consist of charged micro particles suspended in a somewhat ionized water. We will return to that example later in the book describing the so called “red wine effect” in PV.
Note that junction fields require electronic exchange between two materials while their direct physical contact is not necessary. As an illustration, chemically different metal electrodes of a capacitor will spontaneously acquire opposite charges proportional to the difference in their work functions. That process often called the ‘dielectric absorption’ takes time sufficient for the inter-plate electron transfer. Along the same lines, two different metals separated by a dielectric or semiconductor layer will exchange electrons forming the built-in electric field throughout that layer as described more in detail next (Sec. II).
B. Fundamental Material Requirements
A well known feature of all PV devices is that at least some of their constituting materials must have a not-too-wide forbidden gap, say G ~ 1–2 eV. The origin of that criterion is that larger band gaps exceeding the energies of most of sun spectra photons would not allow efficient light absorption necessary to produce enough electrons and holes. However, there is also the opposite requirement of those gaps being not too small, so that efficiently absorbing narrow band semiconductors are not good for PV either. As a result, semiconductors with substantial but not-too-wide forbidden gaps G ~ 1–2 eV, such as Si, Ge, CdTe, CIGS and some others are most suitable for PV.
The not-too-narrow gap limitation is less intuitive and may be worth explaining here. It is dictated by PV functionality as a power source. The power is a product of electric current and voltage, P = IV where both I and V components must be not too small. I is proportional to the light induced charge generation rate favoring significant absorption coefficients in the sun spectral region of ħω ~ 0.5–2 eV. Forbidden gaps G ~ 1–2 eV of many semiconductors fall in that region. To the contrary, the typical dielectric gaps G ≳ 4 eV are too wide for sufficient absorption (for example, window glass that is practically transparent and does not absorb light).
The requirement that undermines the suitability of narrow gap semiconductors (despite their strong absorption coefficients) is related to the voltage component: V ≤ G/q, where q is the electron charge. To explain the latter inequality we note that V can be related to the difference in Fermi energies in two metal electrodes as illustrated in Fig. 2. We recall that the Fermi (quasi-Fermi) energy describes the energy change due to removing one particle from the system. Therefore, ΔEF ≡ EF1 − EF2 gives the energy change due to transferring one electron between the two metals, and so does qV. On the other hand, the metal Fermi energies must not overlap with the semiconductor conduction or valence bands because such an overlap would mean that the semiconductor has in reality metal conductivity (no gap between the Fermi level and forbidden gap edges). As illustrated in Fig. 2, G presents the upper limit of the difference between the electron and hole Fermi levels allowing their steady state spatial separation. Increasing V beyond G/q would shift the Fermi levels beyond the forbidden gap turning the semiconductor into metal thus shorting the built in field and the circuit.
Fig. 2 Band diagram of a metal/semiconductor/metal structure where EF1 and EF2 represent quasi-Fermi levels determined by voltage drop V across the semiconductor.
Another wording of the same is that electrons and holes recombine very efficiently when the two Fermi levels are close thus suppressing their spatial separation and the built-in field. Assuming point defect mediated recombination, it can be shown more quantitatively [12] that the electron-hole recombination rate strongly accelerates with decrease of the gap G. As a result, there exists a range of gaps optimizing PV performance, G ≲ 2 eV. It should be remembered however, that the latter optimum gap prediction was derived under certain assumptions about the nature of (defect facilitated) recombination, lack of traps, insignificant leakage due to shunts, and others clearly outlined in the original work [12].
C. Charge Transport. Definition of Thin Film PV
We now consider charge carriers transport in the junction region where the built in field is significant; that region is often called the space charge region, simply because the field and charge density are ∇E = 4πρ (where E and ρ are correspondingly the field and charge density, and we use the Gaussian system of units). The built-in field extends through a limited thickness lE determined by the condition that the change of electron energy through lE equals the difference in Fermi levels ΔEF of the materials involved. In the order of magnitude, the latter condition yields
In the built-in field region, the charge carrier transport is dominated by drift with velocity v = μF where μ is the mobility and F = qE = qV/lE is the electric force. The diffusion with coefficient D = μkT (according to the Einstein formula where k is the Boltzmann constant and T is the temperature) is insignificant contributing to the transport time a relatively small fraction of kT/qV ≪ 1 assuming the typical V ~ 1 V and kT ~ 0.025 eV (room temperature).
The drift transport approximation is sufficient if the light absorption is limited to the space charge region, which applies to many thin-film structures. That approximation is well justified when the light absorption length is short enough, labs ≲ lE, limiting charge carrier generation to the built-in field region, which takes place in CdTe, CIGS, and a variety of other thin-film PV materials. However, some crystalline structures, such as Si and Ge, possess the non-direct band structures with absorption lengths in the hundred of microns range. In such materials, charge carriers generation extends way beyond the built-in region, and the transport is dominated by diffusion rather than drift. We recall that the characteristic diffusion distance and time are related as
The above discussed drift and diffusion times,
(1)
describe how long it take for a charge carrier to travel distance l to the device terminals. These times must be short enough to avoid significant electron-hole recombination. If the characteristic recombination time is τr, we must require that the relevant transport time to device terminals, τE or τD be shorter than τr. The corresponding criteria are discussed in Sec. XVI below. Here, it suffices to note that τr is extremely sensitive to material parameters and device structure, which brings in multiple elements of materials science and PV technology. In particular, recombination processes are strongly facilitated by structural defects (imperfections, impurities, surface states) that depend on
