Debye length semiconductors

With electrochemically studied semiconductor samples, the evaluation of t [relation (39)] would be more straightforward. AU could be increased in a well-defined way, so that the suppression of surface recombination could be expected. Provided the Debye length of the material is known, the interfacial charge-transfer rate and the surface recombination... 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

This same theoretical approach can also apply to the space charge layer formed in solid semiconductors. Instead of the concentration of ions in aqueous solution, however, the concentration of electrons or holes is used with the space charge layer in semiconductors. Then, the Debye length is given by Eqn. 5-7 ... 

The thickness of these layers is in the range of <2h = 0.4 to 0.6 nm for the compact layer, space charge layer, and c(d = 1 to 10 nm for the diffuse layer. The thickness of space charge layer, dac, and the thicknesses of diffuse layer, (fd, depend on the concentrations of mobile charge carries Tii in the semiconductor and in the aqueous solution, respectively. The Debye length, Ljy, may be used as a measure of the thickness of these two respective layers as shown in Eqn. 5-61 ... 

Further, the thicknesses of the diffuse and space charge layers depend on the potentials Ma and i sc across the respective layers for the space charge layer the thickness, dgc, is expressed, to a first approximation, by dsc = 2Lox (eA /kT)- [Memming, 1983]. The Debye length, Ld, is about 100 nm in usual semiconductors with impurity concentrations in the order of 10 cm and is about 10 nm in dilute 0.01 M ionic solutions. 

Figure 5-47 shows the Mott-Schottky plot of n-type and p-type semiconductor electrodes of gallium phosphide in an acidic solution. The Mott-Schottl plot can be used to estimate the flat band potential and the effective Debye length I D. . The flat band potential of p-type electrode is more anodic (positive) than that of n-type electrode this difference in the flat band potential between the two types of the same semiconductor electrode is nearly equivalent to the band gap (2.3 eV) of the semiconductor (gallium phosphide). 

The thickness of depletion and deep depletion layers may be approximated by the effective Debye length, Lo, ff, given in Eqn. 5-70 Ld, is inversely proportional to the square root of the impiuity concentration, In ordinary semiconductors... 

Note. The Debye length (LD), although not introduced into the present simplified discussion, is a parameter frequently referred to in the gas-sensor literature. It was originally introduced into ionic solution theory and later applied to semiconductor theory where it is especially applicable to semi con -ductor/metal and semiconductor/semiconductor junctions. It is a measure of the distance beyond which the disturbance at the junction has effectively no influence on the electron distribution and therefore closely related to d (see Eq. (4.49)). It is a material parameter given by LD = (j kl /e2(, )12 where cQ is the undisturbed electron concentration, essentially the extrinsic electron concentration in the case of doped n-type tin oxide, and the other symbols have their usual meaning.)... 

Although this is clearly an extreme case, and mobilities are commonly much higher than this and Debye lengths smaller, nevertheless, oxide semiconductors may well be limited in practical application by carrier transport. Naturally, if the bias is such that the semiconductor is not in depletion, there will be no restriction arising from transport indeed, the semiconductor will behave like a metal under these circumstances. 

Figure 18. Photogeneration of electron-hole pairs in the field-free region and depletion layer for an n-type semiconductor-electrolyte interface. The characteristic regions defined by the depletion layer (W), Debye length (Ld) and the light penetration depth (1/a) are also compared.

Figure 12.6 Potential distribution for an n-GaAs electrode in contact with a selenium redox couple with fast interfacial reactions curve a in the absence of illumination curve b at open circuit with 882 W/m illumination and curve c under illumination near the short-circuit condition (-23.1 mA/cm ). The Debye length in the electrolyte was 0.2 nm, and the Debye length in the semiconductor was 70 nm. (Taken from Orazem and Newman.

Calculate the Debye length in units of expected for an n-type GaAs semiconductor with a dopant concentration of 10. Compare the value you obtain to the Debye length obtained for an electrol) c system with a NaCl concentration of 0.1 M. 

Another prediction of Vorkenstein s theory is that crystallite size influences semiconductor electronics. Figure 4.16 shows the bending of energy levels at the surface, the so-called Debye length. Since catalytic crystallites are much smaller than this dimension, the phenomenon is not found in these materials." Catalysts may be treated as two-dimensional semiconductors, a fact that greatly simplifies theoretical models. 

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