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

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44<br />

Qsi — charge density induced in the <strong>silicon</strong><br />

Qit — interface state charge density<br />

Qf — density <strong>of</strong> dielectric-induced fixed charges<br />

ψ — electrostatic potential<br />

— surface potential<br />

— quasi-Fermi potential <strong>of</strong> electrons <strong>and</strong> holes, respectively<br />

For a continuum <strong>of</strong> noninteracting surface states, Us is obtained <strong>by</strong> an integration<br />

over the b<strong>and</strong> gap:<br />

where, ns <strong>and</strong> Ρs are the electron <strong>and</strong> hole concentration at the surface, ni<br />

represents the intrinsic carrier concentration, Εi is the intrinsic Fermi level, Ε is the<br />

bottom <strong>of</strong> the conduction b<strong>and</strong>, Ε is the top <strong>of</strong> the valence b<strong>and</strong>, Ε is the interface trap<br />

energy level, k is the Boltzman constant, T is the absolute temperature, σ,,, σp are the<br />

capture cross sections for electrons <strong>and</strong> holes, respectively, Di t is the interface state<br />

density <strong>and</strong> stn is the carrier thermal velocity.<br />

Thus, the effective surface recombination velocity, Sef, at the edge <strong>of</strong> the surface<br />

space charge region can be calculated:

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