Structural aspects of adamantine like multinary chalcogenides

Abstract

The present state of knowledge of structure, phase relations and metal ordering in 2(ZnX)_x(CuBX₂)_1 − x (B = Ga, In and X = S, Se, Te) and Cu₂Zn_xFe_1 − xSnS₄ multinary compounds is discussed. The chemical disorder process in 2(ZnX)_x(CuBX₂)_1 − x alloys leads to a phase separation, i.e. in a certain composition range (2-phase field) two phases, tetragonal domains and a cubic matrix, coexist. Its width depends on the three-valent cation only and is independent from the size of anion. In the subsolidus region of the 2(ZnX)_x(CuBX₂)_1 − x system the stability range of tetragonal mixed crystals as well as the miscibility gap is decreasing, the stability range of cubic mixed crystals is increasing. The process of structural disorder in 2(ZnX)_x(CuBX₂)_1 − x as well as Cu₂Fe_1 − xZn_xSnS₄ alloys is connected to the cation substructure. In tetragonal 2(ZnX)_x(CuInX₂)_1 − x alloys a non-random Zn distribution on the both cation positions of the chalcopyrite-type structure was revealed, whereas a random distribution of Zn and Cu on two different sites of the kesterite type structure was obtained in Cu₂ZnSnS₄ in contradiction to literature. The crossover from stannite (x = 0) to kesterite (x = 1) in Cu₂Fe_1 − xZn_xSnS₄ is considered as a three-stage process of cation restructure involving Cu⁺, Zn²⁺ and Fe²⁺, whereas Sn⁴⁺ does not take part in this process. In tetragonal 2(ZnX)_x(CuInX₂)_1 − x alloys the anion displacement is decreasing with increasing ZnX content in CuInX₂ indicating a decreasing tetragonal distortion. Here the disorder process in the cation substructure and the displacement process in the anion substructure are coupled.

Introduction

In the well known diamond structure (space group Fd3¯m) each atom is surrounded by four nearest neighbours situated at the corners of a regular tetrahedron forming a tetrahedrally bonded structure. Its lattice can be foreseen as two interpenetrating face centered cubic sub-lattices. The diamond structure forms the source of a family of structures based on the ordering of atoms on the two substructures [1]. An important feature of all tetrahedral structures is that each atom may be pictured as making four covalent bonds and thus requires four valence electrons. All compounds with structures derived from diamond are said to be “adamantine” [1]. Considering the rule that the average number of valence electrons per atom is four a wide range of tetrahedral structures can be derived. In multinary compounds the two substructures are populated with cations and anions respectively. Binaries have the common formula A^NB^8 − N (N = 1; 2; 3) [2]. The well known representatives are A^IIB^VI compounds (N = 2; A = Zn, Cd, Hg; B = S, Se, Te) which crystallize in the cubic sphalerite-type structure (space group F4¯3m) and in the hexagonal wurtzite type (space group P6₃mc). For ternary compounds the formula A^N − 1B^N + 1X₂^8 − N results [2]. The compounds A^IB^IIIX₂^VI (N = 2; A = Cu, Ag; B = Al, Ga, In; X = S, Se, Te) crystallize in the tetragonal chalcopyrite-type structure (space group I4¯2d) [2]. The ordered substitution of the metal in II–VI compounds by two metals (I and III) doubles the identity period of the initial cubic unit cell (by definition along the z-direction) with a tetragonal distortion η = c / 2a ≠ 1 due to different interactions between A–X and B–X resulting in different bond length (R_AX ≠ R_BX) and bond angles. This leads to a displacement of the anions from the ideal tetrahedral site by a quantity |u − ¼| (where u is the anion x coordinate). The parameters η and u are called the structural degrees of freedom of the chalcopyrite-type structure [3]. The prototype of this group is the mineral chalcopyrite (CuFeS₂). Lowering the symmetry one step further leads to the stannite-type structure (space group I4¯2m) named after the mineral stannite Cu₂FeSnS₄ [4]. A symmetry decrease is not only achieved by ordered substitution of the metals, but also by changing the metal ordering, i.e. the arrangement of the cations on the structural sites of the unit cell. By doing so the kesterite type structure (space group I4¯) can be deduced from the stannite-type structure, which is named after the mineral kesterite Cu₂ZnSnS₄ [4].

The anion displacement is increasing with symmetry degradation from the sphalerite (ideal position (¼,¼,¼,)) → chalcopyrite (x,¼,1/8) → stannite(x,x,z) → kesterite (x,y,z) type structure. In this sequence the anion position is characterized by an increasing number of free atomic coordinates, i.e. from one in the chalcopyrite-type structure to three in the kesterite type structure. Note that in the chalcopyrite-type structure two different cations are involved in the cation tetrahedra (A₂B₂X) whereas in the stannite and kesterite type structure three different cations form the tetrahedra (A₂BCX).

An overview of this part of the adamantine compound family is shown in Fig. 1 and Table 1.

The ternary A^IB^IIIX₂^VI chalcopyrites have attracted considerable attention for practical applications, amongst others as absorber layers in thin film solar cells. Moreover the range of commonly used photovoltaic materials can be expanded by crossing over to multinary semiconductors, i.e. alloys between the non-isotype II–VI binaries and I–III–VI₂ ternaries. They offer the advantage to vary the band gap at room temperature from the large value of the binary wide band gap semiconductor (e.g. ZnX) towards the band gap of the ternary chalcopyrite-type end member (e.g. CuInX₂) [5]. Moreover a better match of the lattice metrics between substrate (in case of single crystalline substrates e.g. Ge) and absorber layer is possible. In this connection structural aspects of 2(ZnX)_x(CuBX₂)_1 − x alloys (B = Ga, In and X = S, Se, Te) will be discussed in the present work.

The site preference of Zn²⁺ in tetragonal 2(ZnX)_x(CuBX₂)_1 − x mixed crystals is important, because a non-random distribution gives rise to Cu–In anti-site effects resulting in defects influencing the electronic properties of the material. The elements Cu and Zn are neighbours in the periodic table, Cu⁺ and Zn²⁺ have the same number of electrons (28). Their atomic scattering factor f, determining the structure factor F_hkl by

$$F_{\text{hkl}}=\sum _j{f}_j·exp\left\{2\mathrm{\pi }i\left(h{x}_j+k{y}_j+l{z}_j\right)\right\}$$

which is proportional to the measured intensity in an X-ray diffraction experiment, is identical. Hence both these cations are not distinguishable by conventional X-ray diffraction. The problem can be solved using neutron diffraction, because of the different neutron scattering lengths of Cu and Zn (b_Cu = 7.718 fm, b_Zn = 5.67 fm [6]). In Eq. (1) the atomic scattering factor f is then replaced by the neutron scattering length b.

In case one structural site is occupied by different elements (for instance two different atoms A and B occupy a site j), the average neutron scattering length of the site can be calculated by

$${\overline{b}}_j=A_j·b_A+B_j·b_B\text{.}$$

Here A_j describes the fraction (or occupancy) of atom A on site j and B_j the fraction of atom B on site j (with A_j + B_j = 1). Using Eq. (2) the average neutron scattering length can be calculated (b¯_j(calc)) on the assumption of a distribution model. Otherwise the experimentally obtained site occupancy, determined by Rietveld analysis of the neutron diffraction data, allows to evaluate an experimental average neutron scattering lengths (b¯_j(exp)). By variation of the distribution model a cation distribution which fulfill the condition b¯(exp) = b¯(calc) can be revealed.

The most efficient thin film solar cells these days with a current record efficiency of 18.8% on the laboratory scale [7] contain a Cu(In,Ga)Se₂ absorber layer. Since the availability of indium is an object of discussion regarding the large-scale production of CuInSe₂ solar cells [8], its replacement with other elements, for instance Zn and Sn, is reconceived. The discussion in literature goes about In-free photovoltaics, as for instance compounds belonging to the stannite-type or also kesterite type structure family [9], [10]. In this connection the Cu₂FeSnS₄–Cu₂ZnSnS₄ series will be discussed in the present work. Their two structures, the stannite and kesterite type structures, are based on different distributions of Cu⁺, Zn²⁺ and Fe²⁺ among the positions at (0,0,0), (0,½,¼) and (0,¼,¾) [4]. To get a knowledge about the metal distribution among the tetrahedral cavities in Cu₂Zn_xFe_1 − xSnS₄ neutron diffraction has to be applied. The cations Cu⁺ and Zn²⁺ are involved, causing the differentiation problems in X-ray diffraction as described above.

The work presented here will give an overview and a generalization of our detailed investigations about structure and phase relations as well as metal ordering [11], [12], [13], [14], [15], [17] of adamantine multinary chalcogenides.