The efficiency of solar cells is limited by non- radiative recombination occurring in the bulk via defect states or at the surfaces via surface states. In present day high efficiency silicon solar cells bulk recombination is reduced so far that surface recombination is an important loss mechanism. Surface states are caused by the interruption of the periodical arrangement of the atoms and by the deposition of impurities at the surface. Their density can be as large as 10¹⁵ / cm³, resulting in surface recombination velocities v_s of up to 10⁷ cm/s. The surface recombination velocity v_s defines the surface recombination rate of electrons r_e,s by
r_e,s = v_sn_e,s = s_en_ss,hv_e,thn_e,s (1)
where n_e,s is the density of electrons at the surface, s_e is the capture cross section for electrons of the n_ss,h surface states occupied by a hole and v_e,th is the thermal velocity of the electrons. The strategy forreducing surface recombination would either call for a reduction of the density n_ss of surface states by altering the environment of the surface atoms or a reduction of the density n_ss,h of holes in surface states or a reduction of the density n_e,s of free electrons at the surface. The most effective way of reducing the density of surface states on a silicon surface is by covering it with a carefully grown layer of SiO₂.
In the following, we describe how the remaining surface states at a Si/SiO₂ interface are distributed over energy between the conduction and valence band edges and how the surface recombination rate is determined by the position of the Fermi-energies within this distribution of surface states.
The distribution of the surface states over energy shows up in a measurement of the electrical capacitance between a contact on the SiO₂ and a contact on the Si back side. Due to the depletion of holes in a space charge layer of the p-type Si by a positive voltage on the SiO₂ , a decrease of the capacitance with increasing voltage is expected as shown by the theoretical curve in Fig.1.
The experimental curve is displaced with respect to the theoretical curve to more negative voltages, indicating the presence of a positive sheet charge at the Si/SiO₂ -interface for zero applied voltage. Also the slope of the experimental curve is different from the slope of the theoretical curve, which is due to a change of the sheet charge with applied bias. If we neglect the contribution of a change of the surface charge to the capacitance itself due to the large frequency at which it is measured and consider only variations with the slowly varying bias voltage, then the band bending follows directly from the value of the measured capacitance according to the Mott-Schottky formula. The change of the interface sheet charge with respect to the band bending translates into a change of the occupation of the surface states with respect to the position of the Fermi-energy at the surface. The resulting distribution of the density of surface states which is a typical example for Si/SiO₂-interfaces is shown in Fig.2.
The contact which was applied to the SiO₂ was made by a transparent paste used in electrocardiography. It can be removed without any damage of the SiO₂. Since it is transparent we could illuminate the contact area simultaneously with the electrical measurements and observe the intensity of the photoluminescence which is shown in Fig.3 as a function of the band bending at the surface.

Fig.2	Fig.3

The photoluminescence is caused by the radiative recombination of electrons and holes irrespective of their distance from the emitting surface because of negligible reabsorption in crystalline Si. The minimum of the photoluminescence in Fig.3, observed for a band bending of 0.25 eV corresponding to a position of 0.45 eV above the valence band, therefore reflects a maximum of the non-radiative recombination via surface states. For large accumulation of holes (negative band bending) as well as for large depletion (positive band bending) surface recombination is small.
In high efficiency solar cells, positioning of the Fermi-energy close to the valence band is achieved by a higher doping level at the p-type back surface. The resulting low surface recombination is usually attributed to the so-called back surface field repelling the electrons, but is rather a consequence of the occupation of the surface states.

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