Recombination losses

Once the electron-hole pairs are generated by absorption in the silicon, they are exposed to several recombination mechanisms. These processes occur in parallel and the recombination rate is the sum of those for the individual processes.

Radiative Recombination

Radiative recombination is the inverse process of optical absorption. This process is of minor importance in silicon since energy and momentum conservation require the additional participation of a phonon. For the usual doping concentration of about NA ≈ 1⋅10¹⁶ cm^-3 radiative recombination is negligible and cannot be influenced by the solar cell design and processing.

Auger Recombination

Auger recombination is described by an electron recombining with a hole which gives the excess energy to a second electron or hole instead of emitting light. This third particle then relaxes back to its original energy by emission of phonons. The characteristic lifetime associated with the Auger process is in general inversely proportional to the square of carrier concentration. In low level injection it is described by:

Lower doping levels lead to higher limits of the Auger recombination. Therefore the minority carrier lifetime can be influenced by the design of the emitter diffusion and the doping of the base material.

Recombination through traps

Impurities and defects in semiconductors can give rise to allowed energy levels within the forbidden gap. These defect levels create very efficient two-step recombination processes whereby electrons relax from the conduction band to the

defect level and then relax to the valence band, recombining with a hole. The dynamics of this recombination process were calculated by Shockley, Read [8] and Hall [9]. The recombination rate, USRH for a single defect is given by

)

where τ^{n0 and} τ^p0 are the fundamental hole and electron lifetimes. These are related to the thermal velocity of charge carriers vth≈ 10⁷cm/s, the density of recombination defects N_t and the capture cross sections σ^{n and} σ^p for the specific defect:

n₁ and p₁ are statistical factors defined as follows:



where N_C and N_V are the effective density of states at the conduction band edges, ε^C and ε^G are the conduction band and bandgap energies and ε^t is the energy level of the defect.

The recombination lifetime τ^SRH follows from equation 2-20

n

with n0 and p0 being the equilibrium electron and hole concentrations. The SRH lifetime is a function of the injection level and the doping density as well as the specific defect parameters such as the concentration of traps, their energy level and their capture cross sections. Deep levels with energies close to the middle of the gap are more detrimental recombination centres than shallow levels near the band edges. Technological ways to reduce recombination following the Shockley-Read-Hall mechanism are the avoidance of contamination of the material, the removal of impurities by gettering or the passivation of defect levels.

Recombination at surfaces

Surfaces are rather severe defects in the crystal structure and produce a continuum of allowed states within the forbidden gap. Recombination can therefore occur very effectively via the Shockley-Read-Hall mechanism. The

analysis needs to be reformulated in terms of recombination per unit surface area (rather than unit volume). For a single defect the recombination rate U_S is given by

0

where n_S and p_S are the concentrations of electrons and holes at the surface. S_n0 and S_p0 are related to the density of surface states per unit area N_tS. Using the capture cross sections σ^{n and} σ^p for electrons and holes, S_n0 and S_p0 can be written as: The defect levels at the surface are so numerous that a continuous distribution throughout the bandgap is assumed. Using the interface density of states D_it(ε^{) and} integrating over the entire bandgap results in

( )

Similar to the definition of the lifetime, the surface recombination velocity is defined via

S

S S n

U ≡ ∆ _2-56

which is typically used for quantifying surface recombination processes.

The two fundamental possibilities to reduce surface recombination are:

• Reduction of the density of interface states. This can be achieved by growing an appropriate dielectric layer like SiO₂ which passivates many of the dangling bonds with oxygen or hydrogen atoms and reduces D_it(ε^).

• Reduction of the surface concentration of electrons and holes. Equation 2-53 shows that a reduction of one carrier type can strongly reduce carrier recombination. Minimisation of these therefore reduces recombination. This can be achieved by doping the surface to reduce the minority carrier concentration like in a back-surface-field (BSF). Alternatively, fixed charges in an overlying dielectric layer can be used to hold off either the minority carriers (for a p-type wafer negative charges repel free electrons) or in the extreme case invert the surface (large amounts of fixed positive charge invert the surface of a p-type silicon wafer). This is also known as field effect passivation, since an electric field is established near the surface.

In reality the methods for reducing surface recombination in actual devices rely on both mechanisms to some extent. The most prominent dielectric layers used to passivate the surfaces in silicon solar cells are thermal oxidation of the silicon surface and a deposited silicon nitride layer. Silicon oxide drastically reduces the interface state density (and additionally contains some fixed charges), silicon nitride mainly passivates via the field effect (in addition to a reduction of interface states). Gradients in the dopant concentration are commonly realised with highly doped regions of phosphorus or boron underneath local contacts or, on an industrial scale, via alloyed aluminium back-surface-fields.