Surface and bulk passivation of multicrystalline silicon solar cells by ...

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carrier recombination within the damaged layer, which occurs within the SCR. Based on
this, one must include recombination in the SCR. Α similar conclusion was arrived at by
Schmidt [93], but his reasoning did not include the surface damage. However, one can
follow his approach to calculate the effect of increased recombination near the damaged
surface. Once SCR exists beneath the surface of the wafer, its detailed characteristics are
uniquely determined by the shape of the potential barrier. Α full derivation of
approximate solutions to the recombination velocity in SCR can be found in the literature
[94, 95]. The surface potential distribution across the space charge region is given by:
ψ(z) =ψS •e -z/L,
where, z is the vertical distance from the surface, and Ys is the surface potential at
the surface or at one end of SCR ( z = 0 ), which can be found by an iterative approach of
Shockley-Read-Hall (SRH) formalism. L is the extrinsic Debye length and is defined as:
where, nb, pb denote carrier density of electrons and holes in the bulk,
respectively, and εb is the dielectric constant of the semiconductor.
In the SCR, the carrier densities are functions of the position z:
n(z) = n b eβψ, p(z) = pbeβψ
The definition and parameterization of recombination rate in the SCR, USCR(z)
parameterization can be found in the literature [96]. The recombination velocity in the
SCR is calculated by: