Thickness of the space charge layer

The formation of two-layer PS on p-Si involves two different physical layers in which the potential-current relations are sensitive to the radius of curvature. The space charge layer of p-Si under an anodic potential is thin, which is responsible for the formation of the micro PS. The non-linear resistive effect of the highly resistive substrate is responsible for that of macro PS. The effect of high substrate resistivity should also occur for lowly doped n-Si. However, under normal conditions, the thickness of the space charge layer under an anodic potential, at which macro PS is formed, is on the same order of magnitude as the dimension... 

The fundamental reason for the uneven distribution of reactions is that the rate of electrochemical reactions on a semiconductor is sensitive to the radius of curvature of the surface. This sensitivity can either be associated with the thickness of the space charge layer or the resistance of the substrate. Thus, when the rate of the dissolution reactions depends on the thickness of the space charge layer, formation of pores can in principle occur on a semiconductor electrode. The specific porous structures are determined by the spatial and temporal distributions of reactions and their rates which are affected by the geometric elements in the system. Because of the intricate relations among the kinetic factors and geometric elements, the detail features of PS morphology and the mechanisms for their formation are complex and greatly vary with experimental conditions. 

Equation (20) is an approximation being valid only in the depletion layer, where the majority carrier density at the surface (ns for n-type ps for p-type) is smaller than the corresponding bulk concentration. The thickness of the space charge layer can be defined by the relation dsc = eeo/C which is valid for a normal capacitor. Inserting Eq. (20), for the thickness of the space charge layer, one obtains ... 

To obtain relations between carrier density at the interface and at the inner edge of the depletion layer (the thickness of the space charge layer dsc is defined by Eq. (22)), we assume Boltzmann equilibrium for the carriers across the space charge layer. Using Eqs. (3a) and (3b), we have... 

The optimum conditions would arise for the size of Pt particles comparable with the thickness of the space charge layer. Such an adjustment would certainly be favored by the Pt encapsulation and by a decrease of the space charge layer thickness, around Pt particles, due to the increase of the donor concentration. 

This relation is valid only for a space-charge region where the majority-carrier density is depleted with respect to the bulk density. The thickness of the space-charge layer, defined as w = decreases as doping increases. For a typical carrier... 

Accordingly, the space charge capacity can only be measured for < Ch- This condition can usually fulfilled with semiconductors of a carrier density smaller than uq = 10 cm". In addition a thickness of the space charge layer, can be derived using the relation d = eeo/C (valid for a capacitor with fixed plates). Applying this to a depletion layer, one obtains from Eq. (5.27)... 

The fact that the dimensions of the particles approaches, or becomes smaller than, the critical length for certain phenomena (e.g., the de Broglie wavelength for the electron, the mean free path of excitons, the distance required to form a Frank-Reed dislocation loop, thickness of the space-charge layer, etc.). 

The thickness of the space charge layer can be derived using the relation d = eeo/C for a normal capacitor, and then one obtains from (10)... 

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