Spectroscopic ellipsometry study of Cu2ZnGeSe4 and Cu2ZnSiSe4 poly-crystals

Materials Chemistry and Physics 141 (2013) 58e62

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Spectroscopic ellipsometry study of Cu2ZnGeSe4 and Cu2ZnSiSe4 poly-crystals M. León a, *, S. Levcenko b, e, R. Serna c, A. Nateprov b, G. Gurieva b, e, J.M. Merino a, S. Schorr d, E. Arushanov b a

Department of Applied Physics C-XII, Universidad Autónoma de Madrid, Madrid, Spain Institute of Applied Physics, Academy of Sciences of Moldova, Chisinau MD 2028, Republic of Moldova Optics Institute, CSIC, 28006 Madrid, Spain d Free University Berlin, Institute of Geological Sciences, Malteserstr. 74-100, Berlin, Germany e Helmholtz-Zentrum Berlin fuer Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany b c

h i g h l i g h t s
Cu2Zn(Si,Ge)Se4 pseudodielectric function and optical constants were measured by SE.
Dispersion of the optical constants was modeled by Adachi model dielectric function.
Fundamental band gap and high-energy transitions were determined.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 March 2012 Received in revised form 5 March 2013 Accepted 26 April 2013

We report the room temperature spectroscopic ellipsometry study of Cu2ZnGeSe4 and Cu2ZnSiSe4 crystals, grown by modified Bridgman technique. Optical measurements were performed in the range 1.2e4.6 eV. The spectral dependence of the complex pseudodielectric functions as well as pseudocomplex refractive index, extinction coefficient, absorption coefficient, and normal-incidence reflectivity of Cu2ZnGeSe4 and Cu2ZnSiSe4 crystals were derived. The observed structures in the optical spectra were analyzed by Adachi’s model and attributed to the band edge transitions and higher lying interband transitions. The parameters such as strength, threshold energy, and broadening, corresponding to the E0, E1A and E1B interband transitions, have been determined using the simulated annealing algorithm. Ó 2013 Elsevier B.V. All rights reserved.

Keywords: A. Semiconductors C. Polarimeters and ellipsometers C. X-ray scattering D. Optical properties D. band-structure

1. Introduction Cu2ZnGeSe4 (CZGeSe) and Cu2ZnSiSe4 (CZSiSe) are interesting and promising p-type semiconductor materials for optoelectronics [1], solar cells [2] and thermoelectric applications [3]. The CZGeSe and CZSiSe compounds belong to the large family of I2eIIeIVeVI4 quaternary compounds and crystallizes in the tetragonal and orthorhombic crystal system, respectively, in which each of Se atom are surround by two Cu, one Zn, and one Ge or Si and every cation is tetrahedrally coordinated by Se [4e6]. Recently, Parasyuk et al. [7] has investigated the phase diagram of Cu2GeSe3eZnSe and found that the formation of the quaternary compound Cu2ZnGeSe4 was

* Corresponding author. E-mail address: [email protected] (M. León). 0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.04.024

incongruent. More recently, several first-principles studies [8e11] have been performed to investigate phase stability and electronic structure of these materials. However, much less amount of the experimental information is available about their basic physical properties and in particular about their optical properties, partially due to difficulty of preparing suitable size, compositionally homogeneous crystals. There have been few experimental reports on the optical properties of CZGeSe and CZSiSe studied using various techniques, such as absorption [5,6,12e15], far infrared spectroscopy [16] and Raman [17], photoluminescence [17] and electrolyte electroreflectance [18]. However, there has been no data on the optical constants of these materials. The detailed knowledge of the optical constants is of great importance for development of the optoelectronic applications based on it, while character of spectra of the optical constants can provide important information of the band structure of the semiconductor material.

M. León et al. / Materials Chemistry and Physics 141 (2013) 58e62

In the present work, the room temperature complex pseudodielectric function spectra for CZGeSe and CZSiSe crystals, grown by modified Bridgman method, have been measured by spectroscopic ellipsometry (SE) over the photon energy range from 1.2 to 4.6 eV. The determined pseudo-optical constants of the CZGeSe and CZSiSe quaternary compounds have been modeled using Adachi’s model for the electronic interband transitions. 2. Experimental details CZGeSe and CZSiSe crystals were grown by the modified Bridgman method. Energy dispersive X-ray microanalysis (EDAX) measurements yield some variations between the ratio of Cu and Zn among the examined samples. However, the average atomic ratio of Cu:Zn:Ge(Si):Se was found to be close to stoichiometry, Cu:Zn:Si:Se ¼ 26.1:11.8:13.3:48.9 with Cu/Zn þ Si ¼ 1.04 and Zn/ Sn ¼ 0.89 for Si containing samples and slightly Cu rich and Zn poor (29.2:10.3:12.6:47.9 with Cu/Zn þ Ge ¼ 1,27 and Zn/Ge ¼ 0.82) for Ge contained samples. The XRD data reveal, that the quaternary phases Cu2ZnSiSe4 and Cu2ZnGeSe4 are the main phases of the Bridgman grown polycrystalline material, and no preferential orientation has been found. Moreover the XRD measurements show (Fig. 1), that the compound Cu2ZnSiSe4 crystallizes in the orthorhombic structure (wurtz-stannite or wurtz-kesterite), whereas Cu2ZnGeSe4 crystallizes in a tetragonal structure (stannite or kesterite). Secondary phases, which are in the minority, are ternary and binary compounds. On the basis of the EDX and XRD measurements it can be concluded, that the crystals chosen for the optical measurements are the quaternary compounds Cu2ZnSiSe4 and Cu2ZnGeSe4. The optical measurements were carried out with a variable-angle spectroscopic ellipsometer at room temperature in the photon energy (E ¼ Zu) range from 1.2 to 4.6 eV, at two incidence angles F, 60 and 70 in standard ellipsometry mode assuming that the sample can be treated as an isotropic medium. It is worth noting that tetragonal CZGeSe and orthorhombic CZSiSe are unaxial and biaxial crystals, respectively, so that their optical properties are anisotropic in general case. Moreover the anisotropy of the optical transitions near the band edge region on CZSiSe single crystals was observed by absorbance [15] and electrolyte electroreflectance [18] measurements. Considering a medium composed of uniaxial/biaxial crystals oriented in random directions the optical response of polycrystalline material will correspond to a mean effective value of tensorial dielectric function of anisotropic crystal [19].

59

A special attention was paid to the preparation of good quality “pure” surface as was proposed by Albornoz et al. [20]. The real and imaginary parts of the pseudodielectric function 3 (E) ¼ 3 1(E) þ i3 2(E) may thus be obtained from the equation of two-phase (substrate-ambient) model [21]. For the case when the dielectric function of ambient is equal to unity the two-phase model is given by

3


   1r 2 ¼ sin2 F 1 þ tan2 F 1þr

(1)

where F is the incidence angle of the photon beam and r is the complex ratio of the Fresnel coefficients for light parallel (p) and perpendicular (s) to the plane of incidence, respectively.

3. Theoretical model The Adachi’s model for the dielectric function (MDF), which describes features of the complex dielectric function 3 (E) of crystalline materials in terms of electronic transitions in the neighborhood of critical points (CP), has been employed in this work [22,23]. The MDF has successfully applied to model the dielectric function and the optical constants of close related IeIIIe VI2 chalcopyrite compounds [24e27] and quaternary chalcogenide Cu2ZnGeS4 [28] semiconductor. The complex pseudodielectric function of CZGeSe and CZSiSe was described by the sum of three terms corresponding respectively to the one-electron contributions at the E0 and E1b critical points, where b ¼ A, B refers to different energy transitions after the main one, and an additional constant 3 1N: 3 ðEÞ

¼

3

ð0Þ

ðEÞ þ 3 ð1Þ ðEÞ þ 3 1N

(2)

(0)

The first term, 3 (E), corresponding to the fundamental gap, E0, is assigned to the three-dimensional (3D) M0 CP 3

ð0Þ

3=2 2 c0

ðEÞ ¼ AE0



2  ð1 þ c0 Þ1=2  ð1  c0 Þ1=2



(3)

with c0 ¼ (E þ iG0)/E0, where A and G0 are the strength and the damping energy of the E0 gap respectively. The second term, 3 (1)(E), corresponding to the higher criticalpoints E1b (b ¼ A, B), is assigned both to the two-dimensional 2DM0 and 2D-M1 CP and is given by 3

ð1Þ

h i1 ðEÞ ¼ B1A 1  ðE=E1A Þ2  iðE=E1A ÞðG1A =E1A Þ   2  B1B c2 1B Ln 1  c1B

(4a)

for CZGeSe, and 3

Fig. 1. XRD patterns of Cu2ZnGeSe4 and Cu2ZnSiSe4 polycrystalline samples.

ð1Þ

  2 ðEÞ ¼ B1A c2 1A Ln 1  c1A h i1 þ B1B 1  ðE=E1B Þ2  iðE=E1B ÞðG1B =E1B Þ

(4b)

for CZSiSe with c1b¼(E þ iG1b)/E1b, where B1b and G1b are the strength and damping constants of the E1b transitions. The inclusion of an additional term, 31N, in the theoretical model usually improves the fit of 3 1(E) experimental data [22e30]. This term contains the contributions of higher lying interband transitions and in our calculations this parameter has been taken as photon energy independent constant. The unknown parameters of the optical transitions entering in Equations (2)e(4) were obtained using the simulated annealing

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M. León et al. / Materials Chemistry and Physics 141 (2013) 58e62

(SA) algorithm [31] through the minimization of the following objective function [27,32]:

   !2  3 ðE Þ   3 ðE Þ  N X  1 i   2 i  F ¼  1 þ  expt  1  expt 3  3  ðEi Þ ðEi Þ i¼1

1

(5)

2

where N is the number of photon energies at which 3 (E) was (Ei), 31 (Ei) 3 expt (Ei), 3 2 (Ei) are respectively the measured, and 3 expt 1 2 experimental and calculated values of the real and imaginary parts of the complex pseudodielectric function at Ei point.

E1A and E1B region, for both compounds as it has been explained above. The different shape of the 3 (E) spectra in high photon energy region between CZGeSe (Fig. 2a) and CZSiSe (Fig. 2b) is probably related to different type of CP. Consequently a better agreement was achieved for 2D-M1 plus 2D-M0 description for, respectively, E1A and E1B transitions in CZGeSe spectra, and 2D-M0 plus 2D-M1 description for, respectively, E1A and E1B transitions in CZSiSe. Additionally, to match the shape of 3 (E) theoretical curves, Gaussian-like energy dependent broadening functions were employed for the broadening parameters of each transitions, which allows one to adjust continuously parameters Gi (Equations (2), (4a) and (4b)) from a Lorentzian to Gaussian type of broadening [32]:

4. Results and discussion Fig. 2a and b show the 3 1(E) and 3 2(E) pseudodielectric functions of CZGeSe and CZSiSe crystals, derived from the SE measurements by using Equation (1). As seen in the figures, the 3 (E) spectra reveal clear structures E0, E1A, E1B labeled in Fig. 2a and b. In the region below 1.7 eV for CZGeSe (Fig. 2a) and 2.7 eV for CZSiSe (Fig. 2b) the energy thresholds of the fundamental absorption edge E0 ¼ Eg is observed, respectively. A second E1A energy thresholds appear in the intermediate region of 3 (E) spectra between 2 and 3 eV for CZGeSe and from 3 to 3.8 eV for CZSiSe. At higher photon energy of 3 (E) spectra a third E1B energy threshold appear for both compounds. The Adachi’s model (Equations (2)e(4a) and (4b)) was applied to calculate the pseudodielectric function of the studied crystals. The resulting analytical lines from the fits of the experimental data in Fig. 2a and b have been obtained considering CP’s of the threedimensional-type 3D in the E0 region and of the 2D -type in the

a)



G0i ðEÞ ¼ Gi exp  si



E  Ei

2  (6)

Gi

where si and Gi are the adjustable model parameters, Ei is the transition energy, and i ¼ 0, 1A, 1B. It was found, that introducing energy dependent broadening of E1A and E1B transitions leads to better agreement between the experimental and theoretical 3 (E) for CZSiSe. However, we omitted this modification of Adachi’s model for CZGeSe as it has much smaller effect on the final value of the objective function F (Equation (5)). As can be seen from Fig. 2, all features present in the experimental spectra are very well reproduced by the model fit. The model parameters A, B, E0, E1A, E1B, G, s, 3 1N and 3 N were calculated using the global optimization routine (SA algorithm), which enables to obtain a good fit without providing good initial estimations for the unknown parameters. The determined values of these parameters are listed in Table 1. As an indication of the accuracy with respect to the experimental values, the relative errors, D3 1 and D3 2, have also been calculated and they lie in the D3 1 ¼ 0.8e2.8% and D3 2 ¼ 1.8e2.1% ranges for the real and the imaginary parts, respectively (Table 1). In addition, the value of the high-frequency dielectric constant (3 N) was estimated from the derived parameters of the Adachi model by using the approximation formula [33]



3 N zA=

 4E01:5 þ B1A þ B1B þ 3 1N

(7)

for long wavelengths (l / N). The obtained 3 N value for CZGeSe 8.42 is larger than those obtained for CZSiSe, 7.04, and for Cu2ZnGeS4, 6.61e6.65, obtained from the Adachi model parameters presented in Ref. [28].

Table 1 Model parameter values. Materials

1.5

b)

A (eV ) E0 (eV) G0 (eV) B1A E1A (eV) G1A (eV) s1A B1B E1B (eV) G1B (eV) s1B 3 1N

Fig. 2. Experimental spectral dependence of pseudielectric function 3 (E) ¼ 3 1(E) þ i 3 2(E) and numerically calculated (solid lines) using the MDF model and the SA algorithm for (a) CZGeSe and (b) CZSiSe crystals. The obtained values of the transition energies denoted as E0, E1A and E1B are indicated by the arrows.

3N

a

Cu2ZnGeSe4

Cu2ZnSiSe4

5.83  0.06 1.41  0.02 0.17  0.01 (1.29  0.02)a (2.46  0.03) (0.35  0.02) e 5.4  0.1 3.67  0.04 0.66  0.02 e 0.86  0.01 8.42

39.9  0.8 2.42  0.03 0.12  0.01 2.80  0.04 3.44  0.04 0.19  0.01 0.20  0.01 (1.19  0.03) (4.59  0.05) (0.56  0.02) (1.10  0.05) 0.43  0.01 7.04

D3 1

D3 2

D3 1

D3 2

2.8%

1.8%

0.8%

2.1%

Data given in brackets correspond to 2DM1 CP.

M. León et al. / Materials Chemistry and Physics 141 (2013) 58e62

The determined values of E0 transition are 1.41 eV for CZGeSe and 2.42 eV for CZSiSe (Table 1). The value of CZGeSe band gap is larger than the first reported 1.29 eV [6] and smaller than the values 1.63 and 1.52 eV found by H. Matsushita et al. [13] and Lee and Kim [14], respectively. On the other hand, in relation with the CZSiSe compound, our applied model for the description of 3 (E) doesn’t take into account the contribution of an indirect transition since such mechanism is expressed by a second order process in the perturbation and hence the reported values, 2.20 eV, by Yao et al. [6] and 2.08 eV, by Levcenco et al. [15] for the indirect band gap of CZSiSe cannot be compared with our values. However, the values of the lowest direct band gaps obtained from electroreflectance study (2.35, 2.41 eV) [18] and transmittance measurements (2.32 eV) [5] are in a good agreement with our result 2.42 eV for CZSiSe. Following Chen et al. [9] the GGA (generalized gradient approximation) -corrected direct band gaps for CZGeSe kesterite and stannite type are 1.50 and 1.32 eV, respectively. On the other hand, Nakamura et al. [8] calculated with screened-exchange local density approximation theoretical gaps 1.10 (1.48), 0.76 (1.07) and 0.87 (1.17) eV for kesterite, stannite and wurtz stannite structures of CZGeSe (CZSiSe). Our experimental results for CZGeSe agree with predictions of Chen et al. [9] but they differ considerably from theoretical values of Nakamura et al. [8] for both CZGeSe and CZSiSe compounds. Based on these band structure calculations we assign E0 to an electronic transition at the G:(000) point, which correspond to a direct transition from the valence band maximum to the conduction band minimum (CBM) [8,9]. The energies of the second E1A and third E1B energy thresholds are 2.46 (3.4) and 3.6 (4.6) eV for CZGeSe (CZSiSe), respectively. By analogy to the assignment done on Cu2ZnGeS4 [28], we may attribute these transitions for CZGeSe as transitions at the high critical points N(A):2p/a(0.5 0.5 0.5) and T(Z):2p/a(0 0 0.5) of the first Brillouin zone, based on the

61

Fig. 4. Experimental spectral dependence of pseudo- absorption coefficient a, and pseudo- normal-incidence reflectivity R for (a) CZGeSe and (b) CZSiSe crystals. The solid lines represent numerically calculated n and k using the MDF model and the SA algorithm.

theoretical band diagram (Fig. 5) of reference [9]. However, to the best of our knowledge there are no available theoretical band structure for the wurtz stannite quaternary compounds, so that possible origin of the E1A and E1B transitions observed in CZSiSe remains unclear. It is worth also noting that the energy of the E1B transition for CZSiSe is at the end of our experimental range and in order to determine more accurately model parameters of this transition the measurements beyond 4.6 eV are called for. Once determined the pseudodielectric functions for CZGeSe and CZSiSe materials, the pseudo-optical constant that are of interest for applications design, namely, the complex refractive index n* ¼ n þ ik, the normal-incidence reflectivity R, and the absorption coefficient a, can be readily computed from well-known equations (see Equations 5e7 in Ref. [25]). The experimental spectral dependences of n and k, as well as the calculated ones using the Adachi’s model and the SA algorithm, are presented in Fig. 3 for the studied samples. Fig. 4 shows the comparison between experimental and numerically calculated a and R using the Adachi’s model and the SA algorithm. A good agreement is observed for both studied materials. Similarly to 3 (E) the n*(E), a(E) and R(E) spectra reveal several structures at E0, E1A and E1B CP’s. 5. Conclusions

Fig. 3. Experimental spectral dependence of the pseudo-real refraction index n and pseudo-extinction coefficient k for (a) CZGeSe and (b) CZSiSe crystals. The solid lines represent numerically calculated n and k using the MDF model and the SA algorithm.

The pseudo-optical constants for Cu2ZnGeSe4 and Cu2ZnSiSe4 polycrystalline quaternary compounds have been determined. The spectral dependence of the complex pseudodielectric function and pseudo-refractive index, normal-incidence reflectivity and the absorption coefficient for the crystals have been modelled in the 1.2e 4.6 eV photon energy range using the Adachi’s model dielectric function and described by E0, E1A and E1B interband transitions. A good agreement with the experimental data has been achieved and

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M. León et al. / Materials Chemistry and Physics 141 (2013) 58e62

the model parameters (strength, threshold energy and broadening) of the interband transitions have been calculated by the simulated annealing algorithm. The high-frequency dielectric constant (3 N) was estimated by the extrapolation of the Adachi’s model. Pseudooptical constants, easily computed using the parameters of E0, E1A and E1B interband transitions, could be useful for the design and analysis of optoelectronic devices based on the Cu2ZnGeSe4 and Cu2ZnSiSe4 materials. Acknowledgments Financial supports from BMBF MDA11\002, Spanish MINECO KEST-PV; ENE2010-21541-C03-01/-02/-03 and IRSES PVICOKEST 269167 projects are acknowledged. S.L. thanks the Humboldt foundation for support. References [1] T. Oike, T. Iwasaki, AH01L2915FI (2008) http://www.faqs.org/patents/app/ 20080303035#ixzz0iW8PX6KV. [2] G.M. Ford, Q. Guo, R. Agrawal, H.W. Hillhouse, Chem. Mater. 23 (2011) 2626e 2629. [3] M. Ibañez, R. Zamani, A. Lalonde, D. Cadavid, W. Li, A. Shavel, J. Arbiol, J.R. Morante, S. Gorsse, G.J. Snyder, A. Cabot, J. Am. Chem. Soc. 134 (2012) 4060e4063. [4] W. Schafer, R. Nitsche, Mater. Res. Bull. 12 (1974) 645e654. [5] D.M. Schleich, A. Wold, Mater. Res. Bull. 12 (1977) 111e114. [6] G.Q. Yao, H.S. Shen, E.D. Honig, R. Kershaw, K. Dwight, A. Wold, Solid State Ionics 24 (1987) 249e252. [7] O.V. Parasyuk, L.D. Gulay, Ya. E. Romanyuk, L.V. Piskach, J. Alloys Compd. 506 (2001) 202e207. [8] S. Nakamura, T. Maeda, T. Wada, Jpn. J. Appl. Phys. 49 (2010) 121203, 3 pp. [9] S. Chen, X.G. Gong, A. Walsh, S.-H. Wei, Phys. Rev. B 79 (2009) 165211, 10 pp.

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