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.

metastabilities. 52,61 The device was therefore left in the dark at 300K over night (at least 10 h) prior to an admittance measurement in order to put the device into an equilibrium state. At low-T (up to 203K) the spectra converge at the highest frequency to a low capacitance value, namely the geometric capacitance of the cell (C g ). The converging frequency is denoted as inflection frequency ƒ t and the transition to C g reflects the dielectric freeze-out. At high-T the capacitance transition fits a Gaussian broad deep defect distribution, as described elsewhere. 53 The inflection frequencies are obtained from measured capacitance spectra from the derivative of the capacitance: . An Arrhenius plot '(ƒ) = ƒ * ƒ drawn with ln versus 1/T results in a straight line where the slope represents the defect energy E a ƒ -2 (C ƒ -T). For CV measurements the voltage was forward swept from -1 to 0.5 V at a frequency of 1 kHz. External quantum efficiency (EQE). The measurement was measured using a grating spectrometer (CS260-RG-4-MT-D) to create monochromatic light combined with a tungsten halogen light source.

Electroluminescence (EL) and Photoluminescence (PL
The monochromatic light was chopped at ~300 Hz, and a Stanford Research Systems SR380 lock-in amplifier with an internal transimpedance amplifier of 106 V/A was used to detect the photocurrent.
Long pass filters at 610, 715, 780, 850, and 1000 nm were used to filter out the scattered light from the monochromator. The spectra were taken from 300 to 1300 nm and calibrated by a silicon photodiode and a calibrated germanium photodiode.
JV characterization was carried out on 9 different cells for each Sn concentration, while all the other opto-electronic (JVT, CfT, CV, EL, PL and EQE) measurements were carried out on the single best representative among those 9.  S6 Figure S4 shows illuminated and dark IV measurements for the champion device (device C) and a band gap of 1.14 eV as obtained from the inflection point of the first derivative of EQE curve.  Figure S5 Electroluminescence spectra of the four device types used to determine the band gap, along with the fit used to extract the band gap value.

XRF AND XRD OF THE DIFFERENT ABSORBERS
We fit the electroluminescence of the cells using a model for the sub band gap absorption presented by Katahara et al. 4 . By convoluting a tail model and an ideal square root dependence above the band gap, the absorption coefficient can be expressed as :     Focussing on the devices with the highest and lowest Sn contents (devices A and D, respectively), we first note that the calculated from is similar to for device A whereas it is higher by oc,SQ g,EL oc,rad

TEMPERATURE DEPENDENT CAPACITANCE-FREQUENCY (CF-T) PLOTS FOR THE REMAINING DEVICES
Device B: Frequency (s -1 ) 32.9 at.% Sn S11 Figure S7: Temperature-dependent capacitance frequency measurements in the temperature range from 123 to 323 K with 10 K steps and frequencies from 100 Hz to 1MHz of devices B, C and D (Sn content of 29.5%, 31.2% and 32.9% respectively). The data for A are shown in the main text.

TEMPERATURE-DEPENDENT CURRENT DENSITY-VOLTAGE PLOTS FOR THE REMAINING DEVICES.
Device B: The presence of a second peak in the PL of figure S10a is unusual and as for now not fully understood, it was observed under different light intensities and on different samples. However, the measured EL did not show the second peak. Same applies for PL measurements made at EMPA (figure S10b) under different conditions.