Spectroscopic ellipsometry study of Cu2ZnSnS4 bulk poly-crystals

Department Structure and Dynamics of Energy Materials, Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz, D-14109 Berlin, Germany Berlin, Germany Institute of Applied Physics, Academy of Sciences of Moldova, Academiei 5, MD 2028 Chisinau, Moldova Department of Applied Physics M12, Universidad Autónoma de Madrid, C/ Francisco Tomás y Valiente 7, 28049 Madrid, Spain Laser Processing Group, Instituto de Optica, IO, CSIC, Serrano 121, 28006 Madrid, Spain Belarusian State University of Informatics and Radioelectronics, P. Brovka 6, 220013 Minsk, Belarus IREC, Catalonia Institute for Energy Research, C. Jardins de les Dones de Negre 1, 08930 Sant Adrià del Besòs (Barcelona), Spain INUB, Departament d’Enginyeria Electrònica i Biomèdica, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain *Corresponding author: S. Levcenko; email sergiu.levcenco@helmholtz-berlin.de

The linear optical properties of Cu 2 ZnSnS 4 bulk poly-crystals have been investigated using spectroscopic ellipsometry in the range of 1.2-4.6 eV at room temperature.The characteristic features identified in the optical spectra are explained by using the Adachi analytical model for the interband transitions at the corresponding critical points in the Brillouin zone.The experimental data have been modeled over the entire spectral range taking into account the lowest E 0 transition near the fundamental absorption edge and E 1A and E 1B higher energy interband transitions.In addition, the spectral dependences of the refractive index, extinction coefficient, absorption coefficient, and normal-incidence reflectivity values have been accurately determined and are provided since they are essential data for the design of Cu 2 ZnSnS 4 based optoelectronic devices.Published by AIP Publishing.https://doi.org/10.1063/1.5024683 In the span of the last decade, much progress has been made in kesterite based Cu 2 ZnSnS 4 (CZTS) thin film solar cells.This is because kesterites show excellent properties as absorber materials such as an optimal bandgap of $1.5 eV (Refs.1-3) which can be tuned by adjusting anion and cation compositions 4,5 and a high optical absorption coefficient 6,7 over $10 4 cm À1 .Moreover, kesterites are composed of lowcost elements with low toxicity and abundant in the Earth's crust, which allows avoiding the use of critical raw materials.The best solar cell efficiency has reached values of 9% for CZTS based solar cells 8 and 12.6% for alloyed kesterite photovoltaic devices. 5Other possible applications of CZTS range from utilization as a wide-gap p-type thermoelectric material 9 to a photoelectrode layer in water splitting devices. 10espite the considerable efforts aimed at the development of kesterite thin film technology and the photovoltaic conversion improvements, there are still a limited number of works centered on their fundamental material properties.,13 However, for optoelectronic applications, it is mandatory to have deeper and more accurate knowledge on the optical properties in a wide photon energy range.An examination of the spectroscopic ellipsometry (SE) literature shows that the dielectric function data, e, have been reported for CZTS thin films. 7,20,21However, the optical response of the thin film has been often treated using the multi-layer stack model composed of three to six sublayers, 7,21 which has a limited accuracy.In this context, the data obtained from the bulk poly-crystals are in principle more reliable.Besides, they are also more relevant than those obtained for bulk singlecrystals, which show a strong polarization dependence of the dielectric function, because for the design of actual solar cell devices, polycrystalline materials will be used.In this letter, from the SE measurements performed in a wide spectral range of 1.2 to 4.6 eV, we determine the intrinsic dielectric function of CZTS bulk poly-crystals by taking into account the presence of a roughness layer on the surface of the specimens induced by chemical and mechanical sample preparation procedures.The dispersion of the dielectric function has been parameterized based on the Adachi model for the interband transitions, which in turn enables us to calculate the CZTS optical constants over the wide spectral range relevant for device applications.
Cu 2 ZnSnS 4 crystals were grown by the modified Bridgman method. 3The chemical composition was investigated by Energy Dispersive X-ray microanalysis (EDX) measurements (Oxford instruments, model INCA Xsight) using a Hitachi S-3000N scanning electron microscope.The Cu/(Zn þ Sn) ratio varies from 0.8 to 1.1, and the Zn/Sn ratio lies in the range of 0.9-1.3 in the selected samples (Table I).
To determine the possible presence of secondary phases in CZTS poly-crystals, we carried out Raman measurements by using a LabRam HR800-UV Horiba Jobin Yvon spectrometer coupled with a CCD detector.Under 532 nm a) Author to whom correspondence should be addressed: sergiu.levcenco@helmholtz-berlin.de0003-6951/2018/112(16)/161901/5/$30.00 Published by AIP Publishing.112, 161901-1 excitation [Fig.1(a)], all the detected peaks, including the most intense peaks at 339 and 289 cm À1 , correspond to vibrational modes of CZTS. 18,19The relatively low value of full width at half maximum of the most intense peaks ($9 cm À1 in S1, $6 cm À1 in S2, and $7 cm À1 in S3) as well as the detection of the low intensity CZTS peaks denotes a good sample crystallinity.The spectra excited with a He-Cd laser (line 325 nm) were used to exclude the possible presence of the ZnS phase. 22Figure 1(b) shows that under the UV excitation, an enhancement of the peak at 320 cm À1 and the appearance of a small additional peak at 677 cm À1 occurred.The first of them is identified with a CZTS characteristic mode, 18 while the second is attributed to the second order of the main CZTS peak. 19Experimentally, we have observed that excitation of the Raman spectra with a NIR laser (line 785 nm) improves the detection of SnS and Cu 2 SnS 3 phases, as this laser line is closer to the resonant conditions for these compounds.Figure 1(c) shows a typical spectrum obtained under NIR excitation, but none of the peaks could be attributed to the SnS or Cu 2 SnS 3 phases. 23,24inally, for any of the used excitation conditions, it has not been possible to observe the presence of the Cu 2-x S phase, which has a dominant peak at 475 cm À1 . 25According to the Raman data, no evidence has been obtained in the presence of any secondary phase in the investigated samples.
The optical response of CZTS poly-crystals is analyzed by considering a three-phase model 26 composed of air, a rough surface layer, and a bulk material.We have modeled the thin roughness layer as a mixture of air voids and bulk CZTS with the fixed 50% ratio of each component.The Bruggeman effective medium approximation (EMA) was applied to describe the dielectric function of this effective medium. 27Thus, our model includes the thickness of the roughness surface layer as an additional parameter in comparison to the ideal two-phase model. 28llowing Adachi, 29,30 we adopted the model for the dielectric function (MDF) to describe the complex dielectric function, e(E) ¼ e 1 (E) þ ie 2 (E), as a function of the photon energy, E, over the spectral range from the absorption edge up to 4.6 eV in CZTS.This is similar to the previous SE studies on Cu 2 Zn(Sn,Ge)Se 4 quaternaries with a tetragonal type structure. 31,32The general expression for e(E) includes three terms where e (0) (E) is the contribution from the electronic transitions near the bandgap region, e (1) (E) is the combined contribution from the interband transitions near the 2D-M 1 and the 2D-M 0 critical points (CPs), and e 11 accounts for the higher energy CPs outside the experimental range. 29he assumptions on the parabolic nature for the valence and conduction bands for the lowest energy transitions and the 3D M 0 type character of the CP result in e (0) (E) of the form with v 0 ¼ (E þ iC 0 )/E 0 , where A and C 0 are the strength and the broadening energy of the E 0 transition, respectively.The e (1) (E) component is given by where B 1A and C 1 A are the strength and the broadening parameters of the E 1A transition at the 2D-M 1 CP and )/E 1B , with B 1B and C 1B being the strength and the broadening energy of the E 1B transition near 2D-M 0 CP.
To have a more accurate description of e(E) in Eq. ( 1), a Gaussian type broadening mechanism has been assumed for the interband transitions, after Kim 33 where s i is the non-dimensional parameter, C i is the broadening parameter, E i is the transition energy, and i is 0, 1A, or 1B.The use of the simulated annealing (SA) algorithm 34 has enabled us to perform a global minimization procedure and to calculate the MDF parameters.The following objective function 35 was selected in the minimized routine where D exp (E i ), W exp (E i ) and D(E i ), W(E i ) are the experimental and calculated values of the ellipsometry parameters at the E i point, respectively, and N is the number of experimental points.The optical measurements were performed using a variable-angle spectroscopic ellipsometer (J. A. Woollam VASE) at 300 K and at two incidence angles U, 60 and 70 , in the photon energy range of 1.2-4.6 eV.The information on the preparation of the good quality "pure" sample surface can be found in Ref. 36. Figure 2 shows the plot of typical experimental (D exp , W exp ) curves as a function of E for samples S1 and S3.Over the measured spectral range, the experimental results agree well with the theoretical predictions for the interband transitions [Eqs.( 1)-( 4)], which are also plotted in Fig. 2 as solid lines.The relative errors for the obtained (D, W)-ellipsometric parameters range between 2% and 4%.Table II lists the MDF parameters for the different samples.The calculated values of the surface layer thickness are in the range of 6-8 nm, which are acceptable values taking into account the specific surface preparation for the SE measurements. 37From the global fitting procedure, the value of the e 11 parameter was found to be negligibly small and was omitted in Table I.We found that introducing the Gaussian broadening mechanism [Eq.( 4)] for the E 0 transition does not have any influence on the value of F [Eq. ( 5)] in contrast to E 1A and E 1B CPs. Figure 3(a) shows the calculated real and imaginary parts of the e-function for the three samples.The line shapes of the e(E)-curves for S1 and S3 samples are quite similar but shifted by about 0.1 eV in energy.This is not an unexpected result as a spectral similarity can already be noticed in the raw (D, W) data (Fig. 2).e 2 (E) from the S2 sample resembles the e 2 (E) shapes of S1 and S3 samples, too, but composed of broadened features.Quantitatively, the similarity between the CZTS samples can be concluded from the calculated MDF parameters (Table II).We can also define analytically the high frequency dielectric constant, e 1 , for CZTS.Developing Eq. ( 1) for E % 0 and assuming e 11 % 0, we get e 1 % A/(4 Â E 0 The obtained values of e 1 are in the range of 7.0-7.2for the studied samples, while the recent ab-initio calculations give close but lower values of 6.5-6.8 depending on the employed functional. 7t us now consider the obtained energies of the interband transitions.For the E 0 transition, we get a value from 1.53 to 1.67 eV, which can be assigned to the transition between the valence band maximum (VBM) and the conduction band minimum (CBM) at the C(0,0,0) point in the Brillouin zone (BZ). 7,13These values reasonably agree with the bandgap values of 1.51-1.59eV on thin films derived from the SE 7,21 but larger than the earlier reported 1.30 eV. 20otably, the decrease in E 0 correlates with the reduction in the Cu/(Zn þ Sn) ratio (Table I).However, this tendency is opposite to those found in Cu 2 ZnSnSe 4 , where the bandgap increases with copper deficiency. 38On the other hand, the Cu-Zn lattice disorder in CZTS can induce a change in the bandgap of about 0.2 eV. 39According to this concept, an increase in the bandgap is related to an increase in the degree of ordering in the samples.Unfortunately, the amount of Cu-Zn lattice disorder is not known in the studied poly-crystals and the actual mechanism responsible for the E 0 variation cannot be determined at this stage.
The E 1A CP energies are obtained in the range of 2.86-2.97eV which can be attributed to the transition from VBM to the second conduction band at the C(0,0,0) point 13 or to transitions at the P(1/2,1/2,1/2) point in the BZ. 7In the room temperature SE study on thin films, 7 a value of 3.09 eV is derived from d 2 e(E)/dE 2 spectra, while the thermoreflectance on crystals 13 at 25 K resulted in a dominant transition with 3.3 eV.Interestingly, the transition of the E 1A CP is about 1.3 eV higher in energy than the E 0 CP for all the investigated samples.A slightly larger difference (1.4 eV) has also been found in the SE study from sulfoselenide thin films. 7he high-energy transition of the E 1B CP is found to be 4.8-5.0eV and contains numerous contributions with different types of transitions occurring over a wide region of BZ, and so, the amplitudes of these CP structures become relatively large due to the close locations of multiple transitions.
Tentatively, E 1B CP can be associated with the transition at the T(0,0,1) point in the BZ. 13 According to the thermoreflectance at 25 K, the energy of this transition is 4.8 eV. 13 However, it should be noted that our experimental spectral range limits the accurate determination of the E 1B transition parameters and higher energy data points are necessary to better analyze its characteristics.
In view of the application, design, and optimization of the CZTS solar cells as a multilayer thin film system, we present the dielectric function related optical constants such as the refractive index and extinction coefficient [Fig.3   In conclusion, the intrinsic optical constants for Cu 2 ZnSnS 4 bulk polycrystalline samples, grown by the modified Bridgman method, have been determined by using the three-phase model from the SE measurements in the photon energy range of 1.

(Received 2
February 2018; accepted 6 April 2018; published online 19 April 2018) (b)], as well as the normal incidence reflectivity and absorption coefficient [Figs.3(c)and3(d)].Similar to the e(E) spectra, the optical constants reveal distinct structures near the analyzed E 0 , E 1A , and E 1B CPs.

FIG. 2 .
FIG.2.Experimental W and D spectra (points) and numerically calculated ones (solid lines), using the three phase model (air, surface, and bulk layers) for S1 and S3 samples of the CZTS poly-crystals.
2-4.6 eV.Multi-excitation wavelength Raman scattering measurements support the high crystalline quality of the bulk samples and show no evidence of the presence of secondary phases.To describe the optical spectra, we propose the application of Adachi's model, which includes the E 0 , E 1A , and E 1B interband transition contributions to the dielectric function.The obtained analytical description of the dielectric function will be useful for the design of optoelectronic devices and for the analysis of optical measurements of multilayer structures based on the Cu 2 ZnSnS 4 material.The research leading to the presented results was partially supported by the European Project INFINITE-CELL (Ref.H2020-MSCA-RISE-2017-777968, 2017-2021, www.infinitecell.eu) and the Spanish MINECO Projects "WINCOST" (ENE2016-80788-C5-2-R) and PHOTOMANA (TEC2015-69916-C2-1-R).The authors from the Institute of Applied Physics appreciate the financial support from STCU 6224 and from the Institutional Project No. CSSDT 15.817.02.04A.

TABLE I .
Chemical composition of the CZTS samples.

TABLE II .
Model parameter values.