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

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

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41 surfaces and interfaces are more likely to contain impurities since they are exposed during the device fabrication process. As discussed above, the trap-assisted recombination is described by the SRH theory. In order to calculate the recombination rate, a number of simplifying assumptions are made [79] : (a) no radiative recombination or Auger recombination; (b) the semiconductor is not degenerate; (c) the energy level of the defects does not change with charge condition; (d) the relaxation time of the charge carriers caught by the defect is negligibly small compared to the average time between two emission processes; (e) the defect concentration is very small compared to the doping density; (f) Fermi-Dirac statistics apply; (g) the defects do not interact with each other (i.e., an electron cannot make a transition from one defect level to another). Based on these assumptions, the SRH theory predicts the following recombination rate Ut (unit cm-3/s) for a single -level defect located at an energy Εt [79] : τρ0 = 1/σpvthΝt τnO TnO = 1/σnvthΝt 1 _ 1

42 σ and σp are the capture cross sections of electrons and holes, νth is the thermal velocity of the electron or hole. The electron and hole concentrations are n and p, respectively. Νt is the volume density of deep levels and Εt is the energy level of the traps, τ„ ο and τ ο are the so-called capture time constant of electrons and holes. Typical values for the capture cross sections of bulk defects in silicon are in the range of 10 i2 10' 18 cm2. The recombination rate is proportional to the thermal velocity and the defect concentration. The driving force for this recombination process is the term np-ni2, which describes the deviation of carrier concentration from the thermal equilibrium values. The SRH recombination rate has been derived in most semiconductor textbooks (Grove and Fitzgerald, 1966; Sze, 1981) and is shown to be [80, 81]: For a doped semiconductor, one has either n0»ρ0 (n-type) or ρo»no (p-type). First, taking the case of an n-type material, one can derive the recombination rate for holes at a single energy level, Ε1, in the forbidden gap. This case is completely symmetrical to that of electron recombination in p-type material. In this expression, n o = ND and p0'0. Therefore, where, p is injection level.

42<br />

σ <strong>and</strong> σp are the capture cross sections <strong>of</strong> electrons <strong>and</strong> holes, νth is the thermal<br />

velocity <strong>of</strong> the electron or hole. The electron <strong>and</strong> hole concentrations are n <strong>and</strong> p,<br />

respectively. Νt is the volume density <strong>of</strong> deep levels <strong>and</strong> Εt is the energy level <strong>of</strong> the<br />

traps, τ„ ο <strong>and</strong> τ ο are the so-called capture time constant <strong>of</strong> electrons <strong>and</strong> holes. Typical<br />

values for the capture cross sections <strong>of</strong> <strong>bulk</strong> defects in <strong>silicon</strong> are in the range <strong>of</strong> 10 i2<br />

10' 18 cm2. The recombination rate is proportional to the thermal velocity <strong>and</strong> the defect<br />

concentration. The driving force for this recombination process is the term np-ni2, which<br />

describes the deviation <strong>of</strong> carrier concentration from the thermal equilibrium values.<br />

The SRH recombination rate has been derived in most semiconductor textbooks<br />

(Grove <strong>and</strong> Fitzgerald, 1966; Sze, 1981) <strong>and</strong> is shown to be [80, 81]:<br />

For a doped semiconductor, one has either n0»ρ0 (n-type) or ρo»no (p-type).<br />

First, taking the case <strong>of</strong> an n-type material, one can derive the recombination rate for<br />

holes at a single energy level, Ε1, in the forbidden gap. This case is completely<br />

symmetrical to that <strong>of</strong> electron recombination in p-type material. In this expression, n o =<br />

ND <strong>and</strong> p0'0. Therefore,<br />

where, p is injection level.

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