CHAPTE R 6
Solar Cells Based on Hot Carriers and Quantum Dots Santosh Shrestha, Gavin Conibeer, Shujuan Huang School of Photovoltaic and Renewable Energy Engineering, The University of New South Wales, Sydney, NSW, Australia
6.1 The Hot Carrier Solar Cell 6.1.1 Introduction The hot carrier (HC) solar cell aims to extract energy from photogenerated carriers before they thermalize to the band edges to generate electric power. The excess carrier energies above the respective conduction and valence band edges contribute to a higher energy conversion efficiency than conventional, single-junction solar cells. The limiting efficiency of HC solar cells is 66% under unconcentrated sunlight (1 sun) and 85% at maximum concentration (46,200 suns), assuming ideal operation under detailed balance (Ross and Nozik, 1982; Würfel, 1997; Green, 2003). Fig. 6.1 shows a schematic band diagram of a HC solar cell. It consists of an absorber with band gap, Eg, which is ideally a narrow band-gap material that can absorb a wide range of solar spectra. The most important property of the absorber is to slow the rate of carrier cooling to allow extraction of the carriers while they are at elevated energies i.e., hot. The hot carriers are extracted through two contacts on the either side of the absorber. These energyselective contacts (ESCs) allow only carriers within a narrow energy range, δE, to pass through, above the band edges. Hence, a higher voltage (compared to that achieved from p-n junction solar cells of the same band-gap material) is achieved which contributes to higher efficiencies. The carrier distribution of photogenerated electron-hole pairs in the absorber is described by a high carrier temperature, TH; and a quasi-fermi-level splitting, ΔμH = μe − μh ≠ 0, is the difference between chemical potential of electrons (μe) and holes (μh) at a hot thermal equilibrium temperature, TH. The ESCs are designed to extract the carriers at the optimal e h , and holes at an energy Eext . Carriers with energies energy, electrons at an energy Eext above and below these levels are reflected back into the absorber. The ESC level, ES, is in Advanced Nanomaterials for Solar Cells and Light-Emitting Diodes. https://doi.org/10.1016/B978-0-12-813647-8.00006-0 © 2019 Elsevier Inc. All rights reserved.
175
176 Chapter 6 Selective contacts Electrode n TC
mn
Absorber TH
Electrode p TC Eexte
δE
me Eg
mh
∆mg
mp
δE
qV
Eext
Eexth
Fig. 6.1 Band diagram of an ideal HC solar cell. Photogenerated carriers are generated in the absorber, which are collected over a narrow energy range above the band edges through selective energy contacts. From Le Bris, A., Guillemoles, J.-F., 2010. Hot carrier solar cells: achievable efficiency accounting for heat losses in the absorber and through contacts. Appl. Phys. Lett. 97 (11), pp. 113506(1–3).
the conduction band for the electron contact and in the valance band for the hole contact. Ideally, the ESC extracts carriers only within a very narrow range of energies, δE, so that a minimal energy is lost due to the increase in entropy caused by the cooling of hot carriers to the ambient temperature, TA, at the external contacts. The energy extracted from the e h − Eext , which is ideally larger than the band gap of the absorber. device is given by Eext = Eext The potential between the quasi-Fermi levels on the other sides of the ESCs represents the device’s operating voltage, which is given by V = (μn − μp)/q.
6.1.2 Modeling of the HC Solar Cell Efficiency A number of models have been proposed to estimate the theoretical efficiency of HC solar cells. These models are based on a detailed balance approach that defines the electrical power output of a device, Pout = Pabs − Ploss, where Pabs is the power absorbed and Ploss is the total power loss. According to the Shockley and Queisser detailed balanced model (Shockley and Queisser, 1961), the current generated by a solar cell is given by (6.1) J = q ( FA − FE ) , where J (A/m2) is the electric current density, FA (m−2 s−1) is the absorbed photon flux, and FE (m−2 s−1) is the emitted photon flux. Considering black-body radiation from the Sun at TS, the total absorbed photon flux can be expressed as FA =
1 4π 2 3c 2
Ω A E 2 dE ∫EG e E / kTs − 1 , ∞
(6.2)
Solar Cells Based on Hot Carriers and Quantum Dots 177 where E is the photon energy, TS is the temperature of the Sun, EG is the band gap of the solar cell, and ΩA is the solid angle subtended by the Sun, which equals the concentration ratio divided by the maximum possible concentration ratio. It is assumed that the absorptivity for above band-gap photons is 1 and for below band-gap photons is zero. The emitted photon flux is given by FE =
q 2 3 2 4π c
∫
∞
E 2 dE
, (6.3) e( E − ∆µH ) / kTC − 1 where TC is the carrier temperature, which is the same as the cell/lattice temperature; and Δμ is the difference between the electrochemical potentials of electrons and holes. In conventional solar cells, Δμ = q ΔV, neglecting the contact losses and assuming infinite mobility. J-V characteristics the solar cell can be calculated by solving Eqs. (6.1)–(6.3). The maximum solar energy conversion efficiency limit for a single-junction solar cell is about 33.7% and 44% using an AM1.5 solar spectrum, and for maximum concentrations, respectively. EG
Ross and Nozik introduced the concept of the HC solar cell based on particle conservation (Ross and Nozik, 1982). In this model, electrons and holes are extracted separately through ESCs at TH, which is higher than the lattice temperature TC (i.e., before they thermalize to the conduction and valance band edges). In this case, the current density from the solar cell becomes 2 ∞ Ω E q E2 J = q ( FA − FE ) = 2 3 2 ∫ E / kTA s − ( E − ” µ ) / kT dE , H s (6.4) 4π c EG e −1 e − 1 where ΔμH is the difference between chemical potential of electrons (μe) and holes (μh) at the hot thermal equilibrium temperature TH. If the hot electrons and holes are extracted only at specific energies (Ee and Eh, respectively), then the electric potential across the cell is given by T T qV = Eext 1 − C + ∆µH C . (6.5) TH TH Also, JEext =
q 2 3 2 4π c
ΩA E 2 E2 E − ∫EG e E / kTs − 1 e( E −” µH )/ kTs − 1 dE. ∞
(6.6)
By solving Eqs. (6.4)–(6.6), the J-V characteristic of the solar cells can be calculated for a given EG and Eext. The power conversion efficiency predicted by this model is about 65% at 1 sun and 85% at maximum concentrations, which is only slightly lower than the limiting efficiency of infinite-junction tandem solar cells (Green, 2003). In this model, particle conservation is assumed, but Auger recombination (AR) and impact ionization (II) are neglected. However, at high carrier temperatures, AR and II can be significant so that particle conservation is no longer valid. Würfel proposed another approach that incorporates
178 Chapter 6 AR/II and assumes infinitely short lifetimes for these two processes, much faster than the carrier extraction (Würfel, 1997). Very high AR/II rates tend to reduce the splitting of quasiFermi levels, and for ultrafast AR/II, ΔμH is considered to be zero (i.e., electron and hole populations have a common hot temperature). The limit of efficiency in that case is 53% under nonconcentrated 6000 K black-body illumination, and 85% under full concentration. The ideal detailed balance efficiencies for the HC solar cell as a function of the absorber band gap calculated from Ross and Nozik (Δμ < 0) and Wurfel (Δμ = 0) models are shown in Fig. 6.2 for 1-sun (diffuse) and maximum-concentration (direct) illumination. Ross and Nozik predicted a limiting efficiency of about 65% at 1 sun for an absorber with a band gap of about 0.3 eV and a carrier temperature of 3600 K, and 85% at maximum concentration with a band gap approaching zero and a carrier temperature of 4200 K. Unlike normal p-n junction solar cells, the extracted voltage from the HC solar cell is decoupled from the band gap. The highest efficiency at the maximum concentration is achieved at zero band gap because in this case, most photons are absorbed and the current is highest. At 1 sun, the maximum efficiency is achieved at nonzero band gap. This is because being a reciprocal converter, the absorber must emit photons at any wavelength at which it can absorb them. At 1 sun, the device emits into the full half-hemisphere but only absorbs over the small solid angle of the Sun. At lower photon energies, the number of photons in the solar spectrum progressively decreases until it reaches the point at which a larger number of photons would be emitted into the hemisphere than can be absorbed from the solid angle of the Sun. This is the optimum band gap for the HC solar cell
Fig. 6.2 Detailed balance efficiencies for the HC solar cell as a function of an absorber band gap for 1-sun (diffuse) and maximum-concentration (direct) illumination. Efficiency curves for Ross and Nozik (Δμ < 0) and Wurfel (Δμ = 0) models are shown. After Green, M.A., 2003. Third Generation Photovoltaics: Ultra-High Efficiency at Low Cost. Springer-Verlag.
Solar Cells Based on Hot Carriers and Quantum Dots 179 for 1 sun. It decreases as the concentration ratio increases, until it reaches zero at maximum concentrations, when the solid angle of emission equals the solid angle of absorption. The Ross-Nozik and Wurfel models represent two extreme conditions for ideal materials with no electron and hole interaction (zero Auger coefficients) and infinitely fast Auger processes (instantaneous impact ionization), respectively. For real material systems, the Auger coefficients lie somewhere between these two extremes, with partial impact ionization primarily for high-energy carriers well above the band gap (Jung et al., 1996). Takeda et al. expanded the particle conservation and II/AR models by introducing a thermalization time for the hot carriers, considering the electronic band structure of the absorber (Takeda et al., 2009a,b). The relative lifetimes of II and AR processes were compared with the retention time of the hot carriers. The power output from the cell was derived from conservation of energy, expressed as ∞
J ∆E = ∫ d ε ( ε I A − ε I E ),
(6.7)
ε = ε F + (1 − F ) (ε g + 3kBTRT )
(6.8)
F = exp [ −τ re / τ th ] ,
(6.9)
EG
where
where ε represents the decrease in absorbed energy due to thermalization of the carrier, τre is the average retention time, and τth is the thermalization time of electrons and holes, which is normally assumed to be the same. Using this model, the relationship between carrier concentration, thermalization time, temperature, and irradiation intensity can be determined by the following two equations: nC =
8 2π me3/ 2 h3
∫
∞
ε g /2
d ε ε − (ε g / 2 )
1 exp ( ε − µe ) / k BTC + 1
nC = J absτ re / d ,
(6.10) (6.11)
where d is the thickness of the absorber. Eqs. (6.10) and (6.11) show the carrier density’s dependency on the chemical potential of the electrons, μe, and the carrier retention time, τre, respectively. This model allows performance evaluation of the HC solar cell in terms of factors affecting the carrier density, such as impact ionization and Auger recombination. Furthermore, it helps to determine the conditions in which Ross-Nozik and Wurfel models can apply. When AR/II lifetimes are much longer than the carrier retention time, the effects of AR/II are negligible; and hence, the particle conservation model holds. However, at high carrier densities (e.g., due to high carrier temperatures), AR/II processes dominate.
180 Chapter 6 Fig. 6.3 shows the dependence of efficiency on the carrier density, calculated using the particle conservation (PC) and the impact-Auger (IA) models for a 100-nm absorber under 1000× solar irradiation (Takeda et al., 2009a). In this case, thermalization of the carriers is not considered [i.e., F = 1 in Eq. (6.9)]. Strong dependence of efficiency on carrier density is obvious, with maximum efficiency achievable for carrier densities of about 1018 cm−3. However, the carrier density in a real material system is affected by factors such as concentration ratio, carrier thermalization time, and carrier retention time, and has been suggested to be much lower (around 1015 cm−3) for an observer with d = 100 nm, and have practically achievable τre = 100 ps and τth = 1 ns and concentration ratio of 1000 (Takeda et al., 2009a). Aliberti et al. applied a hybrid model considering both particle balance and energy balance to estimate the maximum achievable efficiencies for HC solar cells using a wurtzite InN absorber (Aliberti et al., 2010). The model also considered the influence of actual AR and II rates and thermalization losses on cell performance. The detailed band structure of the wurtzite bulk InN has been considered in performing computation of carrier densities, pseudo-Fermi potentials, and II-AR time constants. The maximum efficiency was calculated to be 43.6% for the absorber under 1000 suns, energy extraction level at 1.44 eV, and thermalization constant of 100 ps and 52% for maximum solar concentration. The results have been calculated considering ideal ESCs, which means that the contacts have very high conductivity and a discrete energy transmission level. This model has been further developed by Aliberti et al. and Feng et al. (Aliberti et al., 2011; Feng et al., 2012), considering nonideal ESCs (i.e., carriers are extracted in a finite energy
Fig. 6.3 Dependence of conversion efficiency on the carrier density for carrier temperature TC = 600, 1200, and 1800 K for the PC model. Thickness of the absorber d = 100 nm, and illumination is 1000× concentration. From Takeda, Y., et al., 2009a. Impact ionization and Auger recombination at high carrier temperature, Solar Energy Mater. Solar Cells 93 (6–7), 797–802.
Solar Cells Based on Hot Carriers and Quantum Dots 181 window), making the model more realistic. The InN absorber and InGaN/InN/InGaN double barrier resonant tunneling structure for ESCs have been considered, and the results are shown in Fig. 6.4. The maximum achievable efficiency of 39.6% is achieved for ΔE = 1.15 eV and δE = 0.02 eV, considering compete absorption and under 1000-sun illumination. It can be observed from Fig. 6.4A that the limiting efficiency decreases with the increase of energy width of ESCs, δE, and the optimum extraction energy, ΔE, and shifts to the higher value with the increase of the energy width of ESCs, δE. This is because carrier extraction at higher energies is associated with a higher resistive loss because of the lower carrier density at these energy levels. Fig. 6.4B shows that the optimum value of δE is related to ΔE. With the increase of ΔE, the δE that gives the optimum efficiency also increases in order to maintain the carrier extraction rate. The efficiency is lower if δE is too wide, in contrast to the less reduced efficiency that is calculated without considering Auger recombination (Le Bris and Guillemoles, 2010). However, in practical hot carrier solar cells, Auger recombination
Fig. 6.4 (A) Calculated HC solar cell efficiency versus extraction energies, ΔE, under 1000-sun illumination for different extraction energy window widths, δE; and (B) calculated HC solar cell efficiency versus extraction energy window, δE, under 1000-sun illumination for different extraction energies, ΔE. From Feng, Y., et al., 2012. Non-ideal energy selective contacts and their effect on the performance of a hot carrier solar cell with an indium nitride absorber. Appl. Phys. Lett. 100(5), pp. 053502(1–4).
182 Chapter 6 is expected to continue to supply high-energy carriers well above ΔE that are extracted by a wide δE and then thermalized in the contacts, causing a larger entropy increase.
6.1.3 HC Solar Cell Absorbers The requisites of HC absorbers are described in detail by Conibeer et al. (2015). Of these, arguably the most important property of an absorber is its slow cooling rate. If the carrier thermalization (i.e., thermal equilibration of carriers with the lattice) is reduced sufficiently, then the conversion of the total available energy into potential energy is possible, which leads to higher conversion efficiency. Immediately after photon absorption, the energy distribution of the photogenerated carriers is a nonequilibrium distribution that depends on the energy distribution of the incident photons, as well as electron and hole effective masses and their respective density of states. The carrier-carrier scattering time constant is typically much <1 ps, and it decreases with increasing carrier density. The time constant for the carrier-phonon interaction, however, is on the order of several picoseconds. If the thermalization rate is less than the excitation rate and the carrier-carrier scattering rate, a steady-state hot distribution can be established, and the carrier kinetic energy, which is usually lost as heat, can be used and potentially contribute to extracted power, hence boosting conversion efficiency. Under steady-state conditions, there are several possible carrier distributions: • •
•
Hot nonequilibration: The carriers are not yet equilibrated among themselves, and therefore, a common carrier temperature and chemical potential cannot be defined. Hot equilibration: The electron and hole populations reach separate thermal equilibria at different temperatures. This results in hot carrier populations with electron temperature, TH(e), and hole temperature, TH(h), both of which are higher than the lattice temperature, TC. A chemical potential (quasi-Fermi level) can be defined for each carrier type, and strangely enough, in principle, the potential for electrons can be lower than that for holes. The related situation occurs for a strong interaction between electrons and holes (i.e., very fast Auger processes), for which the electron and hole populations reach a common temperature TH, > TC. In this case, the electron and hole chemical potentials are equal. Thermalization: In this situation, hot carriers have lost all their excess energy above the band edges to lattice vibrations (phonons) and are at thermal equilibrium with the lattice. A separate chemical potential can be defined for electrons and holes in the conduction and valence bands, respectively.
A hot carrier absorber should produce a steady-state hot carrier population for enough time to allow extraction to the external contacts. The extraction should be through energy-selective contacts to minimize the energy loss.
Solar Cells Based on Hot Carriers and Quantum Dots 183 6.1.3.1 Slowing of HC cooling The energy dissipation of photogenerated carriers is a multistep process. The inelastic scattering of carriers, which typically occurs in the first few tens of femtoseconds after their generation, normalizes momentum and leads to a distribution of electron energies, which can be described by a Boltzmann distribution and a single high temperature (i.e., a thermal population), and a separate thermal population of holes (Feng et al., 2013). Then the carriers scatter inelastically with phonons, mainly emitting optical phonons in a series of discrete hops, in each of which energy and momentum are conserved in the combination of electrons and emitted phonons. This process takes place over several picoseconds. For polar semiconductors, the major scattering process occurs with longitudinal, optical phonon modes. These optical phonons emitted by the excited carriers then interact with other phonons due to the anharmonic nature of the crystal potential. These overpopulated optical phonons decay into low-energy acoustic phonons through various routes. The final step is the transport of these acoustic phonons, macroscopically illustrated as the heat dissipation to the environment. The carrier-cooling process can be slowed by blocking any of these three processes. Other processes, such as direct emission of acoustic phonons and diffusion of optical phonons, are not significant for polar semiconductors. The cooling of carriers by emission of optical phonons leads to the buildup of a nonequilibrium hot population of optical phonons which, if it remains hot, will drive a reverse reaction to reheat the carrier population, thus slowing further carrier cooling. Therefore, the critical factor is the mechanism by which these optical phonons decay into acoustic phonons, or heat in the lattice. The principal mechanism by which this can occur is the Klemens mechanism, in which the optical phonon decays into two acoustic phonons of half its energy and of equal and opposite momenta (Klemens, 1966). The processes require the conservation of energy and momentum. The buildup of emitted optical phonons is strongly peaked at the zone center, both for compound semiconductors due to the Fröhlich interaction and for elemental semiconductors due to the deformation potential interaction. The strong coupling of the Fröhlich interaction also means that high-energy optical phonons are also constrained to near the zone center, even if parabolicity of the bands is no longer valid, as is the case for high-energy carriers well above the band minima (Conibeer et al., 2015). This zone center’s optical phonon population determines that the dominant optical phonon decay mechanism is this pure Klemens’ decay. The thermalization of carriers occurs in three stages, each of which could be interrupted in order to slow the cooling. The first of these is the Fröhlich interaction between electrons and optical phonons, which can potentially be blocked by modifying bond polarization. The second is decay of optical phonons decay into acoustic modes, which can be modified by a phonon bottleneck effect. And the third is the buildup of nonequilibrium acoustic phonons, which could also contribute to reducing carrier energy relaxations. To understand the mechanism of slow relaxation rates in different types of materials, these three interaction processes must be considered.
184 Chapter 6 The dispersion relations of phonon modes are regarded as important for the purpose of realizing the hot carrier cell. The phonon-bottleneck effect plays an important role in slowing down the carrier-cooling processes, especially for polar semiconductors. This is because prevention of further phonon decay leads to a nonequilibrium phonon population and an increased probability of the back reaction occurring, which transfers the phonon energy back to electrons or holes. Hence, by restricting the energy dissipation of optical phonons, they feed energy back to electrons and impede the process of carrier energy loss. 6.1.3.2 Bulk materials with large phononic band gap Bulk materials with a large energy gap between optical phonon energies and acoustic phonon energies can inhibit the decay of optical phonons. The compounds in which there is a large difference in masses of the constituent elements can have a large gap between the acoustic and optical phonon energies. If the phonon band gap (i.e., the difference between the minimum optical phonon energy and the maximum acoustic phonon energy) is greater than the maximum phonon energy (i.e., ωoptical(min) > 2·ωacoustic(max)), it can prevent Klemens’ decay of optical phonons because allowed states at half the longitudinal optical (LO) phonon energy do not exist. From a one-dimensional (1D) diatomic chain of atoms, it can be calculated that in a binary compound in which M/m > 4, where m is the mass of the lighter atom and M is the mass of the heavy atom, can give such a phonon band gap (Shrestha et al., 2017). Another most likely mechanism by which carriers cool is the decay of optical phonon decay into one transverse optical (TO) and one low-energy LA phonon (i.e., the Ridley mechanism). Energy loss by this mechanism is much less than Klemens’ mechanism; it occurs if there is a wide range of optical phonon energies at the zone center, which is the case for lower-symmetry structures such as hexagonal. For a high-symmetry cubic structure (or engineered nanostructures), LO and TO modes are close to degenerate at the zone center, and thus the Ridley mechanism is inhibited or largely restricted. A flat dispersion relation is also useful, as it can contribute to small heat conductivity because the group velocity for phonon transport is the tangential slope of the dispersion curves. This inhibits the energy dissipation into the environment. Therefore, inhibiting the hot optical phonon population to acoustic phonons via either the Klemen’s and Ridley mechanism, or both of them, or significantly slowing down this process, allows electron population sufficient time to reabsorb the energy of optical phonons. Materials that possess this property thus can be promising hot carrier solar cell absorbers. Slowed carrier cooing has been observed in a range of materials where there is a large mismatch between the masses of constituent atoms. Indium nitride (In N), in which M/m > 7, has been theoretically and experimentally shown to have a large gap in its phonon dispersion to prohibit Klemens’ decay (Davydov et al., 1997; Pomeroy et al., 2005). Hot carrier thermalization rates of several hundred picoseconds have been measured (Chen et al., 2003). The electronic band gap of In N is also around 0.7–0.8 eV, which is in the range of the optimal
Solar Cells Based on Hot Carriers and Quantum Dots 185 band gap for a hot carrier solar cell (HCSC) to operate under 1-sun conditions (Würfel et al., 2005). Because of these properties, this material has been used to model hot carrier solar cell devices (Aliberti et al., 2010; Feng et al., 2012). However, due to the difficulty of making high-quality In N, high production cost, and also the scarcity of indium in the Earth’s crust, practical HC solar cells using In N is unlikely to materialize. A range of bulk materials have been studied for their potential application as HC absorbers. This includes HfN, ZrN, and TiH2. Theoretical and experimental studies have shown a large phononic band gap and small dispersion of optical modes in these materials (Saha et al., 2010; Shanavas et al., 2016; Christensen et al., 1979; Christensen et al., 1983). The abundance of these materials is also relatively large. HfN and ZrN are metallic, but the higher-nitride materials Hf3N4 and Zr3N4 are semiconductors with band gaps of about 0.9 eV and 1 eV, respectively (Bazhanov et al., 2005). Metallic absorbers can be utilized as hot carrier absorbers. In fact, detailed balance analysis of the hot carrier solar cell device shows that the highest theoretical conversion efficiency is achieved by absorbers with a band gap approaching zero (Ross and Nozik, 1982). However, there are some technical challenges associated with the use of a metallic absorber, such as high level of reflectivity, photon absorption, and carrier collection, which need to be addressed. In Fig. 6.5, transient absorption (TA) spectroscopy of typical HfN, ZrN, and TiH films are shown. The HfN and ZrN films were deposited by RF sputtering (Shrestha et al., 2017), whereas TiH films were prepared by evaporation of Ti on a glass substrate, followed by hydrogenation (Wang et al., 2017). HfN and ZrN films grown on (100) silicon substrate were reported to be polycrystalline, with preferential growth in the (100) direction, and films grown on MgO substrates had better crystal quality, which was attributed to a smaller lattice mismatch between HfN (or ZrN) and MgO. Films were typically metal rich. The crystal size of TiH estimated from XRD was comparable to the thickness of the TiH film, suggesting the crystal growth is continuous throughout the film in the growth direction. A good description of the TA technique can be found in the literature (Hartland, 2010). In short, the sample of interest is excited by a pump pulse, and a weak probe with different delays with respect to the pump is used to monitor the change in optical density (∆OD) before and after the pump. The ∆OD is directly related to the carrier dynamics and thus can be studied as carriers relax back to steady-state conditions. HfN and ZrN films grown on quartz substrates were used, although the crystal quality of these films were inferior to the films grown on silicon or MgO substrates, as transmitted signals are detected via this method. The TA measurements were performed using a 400-nm excitation pump source with 100-fs duration and 1-kHz repetition rate. White light continuum was used as the probe beam and detected by a polychromator CCD. In Fig. 6.5A, C, and E, TA spectra at various time delays are shown. The changes in optical density, ∆OD, before and after the pump are plotted as a function of the probe wavelength.
186 Chapter 6
Fig. 6.5 Transient absorption spectroscopy results of typical HfN, ZrN, and TiH films. (A) TA spectra of a typical HfN sample deposited at 450°C in the visible range. (B) ΔOD as a function of delay time measured at 730 nm for the sample shown in (A). The red curve is the exponential fit. (C) TA spectra of a typical ZrN sample deposited at 500°C in the visible range. (D) ΔOD as a function of delay time measured at 730 nm for the sample shown in (C). The red curve is the exponential fit. (E) TA spectra of a TiHx thin film. LOWESS has been applied for each time delay. (F) ΔOD as a function of delay time measured at 700 nm for the sample shown in (E). The red curve is the exponential fit. An adjacent-averaging function on every five points has been applied to smooth the data.
Solar Cells Based on Hot Carriers and Quantum Dots 187 TA spectra for HfN show an excited state absorption peak of around 440 nm and a bleaching peak of around 730 nm, whereas a bleaching peak is not observed in the case of ZrN and TiHX. In the wavelength range shown in the figure, ∆OD for the ZrN film is always positive; and in the case of TiHX, ∆OD fluctuates from negative to positive. In Fig. 6.5B, D, and F, the time evolution of ∆OD at a particular wavelength is plotted as a function of time delay. Immediately after the pump, a rapid change in ∆OD is observed in the TA spectra of HfN and ZrN (Fig. 6.5B and D), which may be due to electron-electron scattering; and then it slowly decreases with a longer delay time. Although the data for TiHX is very noisy, gradual decrease of ∆OD with time delay can be observed. The data have been fitted with a single exponential fit, which is shown by the red curves. From these fits, decay time constants of about 2900 ± 1200 ps, 470 ± 84 ps, and 285 ± 140 ps can be extracted for HfN, ZrN, and TiHX, respectively, which are quite long, thus making these materials potential candidates for HC solar cell absorbers. 6.1.3.3 Slow carrier cooling in nanostructures Modeling and experimental work have shown that nanostructured materials, such as multiple quantum well (MQW) systems, have significantly slower hot carrier cooling rates compared to their bulk counterparts. Measurement of the carrier lifetime of bulk GaAs as compared to GaAs/AlGaAs MQW using time-resolved transient absorption by Rosenwaks et al. (Rosenwaks, 1993), recalculated to show effective carrier temperatures as a function of carrier lifetime by Guillemoles (Guillemoles et al., 2006), shows that the carriers remain hotter by over an order of magnitude for significantly longer times in the MQW samples, particularly at the higher injection levels. This is due to an enhanced phonon bottleneck in the MQWs that allows the threshold intensity at which a certain ratio of LO phonon reabsorption to emission is reached, which allows the maintenance of a hot carrier population to be achieved at a much lower illumination level. Work on strain-balanced InGaAs/GaAsP MQWs by Hirst et al. has also shown carrier temperatures significantly above ambient temperatures (Hirst et al., 2014). Increase of the indium content to make the wells deeper and to reduce the degree of confinement is seen to increase the effective carrier temperatures. A more recent study by Conibear et al. on strain-balanced GaAs/AlAs MQW also has shown that the carrier stays hot for several nanoseconds, as shown in Fig. 6.6 (Conibeer et al., 2017). The figure shows fitting of time-resolved spectroscopy results to estimate the carrier temperature in MQWs’ varying well thickness but fixed barrier thickness, and varying barrier thickness but fixed well thickness. The results indicate that in general, thicker QWs give lower carrier temperatures but longer hot carrier lifetimes. However, there is complexity in the onset of a phonon bottleneck, leading to reduced carrier cooling rates as the thickness of QWs increases. This would seem to occur at lower illumination intensities as the QW thickness increases for small thicknesses because of a rapid decrease in quantum confinement. For thicker QWs, however, quantum confinement is less important and material quality is probably dominant, leading to longer hot carrier lifetimes for higher-quality thicker QWs.
188 Chapter 6
Carrier temperature (K)
430 420
Sample #1, Lw =6 nm
410
Sample #2, Lw =8 nm
400
Sample #3, Lw =12 nm
390
Sample #4, Lw =30 nm
380
LB =40 nm
370
Single exponential fitting
360 350
t1=749±10 ps, T0=400±7 K
340
t2=1127±22 ps, T0=420±6 K
330
t3=800±10 ps, T0=385±7 K
320
t4=1109±17 ps, T0=380±2 K
310 300 –1
0
1
2
3
Carrier temperature (K)
(A)
4
640 620 600 580 560 540 520 500 480 460 440 420 400 380 360 340 320 300
(B)
5
6
7
8
9
10
11
10
11
Time (ns)
Sample #4, LB =40 nm Sample #5, LB =5 nm Sample #6, LB =2 nm LW =30 nm Single exponential fitting
t4=1109±17 ps, T0=380±2 K t5=1100±15 ps, T0=450±4 K t6=1567±20 ps, T0=580±7 K
–1
0
1
2
3
4
5
6
7
8
9
Time (ns)
Fig. 6.6 (A) Carrier temperature evolution from “high-energy tail fitting” for samples 1–4 with increasing QW LW, but fixed LB of 40 nm. (B) Carrier temperature evolution from “high-energy tail fitting” for samples 4–6 with decreasing QW LB, but fixed LW of 30 nm.
For variations in barrier thickness, thinner barriers are seen to give both higher carrier temperatures and longer hot carrier lifetimes, with temperatures up to 300 K above ambient temperatures at lifetimes of approximately 1.5 ns. This occurs due to differential tunneling through barriers for electrons and holes and for hot and cold carriers, leading to carrier separation and suppression of recombination to give longer hot carrier lifetimes. These MQW materials with thin barriers and wide wells appear to be very suitable, as HC solar cell absorbers, particularly materials with the best transport (superlattices with thin barriers) for
Solar Cells Based on Hot Carriers and Quantum Dots 189 which the highest carrier temperatures and longest hot carrier lifetimes are observed, make hot carrier collection at surfaces much more feasible. The mechanisms for the reduced carrier cooling rate in these MQW systems are not yet clear. There are at least three possible effects that are likely to contribute, more than one of which may well be occurring in parallel. The first of these is that with bulk material, photogenerated hot carriers are free to diffuse deeper into it, and hence 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. On the other hand, in 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 of the emitted optical phonons. Thus, the phonon bottleneck condition could be achieved at lower illumination intensities. The second effect is that for the material systems where there is very little or no overlap between the optical phonon energies of the well and barrier materials, the predominantly zone-center LO phonons emitted by carriers in the wells will be reflected from the interfaces and will remain confined in the wells. This will enhance the phonon bottleneck at a given illumination intensity. Third, 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 1D phononic band gaps (analogous to photonic band gaps in modulated refractive index structures). For specific ranges of nanowell and barrier thicknesses, these forbidden energies can be at just those energies required for phonon decay. It is likely that all three of these effects will reduce carrier cooling rates. None depend on electronic quantum confinement, and hence they should be exhibited in wells that are not thin enough to be quantized, but still quite thin. In fact, it may well be that the effects are enhanced in such nanowells 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, which will enhance the phonon bottleneck for emitted phonons. While 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 determine which of these reduced carrier diffusion, phonon confinement or phonon folding mechanisms, might be dominant.
6.1.4 Energy-Selective Contacts The hot carriers generated in the absorber need to be extracted to an external circuit to do meaningful work. In order to minimize energy loss of the hot carriers, they must be extracted through energy-selective contacts (ESCs) via a narrow energy range to prevent cooling of
190 Chapter 6 the hot carriers at the external metal contacts i.e., with minimum entropy loss on carrier extraction (Conibeer et al., 2008). Carriers with energy above or below this narrow range are reflected back to the absorber, where they renormalize their energy through carrier-carrier scattering and repopulate the carrier at the ESC energy level. This elastic carrier-carrier scattering occurs on the femtosecond timescale, and thus is not expected to affect carrier thermalization, which occurs over several picoseconds in bulk materials. The energy level at which the carriers are collected needs to be optimized in order for a particular device to optimize the efficiency of the device. The carriers collected with energies below the optimum level will decrease the electrochemical potential of the carriers, leading to lower operating voltages, whereas carriers collected with energies above the optimum level will lead to excess cooling of hot carriers in the contact. The extraction energy and width of ESCs determine the voltage and efficiency of HC solar cells. Ideally, hot carriers need to be extracted at a discrete energy through monoenergetic contacts for optimum efficiency, although in this case, the power output from the device would be minimal. In a real HC solar cell device, the width of the ESC, ∂E, is more than zero, which means that entropy will be generated on carrier cooling, thus reducing efficiency. Therefore, in practical HC solar cell devices, ∂E should be kept as small as possible. A rough estimate of ∂E = 25 mV has been recommended as a reasonable value (Conibeer et al., 2008). Aliberti et al. have investigated effect on the conversion efficiency on different carrier extraction energy for HC solar cell devices based on InN absorbers. Under 1000 suns, the maximum efficiency occurs with a ∆E of 1.44 eV, yielding an efficiency of 43.6% (Aliberti et al., 2010). Aliberti et al. also showed under 1000- and 1-sun conditions, there is a broad range of optimal extraction energies located around 1.47 and 1.45 eV, respectively. Having a low extraction energy yields a lower voltage, but having a high extraction energy will limit the current. The short-circuit current decreases as a function of extraction energy due to an increase in the Auger recombination required to raise the carrier energy to the extraction level. Having an extraction energy above the average energy of the absorbed photons, the current density decreases due to losses by Auger recombination, which reduces the carrier temperature significantly in the absorber. In the design of a HC solar cell, the carrier extraction energy needs to be selected in a manner that optimizes the voltage that the device is able to achieve while having a reasonable current density. Takeda et al. and Aliberti et al. added another parameter for the energy width through which the ESCs collect the current (Takeda et al., 2010; Aliberti et al., 2011). Takeda et al. showed that there is a linear decrease in conversion efficiency with an increase in the energy selection width, and suggested that targeting 0.1-eV width for ESCs enables the HC solar cell to compete with the Shockley-Queisser limit under 1 sun of illumination. An increase in width increases the energy loss due to entropy generation and is minimized as the width approaches zero (Humphrey et al., 2002). Aliberti et al. showed that the maximum efficiency is obtained for an extraction energy between 1 and 1.2 eV, with a transmission window of 0.05–0.1 eV,
Solar Cells Based on Hot Carriers and Quantum Dots 191 consistent with work by Takeda et al. (Aliberti et al., 2011). The models used to assess the optimal carrier extraction energy assume a common temperature for hot electrons and holes. However, due to the high effective mass of holes, some models assume holes to be close to the lattice temperature and majority of the “hot” energy, as in the electron population (Takeda et al., 2010, Konig et al., 2012]) Because the majority of the absorbed photon energy is within the electron population, it may also be more practical to use a semiselective or carrierselective contact for holes where there is no upper bound for carrier extraction—a high-pass contact rather than a band-pass contact. 6.1.4.1 Energy-selective contact structures As discussed earlier, good energy selectivity is a crucial requirement for suitable ESCs. Quantum mechanical tunneling structures, such as quantum-dot (QD) and quantum-well (QW) double-barrier-resonant (DBR) structures, are most likely to satisfy this requirement (Conibeer et al., 2003). These structures are expected to give conduction of carriers strongly peaked at the discrete energy level, and lower at other energies. Resonant tunneling devices are characterized by a negative differential resistance (NDR), as seen in I-V measurements, by the tunneling of carriers through barriers through quantized energy levels. For a given QW (or QD) and barrier material combination, the confined energy level can be engineered by controlling the width of QWs (or the size of QDs), barrier thickness, and barrier height. These parameters can be tuned to optimize the extraction of carriers at a specific energy level. The use of QD DBR tunneling structures is ideal, as they can provide total energy selection due to strong quantum confinement in three dimensions (3D), rather than confinement in 1D by QW DBR tunneling structures. However, fabricating QDs of uniform size is very challenging. QD size nonuniformity greatly degrades the quality of the resonance, and hence the carrier selectivity (Veettil et al., 2010). On the other hand, a QW DBR tunneling structure can be more easily controlled than QD, leading to the realization of higher selectivity (Sadakuni et al., 2009). The decrease in 3D selectivity with QW resonance is expected to give only a minor broadening so that the effect on efficiency is expected to be small (Veettil et al., 2010). QD and QW resonant tunneling structures have been intensively studied. A number of papers have reported room-temperature-resonant tunneling with a peak-to-valley current ratio (PVCR) > 1. Most of these devices are based on III-V materials such as InGaAs/AlAs, GaN/ AlN, and GaAs/AlAs, and others are Si-based, like Si/SiGe, Si/Al2O3, and Si/CaF2. Most of these structures were grown by molecular beam epitaxy (MBE) or metal organic chemical vapor deposition (MOCVD), which is very costly. In the following sections, selected work on doublebarrier-resonant (DBR) structures with cheaper fabrication methods is briefly discussed. For ESC applications, a range of DBR structures have been investigated. DBR structures consisting of Si QDs in SiO2 have been shown to give evidence of resonant tunneling at room temperature (Shrestha et al., 2010). Structures were fabricated by thermal annealing of SiO2/Sirich oxide (SRO)/SiO2 layers deposited by RF-sputtering. The thickness of the oxide layers were
192 Chapter 6 typically 5 nm, and the SRO layer varied from 2 to 7 nm. Negative differential resistance (NDR) characteristics were observed in the I-V curves, evidencing resonant tunneling; however, the fullwidth half-maximum (FWHM) of the NDR was >400 mV, which is an order of magnitude larger than the suggested nominal value of 25 mV (Conibeer et al., 2003). The broadening of the NDR peak was attributed to the large distribution of the QD sizes in the sample. Although the average size of the QDs can be controlled by the thickness of the SRO layer, a considerable distribution of QD sizes in the samples was observed (Shrestha et al., 2010). Significant improvements on the quality of resonance peak has been demonstrated with DBR structure using atomic layer deposition (ALD) of Al2O3 barriers and chemically synthesized PbS quantum dots, as well as ALD-deposited Al2O3 barriers and Ge QW deposited by RF sputtering, as shown in Fig. 6.7 (Shrestha et al., 2017). NDR features can be observed in I-V curves of both structures at low temperature, as well as 300 K measurements. FWHM, PVCR, and quality factor (QF = PVCR/ FWHM) of the NDR peaks are labeled. The PVCR and QF increase at lower temperature, which was primarily attributed to the reduction of background current. FWHM of the NDR peaks is about 30 mV, which is very close to the suggested nominal value of 25 mV for the width of ESCs. Improvement on the quality of the resonance peak was attributed to the improved quality of materials as given by ALD and chemical synthesis, as well as uniform size distribution of
4×10−5
(A)
−5
3×10
PVCR= 8 FWHM= 30 mV QF= 264
1.2×10−6
300 K
(C) PVCR= 1.6
300 K
(D) PVCR= 1.6
190 K
FWHM= 26 mV QF= 61
8.0×10−7
2×10−5 4.0×10−7 Current (A)
Current (A)
1×10−5 0 1.2×10
−9
8.0×10−10
(B) PVCR= 15
FWHM= 37 mV QF= 405
90 K
8.0×10−7
FWHM= 20 mV QF= 300
4.0×10−7
4.0×10−10 0.0 0.0
0.0 1.2×10−6
0.0 0.2
0.4 0.6 Voltage (V)
0.8
1.0
0.0
0.2
0.4 0.6 Voltage (V)
0.8
1.0
Fig. 6.7 I-V measurements on (A) Al2O3/Ge QW/Al2O3 structure at 300 K, (B) Al2O3/Ge QW/Al2O3 structure at 90 K, (C) Al2O3/PbS QDs/Al2O3 structure at 300 K, and (D) Al2O3/PbS QDs/Al2O3 structure at 90 K.
Solar Cells Based on Hot Carriers and Quantum Dots 193 barriers, quantum wells, and quantum dots. ALD allows growth of thin films with excellent conformity and precise control of thickness down to atomic levels, which is expected to reduce the broadening of the discrete energy level. At UNSW, monodisperse growth of PbS QDs has been demonstrated (Cao et al., 2016). In addition, interface roughness between Ge and Al2O3 films was only about 0.2 nm, which is good for minimizing the degradation caused by nonuniformity.
6.2 Colloidal Quantum Dot Solar Cells 6.2.1 Introduction Solution-processable quantum dot solar cells have emerged as a promising low-material-cost, low-embodied production energy and high-efficiency photovoltaic technology. Since 2009, small-cell efficiencies have increased from 3% to 12% (Ma et al., 2009; Debnath et al., 2010; Xu et al., 2018). Among the colloidal quantum dot solar cells, Pb chalcogenide (i.e., PbS and PbSe quantum dots) stand out due to their high efficiency, simple fabrication process, and good stability. PbS quantum dot cells with a certified efficiency of 11.28% and 1000 h of stability have been demonstrated (Liu et al., 2017). Due to the quantum confinement effect, the band gap of the material is size dependent. This enables both optimized-band-gap singlejunction cells and multijunction tandem devices. The band gaps of PbS and PbSe quantum dots can be tuned from 0.4 to 1.8 eV, which are suitable for optimal single-junction devices, all-quantum dot tandems, and quantum dot‑silicon tandem solar cells. Owing to the low temperature and solution-processable characteristics, colloidal quantum dot solar cells can be fabricated on light and flexible substrates using a range of low-cost solution processes such as spraying, spin-coating, printing, and blading. These technologies potentially enable the development of solar ink applied to building materials in buildingintegrated photovoltaics (BIPVs). The rapid development of colloidal quantum dot solar cells is largely attributed to the great research results leading to the advancement in materials synthesis, quantum dot surface passivation, and device structure design and fabrication, which will be presented and discussed in this section.
6.2.2 Synthesis of PbS and PbSe Quantum Dots One of the advantages of colloidal quantum dot solar cells is the solution processes for materials synthesis with low temperature and low embodied energy compared to Si, III-V, and CIGS solar cells. With the substantial interest in quantum confinement effects, tunable band gaps, and modified photonic and phononic properties for optoelectronic applications, synthesis recipes for PbS and PbSe quantum dots continue to be of significant interest. The recent advances in solution synthesis of quantum dot materials and surface chemistry have greatly contributed to the rapid progress of the PbS and PbSe QD-based optoelectronic devices, particularly solar cell technology, due to improved size uniformity, reduced surface defect density, controllable doping level, and enhanced stability.
194 Chapter 6 The most commonly used synthesis method for highly performing PbS and PbSe quantum dot solar cells is a so-called hot injection method. The hot injection method has been widely used to synthesize a broad range of colloidal chalcogenide quantum dots, including CdE, CZTE, and PbE (E = S, Se, Te) since a study by Murray (Murray et al., 1993). Three important components in a typical hot-injection synthesis include metal and chalcogenide precursors and organic ligands. The synthesis procedure is relatively straightforward, as implied by the name hot injection, with one of the precursor solutions being injected into the other swiftly at an elevated temperature. The reaction and growth of the nanoparticles follow the classical nucleation and crystallization theory. When the two precursors are mixed, saturation of the precursor ions leads to a rapid nucleation burst, followed by the Ostwald ripening process for the nanoparticles to grow. In this process, the reaction temperature and duration determine the size of the nanoparticles, while the ligand molecules and precursors’ concentration play an important role in controlling the shape, size distribution, and stability (Hines and Scholes, 2003; Murray et al., 2000). For PbS quantum dots, the choice of chemical precursors has been shown to be important in the discovery of the benefits (such as better stability) of halide atomic ligand surface passivation offered by Pb-halide precursors instead of PbO precursors (Hines and Scholes, 2003; Yuan et al., 2015; Weidman et al., 2014; Zhang et al., 2014a; Yuan et al., 2014). Since Tang et al. reported on the impressive air stability provided by halide atoms on the surface of the quantum dots (Tang et al., 2011), a few significant breakthroughs have been achieved using Pb-halide precursors to synthesize PbS quantum dots with narrower size distribution, more air stability, and reduced surface defects. For instance, Zhang et al. achieved effective halide passivation for PbS and PbSe quantum dots via a simple and in situ low-temperature process using metal halide as a precursor (Zhang et al., 2014a). Halide-passivated PbS and PbSe quantum dots have demonstrated significantly increased PL quantum yield and air stability compared to that synthesized by PbO precursors. Despite of the better stability and surface passivation provided by the halide precursors, PbO is still the precursor most used to synthesize PbS quantum dots for the best-performing solar cells (Xu et al., 2018; Liu et al., 2017). However, most recently, Wang et al. reported on PbS quantum dot synthesis using Pb acetate as a Pb source, where acetates can act as efficient capping ligands together with oleic acid, providing better surface coverage and replacing some of the harmful OH ligands during the synthesis (Wang et al., 2018). As a result, a higher efficiency of 10.82% was achieved. This work also highlighted the fact that the precursor engineering has great potential to further improve the quantum dot quality, hence enhancing device performance. Compared to PbS, PbSe has a larger Bohr radius, and therefore a stronger degree of quantum confinement effect for quantum dots of the same size. This should result in a more significant wave function overlap among quantum dots and a stronger electronic coupling in PbSe QD-based devices (Zhang et al., 2014b; Shabaev and Efros, 2013). However, due to the poor
Solar Cells Based on Hot Carriers and Quantum Dots 195 air stability of PbSe quantum dots synthesized by the hot injection method, the progress in PbSe quantum dot based solar cells has largely lagged behind PbS solar cells. However, this situation has changed since a direct cation-exchange method for PbSe quantum dot synthesis from a CdSe quantum dot solution was reported by J. Zhang et al. in 2014 (Zhang et al., 2014b). Synthesis of monodispersed CdSe quantum dots has been well developed over a wide range of sizes. By exchanging Cd cations of CdSe quantum dots using a PbCl2 precursor, highly air-stable PbSe quantum dots can be produced owing to in situ chlorine and cadmium passivation to their surface, as shown in Fig. 6.8A. This has led to a power conversion efficiency (PCE) of over 6% (see Fig. 6.8B), which was further improved to 8.2% in 2017 by postsurface passivation by direct ion exchange between PbSe quantum dots and CsPbX3 (X = Cl, I, Br) nanocrystals, as discussed later in this chapter (Zhang et al., 2017).
6.2.3 Band-Gap Tunability A unique property of quantum dot materials is the quantum confinement effect, which alters the electronic band structure, hence changing the optical and electronic properties. For instance, the band gap of quantum dot materials enlarges when the dot size is smaller than their exciton Bohr radius. Therefore, both optical absorption and photoluminescence spectra shift to higher energy regions, as shown in Fig. 6.9A and B (Weidman et al., 2014). This confinement effect is size-dependent and particularly strong in a semiconductor with larger exciton Bohr radius, rBohr. The tunability of the optical and electronic properties has attracted
Fig. 6.8 (A) Transmission electron microscopy (TEM) image of PbSe quantum dots synthesized by Cd cation exchange and (B) J-V curve of the best-performing device of PbSe quantum dots reported in 2014 (Zhang et al., 2014b).
196 Chapter 6
Fig. 6.9 (A) Optical absorbance and (B) PL spectra of PbS quantum dots with different sizes, showing a wide range of band-gap energies (1.25–0.7 eV) (Weidman et al., 2014). (C) Comparison of band-gap energy as a function of dot size between estimations using Moreels’s et al. (2009) and Weidman’s et al. (2014) equations, EMA equation (Brus, 1984), and our experimental results (Yuan et al., 2015).
a great amount of attention for quantum dot materials in their applications in optoelectronics, such as LEDs, photodetectors, and photovoltaics. Both PbS and PbSe are known as strong quantum confinement materials, with rBohr = 18 nm and 46 nm, respectively. Owing to recent advancements in synthesis, the band gap of PbS and PbSe quantum dots can be tuned in a wide spectral region, ranging from the narrow bulk band gap (0.41 eV for PbS and 0.27 eV for PbSe) to 2 eV for ultrasmall quantum dots. The effective mass approximation (EMA) is often used in determining the absolute confined energy levels for isolated quantum dots (Brus, 1984):
Solar Cells Based on Hot Carriers and Quantum Dots 197 Eg ( r ) = Eg + ∆E = Eg +
2 2π 2 1 1 + , 2 d me mh
where Eg is the band gap of the bulk material, ΔE is the band gap increase, d is the dot size, and me and mh are the effective mass of electrons and holes of the bulk, respectively. Although this method relies on the semiconducting nature of the bulk materials and is arguably valid in the ultrasmall regime, it gives a relatively correct prediction of the band gap widening as quantum dot size decreases. In the research literature, the relationship of the quantum dot band gap with dot size varies slightly with synthesis methods used by different groups. Moreels et al. determined the correlation between the band gap and dot size by an empirical equation that best fits their optical absorption spectra of PbS quantum dots synthesized by using element sulfur and PbCl2 precursors (Moreels et al., 2009): 1 , 0.0252d + 0.283d where Eg is the band gap of the quantum dot and d is the particle size. Eg = 0.41 +
2
Weidman et al. derived the relation between the band gap and the dot size of highly monodispersed PbS quantum dots synthesized by a high Pb:S precursor stoichiometry ratio, as shown by this relation (Weidman et al., 2014): 1 . 0.0392d + 0.114d Fig. 6.9C compares the band gap of experimental data of PbS quantum dots synthesized using PbBr2 precursors by the group at UNSW Sydney (Yuan et al., 2015) with the band gap calculated by Moreels’s and Weidman’s equations, as well as the EMA method. It can be seen that these three equations show excellent consistency when the dot size is larger than 6 nm, while Moreels’s equation gives a slightly lower band gap than the other two in the small regime. Regardless of the discrepancy, using these equations, one can quickly estimate the quantum dot size based on their optical absorption peak position without taking TEM images. Eg = 0.41 +
2
For applications in photovoltaics, it is necessary to effectively utilize all the photons from the solar spectrum. Considering the abundance of photons with wavelengths longer than the visible range, materials with band gaps that can be well tuned within the near-infrared (NIR) and IR range are desirable, particularly for the tandem solar cell configuration. Therefore, PbS and PbSe quantum dots provide huge potential for applications in a high-efficiency single junction, as well as multijunction tandem solar cells, owing to their band gap tunability.
6.2.4 Electronic and Doping Properties In a solar cell, photogenerated carriers need to be separated, usually by some form of junction. In high-efficiency silicon homojunction photovoltaic devices, the p-n junction forms
198 Chapter 6 by an impurity doping process, while heterojunction devices consist of a p-i-n structure where a near-perfect, defect- and impurity-free silicon absorber is sandwiched between two heavily doped thin p- and n-type regions. Either structure requires modification of the electronic band property of the materials by impurity doping. However, impurity doping to quantum dots and nanostructures has been shown to be challenging. There has been much debate in the research literature about whether doping of quantum dots is possible, given the high-formation energies of defects inside small atomic clusters and the high probability that defects or impurities may diffuse to a surface (Mocatta et al., 2011, Kroupa et al., 2017). Fortunately, surface chemistry was found to have a strong influence on the physical properties of the quantum dots, particularly to alter the energy band structure and doping property (Jasieniak et al., 2011). As presented previously, colloidal quantum dots are normally synthesized by surfactantassisted chemical reactions, in which organic ligands stabilize the quantum dot growth by capping the surface. For both PbS and PbSe quantum dots, oleic acid (OA) is the most commonly used ligand in the synthesis, resulting in OA-capped quantum dots for further use in the devices. Therefore, understanding of the physical property of OA-capped quantum dots is crucial to their application in optoelectronics. As discussed in the previous section, the band gap of PbS and PbSe quantum dots can be tuned in a wide energy range, depending on the dot size. Researchers have also demonstrated that the valence and conduction band edge energies are also size dependent. Jasieniak et al. have investigated the energy band structure of OA-capped PbS and PbSe quantum dots using photoelectron spectroscopy (Jasieniak et al., 2011). They demonstrated that the energy edge of conduction and valence band move apart in an asymmetric manner, in which the conduction edge energy increases by a greater extent toward the vacuum level than the decrease of the valence band energy for the same dot size, as shown in Fig. 6.10A. By fitting their results, they formulated the band edge energies shown in Table 6.1, which can be used to predict the band alignment of quantum dot active layers with other carrier transport layers in a device. The influence of surface ligands on the electronic band structure has been a significant research topic in the last decade. With surfactant-assisted synthesis, the synthesized quantum dots are usually capped with long-chain organic ligand molecules, such as oleic acid (CH3(CH2)7CH=CH(CH2)7COOH). However, for application in optoelectronic devices such as solar cells, long-chain molecules lead to a large dot-to-dot distance, which hinders carrier’s transport. To maximize conductivity, the long-chain ligands can be exchanged for short-chain ones such as 3-mercaptopropionic acid (MPA), 1,2-ethanedithiol (EDT), and halide atomic ligands, owing to recent advancements in surface chemistry (Zhang et al., 2014a; Tang et al., 2011; Zhang et al., 2014b). Researchers have found that the physical properties of quantum dots are highly dependent on the surface ligands. Both numerical simulation and experimental work have demonstrated
N-type
Inert
Tetrabutyl ammonium iodide
–4 Cadmium bromide/iodide
–10
16
cm
–1014 cm–3
Inert (Ref 15)
–5
Inert
Valence band –6
2
4
Ethane dithiol
1) I- 2) butylamine Air (Ref 1)
6
3-Mercaptopropionic acid Air
8
PbSe QD diameter (nm)
(B)
–1014 cm–3
10–2 MPA
10–3 DE m = m0 exp kBT
(
–1016 cm–3
10–4 –10
18
–3
cm
Tetramethyl ammonium hydroxide
EDT 0.30 0.26 0.28 Average mid-infrared transition energy, DE (eV)
(D)
P-type
3.5
Conduction band Transport Optical
Energy (eV)
4.0 4.5
Fermi level
5.0
Standard deviation
5.5
BT
EDA
MPA
EDT
TBAF
1,2-BDT
1,3-BDT
1,4-BDT
NH4SCN
TBACI
TBAI
(C)
Valence band TBABr
6.0
Instrument accuracy
Fig. 6.10 (A) The valence and conduction band edge energies of PbSe quantum dots as a function of particle diameter (nm) (Jasieniak et al., 2011), (B) diagram showing doping type and concentration of PbS quantum dots capped with different ligands (Voznyy et al., 2012), (C) band energy-level diagram of PbS quantum dots capped by different ligands (Brown et al., 2014), and (D) electron mobility of PbS quantum dot films capped by different ligands (Tang et al., 2011).
Solar Cells Based on Hot Carriers and Quantum Dots 199
(A)
Br
–3
Mobility (cm2 V–1s–1)
Energy (eV)
Conduction band
10–1
–1018 cm–3
Inert
(
–3
200 Chapter 6 Table 6.1: Valance band energy (Evb) and conduction band energy (Ecb) as a function of quantum dot size d (Jasieniak et al., 2011). PbS Evb (eV) Ecb (eV)
PbSe -0.90
−4.76-0.64d −4.35 + 5.12d-1.27
−4.84-0.77d-2.94 −4.56 + 3.167d-0.86
that the selection of surface ligands can have a dominant effect on the charge carrier type, carrier concentration, and mobility (Carey et al., 2015; Voznyy et al., 2012; Oh et al., 2013). Voznyy et al. have developed a generalized doping framework based on charge-orbital balance analysis for quantum dot materials and found that the doping type is determined by the stoichiometry of the quantum dots. The surface ligand treatment can greatly change the quantum dot stoichiometry during the ligand exchange process, where surface elements may be removed or replaced. This introduces a number of states within the band gap. These states can effectively pin the Fermi level near the band edge, altering the doping property. It is found that Pb-rich PbSe quantum dot thin films tend to be more of the n-type, while the Se-rich counterparts tend to be more of the p-type (Oh et al., 2013). Fig. 6.10B shows the doping types and concentrations of PbS quantum dot thin films capped with a range of common surface ligands. With various ligands, the quantum dot film can have completely reversed carrier types. For example, tetramethylammonium hydroxide (TMAOH)–treated PbS quantum dot film is the p-type, with a doping concentration of >1018 cm−3, while tetrabutylammonium iodide (TBAI)–treated film (in an inert environment) is the n-type, with a doping concentration of about 1017 cm−3. Besides shifting the Fermi-level position, surface ligand bindings also induce a variable dipole moment, hence shifting the band-edge energy (Milliron, 2014). Brown and coworkers have investigated the energy-level shifts of PbS quantum dots treated with 12 different ligands using ultraviolet (UV) photoelectron spectroscopy (UPS) (Brown et al., 2014). They demonstrated that the measured valence band maxima span a range of 0.9 eV, as shown in Fig. 6.10C. These findings have guided the design of cascaded p-i-n energy level architecture, leading to significant device optimization. Surface ligands also affect the mobility of carriers in a quantum dot thin film, as shown in Fig. 6.10D. Ligands such as MPA and EDT, used in quantum dot solar cells, have relatively low carrier mobility, in the range of 10−4 to 10−3 cm2 V−1 s−1 (Tang et al., 2011), while halide ligands such as bromide and iodide improve the mobility to the range of 10−1 cm2 V−1 s−1 (Carey et al., 2015). Therefore, halide-passivated quantum dots are often used to form an absorber layer in photovoltaic devices. The ability to control carrier properties by surface ligand engineering allows the fabrication of quantum dot homojunction, as well as p-i-n heterojunction quantum dot solar cells, simply
Solar Cells Based on Hot Carriers and Quantum Dots 201 by choosing proper ligands. This has played a significant role in the development of most efficient lead chalcogenide quantum dot solar cells.
6.2.5 Advances in Colloidal Quantum Dot Solar Cells 6.2.5.1 Device structure The improvements achieved in the device performance of quantum dot solar cells are mainly attributed to the great research efforts to advance material synthesis chemistry and the understanding of physical properties, as well as the development of a device architecture/structure. There are a few milestones in the development of effective device structures. The first is a simple Schottky device with a structure of TCO/quantum dots/ metal. In such a simple device, a depletion region generated at the quantum dot/metal interface is responsible for carrier separation. In 2008, Sargent’s group at University of Toronto reported on a breakthrough PbS quantum dot Schottky solar cell with 2% efficiency (Johnston et al., 2008). At the same time, Nozik’s group achieved over 2% efficiency for its PbSe Schottky device (Luther et al., 2008). However, the pinning of Fermi levels at the quantum dot/metal interface imposes an upper bound on the built-in potential, leading to a low VOC that is well below what is derived from the band gap of the quantum dots Carey et al., 2015, Kramer and Sargent, 2014). This hinders the further development of Schottky junction devices. In 2014, Bawendi’s group at the Massachusetts Institute of Technology developed a p-i-n heterojunction structure based on a ligand-dependent charge carrier property of quantum dots, which led to a significant breakthrough in quantum dot solar cell research (Chuang et al., 2014). By engineering the band alignment of the quantum dot layers via exchanging surface ligands to control the carrier polarity, a certified efficiency of 8.55% has been reached. Furthermore, the performance of unencapsulated devices remains unchanged for over 150 days of storage in air. The enhanced efficiency from the EDT-passivated PbS as a hole transport layer is due to a favorable band alignment with the PbS quantum dot absorber layer, which blocks electrons and transports holes to the metal electrode, as shown in Fig. 6.11. 6.2.5.2 Device fabrication Being synthesized by surfactant-assisted chemical reactions, colloidal quantum dots are capped by insulating, long-chain OA ligands. To fabricate high-efficiency solar cells, these ligands must be replaced by short ones to enhance conductivity, as well as modify the carrier polarity to align the band energies properly. These ligand molecules usually bond on the surface of quantum dots through covalent-like attachment on the surface ions. Therefore, the surface ligands also serve as passivating molecules to the quantum dots to reduce the number of defect states (Tang et al., 2011; Ip et al., 2012).
202 Chapter 6
Fig. 6.11 (A) A schematic of a p-i-n heterojunction device structure and (B) J-V curve comparison to a device without PbS-EDT hole transport layer. From Chuang, C.-H. M. et al., 2014. Improved performance and stability in quantum dot solar cells through band alignment engineering. Nat. Mater. 13(8), pp. 796–801.
Because different ligands have different molecule sizes, as well as bonding strength to the surface of quantum dots, the passivation effect that they provide can vary. For example, it was reported that MPA ligands cannot passivate some of the hard-to-access sites on the surface of PbS quantum dots (Ip et al., 2012), while halide atomic ligands have a smaller size, as well as a stronger affinity to the Pb2+ cation, hence providing more comprehensive and robust passivation to the quantum dots. Over the last decade, a few important ligand exchange methods have been developed, leading to significant improvement in device performance and stability. Solid-state ligand exchange
Until 2016, most commonly used method to replace OA ligands was the so-called solidstate ligand exchange, as shown in Fig. 6.12A. In this process, the quantum dots with long-chain OA ligands are deposited on an ETL (e.g., a ZnO or TiO2 layer), normally by spin-coating or dip-coating to form a thin film. For a halide ligand exchange to form the intrinsic absorber layer, a halide ligand solution (TBAI or PbI2) is applied to this thin
Solar Cells Based on Hot Carriers and Quantum Dots 203
Fig. 6.12 Schematics of (A) solid-state ligand exchange and film fabrication and (B) solution-phase ligand exchange and film fabrication, where the long-chain ligands are replaced by the [PbX3]− anions with the aid of ammonium protons in a solution. From Liu, M. et al., 2017. Hybrid organic-inorganic inks flatten the energy landscape in colloidal quantum dot solids. Nat. Mater. 16(2), pp. 258–263; Wang, R., 2016. Colloidal quantum dot ligand engineering for high performance solar cells Energ. Environ. Sci. 9, pp. 1130–1143.
quantum dot film and then spun to dry the solvent. In this process, halide atomic ligands replace OA molecules due to their stronger affinity to Pb ions. The film is further rinsed with methanol, followed by spinning to remove the residual OA molecules (Tang et al., 2011; Chuang et al., 2014; Ning et al., 2014; Wang, 2016; Kim et al., 2015). This solidligand exchange process is normally repeated a few times to form a desired thickness for the absorber layer of about 250 nm. To form the HTL p-type layer, MPA and EDT are the most used ligands in high-efficiency colloidal solar cells. They can replace OA using a similar solid-state exchange (Chuang et al., 2014; Labelle et al., 2015). Solution ligand exchange
Despite of the advancement of the solid-state ligand exchange process, which has significantly contributed to the progress of colloidal quantum dot solar cell research, there are some key issues involved in this process that hinder further improvement of device performance. This ligand exchange relies on the penetration of the shorter ligand solution to the originally OA-capped quantum dot film. This often results in incomplete ligand exchange, hence creating defect energy states within the band gap. Repacking and aggregation of quantum dots during the exchange process also cause cracks and uneven morphology in the film, affecting device performance. In 2016, Liu and coworkers have successfully developed
204 Chapter 6 a solution-phase ligand exchange process based on lead halide as a precursor, with submolar amounts of ammonium acetate to stabilize the colloidal quantum dots, as shown in Fig. 6.12B (Liu et al., 2017; Wang, 2016). This process overcomes the drawbacks of the solid-state ligand exchange, leading to reduced defect states in the band gap and closely packed quantum dot film. This results in higher mobility and longer diffusion length, allowing the increase of quantum dot film thickness to absorb more photons in order to generate more current without sacrificing VOC and FF. Their champion device, consisting of a 350-nm-thick active layer made by the solution ligand exchange process, has achieved a record efficiency of 11.28%, with an increased JSC of 27.23 mA/cm2, FF of 68%, and VOC of 0.61 V. Due to more homogenous surface passivation, the devices also demonstrated excellent air stability, retaining 90% of the initial efficiency when stored in air after 1000 h. Direct ion exchange for PbSe quantum dot passivation
PbSe quantum dots possess some properties that are superior to PbS, which may lead to more efficient devices. For example, higher MEG efficiency has been demonstrated in PbSe than PbS. With this advantage, a solar cell can multiply the contribution of photon absorption to current generation (Peterson et al., 2014; Zhang et al., 2015; Padilha et al., 2013; Shabaev et al., 2006). PbSe also has a larger exciton Bohr radius (46 nm) than that of PbS (18 nm), which should further facilitate charge carrier transport and collection due to stronger electronic coupling among the quantum dots (Liu et al., 2017; Johnston et al., 2008; Beard et al., 2010; Davis et al., 2015). However, PbSe quantum dots are very prone to oxidation when exposed to ambient environments (Ning et al., 2014). As a result, surface defects can form upon oxidation and become nonradiative recombination centers, which significantly limit the VOC and FF of a PV device (Beard, 2011, Semonin et al., 2012). Promising results on PbSe quantum dot passivation by halides have been reported with great improvement in air-stability and photoluminescence quantum yield (PLQY) (Beard, 2010). In particular, Zhang et al. developed a cation exchange synthesis method using cadmium selenide (CdSe) quantum dots and lead chloride (PbCl2), which has led to Cl-passivated PbSe quantum dots and the first PbSe quantum dot solar cell with a PCE over 6% (Zhang et al., 2014b). It has been suggested that bromide (Br−) and iodide (I−) should provide better passivation than Cl to lead chalcogenide quantum dots (Wang et al., 2011; PattantyusAbraham et al., 2010). Researchers have reported that the use of metal or organic Br−/I− salts can achieve Br− and I− in situ passivation to PbSe quantum dots (Luther et al., 2008; Davis et al., 2015). However, unintentional removal of the capping ligands may occur due to the presence of extra cations and the strong tendency to form covalentlike Pb-Br and Pb-I bonds (Beard, 2011), which causes particle agglomeration and deterioration in the quantum dot PLQY. This can further lead to disorder of quantum dot packing in a thin film and reduced final device performance (Hoye et al., 2014). Therefore, an alternative passivation method is required to fully realize the potential of PbSe in PV devices.
Solar Cells Based on Hot Carriers and Quantum Dots 205 At UNSW Sydney, Zhang et al. have developed an effective passivation route for PbSe quantum dots using inorganic lead halide perovskite (CsPbX3, X = Br or I) nanocrystals as Br− or I− sources (Zhang et al., 2017). By mixing a small amount of CsPbBr3 nanocrystals into Cl-passivated PbSe quantum dot solution, the PL peak of the perovskite nanocrystals (initially at 513 nm) shows a blue shift to higher energy, while the PL peak of PbSe quantum dots stays unchanged, as shown in Fig. 6.13A and B, but with higher quantum yield. These results suggest that the halide ions from these perovskite nanocrystals can shuttle to defective or weaker Pb-Cl bonding sites on the surface of PbSe quantum dots, resulting in high PL efficiency. At the same time, Cl ions on the PbSe surface migrate to the sites of Br− in the perovskite nanocrystals, forming mixed halide perovskite with an increased band gap, consistent with the blue shift in PL. The PbSe quantum dot solar cells made from the ionexchanged quantum dots have demonstrated increased VOC, FF, and air stability owing to the improvement of the surface passivation. The best-performing device has achieved a PCE of 8.2% (Fig. 6.13C), which is the highest reported efficiency for PbSe-based solar cells to date. 6.2.5.3 Optimization of the p-type layer As presented in the previous section, the development of a solution ligand exchange process has significantly reduced the surface defect density in the halide-passivated PbS absorber layer, hence increasing its carrier mobility and conductivity. Compared to the mobility of halide-capped quantum dots at about 10−1 cm2 V−1 s−1, the commonly used hole transport layer of EDT or MPA capped PbS quantum dots has relatively low mobility, ranging from 10−4 to 10−3 cm2 V−1 s−1. This unmatched mobility would lead to unbalanced carrier transport between the absorber layer and HTL layer, resulting in carrier accumulation at the interface (Fig. 6.14A). In addition, the p-type doping level of EDT- or MPA-capped PbS quantum dot film is still not optimized to form sufficient band bending at the interface to facilitate efficient charge extraction. Therefore, optimizing the p-type doping property is another key research topic that should be addressed urgently. The most effective methods to improve the p-doping property of PbS quantum dot solar cells reported so far is remote molecular doping (Kirmani et al., 2017) and impurity doping (Hu et al., 2018). For the former, Kirmani et al. have applied a large electron affinity metal−organic complex, molybdenum tris(1-(trifluoroacetyl)-2-(trifluoromethyl)ethane1,2-dithiolene), Mo(tfd-COCF3)3, on the PbS-EDT quantum dot layer. As Mo(tfd-COCF3)3 molecules can readily withdraw electrons from the PbS-EDT layer, the Fermi level of the PbS-EDT layer treated by Mo(tfd-COCF3)3 was found to shift toward the valence band edge, resulting in better energy alignment with the PbS-PbX (X = halide) absorber layer. In optimal treatment conditions, the best-performing device has achieved a PCE of 9.5%, compared to 8.5% of the untreated control device, owing to improved carrier extraction. Despite that, impurity doping to quantum dots and nanostructured materials has been shown to be challenging; Hu and coworkers at UNSW have demonstrated significantly improved carrier mobility and concentration, as well as device performance, when using Ag as a p-type
206 Chapter 6
Fig. 6.13 (A) A schematic showing the ion exchange between Cl-passivated PbSe quantum dots and CsPbX3 nanocrystals, (B) photoluminescence (PL) spectra of the original CsPbBr3 and CsPbClyBr3-y nanocrystals after mixing with PbSe quantum dot purification, and (C) J-V curves of the devices fabricated from PbSe quantum dots with different perovskite nanocrystal treatments. From Zhang, Z. et al., 2017. A new passivation route leading to over 8% efficient PbSe quantum-dot solar cells via direct ion exchange with perovskite nanocrystals. Adv. Mater. 29 (41), p. 1703214.
Solar Cells Based on Hot Carriers and Quantum Dots 207 dopant to PbS quantum dots (Hu et al., 2018). To incorporate Ag atoms into the quantum dots, silver acetate with various molar ratios to PbO (Ag/Pb = 0.0%, 0.1%, 0.5%, 1.0%, and 2.0%) was added to the conventional precursor solution for PbS quantum dot synthesis. These Ag-doped PbS quantum dots were deposited on a PbI2-treated PbS quantum dot absorber (PbS-PbI2), and EDT-ligand exchange was performed to form the HTL (Ag-PbS-EDT). Compared with the undoped PbS-EDT layer, an X-ray diffraction (XRD) pattern of Ag-PbSEDT sample showed a slight shift toward larger angles when the Ag doping level increases. This indicates that the introduction of the smaller ionic radius Ag+ leads to a systematic decrease in the lattice constant, suggesting that Ag+ was successfully incorporated into the PbS quantum dots. As a result, both carrier mobility and concentration have increased by an order of magnitude, from 3 × 10−4 to 4 × 10−3 cm2 V−1 s−1 and 6 × 1017 to 6 × 1018 cm−3, respectively. Similar to the remote molecular doping described previously, Ag doping also resulted in a deeper Fermi level. These improved doping properties matched well with that of the PbS-PbI2 absorber layer, consequently reducing the carrier accumulation at their interface and improving carrier extraction (Fig. 6.14B). This led to a significant improvement in device performance, with a maximum PCE of 10.6%, compared to 9.1% of the undoped control device, as shown in Fig. 6.14C. Previously, there has been much debate in the research literature as to whether doping of quantum dots was possible. Significant debate was warranted, given the high-formation energies of impurity sites inside nanometer-sized particles and the high probability that defects or impurities may diffuse to the surface (Mocatta et al., 2011; Kroupa et al., 2017). This research shows an example of a complete photovoltaic device that has been improved by the application of doped quantum dots, demonstrating the significant potential of this approach and motivating further research into doped quantum-confined devices.
6.3 Summary and Outlook Hot carrier solar cells present a promising technology with limited efficiency of over 65% at 1 sun and over 85% at maximum concentrations. Significant progress has been made on various aspects of hot carrier solar cells. Slow carrier cooling has been observed in bulk materials with large gaps in their optical and acoustic phonon energies, as well as in multiple quantum wells, demonstrating that these are promising HC absorbers. Recently, a significant hot-phonon bottleneck effect in carrier thermalization was also observed in perovskites (Price et al., 2015; Yang et al., 2016). Yang et al. showed that the hybrid perovskites have a stronger phonon bottleneck effect than the pure inorganic types (Yang et al., 2017). From the fitting of transient absorption data, a hot carrier cooling lifetime of hundreds of picoseconds has been reported. These suggest that these perovskite materials can also be suitable for hot carrier optoelectronics.
208 Chapter 6
PbS-EDT
PbS-Pbl2 Light
low mobility
ZnMgo
Ag-PbS-EDT
(A)
PbS-Pbl2
high mobility
ZnMgo
Light
Electron Hole
(B) 30
Current density (mA cm–2)
25 20 15 A (%) Voc(mV) Jsc(mA cm–2) 25.2 0.0 613 0.1 621 25.4 0.5 625 25.8 1.0 630 26.2 2.0 629 25.7
10 5
PCE (%) 9.1 9.6 10.0 10.6 10.1
0 –5 0.0
(C)
0.2
0.4
0.6
Voltage (V)
Fig. 6.14 (A) Schematic of the device structure using un-doped HTL showing the drawbacks of low mobility, specifically causing charge accumulation at the PbS-PbI2 and PbS-EDT interface and (B) the Agdoped device structure with modifications to the hole extraction. Higher carrier mobility due to Ag doping in the PbS-EDT layer can leads to greatly reduced charge accumulation. (C) J-V curves of the devices fabricated from un-doped PbS quantum dots and Ag-doped ones with different concentrations (Hu et al., 2018).
Double-barrier structures consisting of quantum wells and quantum dots have been investigated for their applications in ESCs. Some of these structures have shown very good energy selectivity, even at room temperature, and so they appear to be promising. An ESC using double-barrier resonant tunneling is symmetric, and so it does not rectify electrons from holes. Therefore, ways of selectively extracting hot carriers from the absorber are
Solar Cells Based on Hot Carriers and Quantum Dots 209 also essential. Triple-barrier resonant tunneling consisting of two QW or QD layers can be separately tuned to only allow extraction of electrons or holes, and thus it can be used to separate electrons and holes in opposite directions (Conibeer et al., 2009). Such an ESC will also give a much greater energy selectivity. This concept was suggested by Brennan and Summers (Brennan and Summers, 1987) and has been used for energy filtering in quantum cascade lasers. Some progress has also been made on the extraction of hot carriers. Dimmock et al. demonstrated hot carrier photovoltaic devices by using a resonant tunneling AlAs/GaAs/AlAs quantum well structure on an AlGaAs absorber at low temperatures, ranging from 93 to 213 K (Dimmock et al., 2014). More recently, enhanced voltage and current in a semiconductor heterostructure due to the presence of hot carrier population in a single InGaAsP quantum well at room temperature has been demonstrated. While these works demonstrate a photovoltaic effect in a hot carrier device, it is still impractical to use as a solar cell. The combination of III-V MQW and bulk material with wide phononic band gap for an absorber and double/triple-barrier resonant tunneling structures for ESCs seems to be a promising route toward the realization of high-efficiency hot carrier solar cell devices. In particular, devices based on HfN absorbers and HfO2/HfNx/ HfO2 DBR for ESCs (or ZrN absorber and ZrO2/ZrNxZrfO2) offer the possibility of making integrated, large-scale fabrications of complete hot carrier devices using thin-film deposition techniques. Colloidal quantum dot solar cells have demonstrated rapid development in the last few years. According to a review of photovoltaic materials (Polman et al., 2016), PbS quantum dot solar cells have increased absolute efficiency by 1.3% every year since 2010, placing it at the second-fastest among all PV technologies. The highest efficiency was reported as 12% (certified) by Sargent’s group at Toronto University in 2018 (Xu et al., 2018). In this work, they developed a PbI2-hybrid-amine complex solution phase passivation to PbS quantum dots, which enabled the fabrication of a thicker absorber at 500 nm, hence increasing Jsc dramatically to 30 mA/cm2, compared to Jsc at 25–26 mA/cm2 from devices fabricated by a solid-state ligand exchange (Wang et al., 2018; Hu et al., 2018). However, compared with other high-efficiency thin-film solar cells such as perovskite, CdTe, and CIGS, the best PbS quantum dot solar cell, with a Voc at 650 mV, still has a very large voltage loss at 0.45 V and a FF at 64% is well below the theoretical value (Xu et al., 2018; Polman et al., 2016). This may be because the quantum dots have a 10%–15% size distribution that results in a distribution of band-gap energies. The low value of the product of Voc and FF indicates poor carrier collection in the device, which is attributed to the insufficient surface passivation of the quantum dots. As the surface-to-volume ratio in the quantum dots is extremely high, further improvement in surface passivation will be key to reducing defect density and nonradiative surface recombination, hence increasing device performance.
210 Chapter 6 In terms of the device structure, there is still room for improvement. As shown in Fig. 6.10C and discussed earlier in this chapter, the band energy levels in the current PbS quantum dot solar cells do not align well to produce a strong electric field by the difference of Fermi levels of the electron transport and hole transport layers. Further deepening Fermi levels of the hole transport layer and raising Fermi levels of the electron transport layer will enhance the built-in electric field to generate stronger driving forces for the carriers to transport more efficiently. This is particularly important in order for short-diffusion-length materials like quantum dot films to improve device performance.
References Aliberti, P., et al., 2010. Investigation of theoretical efficiency limit of hot carriers solar cells with a bulk indium nitride absorber. J. Appl. Phys. 108 (9). pp. 094507(1−10). Aliberti, P., et al., 2011. Effects of non-ideal energy selective contacts and experimental carrier cooling rate on the performance of an indium nitride based hot carrier solar cell. Appl. Phys. Lett. 99 (22). pp. 223507(1–3). Bazhanov, D.I., et al., 2005. Structure and electronic properties of zirconium and hafnium nitrides and oxynitrides. J. Appl. Phys. 97. pp. 044108 (1–6). Beard, M.C., 2011. Multiple exciton generation in semiconductor quantum dots. J. Phys. Chem. Lett. 2 (11), 1282–1288. Beard, M.C., et al., 2010. Comparing multiple exciton generation in quantum dots to impact ionization in bulk semiconductors: Implications for enhancement of solar energy conversion. Nano Lett. 10 (8), 3019–3027. Brennan, K.F., Summers, C.,.J., 1987. Theory of resonant tunnelling in a variably spaced multiquantum well structure: An Airy function approach. J. Appl. Phys. 61 (2), 614–623. Brown, P.R., et al., 2014. Energy level modification in lead sulfide quantum dot thin films through ligand exchange. ACS Nano 8 (6), 5863–5872. Brus, L.E., 1984. Electron-electron and electron-hole interactions in small semiconductor crystallites: the size dependence of the lowest excited electronic state. J. Chem. Phys. 80 (9), 4403–4409. Cao, W., et al., 2016. Quantification of hot carrier thermalization in PbS colloidal quantum dots by power and temperature dependent photoluminescence spectroscopy. RSC Adv. 6 (93), 90846–90855. Carey, G.H., et al., 2015. Colloidal Quantum Dot Solar Cells. Chem. Rev. 115 (23), 12732–12763. Chen, F., et al., 2003. Time-resolved spectroscopy of recombination and relaxation dynamics in InN. Appl. Phys. Lett. 83 (24), 4984–4986. Christensen, A.N., et al., 1979. Phonon anomalies in transition-metal nitrides: ZrN. Phys. Rev. B 19 (11), 5699–5703. Christensen, A.N., et al., 1983. Phonon anomalies in transition-metal nitrides: HfN. Phys. Rev. B 28 (2), 977–981. Chuang, C.-H.M., et al., 2014. Improved performance and stability in quantum dot solar cells through band alignment engineering. Nat. Mater. 13 (8), 796–801. Conibeer, G., et al., 2003. Selective energy contacts for potential application to hot carrier PV cells. In: Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, pp. 2730–2733. Conibeer, G., et al., 2008. Selective energy contacts for hot carrier solar cells. Thin Solid Films 516 (20), 6968–6973. Conibeer, G., et al., 2009. Progress on hot carrier cells. Solar Energy Mater. Solar Cells 93, 713–719. Conibeer, G., et al., 2015. Hot carrier solar cell absorber prerequisites and candidate material systems. Solar Energy Mater. Solar Cells 135, 124–129. Conibeer, G., et al., 2017. Towards an understanding of hot carrier cooling mechanisms in multiple quantum wells. Jpn. J. Appl. Phys. 091201 (1–8). Davis, N.J.L.K., et al., 2015. Multiple-exciton generation in lead selenide nanorod solar cells with external quantum efficiencies exceeding 120%. Nat. Commun. 6 (1), 8259.
Solar Cells Based on Hot Carriers and Quantum Dots 211 Davydov, V.Y., et al., 1997. Experimental and theoretical studies of phonons in hexagonal InN. Appl. Phys. Lett. 75 (21), 3297–3299. Debnath, R., et al., 2010. Ambient-processed colloidal quantum dot solar cells via individual pre-encapsulation of nanoparticles. J. Am. Chem. Soc. 132 (17), 5952–5953. Dimmock, J.A.R., et al., 2014. Demonstration of a hot-carrier photovoltaic cell. Progr. Photovolt. Res. Appl. 22, 151–160. Feng, Y., et al., 2012. Non-ideal energy selective contacts and their effect on the performance of a hot carrier solar cell with an indium nitride absorber. Appl. Phys. Lett. 100 (5). pp. 053502(1–4). Feng, Y., et al., 2013. Investigation of carrier-carrier scattering effect on the performance of hot carrier solar cells with relaxation time approximation. Appl. Phys. Lett. 102 (24). 243901(1–5). Green, M.A., 2003. Third Generation Photovoltaics: Advanced Solar Energy Conversion. Springer-Verlag. Guillemoles, J.-F., et al. (2006). Proceedings of 21st European Photovoltaic Solar Energy Conference, (Dresden Germany), pp. 234–237. Hartland, G.V., 2010. Ultrafast studies of single semiconductor and metal nanostructures through transient absorption microscopy. Chem. Sci. 1 (3), 303–309. Hines, M.A., Scholes, G.D., 2003. Colloidal PbS nanocrystals with size-tunable near-infrared emission: observation of post-synthesis self-narrowing of the particle size distribution. Adv. Mater. 15 (21), 1844–1849. Hirst, L., et al., 2014. Experimental demonstration of hot-carrier photo-current in an InGaAs quantum well solar cell. Appl. Phys. Lett. 104 (23). pp. 231115(1–4). Hoye, R.L.Z., et al., 2014. Improved open-circuit voltage in ZnO-PbSe quantum dot solar cells by understanding and reducing losses arising from the ZnO conduction band tail. Adv. Energy Mater. 4 (8), 1301544–1301549. Hu, L., et al., 2018. Achieving high-performance PbS quantum dot solar cells by improving hole extraction through Ag doping. Nano Energy 46, 212–219. Humphrey, T.E., et al., 2002. Reversible quantum brownian heat engines for electrons. Phys. Rev. Lett. 89 (11). pp. 116801 (1–4). Ip, A.H., et al., 2012. Hybrid passivated colloidal quantum dot solids. Nat. Nanotechnol. 7 (9), 577–582. Jasieniak, J., Califano, M., Watkins, S.E., 2011. Size-dependent valence and conduction band-edge energies of semiconductor nanocrystals. ACS Nano 5 (7), 5888–5902. Johnston, K.W., et al., 2008. Schottky-quantum dot photovoltaics for efficient infrared power conversion. Appl. Phys. Lett. 92 (15). pp. 151115. Jung, H.K., et al., 1996. Impact ionization model for full band Monte Carlo simulation in GaAs. J. Appl. Phys. 79 (5), 2473–2480. Kim, S., et al., 2015. Air-stable and efficient PbSe quantum-dot solar cells based upon ZnSe to PbSe cationexchanged quantum dots. ACS Nano 9 (8), 8157–8164. Kirmani, A.R., et al., 2017. Molecular doping of the hole-transporting layer for efficient, single-step-deposited colloidal quantum dot photovoltaics. ACS Energy Lett. 2 (9), 1952–1959. Klemens, P.G., 1966. Anharmonic decay of optical phonons. Phys. Rev. 148 (2), 845–848. Konig, D., et al., 2012. Technology-compatible hot carrier solar cell with energy selective hot carrier absorber and carrier-selective contacts. Appl. Phys. Lett. 101 (15). pp. 153901(1–4). Kramer, I.J., Sargent, E.H., 2014. The architecture of colloidal quantum dot solar cells: materials to devices. Chem. Rev. 114 (1), 863–882. Kroupa, D.M., et al., 2017. Synthesis and spectroscopy of silver-doped PbSe quantum dots. J. Am. Chem. Soc. 139 (30), 10382–10394. Labelle, A.J., et al., 2015. Colloidal quantum dot solar cells exploiting hierarchical structuring. Nano Lett. 15 (2), 1101–1108. Le Bris, A. and Guillemoles, J.-F. (2010). Hot carrier solar cells: Achievable efficiency accounting for heat losses in the absorber and through contacts. Appl. Phys. Lett. 97 (11), pp. 113506(1–3). Liu, M., et al., 2017. Hybrid organic-inorganic inks flatten the energy landscape in colloidal quantum dot solids. Nat. Mater. 16 (2), 258–263. Luther, J.M., et al., 2008. Schottky solar cells based on colloidal nanocrystal films. Nano Lett. 8 (10), 3488–3492.
212 Chapter 6 Ma, W., et al., 2009. Photovoltaic devices employing ternary PbSxSe1−x nanocrystals. Nano Lett. 9 (4), 1699–1703. Milliron, D.J., 2014. Quantum dot solar cells: the surface plays a core role. Nat. Mater. 13 (8), 772–773. Mocatta, D., et al., 2011. Heavily doped semiconductor nanocrystal quantum dots. Science 332 (6025), 77–81. Moreels, I., et al., 2009. Size-dependent optical properties of colloidal PbS quantum dots. ACS Nano 3 (10), 3023–3030. Murray, M.B., et al., 1993. Synthesis and characterization of nearly monodisperse CdE(E = sulfur, selenium, tellurium) semiconductor nanocrystallites. J. Am. Chem. Soc. 115 (115), 8706–8715. Murray, C.B., Kagan, C.R., Bawendi, M.G., 2000. Synthesis and characterization of monodisperse nanocrystals and close-packed nanocrystal assemblies. Annu. Rev. Mater. Sci. 30 (1), 545–610. Ning, Z., et al., 2014. Air-stable n-type colloidal quantum dot solids. Nat. Mater. 13 (8), 822–828. Oh, S.J., et al., 2013. Stoichiometric control of lead chalcogenide nanocrystal solids to enhance their electronic and optoelectronic device performance. ACS Nano 7 (3), 2413–2421. Padilha, L.A., et al., 2013. Carrier multiplication in semiconductor nanocrystals: Influence of size, shape, and composition. Acc. Chem. Res. 46 (6), 1261–1269. Pattantyus-Abraham, A.G., et al., 2010. Depleted-heterojunction colloidal quantum dot solar cells. ACS Nano 4 (6), 3374–3380. Peterson, M.D., et al., 2014. The role of ligands in determining the exciton relaxation dynamics in semiconductor quantum dots. Annu. Rev. Phys. Chem. 65 (1), 317–339. Polman, A., et al., 2016. Phtovoltaic materials: present efficiencies and future challenges. Science 352 (6283), 307–318. Pomeroy, J.W., et al., 2005. Phonon lifetimes and phonon decay in InN. Appl. Phys. Lett. 86 (22). pp. 223501(1–3). Price, M.B., et al., 2015. Hot-carrier cooling and photoinduced refractive indexchanges in organic-inorganic lead halide perovskites. Nat. Commun. 6, 8420. Rosenwaks, Y., 1993. Hot-carrier cooling in GaAs: Quantum wells versus bulk. Phys. Rev. B 48, 14675–14678. Ross, R., Nozik, A.J., 1982. Efficiency of hot-carrier solar energy converters. J. Appl. Phys. 53 (5), 3813–3818. Sadakuni, K., et al., 2009. CaF2/Fe3Si/CaF2 ferromagnetic resonant tunneling diodes on Si(111) by molecular beam epitaxy. Appl. Phys. Expr. 2 (6). pp. 063006(1–3). Saha, B., et al., 2010. Electronic structure, phonons, and thermal properties of ScN, ZrN, and HfN: a firstprinciples study. J. Appl. Phys. 107, pp. 033715(1–8). Semonin, O.E., Luther, J.M., Beard, M.C., 2012. Quantum dots for next-generation photovoltaics. Mater. Today 15 (11), 508–515. Shabaev, A., Efros, A.L., 2013. Dark and photo-conductivity in ordered array of nanocrystals. Nano Lett. 13 (11), 5454–5461. Shabaev, A., Efros, A.L., Nozik, A.J., 2006. Multiexciton generation by a single photon in nanocrystals. Nano Lett. 6 (12), 2856–2863. Shanavas, K.V., et al., 2016. Electronic structure and electron-phonon coupling in TiH2. Scientific Report 6, p. 28102. Shockley, W., Queisser, H.J., 1961. Detailed balance limit of efficiency of p-n junction solar cells. J. Appl. Phys. 32 (3), 510–519. Shrestha, S.K., et al., 2010. Energy selective contacts for hot carrier solar cells. Solar Energy Mater. Solar Cells 94, 1546–1550. Shrestha, S.K., et al., 2017. Potential of HfN, ZrN, and TiH as hot carrier absorber and Al2O3/Ge quantum well/ Al2O3 and Al2O3/PbS quantum dots/Al2O3 as energy selective contacts. J. Jpn. Appl. Phys. 56. 08MA03. Takeda, Y., et al., 2009a. Impact ionization and Auger recombination at high carrier temperature. Solar Energy Mater. Solar Cells 93 (6–7), 797–802. Takeda, Y., et al., 2009b. Hot carrier solar cells operating under practical conditions. J. Appl. Phys. 105 (7). pp. 074905(1–8). Takeda, Y., et al., 2010. Practical Factors Lowering Conversion Efficiency of Hot Carrier Solar Cells. Appl. Phys. Expr. 3 (10). pp. 104301.
Solar Cells Based on Hot Carriers and Quantum Dots 213 Tang, J., et al., 2011. Colloidal-quantum-dot photovoltaics using atomic-ligand passivation. Nat. Mater. 10 (10), 765–771. Veettil, B.P., et al., 2010. Impact of disorder in double barrier QD structures on energy selectivity investigated by two dimensional effective mass approximation. Energy Procedia 2 (1), 213–219. Voznyy, O., et al., 2012. A charge-orbital balance picture of doping in colloidal quantum dot solids. ACS Nano 6 (9), 8448–8455. Wang, R., 2016. Colloidal quantum dot ligand engineering for high performance solar cells. Energ. Environ. Sci. 9, 1130–1143. Wang, X., et al., 2011. Tandem colloidal quantum dot solar cells employing a graded recombination layer. Nature Photon. 5 (8), 480–484. Wang, P., et al., 2017. Hot carrier transfer processes in nonstoichiometric titanium hydride. Jpn. J. Appl. Phys. 56. 08MA10. Wang, Y., et al., 2018. In situ passivation for efficient PbS quantum dot solar cells by precursor engineering. Adv. Mater. 30 (16), 1704871–1704878. Weidman, M.C., et al., 2014. Monodisperse, air-stable PbS nanocrystals via precursor stoichiometry control. ACS Nano 8 (6), 6363–6371. Würfel, P., 1997. Solar energy conversion with hot electrons from impact ionisation. Solar Energy Mater. Solar Cells 46, 43–52. Würfel, P., et al., 2005. Particle conservation in the hot-carrier solar cell. Progr. Photovolt. Res. Appl. 13, 277–285. Xu, J., et al., 2018. 2D matrix engineering for homogeneous quantum dot coupling in photovoltaic solids. Nat. Nanotechnol. 13, 456–462. Yang, Y., et al., 2016. Observation of a hot-phonon bottleneck in lead-iodide perovskites. Nature Photon. 10, 53–59. Yang, J., et al., 2017. Acoustic-optical phonon up-conversion and hot-phonon bottleneck in lead-halide perovskites. Nat. Commun. 8. 14120. Yuan, M., et al., 2014. High-performance quantum-dot solids via elemental sulfur synthesis. Adv. Mater. 26 (21), 3513–3519. Yuan, L., et al., 2015. Air-stable PbS quantum dots synthesized with slow reaction kinetics via a PbBr2 precursor. RSC Adv. 5 (84), 68579–68586. Zhang, J., et al., 2014a. Diffusion-controlled synthesis of PbS and PbSe quantum dots with in situ halide passivation for quantum dot solar cells. ACS Nano 8 (1), 614–622. Zhang, J., et al., 2014b. PbSe quantum dot solar cells with more than 6% efficiency fabricated in ambient atmosphere. Nano Lett. 14 (10), 6010–6015. Zhang, Z., et al., 2015. Effect of halide treatments on PbSe quantum dot thin films: stability, hot carrier lifetime, and application to photovoltaics. J. Phys. Chem. C 119 (42), 24149–24155. Zhang, Z., et al., 2017. A new passivation route leading to over 8% efficient PbSe quantum-dot solar cells via direct ion exchange with perovskite nanocrystals. Adv. Mater. 29 (41). p. 1703214.
Further Reading Lugli, P., Goodnick, S.M., 1987. Nonequilibrium longitudinal-optical phonon effects in GaAs-AlGaAs quantum wells. Phys. Rev. Lett. 59 (6), 716–719. Ridley, B.K., 1999. Quantum Processes in Semiconductors. Oxford University Press. Shah, J., 1986. Hot carriers in quasi-2-D polar semiconductors. IEEE J. Quantum Electron 22 (9), 1728–1743. Yu, P.Y., Cardona, M., 1996. Fundamentals of Semiconductors: Physics and Materials. Springer.