Separation of Electrons and Holes: The Solar Cell as Diodeas Diode

We have just seen, in Sect.3.2, that when light is absorbed within a semiconductor, a pair of electrical carriers is generated, i.e. an electron-hole pair is created for each absorbed photon. Now, in a second step, in order to generate electricity, electrons and holes have to be separated. If this does not take place, electrons and holes simply recombine again—thereby heating up the semiconductor.

Drift transport: (Fig.3.8) In a solar cell, there is only one way of separating electrons and holes—by the action of an electric fieldE. Indeed, under the influence of an electric fieldE, electrons, whose charge is negative, will travel in a direction opposite to that of the electric field, whereas holes, whose charge is positive, will travel in the same direction as the electric field. This phenomenon is called “drift” transport and is shown schematically in Fig.3.8.

We now need a semiconductor structure, which has an internal electric field.

The simplest such structure is thediode. Therefore (almost) all solar cells are just semiconductor diodes.

In the case of most solar cells (crystalline silicon solar cells, CIGS, CdTe, GaAs and other similar solar cells), we use ap-n diode, i.e. a diode with ap-doped region immediately adjacent to ann-doped region. Here, the internal electric field is at the border of thep-doped andn-doped regions, in what is called the “depletion region”.

In such ap-ntype solar cell, holes and electrons are photo-generated in the bulk of thep- andn-regions; they then travel by diffusion to the depletion region, where they are separated by the action of the internal electric field. (Note that diffusion is

Fig. 3.8 Drift transport of electrons and holes under the influence of an electric fieldE

3 Solar Cells: Basics 45

Fig. 3.9 p-nType solar cell in the “dark”, i.e. without illumination: transport of electrons (e) and holes (h) by diffusion in the bulk of thep- andn-regions; and their subsequent separation by drift under the influence of the electric fieldE, in the depletion region

a transport mechanism for charge carriers within a semiconductor, whereby carriers move from a zone, where their density is high, to a zone where their density is lower.)

This situation is shown schematically in Fig.3.9.

In amorphous and microcrystalline silicon solar cells, we use p-i-n diodes.

Thereby the letter “i” stands for “intrinsic”. As this type of solar cells is very rarely used, at the present moment, except for “niche applications” (such as power sup-plies for watches, calculators and other small-size devices), we shall in this chapter not give any further development for this case. The reader is referred to Chap. 6, Sect.6.2.1.

The mechanism of (charge) carrier separation and transport is called “carrier collection C”. During the transport of electrons and holes, a part of these charge carriers, as obtained by photo-generationPare lost, through recombination lossR, and the balance is collected. Therefore:

C=P−R

The ratio between recombination lossRand carrier collectionCis, very gener-ally speaking, proportional to the ratio between the “average” or “effective” trans-port distance d_cell for carriers and the average length l_transport of carriers before recombining:

(R/C) proportional to(d_cell/l_transport)

46 A. Shah

Fig. 3.10 p-n Type solar cell under illumination: diffusion of holes through then-type wafer, towards the depletion region, from right to left;p(x) is the carrier profile of the holes;n(x) is the carrier profile of the electrons;L_pis the minority-carrier diffusion length (of the holes);n_p0andp_n0 are the equilibrium concentrations of the minority carriers

p-nsolar cells: (Fig.3.9) Here, one remarks that the transport of electrons and holes occurs mainly in the bulk of the p- and n-regions, where there is no significant electric field; this transport is governed by diffusion. Thus, thep-nsolar cell is called a “diffusion-controlled device”. In order to minimize the recombination lossRand to maximize the collectionC, it is necessary, in ap-nsolar cell, that the minority-carrier diffusion lengths be much larger than the corresponding dimensions of thep- and n-regions [12].

Diffusion transport: (Fig. 3.10) Diffusion is very generally a mechanism, where particles diffuse from a zone of high concentration to a zone of lower concentration.

In semiconductors the particles, which are of interest to us, are the (free) holes and electrons.

Let us look the case of free holes, within ap-ntype solar cell, as shown schemat-ically in Fig.3.10: Holes have to diffuse from right to left; they are separated from the electrons by the electric field in the depletion region, and continue their path up to the very left side of the device.

In Fig.3.10, the sun is shining on the solar cell from the left. Photo-generation of holes and electrons take place throughout the photoactive region. The electrons leave the solar cell on the right side. They have to be transported from their point of generation to the right side of the solar cell. As they are here the majority carriers, their density is very high and their transport is consequently not a problem. The limiting factor are the minority carriers, here the holes. Some of the holes will be generated near the right side contact: The only method, by which they can reach the depletion region, is by diffusion. Indeed, in this example diffusion will take place, because the density of holes just behind the right-side contact is relatively high due to photo-generation. On the other hand, as one approaches the depletion region, the density will be lower, as most of the holes there have been siphoned off by the electric field.

In this zone, at the right of the depletion region, the holes are the minority carriers, because this is ann-type wafer, where the density of holes is very low. The electrical

3 Solar Cells: Basics 47 current carried by these holes is a diffusion current; its current densityJp.diffis given by the equation:

Jp.diff= −Dp∂p(x)

∂x , (3.2)

where Dp is the diffusion constant of the holes andp(x) the carrier profile of the holes.

On the other hand,Lpis the minority-carrier diffusion length (of the holes).Lpis, in its turn, given by the expression

Lp=

Dp×τp, (3.3)

whereτpis the lifetime of the holes.

The minority carrier diffusion lengthLpgoverns the carrier transport on the right side of the device.

p-i-nsolar cells: Inp-i-nsolar cells the transport of the photo-generated carriers is mainly by drift (and not by diffusion). Thus, p-i-n solar cells are drift-controlled devices. The transport length that now intervenes is the drift length (for electrons and holes)

L_drift=μ×τ ×E, (3.4)

whereμis the carrier mobility,τ the carrier lifetime andEthe electric field.

The link between diffusion and drift is given by the so-called «Einstein relation»:

D=(μkT)/q, (3.5)

wherekis the Boltzmann constant,T the absolute temperature andqthe charge of an electron.

For further details, the reader is referred to Chap. 6, Sect.6.2.1.

We will now:

Discuss in more detail, whilst using the corresponding equations, the functioning of a solar cell; the goal here is to look at the main parameters of the solar cell: short-circuit current densityJ_sc, open-circuit voltageV_oc, Fill FactorFFand efficiencyη. We will also give approximate relationships for the dependence ofηon temperature and intensity of the incoming light.

3.4 Solar Cell Characteristics, Equivalent Circuits and Key