Intrinsic charge carrier concentration

Note that, under static equilibrium, the electron and hole concentrations are additionally related by the familiar mass action law, CnCp = n , where rii is the intrinsic charge carrier concentration of the material. 

Here m i and mj are the effective masses of the electron and hole, respectively. For an estimate of the intrinsic charge carrier concentration, n, in a liquid insulator we may assume the effective masses of electron and hole to be equal to the free electron mass (0.91 x 10" kg). Equation 11 then becomes... 

Calculate conductivity from charge carrier concentration, charge, and mobility. Differentiate between a conductor, insulator, semiconductor, and superconductor. Differentiate between an intrinsic and an extrinsic semiconductor. 

For a quantitative treatment analogous to intrinsic charge carriers, we have to take the defect concentration Nd and the energetic defect-band distance Ed into account ... 

The defect concentrations that are the result of thermal disorder are small in most oxides. The formation enthalpy of vacancy pairs in MgO is 7 eV, which gives a vacancy concentration of 10 ppm at 1000°C. In most oxides the bandgap is also large (>4eV) and at 1000°C the charge carrier concentration is lower than 10 ppm. Now, oxides can be made with an impurity concentration of at best 10-100 ppm. The concentration of impurities contributes much more to the defect concentration than the thermal disorder at these low formation equilibrium constants and the thermal (intrinsic) contribution to the defect concentration can usually be disregarded. 

Eq. (16) and subsequent expressions hold adequately only as long as the diffuse layer charge carrier concentrations remain small compared to the concentration of intrinsic entities (atoms or ions) which make up the material. Grimley has given a = 0 treatment, applied specifically to Schottky defect carriers, where this restriction is relaxed. Nevertheless, Eq. (16), which includes no finite-size corrections, has usually been found adequate for liquid electrolyte experimental results. ... 

To determine the conductivity contribution from intrinsic charge carriers at 300 K the carrier concentration of lO"" cm" has to be multiplied by the elementary charge and the mobility, which is found around 10 cmV(V.s) in conjugated polymers [100]. This leads to a value of 1.6 x 10 - cm This value is in accordance with experiments by Chiu et al. [101], who deduced the conductivity of pure PPP to be less than 10 ... 

Finally, at the high end of the temperature scale of Figure 18.17, electron concentration increases above the P content and asymptotically approaches the intrinsic curve as temperature increases. This is termed the intrinsic temperature region because at these high temperatures the semiconductor becomes intrinsic—that is, charge carrier concentrations resulting from electron excitations across the band gap first become equal to and then completely overwhelm the donor carrier contribution with rising temperature. 

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... 

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. 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

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