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In terms of PV material, there are a wide range of solar cell configurations that have been explored [20, 21] and presented in section 1.4.

1.3

Loss Mechanisms in Solar Cell

Fundamental limitations on efficiency have been discussed in many studies, and generally loss mechanisms in solar cells have been classified into optical and electrical losses. Optical losses involve reflection, shadowing and unabsorbed radiation. Electrical losses are mainly classified into ohmic loss, related to the solar cell and contact materials and recombination losses that occur in the emitter, base and space charge regions of the solar cell structure.

1.3.1

Optical losses

In order to maximise the current which can be extracted from the contact of a solar cell, and thus to gain high conversion efficiency, a high rate of generation of electron-hole pairs is required. However, the presence of electrical contact in the p- and n-type regions of the solar cell cause a contact grid on the side exposed to sunlight, and this situation has been avoided in the back contact cell. As the metal contacts are opaque-shading losses can result which can reduce the solar cell efficiency by several percent, and are independent of the light’s wavelength. In the back contact cell, a typical thickness is 120 µm, which entails a loss of potential current equal to the gain obtained by removing the front metal contacts of about 0.8 mA/cm2_{. Furthermore, the quality of the antireflection coating contributes a}

small gain. However, avoidable losses from free carrier absorption and insignificant light trapping are very small, leading to the conclusion that a current density of more than 43 mA/cm2 _{can be achieved in practice with current technology using an optimised back}

contact solar cell or a bifacially contacted cell [22].

A texturing technique for the solar cell surface is used to change the reflection of incident light at a tilted plane towards the solar cell, thus increasing the probability of incoming photons entering the cell. A covering of dielectric layers is also used to reduce reflection losses. On the other hand, the absorbed light in the bulk depends on the wavelength. The indirect bandgap of Si means the absorption probability of low energy (long wavelength) photons (where λ >1 µm) is weak [23]. In contrast, with photons of short wavelengths within several tenths of micrometres, several internal reflections are needed before being absorbed. Light which is not absorbed by the bulk can be lost

1.3 Loss Mechanisms in Solar Cell

through the bulk at the rear, or the front after internal reflection is used [23].

1.3.2

Recombination losses

As this project is interested in the effect of impurities and extended defects in the mc-Si solar cell, it is important to consider some details of the recombination processes that always occur near the upper surface, in the depletion region or on the lower surface of the cell. As mentioned before in section 1.1, absorbing photons of sufficient energy creates electron-hole pairs which are exposed to various recombination mechanisms. Generally, carrier generation and recombination are processes by which mobile charge carriers are created and eliminated, where a recombination process occurs when an electron falls from the Ec into the valence band (Ev) of a semiconductor, with the energy of recombination emerging as a photon of light. In contrast, the generation of an electron-hole pair can occur when a valence electron gives an energy (> the energy gap) which is transferred to the conduction band (Ec).

Generally, there are three types of recombination: the Auger (occurs in the bulk [24]), radiative (occurs in the direct band gap, such as in solar cell-based GaAs) and Shockley- Read-Hall (SHR) [25, 26] recombination (occurs in the case of the existence of defects, where an extra energy level in the forbidden region is unintentionally or deliberately introduced through defects in the crystal lattice).

Radiative recombination represents the inverse of the optical absorption process and is less important in Si than other types, as Si has energy and momentum conservation needs the additional participation of phonons. Radiative recombination is negligible and cannot be affected by the design and processing of the solar cell if the concentration of doping is around 1016 _cm−3 [27]. In this recombination type, an electron from the E

c directly combines with a hole in the Ev and releases a photon. The emitted photon has an energy similar to the band gap and is thus only weakly absorbed in which it can exit the piece of semiconductor.

Auger recombination (Figure 1.3) can occur when an electron and a hole recombine together without emitting heat or photons but where the excess energy of the electron in the Ec is given to a third electron in the Ec, and then the third electron relaxes back to its original energy by emitting phonons. This type of recombination is very important in cases of heavy doping or high level injection of high carrier concentrations under concentrated sunlight.

1.3 Loss Mechanisms in Solar Cell

Figure 1.3: Auger recombination mechanism: (a) e/h recombination with releasing energy to second pushing it high into the Ec; (b) the electron gradually gives off its energy thermally; and (c) relaxes back to the band edge.

The characteristic lifetime (τAuger) associated with this type of recombination, which is

defined as the average time which a carrier spends in an excited state after e/h generation and before they recombine, is inversely proportional to the square of carrier concentration. In the case of low level injunction, τAuger has the following expression:

τAuger = ∆n/R (1.1)

where ∆n is the excess minority carrier concentration and R is the recombination rate [28, 29], which is the sum of the individual recombination processes.

Based on equation 1.1, lower doping yields higher limits of Auger recombination. Hence, the minority carrier lifetime can be affected by the design of the diffusion emitter and the doping of the base material [27].

In general, the presence of impurities and defects in semiconductors can introduce energy levels within the forbidden gap of these materials. These levels create a two-step recombination process. First, electrons relax from the Ec to the defect state, and then the electron and hole recombine in the Ev. Figure 1.4 shows the case of an electron (or hole) that is trapped by this level. It is worth mentioning that the movement of a carrier into the defect level relies on the distance of the introduced energy level from either band edge. If this level is close to either band edge, recombination is less likely as the electron

will probably be re-emitted to the Ec edge rather than recombining with a hole that

transfers into the same energy state from the Ev. Therefore, defect levels close to the mid-gap represent an active region for recombination. The mechanism of this type of recombination is called Shockley-Read-Hall (SHR) recombination [25].

1.3 Loss Mechanisms in Solar Cell

Figure 1.4: The SHR recombination mechanism: (a) via extra energy level; (b) movement of an electron to an extra level in the forbidden gap with the releasing of energy as a photon or multiple photos; (c) a further photon or photons released due to e/h recombination.

This section gives a mathematical description of the SHR recombination process which is used in device simulation in chapter 10 to model carrier exchange between the Ec and the Ev. The SRH recombination rate, RSHR, through a deep single defect level in the gap is given in equation 1.2, which is implemented in the Sentaurus Device in chapter 10:

RSHR ₌ np − n2i

τp0(n + n1) + τn0(p + p1)

(1.2) Here n and p are equilibrium electron and hole densities, and τp0 and τn0 are the fun- damental electron and hole lifetimes respectively which are associated with the thermal velocity of charge carriers (υth ≈ 107 cm/s). The density of recombination defects (Nt) and the capture cross-sections, σn and σp, for the specific defects are given by:

τp0≡ 1 σpυthNt (1.3) τn0 ≡ 1 σnυthNt (1.4) The auxiliary parameters n1 and p1 are statistical factors, which for simplicity take trap-

level energy into consideration and are defined as: p1 = NV/exp E_V − E_d KT  (1.5) p1 = NC/exp E_d− E_C KT  (1.6) Here, NC,V are the effective densities of states at the Ec edges, and EV, EC, and Ed are the energy levels for the Ev, Ec, and the defect bands, respectively. KT is the product of

1.3 Loss Mechanisms in Solar Cell

the Boltzmann constant, k, and the temperature, T .

For the equilibrium electron and hole concentrations, n0 and p0, respectively, the

SHR recombination lifetime (τSHR) can be expressed as a function of the injunction level,

the doping density, and the defect parameters. These defect parameters include the concentration of traps, traps energy levels, and trap capture cross-sections. τSHR has the

following formula:

τSHR =

τn0(p + p1+ ∆n) + τp0(n + n1+ ∆p) n0+ p0+ ∆n

(1.7) Here, ∆n and ∆p are the excess carrier densities taken to be equal in the absence of trapping [30].

As mentioned before, for deep levels when energy levels are near to the middle of the gap, the recombination centres are considered to be more detrimental than those of shallow levels close the band edges. In order to reduce recombination following the SHR process, various techniques can be used to avoid impurities by gettering or the passivation of defect levels [27].

1.3.3

Ohmic loss

Part of the carriers generated will be recombined, as explained previously. The rest of the generated carriers will need to be extracted at the contacts. However, there is a level of power dissipation associated with the extraction process due to non-zero contact resistance that produces ohmic losses. In order to reduce the ohmic losses, wider contact lines are needed. However, increasing the contact area might increase the recombination rate and also the shadowing. It is desirable to make the series resistance of the emitter as low as possible in order to enable a smooth current flow. To this end, a highly doped emitter is required, but it is expected that higher Auger (section 1.3.2) and surface recombination will result [27]. There are two possible ways to minimise the series resistance, by either increasing the base doping, which in turn decreases the minority lifetime (i.e. Auger recombination), or by employing a thinner substrate which decreases the probability of absorption. A reasonable compromise between the aforementioned techniques is to find the optimum design parameters of the solar cell structure.

A large series resistance significantly reduces the fill factor and might reduce the short-circuit current if it is too high. In this work, the impact of iron impurity on series resistance, and hence solar cell performance, is investigated and reported in chapter 10.