The space charge layer within semiconductor particles

2 The space charge layer within semiconductor particles 

These two effects will occur if the semiconductor is under conditions of open circuit. Further variation in the charge stored within the space charge layer may occur if 

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form  

Integration of equation (9.16) using the boundary conditions that = f w and (d f ldr) = 0 at r = (r0 - w), where tv = the width of the space charge layer, yields  

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