2.4 to 8 x 10 m . The [100] samples had... 

Fe Code indicated that final conductivities would not be significantly influenced by the observed range of carrier concentrations. 

For a junction of a conjugated polymer, which has an energy gap of around 3 eV (around the value of the polyphenylenes) and a free carrier concentration n> 1017 cm-3, with a low workfunction metal (e.g. when [Pg.155]

The result can be simplified by making use of the above-defined pinch-off voltage [Eq. (14.54)1 and dielectric capacitance of the semiconducting layer. Further simplifications result from the assumptions that Cs 2> C, (Eq. (14.57)), and that the dopant and carrier concentrations arc equal (Eq. (14.58)). 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

A conjugated polymer of a high charge carrier concentration (n> 1017 cm-3) arranged between two mclal electrodes, can be understood as a MSM structure [40. ... 

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