Analysis of the Voltage Losses in CZTSSe Solar Cells of Varying Sn Content.

The performance of kesterite (Cu2ZnSn(S,Se)4, CZTSSe) solar cells is hindered by low open circuit voltage ( Voc). The commonly used metric for Voc-deficit, namely, the difference between the absorber band gap and qVoc, is not well-defined for compositionally complex absorbers like kesterite where the bandgap is hard to determine. Here, nonradiative voltage losses are analyzed by measuring the radiative limit of Voc, using external quantum efficiency (EQE) and electroluminescence (EL) spectra, without relying on precise knowledge of the bandgap. The method is applied to a series of Cu2ZnSn(S,Se)4 devices with Sn content variation from 27.6 to 32.9 at. % and a corresponding Voc range from 423 to 465 mV. Surprisingly, the lowest nonradiative loss, and hence the highest external luminescence efficiency (QELED), were obtained for the device with the lowest Voc. The trend is assigned to better interface quality between absorber and CdS buffer layer at lower Sn content.

Kesterite solar cells are a promising earth-abundant alternative to existing thin film photovoltaic technologies.[1] Even though their power conversion efficiencies (PCE) have increased significantly during the past decade from 4% in 2004 to 12.6% in 2014,[2] they still lie far below those of competing technologies like Cu(In,Ga)Se2 and CdTe that have surpassed 22%.[3] One of the major issues is the significant Voc deficit in these devices defined relative to the bandgap Eg of the absorber or relative to the Voc in the Shockley–Queisser limit for the same band gap (Voc,SQ(Eg)).[4] Kesterite devices show a deficit (Eg/q − Voc) larger than 0.55 V whereas competing technologies have reduced these losses to less than 0.4 V.[5] In the literature, the lowest values of Voc deficit in devices have been obtained by means of interfacial and compositional optimization[6,7] with the highest achieved Voc relative to the band gap of a kesterite solar cell being still 0.4 V lower than Voc,SQ.[8]

Several mechanisms have been investigated as the origin for the large voltage losses in CZTSSe solar cells.[9−11] A primary mechanism is thought to be related to the high defect density and associated band tailing of CZTSSe materials,[12,13] which are attributed to the multielement composition nature of the quaternary CZTSSe phase. The similar ionic radii, and comparable valences of elements like copper and zinc, lead to a narrow chemical stability region and multiple defects with low activation energies.[14] The best performing devices have an off-stoichiometric absorber composition, more specifically Cu-poor and Zn-rich. This reduces the formation of detrimental defects like interstitials (Cui and Zni) and [2CuZn + SnZn] antisite clusters that adversely affect the solar cell performance, while increasing the concentration of copper vacancies (VCu), which is a beneficial shallow acceptor.[15,16]

It has been shown that CZTSSe absorbers and related sulfur–selenium alloys crystallize in the kesterite-type structure where the band gap varies from 1.0 eV for pure selenide (CZTSe) to 1.5 eV for pure sulfurized (CZTS), opening the possibility to tailor the band gap of kesterite through the S–Se content. Additionally, the structural instability due to the low enthalpy cost of swapping Cu and Zn atoms in kesterites has also been shown to affect the band gap.[17] In fact, the ordered CZTSe (Cu2ZnSnSe4) has a band gap 100 meV higher than the disordered one.[18] Márquez et al. observed that Cu-poor CZTSe had a higher band gap and Voc, linked to an increased ordering of the Cu/Zn sublattice, while the Voc,def remained constant.[19] Similarly, through annealing procedures with increasing temperatures and subsequent rapid cool-down, a reversible order–disorder transition was shown to occur at a critical temperature of about 200 °C, leading to a band gap shift equivalent to the one observed with the change in Cu content.[20]

The strong dependence of the band gap of kesterite absorbers on their composition and processing condition, coupled with the complexity of quantifying the band gap energy of a disordered system such as CZTSSe,[21] raises the question of whether a Voc loss analysis solely related to the band gap energy gives relevant information concerning the origin of the losses and their dependence on material properties. From the reciprocity principle and the measured external quantum efficiency, Rau et al.[22] introduced a radiative limit for the open circuit voltage that incorporates the actual absorption tail of the materials, as expressed via the external quantum efficiency (EQE) spectrum. On the basis of this work, Yao et al. introduced another way to quantify the losses in solar cells,[23] where they differentiated the losses due to an extended absorption onset (ΔVoc,abs) from the losses due to nonradiative recombination (ΔVoc,nrad), that are dependent on the ratio of radiative to nonradiative recombination rates. This approach was used on organic solar cells to distinguish nonradiative losses from the total losses to indicate how changes in material or processing could bring Voc closer to the radiative limit.[24,25]

In this work we focus on a series of CZTSSe solar cells where compositional variation, namely, the Sn content, was shown to affect Voc, as well as the band gap energy of the absorber in a similar manner to the ordering effect of the Cu/Zn sublattice. We first show how a method relying solely on Eg to quantify the Voc deficit depends strongly on the way Eg is calculated. We then use the method described above developed by Yao et al.[23] to calculate the radiative limit of the voltage (Voc,rad). This approach has never been applied to CZTSSe absorbers, but it proves to be very relevant, since the bandgap cannot be reliably determined by traditional methods, due to material complexity.[21] Surprisingly, we find that this Voc increase with Sn content was accompanied by an increase rather than a decrease of ΔVoc,nrad, indicating a negative effect of the Sn content on the nonradiative relative to radiative recombination rate. By measuring both temperature dependent current voltage characteristic (JV-T) and temperature dependent capacitance-frequency (Cf–T), we discard the hypothesis that this improvement is due to a change in the defect distribution in the absorber structure and show that it can be related to the interfacial quality between the absorber and the buffer layers. The type of analysis presented here is applied to further characterize the different recombination mechanisms that limit the Voc of CZTSSe and other devices and identify optimization routes to increase Voc.

Voltage Loss Calculation Method. For solar cells, Voc is defined by the balance between the absorbed photon flux and the recombination flux. In other words, the recombination current density Jrec and the photocurrent density Jph are equal at open circuit, Jrec(Voc) = Jph(Voc). Using the nonideal diode equation we can typically express Voc aswhere nid is the ideality factor, kB is the Boltzmann constant, q is the elementary charge, and J0 is the dark saturation current density (neglecting any effect of shunt resistance at open circuit). Both J0 and nid depend on the dominant recombination process. The Shockley–Queisser (SQ) limit for the open-circuit voltage is similarly given bywhere Jph,SQ is the photocurrent density in the radiative limit and J0,SQ is the SQ dark saturation current density. In practice, Jph,SQ(Voc) can be replaced by the measured short-circuit current density (Jsc) at the corresponding light intensity. As discussed in ref (23), this assumption introduces a small error in the calculation of the open circuit voltages of some millivolts that can be neglected. The J0,SQ is obtained directly from the band gap Eg following the detailed balance of absorption and emission in solar cell as expressed by Shockley and Queisser:[4]where a step function for the external quantum efficiency at the band gap is assumed. ϕBB is the spectral blackbody emission flux density in the forward direction integrated from the surface of the blackbody at the cell temperature Tcwhich is expressed in units of cm–2 s–1 eV–1. Here h is Planck’s constant and c is the speed of light in vacuum (we consider the refractive index of the external medium surrounding the cell to be ns = 1).[26] Using a similar approach, but considering the actual quantum efficiency of the cell (EQE(E)), we can express the radiative dark saturation current J0,rad as the integral of the EL emission from the cellwhere ϕEL is the spectral photon flux density emitted by the cell. We used Rau’s reciprocity principle to write ϕEL as EQEϕBB for the cell at equilibrium.[22] Away from equilibrium, the excess electroluminescence emission (δϕem(E)) is related to the internal voltage Vint experienced by the cellThus, we can calculate EQE(E) by measuring δϕem(E) at different injection currents and by using the known form of ϕBB(E,T). Since electroluminescence can be measured at deeper photon energies in the tail of absorption than photocurrent, we can use the relation between δϕem(E) and EQE(E) to extend the quantum efficiency spectrum to lower energy by several tenths of an electronvolt beyond the range that is accessible through direct electrical measurement. In practice, it is difficult to quantify the internal voltage of the cell at fixed injection current. Therefore, the EQE(E) spectrum extracted from EL at any applied bias is scaled by a constant factor in order to coincide with edge of the measured quantum efficiency spectrum using a calibrated electrical setup. Using the extended quantum efficiency, measured in this way, we can calculate the achievable voltage if only radiative recombination occurs,where we use the fact that nid = 1 for radiative recombination and let J0 = J0,rad in the radiative limit. We can now express the excess voltage losses due to the dominating nonradiative losses as[22,23]where QELED(Voc) is the electroluminescence quantum efficiency of the solar cell at an applied bias of Voc. The latter expression emphasizes the link between the efficiency of a solar cell and that of a light emitting diode. Excess nonradiative voltage losses are detrimental for the efficiency of solar cells.

In the case where one can accurately measure the band gap of the absorber, we can additionally quantify the excess losses due to a nonsharp absorption onset by calculating the SQ limit for the Voc (Voc,SQ).[4] The abrupt absorption edge considered in the SQ theory does not apply in the presence of sub band gap absorption that is clearly observed in CZTSSe devices. This difference allows the excess absorption open circuit voltage loss to be defined asHowever, for CZTSSe devices where strong band tailing complicates the calculation of the band gap, this equation of ΔVoc,abs will be subject to uncertainty. Nonetheless, the use of Voc,rad to quantify the excess nonradiative losses gives reliable information on the nonradiative voltage losses even when Eg is uncertain.

Synthesis of Absorbers and Device Performance. Photovoltaic devices of structure glass/Mo/CZTSSe/CdS/i-ZnO/Al:ZnO/MgF2 are prepared using CZTSSe absorbers in which the Sn content, measured as nominal atomic percentage (at. %), is controlled by varying the SnCl2 concentration in the precursor solution as presented elsewhere.[27] Devices A, B, C, and D correspond to CZTSSe absorbers with nominal Sn concentrations of 27.6, 29.5, 31.2, and 32.9 at. %, respectively. For lower concentrations the formation of the Cu(S,Se) phase is observed, while the highest Sn content is the limit at which Sn(S,Se) phases started to form. These secondary phases cause performance degradation and shunting of the solar cells. The chemical compositions of the absorber layers were determined by X-ray fluorescence (XRF) measurements (Table S1). The Cu/Sn ratio decreased with increasing Sn content as expected, while the ratios Cu/(Zn + Sn) and Zn/Sn are in the Cu-poor and Zn-rich regions compared to stoichiometric Cu2ZnSn(S,Se)4.[15,16] X-ray diffraction measurements (Figure S1b) confirm decreasing disorder of the Cu/Zn sublattice with Sn increasing content, through the shift of the 008 peak toward higher 2θ values (further details are presented in the Supporting Information). However, such a shift could also be caused by an overlap of different kinetics due to change in composition. Therefore, additional experiments would be required to verify this interpretation.

Current density–voltage (JV) characteristics under AM1.5G simulated solar irradiation show an increase in Voc with Sn content until 31.2 at. % (device C) and a subsequent drop for device D (Table and Figure S2). The poor performance of device D appears to be caused by the formation of a Sn(S,Se) secondary phase, as shown with XRD measurements (Figure S1a), whereas this phase is not detected for the rest of the series. Overall, the PCEs of these devices follow a trend comparable to that of Voc (Figure S2) with the highest efficiency achieved for device C with a PCE of 8.3%. Larramona et al.[28] also observed the existence of an optimal Sn concentration for device performance, above which increasing Sn content causes a reduction in efficiency due to the formation of secondary phases.

Table 2

Summary of the Voltage Loss Analysis for the Four Cells with Different Sn Content

label	Sn content (at. %)	Voc,rad (mV)	Voc (mV)	ΔVoc,nrad (mV)	QELED (%)
A	27.6	799	423	376	5.2 × 10–5
B	29.5	840	453	387	3.3 × 10–5
C	31.2	888	485	403	1.8 × 10–5
D	32.9	904	465	439	4.6 × 10–6

Emission and Absorption Properties. In order to understand the origin of the higher Voc in device C compared to the other devices, we proceeded to measure EL, photoluminescence (PL), and sub-bandgap EQE spectra for all devices. Figure a presents their EL spectra, which originate from photons emitted during recombination of the injected or photoexcited charge carriers, respectively. We note that the slight red-shifted emission of the EL emission compared to the PL emission can be attributed to the Moss–Burstein effect[29] (Figure S10 for the PL). Significantly, when increasing the Sn content from 27.6 to 32.9 at. % a blue shift in both the EL and PL peaks is observed. The strong blue shift in the luminescence upon increasing Sn content suggests either an increase in the band gap of the material, probably related to a reduction in disorder of the kesterite crystal,[18] or a change in properties of emissive defects close to the band edges. For example, a blue shift in luminescence could, in principle, result from an increase in the density of shallow defects near the band edge, such as the VCu + ZnCu defects, relative to the density of deep defects, or a decrease in the density of the ZnCu + CuZn defect.[30,31] A similar blue shift of the band gap upon changing Sn content has been observed in such cells when decreasing the Cu content.[32]

Figure 1

(a) Normalized EL spectra for the four different cells. All EL spectra were acquired using an injection current density of 40 mA cm–2. (b) Measured EQE for the four cells (bold lines) and the extended EQE reconstructed one from their EL spectra (short dashed lines). The full PL spectra are presented in the Supporting Information, Figure S10.

Figure b shows the measured EQE as well as the sub-bandgap EQE spectra reconstructed from the EL measurements using eq . The excellent overlap of the measured EQE curve and the reconstructed EQE curve justifies the use of the method to extend the measured EQE using the luminescence measurement.[33] Importantly, the same blue shift that we observed in the EL and PL with Sn content is observed in the sub-band gap EQE. Notably, the slope of the tail of the reconstructed EQE below the EL peak does not change significantly with increasing Sn content. If we consider a model of tail states below those band gap energies,[34] this suggests that the distribution of these tail states does not change with Sn content.

Comparison of Voltage Losses Analysis. First, we estimate the voltage deficit in these cells by comparing the bandgap with the measured open circuit voltage, as is common in the literature.[32] We estimate the band gap of the cells using two different methods, first from the inflection point of the EQE curve when plotted on a linear axes (Figure S4)13 (Eg,EQE), and second by fitting the EL spectrum (Figure S5,Table S2) using the method developed by Katahara et al.[35] (Eg,EL). The band gaps extracted using these methods differ significantly, as shown in Table , and result in very different trends in the voltage losses; if we rely on Eg from the EQE spectrum, the Voc deficit reaches a minimum for device C, whereas for Eg values derived from EL the losses are similar for the first three devices and increase only for device D (Table ). This emphasizes the difficulty of relying on the band gap to understand the trends in voltage losses with material composition in a disordered material such as CZTSSe.

Table 1

Summary of the Band Gap Loss Analysis for the Four Different Devices

label	Sn content (at. %)	Eg,EQE (eV)	Eg,EL (eV)	Voc (mV)	Voc,def,EQE (mV)	Voc,def,EL (mV)
A	27.6	1.13	1.04	423	707	617
B	29.5	1.14	1.07	453	687	617
C	31.2	1.14	1.11	485	655	625
D	32.9	1.15	1.12	465	685	655

In order to obtain more reliable values for the voltage losses, we calculate Voc,rad of the different cells from the extended EQE spectrum. Table shows the calculated values, showing that Voc,rad increases with increasing Sn content, where the device with the highest Sn content (device D) has a Voc,rad that is 100 meV higher than the device with the lowest Sn content (device A). The trend in Voc,rad is a quantitative reproduction of the observed (qualitative) blue shift in the EQE onset as well as the EL and PL peak seen in Figure and can be understood as an increase in the maximum achievable Voc in the radiative limit of these devices with increasing Sn content. Using the two bandgap extracted previously (Table ), we hence calculated Voc,SQ for the four devices and compared it to the calculated Voc,rad values (Table ). From Table S3, it is clear that neither method of calculating the band gap can accurately replicate the trend in Voc,rad.

We proceed to calculate the contribution of nonradiative voltage loss (ΔVoc,nrad) for the above device series using eq and Voc,rad (from Table ) and hence QELED for the different devices in the series. From Table , we note that Voc,rad increases by more than 100 mV across the series, whereas Voc increases by only 60 mV, from 423 to 485 mV. This leads to a ΔVoc,nrad that is higher by more than 60 mV in device D compared to device A, and consequently a lower QELED (Table ). In other words, a larger fraction of charge carriers recombine radiatively rather than nonradiatively in device A as compared to device D. From these results we can say that the CZTSe absorber with the lowest Sn content (device A) has a Voc that is the closest to its radiative limit among this series. Moreover, device A shows the highest QELED of the series with a value around 5 × 10–5%, which is among the highest reported values for CZTSe devices[36,37] but remains several orders of magnitude lower than typical values for CIGS or silicon solar cells which are 0.03% and 0.13%, respectively.[38]

The significantly lower QELED of our investigated CZTSe devices compared to CIGS or silicon suggests enhanced nonradiative recombination. Hence, to further investigate what controls QELED for CZTS devices, we proceeded to use Cf–T and JV-T to understand the trend observed with changing Sn content.

Factors Affecting QE Measuring the temperature dependence of the capacitance of the devices at different frequencies is a commonly used method in the literature to characterize defects in chalcogenide materials or the properties of the interfaces with other layers.[39−41] In this work we have measured Cf–T for the four devices in the series, at temperatures ranging from 123 to 323 K. Figure a shows the Cf–T curves for device A, while the curves for the other devices are presented in the Supporting Information (Figure S5). The inflection point frequency (ft) was subsequently extracted from the C-f curves for different temperatures for all the devices of the series. In previous work ft is assumed to relate to the emission coefficient of the defect state and therefore to its energy.[41,42] Thus, we were able to extract the activation energy of the dominant trap state in a Shockley–Read–Hall representation (Ea,CfT) from the slope of an Arrhenius plot of ft (Figure b). As kesterite absorbers are p-type, Ea,CfT is considered to be the energy difference between the trap energy (E) and the valence band maximum energy (Ev), which can therefore be written as Ea,CfT = Et – Ev. Figure a shows Ea,CfT calculated using this procedure for all the devices, together with the band gap extracted from the EL spectra. Clearly, the relative energy of the dominant trap state around 0.1 eV does not change significantly with Sn content. Similar behavior is observed by Larramona et al.[28] where the activation energy of a shallow defect with energy between 120 and 170 meV is not correlated with Sn content. Further, apparent carrier concentration profiles were extracted from capacitance–voltage (CV) measurements at room temperature for devices A, C and D (Figure S7, device B data are unavailable) with a voltage sweep from −1 to +0.5 V. The profiles are comparable for all the devices, showing a doping concentration on the order of 1016 cm–3 at 0 V. The measured trap state is therefore believed to be related to the defect chemistry in the near-surface region or a transport barrier as reported by Werner et al.[43] Deep defects were not detected with the configuration for capacitance measurements presented here.

Figure 2

(a) Representative temperature-dependent capacitance–density frequency measurements in the temperature range from 123 to 323 K with 10 K steps and frequencies from 100 Hz to 1 MHz of device A (Sn content of 27.6 at. %). (b) Arrhenius plot of the inflection frequencies for device A.

Figure 3

(a) Comparison among band gap energy (Eg,EL) as obtained from EL measurements, activation energy of the main recombination mechanism (Ea,JVT) obtained by JVT measurements, and activation energy of the main defect (Ea,CfT) obtained by admittance spectroscopy for increasing Sn content. (The measurement error is too small to be properly visualized by the error bars.) (b) Temperature-dependent JV measurement (dark curve: dotted line, light curve: solid line) of device A (Sn content of 27.6 at. %). The inset shows a linear fit of Voc extrapolated to T = 0 K; a fitting error of 1% is taken into account.

Note that defect densities and energies are usually expected to strongly affect QELED of the device; however, in the studied series QELED changed significantly with Sn content, while the trap states properties remained unchanged. This observation suggests that the measured change in QELED with Sn content results not from trap states in the absorber inferred from Cf–T in these devices, but from a different cause.

Finally, in order to investigate this further, we carried out temperature-dependent JV measurements for device A under AM1.5G illumination (Figure b), with similar plots for the rest of the series shown in Supporting InformationFigure S6. The crossover of illuminated and dark JV-T curves becomes more pronounced at lower temperatures, whereas the increasing rollover leads to a complete blocking of the current at the lowest temperature of 123 K. The inset shows the temperature dependence of the Voc, where the linear extrapolation to 0 K provides the activation energy of the dominant recombination mechanism Ea,JVT.[44] For device A the obtained Ea,JVT = 0.99 eV is close to the derived bandgap Eg,EL = 1.04 eV; thus the dominant recombination is within the bulk of the absorber rather than at the interface. While the band gap increases with Sn content, Ea,JVT decreases slightly. Possible reasons for this are either worsened interface quality, due to the presence of domains of antibonding boundaries[45,46] shunting paths on the nanoscale,[47] or worsened band alignment, specifically with the CdS buffer layer as Sn is expected to mainly affect the conduction band minimum of the absorber. The latter is supported by first-principles studies showing that the conduction band minimum is dominated by antibonding Sn s and Se p hybrid orbitals while the valence band minimum does not involve Sn orbitals; thus a variation in Sn content will predominantly influence the conduction band.[48,49] Device A shows the smallest difference between Eg,EL and Ea,JVT values, which amounts to about 0.05 eV. This means that the main recombination mechanism has an energy closer to the band gap of the absorber, thus a better band alignment with the buffer layer, than the devices of higher Sn content.[50−52] An increasing mismatch of the absorber layer and buffer layer conduction bands could explain the decreased QELED with Sn content through increasing nonradiative losses via surface recombination at the interface with the buffer layer.

The present study highlights that quantifying the Voc loss as the difference between the measured device Voc and the band gap of the absorber is not the best metric for determining the voltage losses in compositionally complex absorbers like kesterites. By using two different methods to determine the bandgap, using either the absorption or emission spectra of the devices, we showed that the different methods lead to very different values in the Voc deficit relative to the bandgap, and quantitatively different Voc loss trend in a series of solar cells with varying Sn content. Further, we show that by instead using the radiative limit to the open circuit voltage (Voc,rad) calculated from electroluminescence (EL) and external quantum efficiency (EQE) measurements, we can more reliably compare the voltage losses for the different devices in the series and subsequently quantify the electroluminescence quantum efficiency (QELED) of the different devices. Interestingly, for this series of cells, the Voc increases with increasing Sn content from 423 mV to 465 mV, while the QELED decreases from 5 × 10–5% to 5 × 10–6%. This result shows that while increasing Sn content increases device Voc, it actually degrades the radiative efficiency of the device, increasing the loss in Voc due to nonradiative recombination. Regarding the origin of this effect, the decrease in QELED appears not to be related to the defect properties of the absorber as no significant change in defect energy activation was observed. In fact, the solar cell with the best QELED shows the best interface quality of the series as inferred from the JV-T measurement. Further investigations are needed to fully understand what controls QELED in kesterite solar cells and how it is linked to the overall power conversion efficiency of the devices. We anticipate that this type of analysis will prove useful in analyzing the impact of material composition, processing, and device architecture on the voltage losses in other varieties of thin-film solar cells.