The electrical and optical properties of kesterites

Kesterite Cu2ZnSn(SxSe1-x)4 (CZTSSe) semiconductor materials have been extensively studied over the past decade, however despite significant efforts, the open circuit voltage remains below 60% of the theoretical maximum. Understanding the optical and electrical properties is critical to explaining and solving the voltage deficit. This review aims to summarize the present knowledge of optical and electrical properties of kesterites and specifically focuses on experimental data of intrinsic defects, charge carrier density and transport, and minority carrier lifetime and related rate-limiting recombination mechanisms. It concludes with suggestions for further investigation of the electrical and optical properties of kesterite materials.


Introduction
The high interest in kesterite Cu 2 ZnSn(S x Se 1-x ) 4 (CZTSSe) absorber materials for thin film solar cells is a result of a high absorption coefficient of ∼10 4 cm −1 , the opportunity for band gap tuning in the range of 1-1.5 eV, as well as from the earth-abundant and non-toxic nature of the constituent elements [1]. However, despite a growing research body, the open circuit voltage (V OC ) characteristics of the best kesterite solar cells remain at only 60% of the maximum achievable value under the terrestrial solar spectrum. Carrier recombination in the bulk and a high recombination rate at the absorber-buffer interface are considered as the main sources of the large V OC deficit. The bulk recombination involves the extended band tail states, and deep intrinsic defect levels which result in strong non-radiative recombination evidenced by the low luminescence yield and short minority carrier lifetime in kesterite materials [2][3][4][5].
It is known, that CZTSSe crystallizes in the disordered kesterite structure, where the 2d -Wyckoff positions

Intrinsic defects in kesterites
Experimental and theoretical studies of kesterites have identified intrinsic point defects and associated band tailing as the key limiting factors behind the large V OC deficit [3,[24][25][26]. PL and admittance spectroscopy (AS) are the most used experimental methods to study defects in kesterites. PL studies have shown that most of the kesterite materials show properties that are typical for highly doped and compensated semiconductors [2,5,[27][28][29]. In kesterites, the high doping originates from the very high concentration of charged intrinsic defects (>10 20 cm −1 ) that cause widening of the defect levels within the forbidden gap and induce the spatial potential fluctuations and formation of band tails. In a p-type material and in the case of a small effective mass for electrons, like in kesterites, radiative recombination can mainly arise from four different channels: band-to-tail recombination (BT), that comprises a free electron and a hole that is localised in the valence band tail; band-toband recombination (BB), that involves a free electron and a free hole, band-to-impurity (BI) recombination that involves an acceptor state that is deep enough not to overlap with the valence band tail, and donor-acceptor pair (DAP) recombination that involves an acceptor and a donor state that are deep enough not to overlap with the corresponding band tails. All these recombination pathways have been detected in the PL studies of kesterites. In addition to the spatial electrostatic potential fluctuations, detrimental band gap fluctuations due to the structural Cu-Zn disorder and compositional inhomogeneities are present in kesterites, reducing the V OC of the corresponding solar cell devices. One should be aware that the characteristic length of bandgap fluctuations can exceed the typical size of the potential well caused by electrostatic potential fluctuations, allowing localization of electrons in potential minima of the conduction band edge. Typical schematic presentation of a band structure involving both electrostatic and band gap fluctuations is presented in figure 1. Bandgap and electrostatic potential fluctuations contribute to the band tails with a resulting average depth of fluctuations γ that is a combination of both: , where γ E and γ B correspond to the average depth of electrostatic potential and bandgap fluctuations, respectively (see figure 1) [30]. These fluctuations usually determine the asymmetric shape of PL bands, where the shape of the low energy side of the PL spectra is determined by the density of states function. In kesterite samples, γ values in the range γ≈25-80 meV were found [2,3,5,29,[31][32][33][34][35]. Typical low-temperature measurements for kesterites show a broad peak with increasing width and assymmetry for higher sulfur concentrations as shown in figure 2(a). Figure 2(b) presents a strong dependence of the PL peak emission energy on excitation power commonly observed in kesterites, which is a clear indicator of potential or band gap fluctuations.
There are few publications where very shallow defect levels in CZTSe were measured [36,37], but a vast majority of PL bands measured in kesterites are further away from the band gap and show an asymmetric and quite wide shape (full width at half maximum >100 meV). In most cases, the dominant recombination is related to the BI transition where free electrons recombine with holes captured by deep acceptor levels. Also band to tail (BT) and band to band (BB) processes have been detected in kesterites [38][39][40][41][42]. In addition, the quasi donoracceptor pair recombination model is proposed in numerous publications [5,41,43,44]. The word 'quasi' is used to indicate the deviation from the classical DAP model due to interactions between defects. In the case of deep enough acceptor and donor defect levels a different recombination process is possible-deep donor-deep acceptor (DD-DA) pair recombination. DD-DA recombination was detected in many chalcopyrite compounds [45][46][47] and recently also in CZTS [48].
Theoretical calculations [24,49] have predicted a low formation energy of several defect clusters in kesterites which may cause a highly localized reduction of the bandgap energy. These defect clusters are likely to be detrimental to device performance, and their presence has been suggested as the dominant recombination pathway for CZTS using low temperature PL [50].
AS, capacitance-voltage, and drive level capacitance profiling (DLCP) have been applied on kesterite semiconductors for the determination of defect transition levels as well as the quantification of deep defects and the doping density (N A,a ). Figure 3 shows typical admittance data of a Cu 2 ZnSnSe 0.4 S 0.6 kesterite solar cell with ∼9% efficiency [51]. At low temperatures the capacitance approaches the geometric capacitance due to freeze-out of mobile carriers in the absorber. With increasing temperature two distinct capacitance steps are observed. In the case of a classical semiconductor the first step in the capacitance is interpreted with the dielectric turn-on due to shallow dopants, leveling at the capacitance given by the space-charge region. Capacitance steps occuring at higher temperatures are commonly interpreted as deep defects [5]. In kesterites, this first step is typically observed at significantly higher temperatures than in related semiconductor materials such as Cu(In,Ga)Se 2 [52]. This has been explained  with a large series resistance in kesterites at low temperatures arising from either too deep acceptors [53] or a barrier at the back contact [54]. A high series resistance alone, even if temperature independent, could lead to a capacitance step due to circuit response if an inadequate equivalent circuit model is used [55], emphasizing the need to use appropriate models to analyze admittance measurements [5,56,57]. In the literature no complete agreement on this phenomenon is found, e.g. in [58] it was found that the series resistance and the first capacitance step have similar activation energies varying between 20 and 100 meV depending on the kesterite's annealing conditions, while in [5] it was found that the activation energies were different. In some cases two overlapping steps at low temperature can be observed [58,59], which however cannot be distinguished in the measurement shown in figure 3(a). Distinguishing multiple steps at low temperature may require deconvolution techniques [58] and can also be strongly influenced by the measurement conditions, i.e. light exposure or carrier injection [59]. The second capacitance step seen in figure 3(a) associated with deep defects has been found to depend on material parameters, such as composition [51] and annealing conditions [21]. Therefore, it is difficult to generalize results found in literature, and all these parameters and conditions have to be taken into account. Energy levels of intrinsic defects in kesterites determined by AS method are summarized in table 1, mostly reporting activation energies >50 meV. This is consistent with the large formation energy of shallow copper vacancies predicted by DFT in kesterite, which suggest the deeper Cu Zn antisite to be the dominant hole donating acceptor level and also a higher carrier-freeze out temperature.
In order to determine the free charge carrier density from admittance measurements or capacitance-voltage profiling, the measurement conditions (temperature and frequency) should be chosen such that the space charge capacitance but not the capacitance due to deep defects is evaluated. Most authors interpret the capacitance above the first step (grey shading in figure 3(a)) as the space charge capacitance [5,21,53,58,60]. Thus for kesterites, typical measurement conditions to obtain the free carrier density range from (200 K, 1 kHz used in [58]) to (300 K, 100 kHz, used in [51]), which according to figure 3 is expected to yield identical results. Please note that if this first capacitance step would be due to a barrier, the capacitance-voltage profiling with parameters targeting at this plateau still give the correct carrier density, while the space charge region would be slightly overestimated, due to the effect of the barrier [52]. Frequency-dependent capacitance-voltage profiles performed at room-temperature often yield a strong dispersion for kesterites, which indicates that deep defects may be present and respond in the capacitance measurement at lower frequencies [51]. A comparison of the free-carrier densities deduced from capacitance-voltage profiling under different measurement conditions are reported in table S1 (supplementary information available online at stacks.iop.org/JPENERGY/1/044002/ mmedia), and (selectively) plotted together with Hall effect results in figure 5 of section 4 further below.
An overview of the defect levels in kesterite materials determined by PL and admittance measurements as well as from the photoconductivity (σ (T)), photocapacitance (TPC) and surface photovoltage (SPV) measurements, is given in table 1. In most publications defect levels deduced from either PL or AS methods are reported, while in [5] a defect level diagram for the solid solution Cu 2 ZnSnS x Se 1-x with (0<×<1) was constructed from combined PL and admittance measurements. This study proposed the presence of a shallow defect and a deep defect with relatively constant transition levels on an absolute scale, but varying with respect to the valence band edge, because of the upward shift of the valence band maximum with increasing selenium content [5].
According to first-principles calculations the antisite defect Cu Zn has the lowest formation energy and it contributes the most to the p-type conductivity in the stoichiometric kesterites CZTS and CZTSe [24]. The  Table 1. Experimentally determined energy levels of intrinsic defects in kesterites.
TPC [84] highest solar cell efficiencies have been achieved at low Cu and high Zn compositions which should decrease the formation of Cu Zn and promote the formation V Cu . The Zn-rich and Cu-poor compositions of CZTS and CZTSe should also help to avoid the formation of detrimental Sn-related deep defects such as Cu Sn , Sn Cu and Sn Zn and associated defect complexes.
A classification system of kesterites based on stoichiometry has been proposed by Lafond et al [85] and Gurieva et al [86] and includes 12 types corresponding to various defect complexes necessary to achieve a given deviation from stoichiometry (i.e. Cu poor+Zn rich=[V cu +Zn Cu ]). These concepts and the existence of various stoichiometries modifying defect complexes has been verified via neutron diffraction [86]. It is important to emphasize however, that the defect structure depends not only on the elemental composition but also on the the post-growth cooling process or additional thermal treatments which modify the degree of Cu-Zn disordering in kesterites [9]. It has been shown that with reduced disordering, there is a change in the dominant radiative recombination process, involving deeper defects in the case of a less disordered material [34]. This can be one reason why reduced Cu-Zn disordering does not lead to significant improvement in the device performance. More systematic defect studies that would correlate the intrinsic defects in kesterites to the device performance are needed.

The minority carrier lifetime in kesterites
The minority carrier lifetime (τ) is a critical parameter to evaluate when quantifying absorber quality in semiconductors. This parameter is a measure of the net recombination rate of minority carriers in a material. Consequently, τ is directly related to the quasi-fermi level splitting of an absorber and thus the open-circuit voltage (V OC ) of corresponding devices-a parameter of particular concern for kesterites. Therefore, investigations into the low V OC in kesterites greatly benefit from (i) accurately determining τ and (ii) determining the rate-limiting recombination mechanism which governs τ.
However, τ cannot be directly measured for a given material, requiring extraction from measurements such as luminescence/photoconductivity/photovoltage decay or quantitative luminescence. For highly defective materials such as kesterites, complex carrier transport and dynamics as well as high recombination rates make accurate extraction of τ quite challenging. For this reason, early reports of τ for kesterite materials suggested reasonably large values between 1 and 20 ns; a comprehensive overview of τ values reported for kesterites can be found in [4]. However, recent work indicates that the real minority carrier lifetime in kesterite materials is in the sub-nanosecond regime [4,87]. Quantitative PL [4], time-resolved terahertz spectroscopy (TRTS) [87,88], and device simulation [4,89] independently suggest τ values of a few hundred picoseconds. Therefore, it seems that a low minority carrier lifetime is a present limit to further advances in kesterite device performance. Presently, defect recombination in the bulk kesterite material via non-radiative defects is suspected as the culprit for the high recombination rate/low lifetime [90], illustrated in figure 4. Therefore, developing formation pathways that reduce defect formation, exploring novel defect passivation schemes, or further advancing cation replacement strategies are transformative opportunities for the next-generation of high-efficiency kesterite photovoltaics. . Schematic representation of various recombination mechanisms which contribute to the minority carrier lifetime in kesterites, and their relative impact. τ Trap is the trapping/de-trapping time, τ surface is the surface recombination lifetime, τ rad is the radiative lifetime in low injection, and τ nr is the non-radiative lifetime.

Measuring a sub-picosecond lifetime in CZTSSe
To accurately determine the minority carrier lifetime for kesterites, a combination of techniques with consistent results has been used. This strategy is recommended for such non-ideal or early stage materials where numerous electron-defect interaction pathways need to be distinguished. Time-resolved photoluminescence (TRPL) is a common measurement tool used to extract τ, where the characteristic PL decay time is often equated to the minority carrier lifetime. However, for kesterites several factors have demonstrated that the PL decay time is an unreliable estimate for the minority carrier lifetime. First, reported PL decays times between 1 and 20 ns throughout literature do not correlate with the V OC or device efficiency [4]. Second, these reported PL decay times significantly overestimate the expected device performance if interpreted as the lifetime, considering a wide range of simulation parameters [4,89,91]. The reported PL decay times would result in V OC values at 65%-75% of the Shockley-Queisser limit (V OC,Max ) and efficiencies between 14% and 20%. However, corresponding devices have V OC /V OC,Max between 25% and 55% and efficiencies between 1% and 11% [4]. Third, TRPL data measured on devices-at a wide range of bias voltages-generally show negligible bias voltage dependence and/ or no change when measured on bare absorbers or devices [4]. However, the presence of such an electric field is expected to have a dramatic effect on the TRPL response time due to charge separation effects. The above arguments are contrary to theoretical expectations from solid state physics. In addition to this, experimental TRPL data for kesterites are generally reported over a small decay range due to the low signal associated with this material (generally around 1 order of magnitude of signal decay), which makes accurate fitting and interpretation difficult [4]. Furthermore, a limited instrument response function in TRPL measurements can obscure fitting of decay times below about 1 ns.
Recent work using high-resolution intensity-and temperature-dependent TRPL has shown that the characteristic PL decay times for kesterites can commonly be attributed to trapping/de-trapping processes in the material rather than the minority carrier lifetime [4,92]. Trapping is also observed in TRTS measurements [88,93]. The mechanism and defects involved with this minority carrier trapping is an active area of research [94][95][96][97]. Similar results can be expected from photoconductivity decay, photovoltage decay, and related measurements, which probe the decay of excess carriers. In certain cases, trapping/de-trapping may not dominate the decay signal of minority carriers and the recombination lifetime may indeed be measured-as found for CZTS, CZTSe, and CZTSSe single crystals, for example [87,88,98]. However, these cases validate the sub-nanosecond lifetime conclusion for kesterites and alternative high time-resolution measurement techniques are needed such as TRTS. The effect of trapping in kesterite thin films can be mitigated in measurements which probe the excess carrier decay through saturation of trap states at elevated excitation intensities or elevated temperatures during measurement [92,99], however high time-resolution measurement techniques would still be needed to extract τ for kesterites due to fast recombination rates.
As an alternative to carrier decay measurements, the minority carrier lifetime can be extracted from quantitative luminescence analysis. In this approach, τ is related to the internal PL efficiency (η PL ) following η PL =τBp 0 where B is the radiative recombination coefficient and p 0 is the free carrier density [4]. For kesterites, relatively low internal PL efficiencies (e.g. η PL <0.01% ) are ubiquitous-even for state-of-the-art absorbers. Quantitative analysis indicates that a sub-nanosecond lifetime is responsible for the low PL efficiency found in this material.

Determining the origin of rate limiting recombination
As τ reflects the net recombination of carriers, this parameter can vary widely [100] depending on the origin of limiting recombination. Therefore, it is important to rule out various loss mechanism to determine where efforts should be applied to improve τ. For kesterites, various limiting loss mechanisms have been proposed. First, interface recombination was suggested early on as a significant contributor to the V OC deficit in kesterites [54,90,101]. However, the impact of interface recombination may be misinterpreted in kesterites due to the impact of non-ideal device behavior in data analysis [17,26]. To achieve a sub-nanosecond recombination lifetime at the absorber surface (τ Surface ), a surface recombination velocity (S F ) greater then about 2×10 5 cm s −1 is necessary (τ Surface ≈thickness/S F ) [102]; however, a positive conduction band offset extends this range to around 10 7 cm s −1 [89,91]. For CZTSe and CZTSSe, detailed transport modelling/measurements [93,103] estimate surface recombination velocities below 5×10 4 cm s −1 , though values above 10 5 cm s −1 are reported for bare absorbers following various surface treatments [104]. Exhaustive failure-mode-and-effectanalysis [90] and device simulations [4,89,91,105] indicate that surface recombination is not the dominant loss mechanism for CZTSe and CZTSSe absorbers at the current level of device performance. However, surface losses (i.e. a reduced V OC ) may manifest in the device structure due to unfavorable buffer-absorber band alignment-particularly in pure sulfide CZTS, secondary phases at the buffer-absorber interface, interfacial band gap narrowing, and the absence of charge inversion at hetero-interface [90]. However, these factors are distinct from the intrinsic surface and bulk recombination lifetimes of the kesterite absorber.
A general consensus among many kesterite researchers is that limitations in kesterite performance arise from the bulk absorber rather than from its interfaces [90]. Several mechanisms can be responsible for this. First, radiative recombination losses can be disregarded, evident from the low PL yield in this material; a low-injection radiative lifetime (Bp 0 ) of a few hundred nanoseconds can be expected for CZTSe [4]. This leaves non-radiative losses as a dominant recombination path in the bulk kesterite material. While band tails/potential fluctuations have been significantly studied and observed in kesterites, their role in non-radiative recombination is not straightforward. For shallow defect states to efficiently participate in recombination, their energetic position must lie within the demarcation levels for holes and electrons; shallow defects near the band edges will act as trap centers while deeper defects can participate in recombination. For kesterites, reports vary for the degree of potential fluctuations into the energy gap. Early studies suggest a relatively deep penetration of potential fluctuations into the energy gap which efficiently participate in tunneling-enhanced recombination [17,26], while recent work suggest shallow potential fluctuations which are not expected to act as efficient recombination centers [4]. However, shallow defects have been suggested to significantly enhance non-radiative recombination through a multistep process [97]. Further work is needed to quantify the role of potential fluctuations/bandtailing on the minority carrier lifetime in kesterites. Next, grain boundary recombination has been reported to contribute to bulk recombination of carriers [90]. Lastly, a more traditional non-radiative recombination mechanism through deep defects in the bulk are expected to play an important role in explaining the significant non-radiative losses measured in kesterites [90,95]. A relative comparison of the various loss mechanisms discussed here-in is illustrated in the energy band diagram shown in figure 4.

Charge carrier transport in kesterites
Carrier transport properties including carrier type, density and mobility are of fundamental importance to all optoelectronic devices. In solar cells, the carrier type (p or n), will determine the device architecture, the majority carrier density affects recombination lifetime and depletion width, while the carrier mobility, specifically for the minority carriers, affects diffusion length which significantly impacts current collection. For CZTSSe, a range of carrier properties have been reported, which may reflect changes in stoichiometry, doping, fabrication method and sample quality, but may also reflect choice of characterization method.
In figure 5(a) carrier densities obtained from both Hall effect and capacitance-voltage profiling are shown as a function of Cu/(Zn+Sn) content. It can be seen that there is a general trend exhibiting an exponential increase in the carrier density as the Cu/(Zn + Sn) ratio increases linearly. Hall measurements clearly indicate p-type doping for CZTSSe of various compositions. The general correlation of carrier concentration and Cu content is most often ascribed to the dominance of Cu Zn antisite defects, which are predicted to have the lowest formation energy of any defect and provide shallow acceptor states [24]. The defect picture is complicated by extremely high levels of compensated defect complexes, such as [V Cu +Zn Cu ], which enable large variations of stoichiometry without equal levels of free carriers. For stoichiometric material, carrier densities of almost 1×10 19 cm −3 are found. For individual compositions very large deviations can be found, e.g. for the record IBM device with a Cu/(Zn+Sn) = 0.85 and S/(S+Se)=0.25 the carrier density is low 1×10 15 cm −3 [106], while measurements on other samples show up to 1×10 17 cm −3 at the same composition. The data in figure 5 were collected using Hall-effect or capacitance-voltage profiling, which must be performed with distinct sample configurations, the former on absorber layers without back contact, and the latter on a full device structure. Despite the different boundary conditions, the overall agreement is seen to be quite good. Individual samples shown in figure 5(a) may not only vary in copper-content but may also differ somewhat in the Zn/Sn content and sulfur content, and of course sample processing, sodium content, and possibly more. An important point to consider is also that compositional analysis is performed using a variety of different methods in different labs, including inductively coupled plasma mass spectrometry, x-ray fluorescence and energy dispersive x-ray spectroscopy. In addition to calibration challenges and/or different depth bias, these composition measurements usually do not distinguish between the kesterite main phase and the sample composition that includes secondary phases. Thus, similar sample compositions with different secondary phase content may exhibit significantly different compositions of the kesterite phase, as discussed in detail by Just et al [107,108]. Figure 5(b) shows the carrier densities for various samples as a function of S/(S+Se) content for Cu-poor samples. It can be seen that the carrier density varies generally much less than for changing copper content, but tends to decrease for the polycrystalline films with increasing sulfur content, while it slightly increases with sulfur content for the single crystals. The fact that the single crystal values are about an order of magnitude higher and behave different from the polycrystalline films is likely related to the fact the the crystals are nearstoichiometric, compared to the Cu-poor composition of the polycrystalline films. Again, in this figure good overall agreement can be found between carrier densities derived from Hall measurements and those from (room-temperature) capacitance measurements, which indicates that both methods may be reliably applied to estimate charge carrier densities. Best devices typically contain about 20%-30% sulfur and are Cu-poor for which figure 5 would predict a carrier density below 10 16 cm −3 , which indeed has been reported for IBM's champion device [106].
Sodium has been found to be instrumental in increasing the carrier density in Cu-poor Cu(In, Ga)Se 2 , which is achieved either from diffusion of the soda-lime glass or by NaF precursor layers, or post-deposition treatments with NaF [109,110]. The effect of sodium incorporation in CZTSSe has been investigated in several studies on thin films as well as single crystals [111]. In these studies, the increase in the sodium content is generally found to increase the carrier density as measured by Hall effect, although in one recent study a systematic decrease of the carrier density with increasing sodium content was reported [112]. In this study, a NaF layer was deposited and diffused into the absorber after the CZTSe was grown.
For solar cell applications the charge carrier transport to and from electrodes and within the active semiconductor layer plays an important role. The transport of carriers can take place either by drift in electric fields or by diffusion. For both phenomena the carrier mobilities play a decisive role and depending on the type of material and measurement method used can span a very wide range of values from below 1 cm 2 V −1 s −1 for amorphous semiconductors to several thousand cm 2 V −1 s −1 for epitaxial GaAs. Charge carrier mobilities depend on fundamental material properties such as the band structure, in particular the effective masses of the conduction band minimum and valence band maximum, carrier-impurity and carrier-phonon scattering as well as grain boundary scattering, and possible trapping in localized states. Different experimental measurement techniques can be applied to derive the carrier mobility, such as Hall effect [74,[113][114][115][116], Thz spectroscopy (TRTS) [93,[117][118][119][120], or voltage-dependent IQE measurements [17,121]. In contrast to the good agreement of different measurement techniques for the estimation of carrier densities, for carrier mobilities the repercussions of the different required sample geometries often lead to very different results. It is important to stress that the Hall effect is dominated by majority carrier transport while TRTS measurements capture the sum mobility for minority and majority carriers. In a solar cells, on the other hand, carrier transport is generally dominated by minority carriers [93]. In addition, both Hall effect and TRTS are commonly performed on samples without conducting back contact, however for TRTS it has recently been shown that measurements in reflection geometry on back contact substrates also lead to very good results [119]. Figure 6 shows the mobilities as derived from Hall effect and Thz absorption on single crystals (x) and polycrystalline films (px).
Looking at figure 6(a), which displays mobilities as a function of S/(S+Se) content, it is obvious that the carrier mobilities have a huge range of values from about 0.5 cm 2 V −1 s −1 to more than 100 cm 2 V −1 s −1 . A more detailed inspection reveals that the Hall mobilities for the single crystals agree with the TRTS measurements on single crystals as well as TRTS on thin films, while the Hall measurements on polycrystalline films yield much lower values typically below 1 cm 2 V −1 s −1 . This indicates that grain boundary scattering plays a decisive role in the long-range carrier transport, as TRTS measurements in fact probe intragrain transport on a scale of about 30 nm, and single crystals per definition do not have grain boundaries. Overall, the TRTS and Hall measurements on single crystals show a decrease of carrier mobility from pure CZTSe with 140 cm 2 V −1 s −1 to about 10-40 cm 2 V −1 s −1 for the pure sulfide. The larger values of the TRTS measurements compared to Hall in this case can be explained with the fact that Hall measurements probe the majority (hole) mobility and TRTS probes the hole+electron mobility. The true minority carrier mobility can be estimated by substracting the x-Hall values from the TRTS-px values, which leads to values slightly smaller than the TRTS values displayed in figure 6. Majority and minority carrier mobilities have recently been extracted using a new photo-Hall technique [117], as well as from intensity dependent and excitation wavelength dependent TRTS analysis [93]. In the TRTS analysis it was found that for a pure CZTSe polycrystalline layer the electron mobility can be estimated at 140 cm 2 V −1 s −1 while the hole mobility was significantly lower at about 10 cm 2 V −1 s −1 .
As already mentioned grain boundary scattering is expected to affect the carrier mobility, in particular in the case of non-vanishing grain boundary potentials. Comparing the Hall effect hole mobilities measured on single crystals and on polycrystalline thin films in figure 6, we see that grain boundary potentials in kesterites must be larger than kT in order to explain the difference between these measurements. Whether intra-grain transport or transport across grain boundaries is limiting in solar cells strongly depends on the device geometry and sample microstructure i.e. if the grain sizes are large enough (∼500 nm) then carrier absorbed in a single grain most likely do not have to cross a grain boundary in order to reach the pn-junction. On the other hand, for very smallgrained material, grain boundaries may well limit transport processes in the devices.
The effect of Cu-Zn ordering on solar cells has been subject of numerous investigations. Recently, the effect of the amount of disorder present in CZTSe films on the carrier mobility was investigated by TRTS measurements [120]. Here it was found that samples with different degrees of Cu-Zn cation ordering showed no change in the charge carrier mobility, which indicates that the cation-ordering is not the limiting phenomenon for the charge carrier mobility in kesterite Cu 2 ZnSn(S x Se 1-x ) 4 .

Summary and outlook
The optical and electrical properties of kesterite Cu 2 ZnSn(S x Se 1-x ) 4 absorber materials for solar cells have been extensively studied over the past decade and with the evolution of the performance of the solar cells the knowledge about the fundamental physical properties of the kesterites has been improved. From the basic properties, the band structure of kesterite materials has been extensively studied by various experimental methods. It is clear by now that there is direct relationship between the Cu-Zn disorder and the band gap energy of kesterites, an increase in the band gap of about 110 and 200 meV can be obtained by changing the order parameter from 0 to 0.7 in CZTSe and CZTS, respectively. On the other hand, several studies have found no clear correlation between the Cu-Zn disorder and charge carrier mobility as well as the V OC deficit of the solar cells.
The studies of intrinsic defects by different experimental methods have shown the presence of rather deep defect levels within the band gap of kesterites. In addition to the rather deep defect levels, the bulk recombination was found to also involve the extended band tail states. The average depth of the band edge fluctuations was found in the range 25-80 meV. The current understanding is that non-radiative recombination in the bulk kesterite is behind the overall low luminescence yield of these materials leading to a high recombination rate and short carrier lifetime in kesterites.
Recent publications which report that the true minority carrier lifetime in kesterites is in the range of a few hundred picoseconds is of particular concern in improvement of the kesterite solar cell device performance. Therefore, developing formation pathways which reduce defect formation, exploring novel defect passivation schemes, or further advancing cation replacement strategies are transformative opportunities for the nextgeneration of high-efficiency kesterites photovoltaics. Further work is also needed to quantify the role of band edge fluctuations and grain boundaries on the minority carrier lifetime in kesterites.
An overview of the charge carrier transport indicates good agreement between the values of the carrier densities obtained with different characterization techniques despite the fact that they require distinct sample configurations for the measurements. Different conclusions can be made about the determination of the carrier mobility values by using different methods. Comparison of the Hall and Thz spectroscopy results from single crystal and polycrystalline thin film samples indicates that grain boundary scattering plays a decisive role in the long range carrier transport in kesterites, which however is not expected to limit (perpendicular) intragrain transport in absorber layers used in typical thin film solar cells.