Carrier freeze-out

As the temperature increases, the intrinsic carrier concentration rises exponentially so that at some point n p rather than n Nd+. Likewise, as the temperature falls, Ea — Ev becomes large compared with KT and carrier freeze-out occurs below about 100 K so that n Nd+ < Nd. All of this assumes that n < Nc or p < Nv> corresponding to Ep in the energy gap. When enough donor atoms are added so that n > 10 Nc the Fermi level moves... 

The results of these pressure measurements can be transferred to the AlxGai.xN system, suggesting that 0, though a shallow donor for low values of x, will form a deep trapping level for x > 0.4. This is qualitatively in accord with the experimental observations reported below of carrier freeze-out for x > 0.2. Si is predicted to act as a shallow donor for Al fractions up to at least 0.56, though experimental data suggest that Si-doped alloys also show significant carrier freeze-out. 

In summary, (a>) is characteristic of strongly localized electrons (t 10 s) for samples E-G far from the IMT. For samples A-D near the IMT, a small fraction of the carriers become macroscopically delocalized (t > --- 10 s) while the majority of carriers are still strongly localized (t 10 s). The difference between metallic sample A and insulating sample D is that the free carriers freeze out in sample D at low T. This behavior is characteristic of percolating systems. Unlike the usual percolating systems, the percolation for doped polymers can be temperature-dependent. The dielectric response of oriented materials clearly points out the importance of dimensionality in the electronic behavior. 

The rate constants for electron transfer and recombination are readily separated because in the limit ca 0), Eq. 4.17 tends to ktr/ kir + krec), and the maximum of the semicircle occurs when ca = Inf = ktr + krec- In the absence oi RC attenuation effects (see section 4.2), the high frequency intercept of the IMPS plot d>((u —> oo) is unity, so that the ac photocurrent can be used to determine gac, the Gartner flux of minority carriers. Measurements of gac as function of potential (band bending) can be used to determine the minority carrier lifetime and absorption coefficient [44]. The main advantage of using the IMPS data rather than dc measurements of the photocurrent is that the high frequency limit of the IMPS effectively freezes out the effects of surface recombination which are responsible for substantial deviations of the dc photocurrent from the Gartner equation. 

Figure 20.6 shows the carrier concentration in -doped Si calculated from the above analysis plotted against 1/T. The intrinsic, saturation, and freeze-out regions can easily be identified. 

At low temperatures, not all of the donors (or acceptors) are ionized and the number of carriers (or p) exp —(AE/2fcT), where A is the ionization energy of the donor (or acceptor). This energy can be determined by making Hall measurements in this freeze-out region. 

Fig. 2.9. Basic types of freeze drying chambers. A, bell jar or vertical cylinder b, rectangular or cylindrical chamber with one (or 2) door(s) c, tunnel dryer, in which the trays are transported in and out by a system (shown as a carrier on a monorail).

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