Metastable defect response in CZTSSe from admittance spectroscopy

Cu₂ZnSn(S,Se)₄ (CZTSSe) has been the focus of extensive research as a potential absorber layer for photovoltaic applications due to its direct band gap and high absorption coefficient and because it is comprised of earth abundant elements.^1,2 Admittance spectroscopy (AS) has been used to study CZTSSe by several research groups^3–6 as this technique is useful to quantify defect activation energies and distributions as well as the dielectric constant of the depleted semiconductor.⁷ Typically, one or two capacitance signatures are observed in admittance spectroscopy of kesterites, with a range of activation energies (E_A) reported by various research groups.^3–6,8 Such variations in the reported capacitance signatures have been linked with variations in absorber processing conditions, compositional variations, and alkali content in the absorber layer. However, an additional influence on the capacitance response can originate from metastable defect behavior, which has been demonstrated in the similar Cu(In,Ga)(S,Se)₂ (CIGSSe)^9,10 material system. The impact of metastabilities on the analysis of AS has not been shown for the kesterite material system, despite the observed influence this behavior has on other optoelectronic measurements such as current-voltage (JV) measurements^11,12 and quantum efficiency (QE) measurements.¹³ In particular, charge-trapping into defect states—recently observed for kesterites^14,15—can have a significant impact on AS measurements; since AS utilizes a small voltage perturbation with no current injection, metastable responses can be activated upon carrier injection under various measurement conditions. Therefore, the experimental conditions require careful consideration.

In this work, we demonstrate the large impact the metastability in CZTSSe has on AS measurements before and after metastable changes are induced. We find that the metastable defect response occurs due to charge trapping following the injection of carriers into a relaxed device. Therefore, the interpretation of capacitance signatures in admittance spectroscopy of kesterites can be significantly affected by the measurement conditions. Specifically, capacitance signatures are dependent upon the voltage and illumination history of the device. Here, a relaxed CZTSSe sample exhibits a single capacitance signature while two capacitance signatures are observed on the device following low-level carrier injection. Following carrier injection, both capacitance signatures have higher activation energies than that of the relaxed measurement. Voltage dependent AS indicates that the capacitance signatures are due to bulk defects in the kesterite absorber.

CZTSSe solar cells discussed here-in were fabricated by the selenization of CZTS nanoparticles on a Mo substrate, as described by Miskin et al.¹⁶ Devices were completed with the structure CdS (50 nm)/ZnO (80 nm)/ITO (220 nm)/Ni-Al grids. The device used in this study demonstrates 8.1% total area power conversion efficiency under AM1.5 illumination conditions at 1 sun; light and dark IV curves are shown in Fig. S1 of the supplementary material. AS measurements were performed with an Agilent 4294A impedance analyzer. All capacitance is calculated assuming a parallel circuit model shown in Fig. S2 of the supplementary material.⁷ All measurements were performed using a 15 mV_rms AC signal with frequencies ranging from 100 Hz to 1 MHz and completed in the dark. The measurements were completed starting at low temperatures (ca. 60–80 K) and increasing to room temperature (ca. 300 K). The relaxed sample was allowed to equilibrate in the dark at the lowest temperature for 2 h with no voltage or current source. Metastable defect response was activated by a carrier-injection pretreatment (CIP) which consists of sourcing the sample with 1 mA/cm² forward bias current for 5 min prior to each frequency sweep measurement; the CIP treatment was repeated at each fixed temperature and fixed DC voltage bias. Similar behavior is observed following carrier injection from illumination of the device. Note that the device can take as long as 2 h to fully relax at cryogenic temperatures following carrier-injection. The relaxation process is monitored by comparing Nyquist (i.e., reactance vs. resistance) plots over time until changes are no longer observed. For the voltage dependent AS experiment, the cell was subjected to a DC voltage bias ranging from −1.0 to +0.2 V_DC with a 0.1 V_DC step size.

Capacitance as a function of frequency and temperature is shown in Fig. 1 for the CZTSSe sample under relaxed conditions and following CIP to activate metastable defect response; a large variation in the sample response between the two measurement conditions is observed. The relaxed sample exhibits a single capacitance signature (D1) of ca. 12–15 nF/cm² followed by a rise in the capacitance with increasing temperature. This rise in the capacitance signal following the D1 response is attributed to contributions from deep defects. Comparing this with the measurement after the CIP, there is a similar capacitance signature of ca. 12–15 nF/cm² (D1) but an additional capacitance signature of ca. 30 nF/cm² (D2). For the device following the CIP, there is also a rise in capacitance at higher temperatures following the D1 and D2 response, indicating that deeper defects play a similar role in both conditions. At low temperature and high frequency, both measurements converge to ca. 8.5 nF/cm², which we interpret as the geometric capacitance (C_G) of the absorber layer. This results in a dielectric value of approximately 8.5ε₀ (where ε₀ is the permittivity of free space), similarly reported by our group⁸ and several others.^3,4 It should be noted that the absence of the D2 capacitance signature in the relaxed measurement reduces the overall capacitance signal, even at room temperature. Relaxation at low temperature in the dark is required to recover the behavior observed for the relaxed measurement at all temperatures. Note that this behavior is reversible; following a relaxation event, the CIP capacitance spectra can be recovered by performing another CIP treatment.

Assuming that the capacitance response originates from a defect, the data were further analyzed to quantify the activation energies associated with the capacitance signatures following a thermally activated trap response, described by Eq. (1)⁷ 

where ω₀ is the demarcation angular frequency, A₀ is the temperature independent prefactor, and E_A is the defect activation energy. A₀T² represents the product of the valence band density of state (N_V, ∝ T^3/2), thermal velocity of carriers (⟨v_th⟩, ∝ T^1/2), and the electron capture cross section (σ_n).

Arrhenius plots of the relaxed and CIP capacitance signatures are shown in Figs. 2(a) and 2(b), respectively. The single capacitance signature from the relaxed measurement has an activation energy of 59 ± 3 meV, while the two observed capacitance signatures in the CIP measurement result in defect activation energies of 90 ± 2 meV (D1) and 157 ± 2 meV (D2). Additionally, the exponential prefactor A₀ increases for the sample measured under CIP conditions relative to the relaxed measurement, from ca. 6 × 10⁴ s⁻¹K⁻² to ca. 1.2 × 10⁶ s⁻¹K⁻² (D1) and 5 × 10⁵ s⁻¹K⁻² (D2). We attribute the observed increase in A₀ to σ_n, as expected due to the increasing E_A in accordance with the Meyer-Neldel rule.¹⁷ 

Defect energetic profiles, shown in Fig. 2(c), were constructed using the method described by Walter et al.¹⁸ where E_t [see Eq. (S1) in the supplementary material] was calculated using the A₀ values extracted from the Arrhenius fits. The ordinate of these profiles is proportional to the density of defects while the abscissa is the energy relative to the valence band. Note that the CIP profile has a transition from using A_0,D1 to A_0,D2 at 115 meV. The relaxed sample has a single lower energy peak (ca. 60 meV) and what appears to be a very broad peak (ca. 100–150 meV). These results demonstrate how large an impact metastable defects in CZTSSe have on AS results. Weiss et al.⁵ completed this analysis using pure selenide CZTSe fabricated from the co-evaporation process which showed a similar distribution to the CIP method.

It is clear that carrier injection causes a significant change in the admittance spectroscopy measurements. This is important because AS is often combined with IV(T) measurements, or devices are exposed to light before/during measurement, which can significantly alter the AS results and extracted defect properties for kesterites. As metastable response is measured following carrier-injection (i.e., forward bias or light), we attribute this effect to charge trapping following carrier injection. Charge trapping/carrier localization has also previously been reported for kesterites from TRPL¹⁴ and time-resolved terahertz spectroscopy.¹⁵ Such charge trapping is especially important at low temperature as thermal emission from a trap state is exponential dependent on the temperature. The increase in activation energy of the lower energy D1 defect following the CIP is attributed to charge trapping, which can alter the local energetic potential influencing the capture cross section and/or defect potential. This has similarly been reported in CISe₂ where the change in the charge state of a defect results in large lattice relaxation, which consequently shifts the energetic level of the defect to lower energy.¹⁹ Here, low temperature relaxation is required to relax the absorber as it removes trapped charges higher than thermalization and therefore ensures that subsequent higher temperature measurements do not need further relaxation.

Finally, voltage-dependent admittance spectroscopy was completed in order to determine the nature of the measured capacitance signatures, analyses of which are described by Decock et al.²⁰ All measurements were completed following CIP measurement conditions, as voltage-dependent measurements inherently result in carrier injection in forward bias. Linear fits to the Arrhenius plots were optimized simultaneously with the assumption that N_V, ⟨v_th⟩, and σ_n are voltage independent. Once the mean squared error was minimized on all fits, the activation energies extracted from the slopes were plotted vs. voltage shown in Fig. 3(a). We find that both the D1 and D2 activation energies are independent of voltage, which is similarly reported by Sun et al.²¹ Since the activation energies are voltage independent, these capacitance signatures are not likely to originate from the interface. If the response did originate from the interface, we expect that the activation energy would change with voltage since the distance between the Fermi level and the conduction band at the interface also changes significantly with voltage.²² Note that this assumes a continuous distribution of defect states at the interface, no Fermi level pinning, and the n-type layer dominates the admittance response in this region, resulting in electrons as the majority carrier.

Defect energetic profiles were also constructed from the voltage dependent AS measurements and fit with Gaussian distributions; fitting parameters are listed in Table S1 (supplementary material). Figure 3(b) shows the 0 V_DC and −1 V_DC case [created using the same method as in Fig. 2(c)]. Figure 3(c) shows the peak values of the D1 and D2 energetic profiles as a function of DC voltage. We find that the peak values of the energetic profiles are voltage-independent for D1, while D2 shows an increase in forward bias. As the peak of the energetic profiles of the D1 signature is voltage independent, we interpret this signature as being related to carrier freezeout; shallow level defects are no longer responding to the probing signal.²⁰ This conclusion requires the absorber layer to be almost entirely depleted (in which case the depletion capacitance is voltage-independent), resulting in the geometric capacitance for values below the D1 response.

It is obvious that the D2 defect is primarily a metastable defect and is only electrically active following carrier injection. The D2 peak values (i.e., the magnitude of the fitted Gaussian distributions at E_A,D2) plotted in Fig. 3(c) are ∝ (V_BI-V_DC)⁻¹ as shown by the best fit line, where V_BI is the built in potential (0.48 V, estimated from the Mott-Schottky plot at 142 K). Note that this temperature was chosen for the V_BI estimate as the D2 capacitance signature in Fig. 1(b) is clearly defined at 142 K. Therefore, we conclude that this defect has a parabolic defect spatial distribution.²⁰ 

In conclusion, we have demonstrated the large impact the metastable behavior in CZTSSe has on admittance spectroscopy measurements by comparing a device under electrically and optically relaxed conditions and with a carrier-injection pretreatment. The relaxed measurement contains a single capacitance signature, while the carrier-injection pretreatment contains two capacitance signatures. Additionally, voltage dependent admittance spectroscopy demonstrates that the activation energy associated with these two capacitance signatures is voltage independent and suggests an origin due to bulk defect responses. These results indicate that the higher energy metastable capacitance signature is activated by charge trapping within the absorber layer. Therefore, it is recommended that great care and consideration must be taken when measuring and analyzing non-ideal and metastable devices using admittance spectroscopy as the electrical and optical history of the device can greatly impact the results and can explain the wide variations reported in admittance for kesterites.

See supplementary material for additional information including the light and dark IV response of the tested solar cell, the equivalent AC circuit model, and additional information on the Gaussian fits of the defect energetic profiles.

This work was supported by the DOE through a non-proprietary partnering (NPO) with NREL, NSF Solar Economy IGERT 0903670-DGE, and the Solar Energy Research Institute for India and the United States (SERIIUS) DE AC36-08G028308. The authors would like to thank Dr. Sukgeun Choi for his assistance and discussion throughout the NPO project.