Semiconductors depletion region

Similarly, when a voltage V is applied across a semiconductor/metal junction, the total voltage drop in the semiconductor depletion region is Vbi -F V, so we obtain an analogous Boltzmann relationship away from eqnihbrinm ... 

Fig. 2. Potential distribution at the semiconductor/electrolyte interface in the presence of a (fixed) positive charge at the semiconductor surface. Curves (a)-(c) show the effect of a steadily increasing positive bias which, as for Fig. 1, is accommodated entirely within the semiconductor depletion region.

The potential across the semiconductor depletion region, marked... 

When electrons are injected as minority carriers into a -type semiconductor they may diffuse, drift, or disappear. That is, their electrical behavior is determined by diffusion in concentration gradients, drift in electric fields (potential gradients), or disappearance through recombination with majority carrier holes. Thus, the transport behavior of minority carriers can be described by a continuity equation. To derive the p—n junction equation, steady-state is assumed, so that = 0, and a neutral region outside the depletion region is assumed, so that the electric field is zero. Under these circumstances,... 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

Figure 45. (a) Schematic of PMC signal behavior in accumulation region (i), flatband region (ii), and depletion region (iii) with (b) visualization of energy band situation of an n-type semiconductor. 

To understand the role of the noble metal in modifying the photocatalysts we have to consider that the interaction between two different materials with different work functions can occur because of their different chemical potentials (see [200] and references therein). The electrons can transfer from a material with a high Fermi level to another with a lower Fermi level when they contact each other. The Fermi level of an n-type semiconductor is higher than that of the metal. Hence, the electrons can transfer from the semiconductor to the metal until thermodynamic equilibrium is established between the two when they contact each other, that is, the Fermi level of the semiconductor and metal at the interface is the same, which results in the formation of an electron-depletion region and surface upward-bent band in the semiconductor. On the contrary, the Fermi level of a p-type semiconductor is lower than that of the metal. Thus, the electrons can transfer from the metal to the semiconductor until thermodynamic equilibrium is established between the two when they contact each other, which results in the formation of a hole depletion region and surface downward-bent band in the semiconductor. Figure 12.6 shows the formation of semiconductor surface band bending when a semiconductor contacts a metal. 

The speed of response of the photodiode depends on the diffusion of carriers, the capacitance of the depletion layer, and the thickness of the depletion layer. The forward bias itself increases the width of the depletion layer thus reducing the capacitance. Nevertheless, some design compromises are always required between quantum efficiency and speed of response. The quantum efficiency of a photodiode is determined largely by the absorption coefficient of the absorbing semiconductor layer. Ideally all absorption should occur in the depletion region. This can be achieved by increasing the thickness of the depletion layer, but then the response time increases accordingly. 

The electronic charge distribution in a semiconductor varies with applied electrode potential (Uf), which in turn determines the differential capacitance at the interface [11,78]. Relating charge density and electric field, the capacitance of a space charge (or depletion) region can be quantitatively derived. For an n-type semiconductor Poissons equation can be written ... 

Fig. 4.2 For an n-type bulk semiconductor in the presence of an electrolyte illustrated is (left) no space charge layer, (center) a space charge layer in a depletion region, (right) a space charge layer in an accumulation region.

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