Recombination in Solar Cells

Generally, the recombination process of charge carriers is defined as the reverse process of their generation. The thermal-equilibrium condition of a semi-conductor (in the dark) can be disturbed by illuminating the device, increasing the charge carrier concentration bygenerationof electron-hole pairs [35]. Af-ter generation, the carriers tend to return to their original state of equilibrium through the event ofrecombination. Thus, the two mechanisms to disturb the equilibrium-condition are [52]: the recombination process of the electron-hole pairs (undesirable) and the thermal generation through photon illumination (re-quired). Both mechanisms must fulfill the principle of conservation of energy^††.

In solar cells the recombination leads to an undesirable reduction of solar cell efficiency due to the losses of generated carriers. The generation increases by optimizing the absorption of photons from the incident light on the solar cell device, increasingη. The event of generation is the most important process in a solar cell, for converting the incident sunlight into electrical energy.

In semiconductors there are three fundamental recombination possibilities [35, 76], which are the band-to-band radiative recombination, the band-to-band Auger recombination (non-phononic mechanism) and the recombination through defect levels or traps (phononic mechanism) (see Figure 3.2).

The last two events dominate in Si solar cells.

Band-to-band Radiative Recombination

The radiative recombination is the reverse of the absorption and occurs when an electron jump from the conduction band,EC, into the valence band,EV, and this event is therefore faster in a direct-bandgap (E_g) semiconductors than in an indirect one. Direct-bandgap semiconductors (as GaAs) have the minimum of E_C and the maximum ofE_V at the same wave vector, k [66]. An electron with the necessary energy to jump from the valence band into the conduction band becomes free to move in the crystal. By the transition of the electron to the conduction band, a hole is created, which is as well free to move in the valence band (generation, see reference [66]). An electron, however, can also lose energy and fall back into the valence band, recombining with a free hole (see reference [66]). The energy by this recombination event is released in the form of a photon. Hence, this is a 3-particle process [35]. Their energy is near to the visible range and therefore this process is exploited in devices such as light-emitting

††The energy of an electron in transition is conserved by emitting a photon (radiative recombination) or by transferring the energy to another electron or hole, exciting its state to a higher level instead of emitting light (Auger recombination) [35, 52].

3.2. Loss Mechanisms of Solar Cells 31

diodes (LEDs). Due to the indirect bandgap in most group IV-semiconductors (Si, Ge), the radiative recombination is unlikely to occur and is normally negligible.

Auger Recombination

The Auger recombination is defined as to-band recombination. In the band-to-band Auger process, an electron atEC falls back to the EV by transferring its original energy to an electron inE_C, which is excited to a higher level in the Brillouin zone. The separation of the wave vector,k, in indirect-semiconductors assist the occurrence of an Auger event with minimal activation energy. The Auger mechanism dominates the recombination in heavily doped silicon or when silicon is in high-injection levels [57]. The Auger recombination is the direct recombination between an electron and a hole and, in solar cells, occurs when holes are injected into the heavily doped n⁺-region (emitter) [52]. _η is affected by the minority carrier lifetime in the heavily doped regions [76]. Good quality bulk materials are predominantly affected by Auger recombination [33, 76]. Furthermore, the quantum efficiency and the emitter saturation current of highly doped emitter layers are affected at low injection conditions [77].

This recombination process is quantified via the Auger coefficients [78].

Recombination Through Defect Levels, Shockley-Read-Hall

Impurities, incorporated in the bulk material during crystal growth, doping, process-ing, and so forth, can act as recombination centers located within the bandgap [66].

The resulting Shockley-Read-Hall (SRH) [80, 81] recombination process is the predominant recombination process in Si bulk devices [57]. Electrons within non-pure materials and in transition between bands are affected by the energy

E_V

Figure 3.2: Recombination in semiconductors as discussed in the present section (after reference [79]).

32 Chapter 3: Basic Principles of Solar Cells

states created within the band gap (impurity in the lattice).

Excess Carrier Lifetime

Lifetime can be understood as the average time between the generation event of a free carrier and its recombination. It depends on many parameters as the temperature, carrier concentration, energy gap, and others. It was defined by Beattie and Landsberg [82] as the ratio of the non-equilibrium number of electron-hole pairs (N) to the total recombination rate (R). When neglecting the effect of defect traps, the lifetime is obtained by:

τ≡N

R (3.15)

The total bulk recombination rate is the sum of the individual rates of each recombination event [35]. Thus, the total bulk carrier lifetime is given by:

1 As shown by Equation 3.16, the total bulk carrier lifetime is limited via several recombination processes, which occur in the semiconductor at different doping concentrations. The lifetime decreases with increasing dopant concentration:

at high doping concentrations (N_A>2x10¹⁸cm⁻³orN_D >6x10¹⁸cm⁻³) lifetime is Auger-limited and decreases quadratically with increasing dopant concentra-tion [78]. In moderately and low doped regions, recombinaconcentra-tion via defect levels dominates [76], where lifetime is SRH-limited and decreases quadratically with increasing temperature [78].

Diffusion Length

The mean distance travelled by a charge carrier, immediately after its generation and until annihilation, is given by the square root of the lifetime_τ, as:

L=p

Dτ (3.17)

In equation 3.17,D is the diffusivity depending on the temperature, doping concentration, and mobility [83]. Thus, the diffusion length (L) is a function of temperature and lifetime. Equation 3.17 is normally used to calculate the diffusion length of charge carriers in the semiconductor bulk. Both the bulk diffusion length and the bulk lifetime are limited by recombination.

WhenL<<W, the dark saturation current, I₀, which summarizes recombi-nation events in the solar cell, is independent of the rear surface passivation qualities. In the desirable case,L>>W, the charge carriers come in contact with