The final approach for increasing efficiencies, strategy (c) is to allow absorption of a wide range of photon energies but then to collect the photogenerated carriers before they have a chance to thermalise. A hot-carrier solar cell is just such a device that offers the possibility of very high efficiencies (the limiting efficiency is 65% for unconcentrated illumination) but with a structure that could be conceptually simple compared with other very high efficiency PV devices, such as multijunction tandem cells. (Again the physics and limiting efficiency
calculations for hot-carrier cells are outlined in Section 2.4.2.) For this reason, the approach potentially lends itself to thin-fllm deposition techniques with their attendant low material and energy usage costs and the ability to use abundant, nontoxic elements.
The concept underlying hot-carrier solar cells is to slow the rate of photoexcited carrier cooling, which is caused by phonon interaction in the lattice, to allow time for carriers to be collected while they are still at elevated energies (‘hot’). This allows higher voltages to be achieved by the cell [Wurfel, 1997; Ross and Nozik, 1982]. It thus tackles the major PV loss mechanism of thermalisation of carriers (1 in Figure 9.1). In addition to an absorber material that slows the rate of carrier relaxation, a hot-carrier cell must allow extraction of carriers from the device through contacts that accept only a very narrow range of energies (selective-energy contacts), as shown in Figure 9.14.
Slowed carrier cooling has been observed at very high illumination intensities via a phonon-bottleneck effect in which carrier energy decay mechanisms are restricted. Compounds with large mass difference between their anions and cations have a gap in their allowed phonon modes that can slow down these decay mechanisms and enhance the bottleneck effect [Conibeer and Green, 2004]. Examples are GaN and InN, with some experimental evidence for slowed cooling in the latter [Chen and Cartwright, 2003].
Whilst the III-nitrides look very attractive because of their large phonon bandgaps, the inclusion of the rare element Indium in a final technology is problematic. Analogues of InN with abundant elements, but also with wide phonon bandgap and narrow Eg include II-IV-VI compounds such as ZnSnN2, IIIA nitrides such as LaN and YN, which should have large phonon gaps, and IVA nitrides such as ZrN and HfN that have measured large phonon bandgaps and are readily available. Bi and Sb compounds should also have large phonon gaps but are not abundant. Group IV compounds have large calculated gaps and small Egs, as well as several other advantages [Conibeer et al., 2011]. Figure 9.15 shows calculations of phonon dispersions for group IV compounds that have large phonon bandgaps, sufficient to block Klemens’ decay.
Theoretical work on replicating this effect by modifying the phononic band structures of QD nanostructure superlattices has shown that phonon dispersions of simple cubic (SC) SLs of core-shell QDs are expected to exhibit large phonon bandgaps for light-shell thicknesses on the order of a monolayer [Patterson et al., 2009]. Nanoporous materials with gas filled pores also show potential as candidate hot-carrier absorber materials. Fabrication of such highly ordered arrays from uniformly sized core-shell nanoparticles has been attempted experimentally using the Langmuir-Blodgett (LB) technique [Treiber et al., 2008]. This technique allows transfer of highly ordered monolayers onto a wide range of solid substrates such as glass or Si wafers [Huang et al., 2004]. By controlling the interspacing between adjacent particles, i. e. the shell thickness, optimised nanostructures for phonon bandgap materials may be achieved.
Low-dimensional multiple quantum well (MQW) systems have also been shown to have lower carrier cooling rates. Comparison of bulk and MQW materials has shown significantly slower carrier cooling in the latter. Figure 9.16 shows data for bulk GaAs as compared to MQW GaAs/AlGaAs materials as measured using time-resolved transient absorption by [Rosenwaks et al., 1993], recalculated to show the effective carrier temperature as a function of carrier lifetime by [Guillemoles et al., 2006]. It clearly shows that the carriers stay hotter for significantly longer times in the MQW samples, particularly at the higher injection levels by 11/2 orders of magnitude. This is due to an enhanced ‘phonon bottleneck’ in the MQWs allowing the threshold intensity at which a certain ratio of LO phonon reabsorption to emission is reached that allows maintenance of a hot-carrier population, to be reached at a much lower illumination level. More recent work on strain-balanced InGaAs/GaAsP MQWs by [Hirst et al., 2011; Hirst et al., 2012] has also shown carrier temperatures significantly above ambient, as measured by PL. Increase in In content to make the wells deeper and to reduce the degree of confinement is seen to increase the effective carrier temperatures.
The mechanisms for the reduced carrier cooling rate in these MQW systems are not yet clear. However, there are three effects that are likely to contribute. The first is that in bulk material photogenerated hot carriers are free to diffuse deeper into the material and hence
Carrier temperature, shifted from room temp data (T-300K)
Figure 9.16 Effective carrier temperature as a function of carrier lifetime for bulk GaAs as compared to GaAs/AlGaAs MQWs: time-resolved transient absorption data for different injection levels, from [Rosenwaks et al., 1993], recalculated by Guillemoles et al. [Guillemoles et al., 2006].
to reduce the hot-carrier concentration at a given depth. This will also decrease the density of LO phonons emitted by hot carriers as they cool and make a phonon bottleneck more difficult to achieve at a given illumination intensity. Whereas in a MQW there are physical barriers to the diffusion of hot carriers generated in a well and hence a much greater local concentration of carriers and therefore also of emitted optical phonons. Thus, the phonon bottleneck condition is achieved at lower intensity.
The second effect is that for the materials systems that show this slowed cooling, there is very little or no overlap between the optical phonon energies of the well and barrier materials. For instance, the optical phonon energy ranges for the GaAs wells and AlGaAs barriers used in [Rosenwaks et al., 1993] at 210-285 meV and 280-350 meV, respectively, exhibit very little overlap in energy, with zero overlap for the zone-centre LO phonon energies of 285 and 350 meV [Colvard et al., 1985]. Consequently, the predominantly zone centre LO phonons emitted by carriers cooling in the wells will be reflected from the interfaces and will remain confined in the wells, thus enhancing the phonon bottleneck at a given illumination intensity.
Thirdly, if there is a coherent spacing between the nanowells (as there is for these MQW or superlattice systems) a coherent Bragg reflection of phonon modes can be established that blocks certain phonon energies perpendicular to the wells, opening up one-dimensional phononic bandgaps (analogous to photonic bandgaps in modulated refractive index structures [Conibeer and Green, 2004]. For specific ranges of nanowell and barrier thickness these forbidden energies can be at just those energies required for phonon decay. This coherent Bragg reflection should have an even stronger effect than the incoherent scattering of the second mechanism above at preventing emission of phonons and phonon decay in the direction perpendicular to the nanowells.
It is likely that all three of these effects will reduce carrier cooling rates. None depend on electronic quantum confinement and hence should be exhibited in wells that are not thin enough to be quantised but are still quite thin (perhaps termed ‘nanowells’). In fact, it may well be that the effects are enhanced in such nanowells as compared to full QWs due to the former’s greater density of states and in particular their greater ratio of density of electronic to phonon states that will enhance the phonon bottleneck for emitted phonons. The fact that the deeper and hence less-confined wells in [Hirst et al., 2012] show higher carrier temperatures is tentative evidence to support the hypothesis that nanowells without quantum confinement are all that are required. Whilst several other effects might well be present in these MQW systems, further work on variation of nanowell and barrier width and comparison between material systems, will distinguish which of these reduced carrier diffusion, phonon confinement or phonon folding mechanisms might be dominant.
Nanostructures such as QW and QD materials are also of importance in energy-selective contacts. Initial experimental progress has been made using double-barrier resonant tunnelling structures, with a single layer of Si QDs providing the resonant level [Jiang and Green, 2006; Conibeer et al., 2008]. A significant proof of concept has been achieved with negative differential resistance (NDR) observed at room temperature for a double-barrier quantum dot structure. The NDR resonance does not appear to be strong but nonetheless such a result at room temperature is very encouraging as evidence for 1D energy selection. Work now is focused on improving the quality factor for such NDR, using other barrier QD combinations and using QWs that, whilst not quite as effective in theory, are much easier to fabricate in high quality in practice.
Complete hot-carrier devices for proof of concept are likely in the near future. These are likely initially to combine double-barrier QW ESCs and MQW absorber in the same lattice-matched III-V system, most likely in the InGaN/InN system. A transition to other bulk and nanostructured thin-fllm-type systems of higher material abundance is anticipated subsequently.