Local lattice distortions in oxygen deficient Mn-doped ZnO thin films, probed by electron paramagnetic resonance

Abstract

The structure and functional properties of metal oxide films for device applications are largely affected by oxygen vacancies. While the macroscopic relationship between functionality and oxygen supply during growth is easy to access, the local influence of changing oxygen content on the incorporated metal atoms has been rarely investigated. As a model system, we use Mn as a local probe in hetero- and homoepitaxial ZnO thin films for electron paramagnetic resonance (EPR). Mn is expected to be incorporated as Mn²⁺ in the Zn-lattice site of ZnO films grown in a wide range of oxygen partial pressures. The zero field splitting (ZFS) parameter D depends on the crystallographic c/a ratio of ZnO : Mn lattice constants as it measures the trigonal distortion of oxygen tetrahedra at the Zn²⁺ site with respect to the Mn²⁺ site. The ZFS parameter D correlates linearly with displacement of Mn²⁺ ions along the c-axis in the MnO₄ tetrahedra and the corresponding bond lengths between the Mn²⁺ ions and the axial oxygen ion.

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1. Introduction

Oxide materials, in particular oxide thin films, gain more and more attention from both basic and applied points of view, due to interesting phenomena such as strong electron correlations and transparent oxide electronics. The functional properties of metal oxide thin films may be controlled by tuning the preparation conditions. However, in the interplay of structure, morphology and the functional properties such as conductivity or the ferroic properties, often an oxygen deficient growth environment is chosen because of the requirements of a smooth surface and an interface.¹ In pulsed laser deposition (PLD), one of the most flexible growth methods of oxide thin films,² the oxygen partial pressure during growth controls the distribution of oxygen vacancies.³ Thus, oxygen vacancies are a common phenomenon in functional oxides, due to the often used oxygen deficient growth conditions. The effect of oxygen vacancies on structures and macroscopic functional properties is a highly interesting and current topic of interest, as the following examples show.

In the high-T_c superconductor Y₁Ba₂Cu₃O_7-δ, under-doped surfaces with ordered oxygen vacancies result in an ortho-II band folding of the Fermi surface.⁴ Detailed point defect analysis using both computational modeling and PLD growth of SrTiO₃ shows that precise growth control allows tuning of the concentration of anion and cation vacancies and tailoring the performance of doped perovskite films.⁵ Borisevich et al. report on the increasing consideration of “oxygen vacancies… to play a role in phenomena observed at transition-metal oxide interfaces”.⁶ There, cation displacements are observed at SrRuO₃/La_0.7Sr_0.3MnO₃ (LSMO) interfaces, indicating interface dipoles between the two metallic oxides. Magnetic exchange bias and coercive fields in LSMO/SrTiO₃ were found to increase with decreasing oxygen growth pressure in PLD and sputtering, thus opening a route for tuning exchange bias by the oxygen vacancy concentrations.⁷ Detailed structural and X-ray photoelectron spectroscopy on LSMO revealed clear correlations of structural, electronic and transport properties with oxygen vacancy concentration from 0 to about 7%.⁸ Other recent experimental examples are the effect of oxygen vacancies on resistive switching in TiO_2−x films⁹ and on the two-dimensional electron gas at the SrTiO₃ surface.¹⁰ In addition, first principle and density functional theory investigations have been performed on native point defects in LaAlO₃,¹¹ on magnetic properties of Mg doped BiFeO₃ with and without oxygen vacancies,¹² and on energetics of intrinsic defects and their complexes in ZnO.¹³ Lany and Zunger calculated the donor level energy of the oxygen vacancy in ZnO to be at or below the midgap, using GW approximation calculations.¹⁴

The above examples show that the macroscopic correlation between functionality and oxygen supply during growth seems to evoke a lot of interesting phenomena. However, much less is known about the local atomic structure of the functional oxides on the availability of oxygen. To contribute to this question, we use as a model system, Mn²⁺ ions as paramagnetic probes in heteroepitaxial ZnO. The ZnO : Mn thin films are grown by PLD on a-plane sapphire substrates in a wide range of oxygen partial pressures. Electron paramagnetic resonance (EPR) spectroscopy of the Mn²⁺ ions allows monitoring the influence of the oxygen growth pressure on the structural properties of the films on a local scale by precise measurements of the zero field splitting (ZFS) of the divalent manganese ions. The Mn²⁺ ZFS parameters are then correlated with (volume-averaged) in-plane and out-of-plane lattice constants a and c of the thin films, respectively, as obtained by high-resolution X-ray diffraction (HR-XRD).

2. Electron paramagnetic resonance of Mn²⁺ in ZnO thin films

The incorporation site and the electronic state of paramagnetic transition metal ions in ZnO bulk materials have extensively been studied by EPR spectroscopy.^15,16 Divalent ions such as Mn²⁺ are incorporated in the trigonally distorted tetrahedral Zn lattice sites (C_3v symmetry). Therefore, the Mn²⁺ EPR spectrum in ZnO displays a characteristic ZFS with an axial ZFS parameter D = −707 MHz as observed for weakly Mn-doped ZnO single crystals.^17,18 The D parameter is considered as a measure of the trigonal distortion of the oxygen tetrahedra by the Mn²⁺ ions substituting Zn²⁺ at the metal ion sites in the ZnO wurtzite structure. Indeed, a linear correlation D ∝ ε_V between D and the volume compression ratio of the unit cellwas proposed for manganese doped ZnO thin films grown on c-plane sapphire substrates recently.¹⁹ Here a₀ and c₀ are the lattice parameters of the undoped ZnO single crystals. Diaconu et al. state that while in single crystals both lattice axes a and c increase with increasing Mn content only the c-axis increases with increasing Mn content in thin films. Obviously, in such a case with a constant in-plane lattice parameter a, the ZFS parameter D will become proportional to the axial compression ratio ε_c = c/c₀ − 1. In that work the lattice parameters of the thin films were changed by different Mn²⁺ doping concentrations in the range 0.1 at% to 9.1 at% whereas other growth parameters were kept unchanged.¹⁹ However, except for the lowest manganese concentration the complete 30 lines Mn²⁺ EPR spectrum could not be resolved in the spectra due to dipolar spectral broadening leading to appreciable errors in the estimated D parameters and preventing further the analysis of the distribution widths of the ZFS parameters. The latter may give additional local information about strain effects in the thin films.

Therefore, in the present work we choose only low manganese concentrations of either 0.2 or 0.02 at% to avoid dipolar line broadening and to access the full spectral information of the Mn²⁺ EPR spectra. Moreover, the low doping levels prevent a significant increase in the c-axis lattice parameter of the films that might already be caused by the direct Mn²⁺ incorporation in the Zn sites of ZnO films.^19,20 In that way, we are now able to measure precisely both c-plane and a-plane lattice parameters of the ZnO thin films and the Mn²⁺ ZFS parameters and their distribution widths that are dependent on the oxygen partial pressure during their PLD growth process without the interference of other crucial parameters. The ZFS parameters are correlated with the c- and a-lattice constants of the films and the displacement of the Mn²⁺ in the oxygen tetrahedra along the c-axis using the superposition model.

3. Results

3.1. Structural characterization

Fig. 1 shows typical results of the structural investigations by XRD and HR-XRD. All ZnO films grow with perfect c-axis orientation on a-plane sapphire (Fig. 1a) and c-plane ZnO, in agreement with previous investigations.²¹ The HR-XRD rocking curves and reciprocal space maps (RSMs) show remarkable differences for hetero- and homoepitaxial samples, for numerical values of the FWHM of the ZnO(002) rocking curves see Table 1. Fig. 1b shows three typical ZnO(002) rocking curves with FWHM from 0.0129° to 0.320°, indicating huge differences in tilt mosaicity of the sample types. The different structural quality of hetero- and homoepitaxial ZnO is further explained by the RSMs in Fig. 1c–f. Here, in addition to the tilt mosaicity expressed by the horizontal broadening of (002) reflections, the broadening of skew-symmetric (101) reciprocal lattice points demonstrates the twist mosaicity, because these peaks are measured with a high chi-tilt angle of 61.61° in HR-XRD. In contradiction to the clearly higher tilt and twist mosaicity of the heteroepitaxial films, the uncertainty of d-spacing as expressed by the vertical broadening of the reciprocal lattice points, is much lower. The extrapolated out-of plane and in-plane lattice constants of all samples are listed in Table 1.

Fig. 1 Typical XRD results of the hetero- and homoepitaxial ZnO : Mn films: (a) wide-angle 2θ − ω scan shows only ZnO(002), (004) and Al₂O₃(110), (220) peaks. (b) shows typical rocking curves of the ZnO(002) peak as a measure of tilt mosaicity. For the homoepitaxial sample G4207, ZnO : Mn film and ZnO substrate peaks cannot be separated. (c) and (e) are ZnO(002) and (101) reciprocal space maps (RSMs) of the heteroepitaxial sample G4004, respectively, while (e) and (f) are the corresponding RSMs for the homoepitaxial sample. Obvious are the differences in horizontal and vertical broadening of the reciprocal lattice points, accounting for tilt (002) and twist (101) mosaicity, and d-spacing blurring, respectively.

Table 1 Oxygen partial pressures p_O2 during PLD, manganese concentrations in the PLD target c_MnO, extrapolated HR-XRD c- and a-axis lattice parameters, FWHM of the ZnO(002) rocking curve, and ZFS parameter D with ZFS distribution widths ΔD and ΔE, of the ZnO : Mn thin films on a-plane sapphire. Sample G4207 was homoepitaxially grown on c-plane ZnO (O-face)

Sample	p O2 (mbar)	c MnO (%)	c (Å)	a (Å)	FWHM (°)	D (MHz)	ΔD (MHz)	ΔE (MHz)
a For Mn^2+ in the ZnO single crystalline substrate, which, however, also contains Fe, Co, Ni. Assuming a homogeneous Fe distribution in the film and the substrate, cFe(III) is 2.3 × 10^15 ions per sample.
G4438	6 × 10^−5	2 × 10^−2	5.2305	3.242	0.452	—	—	—
G4437	3 × 10^−4	2 × 10^−2	5.2267	3.246	0.357	−584	140	40
G4009	2 × 10^−3	2 × 10^−2	5.2233	3.249	0.195	−611	110	40
G4005	2 × 10^−3	2 × 10^−1	5.228	3.245	0.225	−611	100	40
G4592	5 × 10^−3	2 × 10^−2	5.2263	3.246	0.160	−606	95	20
G4207^a ZnO substrate	1.6 × 10^−2	2 × 10^−2	5.2063	3.2497	0.0129	−707	10	0
G4008	1.6 × 10^−2	2 × 10^−2	5.2131	3.247	0.148	−650	35	15
G4004	1.6 × 10^−2	2 × 10^−1	5.2130	3.246	0.130	−653	40	20
G4591	5 × 10^−2	2 × 10^−2	5.2085	3.249	0.134	−674	35	15
G4436	8 × 10^−2	2 × 10^−2	5.2065	3.249	0.568	−703	180	40
G4206	1.6 × 10^−1	2 × 10^−2	5.2061	3.250	0.320	−707	120	40
G4590	5 × 10^−1	2 × 10^−2	5.2084	3.2475	0.194	−671	90	20

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Fig. 2 shows the oxygen partial pressure dependence of the c- and a-axis lattice parameters and the FWHM of the ZnO(002) rocking curves. The lattice parameters of all samples show an almost smooth variation with the oxygen partial pressure, indicating c-axis expansion and a-axis compression of ZnO with decreasing oxygen pressure, i.e. increasing concentration of oxygen vacancies (Fig. 2a and b).²² This in-plane contraction and out-of-plane expansion of the c-axis oriented ZnO unit cells are in qualitative agreement with calculated local atomic relaxations around the neutral oxygen vacancy V⁰_O, see Fig. 4 in ref. 23, as obtained from first-principle local density approximations.

Fig. 2 Oxygen partial pressure dependence of (a) out-of-plane c-axis lattice parameter, (b) in-plane a-axis lattice parameter, and (c) FWHM of the ZnO(002) rocking curves. Data of the homoepitaxial sample (the ZnO single crystal) are marked by the gray filled symbols.

Fig. 3 Experimental and simulated EPR spectra at 297 K of the ZnO : 0.02% Mn (p_O2 = 1.6 × 10⁻² mbar) thin film sample G4008 for B⃑||c and B⃑⊥ c.

Fig. 4 Experimental EPR spectra at 297 K of (a) ZnO : 0.02% Mn (G4008) and (b) ZnO : 0.2% Mn (G4004) thin films both grown at p_O2 = 1.6 × 10⁻² mbar B⃑⊥ c.

For the FWHM (002), three samples were intentionally included which do not follow the general behavior of the majority of films, probably because of substrate issues (top right in Fig. 2c). However, all samples from Fig. 2c fit well the results discussed further below, demonstrating the general validity of our work.

3.2. EPR spectroscopy

The EPR spectra of the heteroepitaxial ZnO : Mn thin films (Fig. 3 and 4) and of the homoepitaxial ZnO : Mn films (Fig. 5a) display the typical thirty line spectrum of Mn²⁺ ions with their 3d⁵ electronic configuration having a ⁶S_5/2 electronic ground state for the two orientations of the external magnetic field, parallel or perpendicular to the crystallographic c-axis. Here the total electron spin S = 5/2 gives rise to a zero field splitting into five fine structure (fs) transitions, each split into six hyperfine (HF) interaction lines due to the HF interaction with the nuclear spins I = 5/2 of the ⁵⁵Mn nuclei. If we assume isotropic electron Zeeman and ⁵⁵Mn HF interactions the EPR spectra of the Mn²⁺ ions can be described by the following spin Hamiltonian,^17,18,24where g is the electron g-factor and A the ⁵⁵Mn HF interaction parameter. The ⁵⁵Mn nuclear quadrupole interaction has been neglected in eqn (2) as it has no effect on the allowed EPR transitions in the spectra recorded for B⃑ ‖ c and B⃑ ⊥ c that have been analyzed here. D refers to the axial ZFS and a and F are the cubic ZFS parameters. The (x, y, z) and (ξ, η, ζ) coordinates refer to the trigonal and cubic axes of the crystal field, respectively. Although the Mn²⁺ ions are incorporated in nominally axially symmetric Zn²⁺ lattice sites (C_3v symmetry) a rhombic contribution to ZFS measured by the parameter E has been included in the spin Hamiltonian. It may allow for possible rhombic distortions of the crystal field in the heteroepitaxial ZnO : Mn films acting on the manganese ions due to strains caused by the sapphire substrate.

Fig. 5 Experimental single crystal EPR spectrum (sample G4207) (a) and EPR spectra of ZnO : 0.02% Mn thin film samples grown under oxygen partial pressures of (b) p_O2 = 1.6 × 10⁻³ mbar (G4009) and (c) p_O2 = 1.6 × 10⁻² mbar (G4008). The spectra were recorded at 297 K for B⃑⊥ c. Asterisks indicate signals of Fe³⁺ impurities in either the sapphire substrate (films) or the ZnO single crystal G4207.

As a typical example for a heteroepitaxial ZnO : Mn film Fig. 3 illustrates the experimental Mn²⁺ EPR spectra of the ZnO:0.02% Mn (p_O2 = 1.6 × 10⁻² mbar) thin film sample G4008 for B⃑ ‖ c and B⃑ ⊥ c together with simulated spectra based on the spin Hamiltonian in (2). The line widths of the five fs transitions centered at 265 mT (m_S = 5/2 ↔ 3/2), 306 mT (m_S = 3/2 ↔ 1/2), 351 mT (m_S = 1/2 ↔ −1/2), 396 mT (m_S = −1/2 ↔ −3/2), and 441 mT (m_S = −3/2 ↔ −5/2) for B⃑ ‖ c differ significantly and increase with increase in the magnetic spin quantum number m_S. Such a behavior is indicative of a distribution in the ZFS parameters and has been taken into account by Gaussian distributions of the ZFS parameters D and E with the corresponding distribution widths ΔD and ΔE in our spectral simulations. We have to note that the spectra for B⃑ ‖ c are only influenced by the axial ZFS parameter D in the case of isotropic g-tensors whereas the spectra are sensitive to both, D and E, for B⃑ ⊥ c. Therefore, the distributions ΔD and ΔE can be separated from each other by simulations of spectra recorded for the two different orientations.

The simulations revealed an axial ZFS parameter D = −650 MHz with distribution width ΔD = 35 MHz and a small distribution ΔE = 15 MHz of the rhombic ZFS parameter about E = 0 (Table 1). The D parameter is in the typical range reported for Mn²⁺ incorporated in Zn²⁺ lattice sites in ZnO.^17–19 The overall axial symmetry of the ZFS interaction (E = 0) was confirmed by a rotation of the magnetic field perpendicular to the c-axis of the film where no significant changes of the positions or line widths of the four outer fs transitions (m_S = ±3/2 ↔ ±1/2, m_S = ±5/2 ↔ ±3/2) have been observed for sample G4008. In the simulations an isotropic g-value g = 2.001 and an isotropic ⁵⁵Mn HF interaction parameter A = −222 MHz was assumed. The negative sign of the D parameter can be deduced from the spectral simulations. In particular the field positions of the m_S = ±3/2 ↔ ±1/2 transitions depend on the sign of the parameter ratio A/D. The cubic ZFS parameters a = 18 MHz and F = 12 MHz were taken from a single crystal study of Mn²⁺ ions in ZnO.

The influence of the Mn²⁺ concentration on the ZFS parameters has been examined at two distinct oxygen partial pressures, p_O2 = 1.6 × 10⁻² mbar (samples G4008 and G4004) and p_O2 = 2 × 10⁻³ mbar (samples G4009 and G4005), during the PLD process. Although the Mn²⁺ concentrations differ in each case by one order of magnitude the ZFS parameters D and E as well as their distribution widths ΔD and ΔE as determined by spectral simulations do not vary significantly (Table 1). However, the higher Mn²⁺ doping results in a substantial increase in the homogeneous EPR line widths ΔB^hom_pp as seen in Fig. 4 for the samples G4008 and G4004 due to enhanced dipolar interactions between the paramagnetic ions in the higher doped films. Here ΔB^hom_pp increases from 9 MHz to 18 MHz with increasing Mn concentration whereas for samples G4009 and G4005 ΔB^hom_pp increases even by a factor of 3 (12 MHz versus 36 MHz).

In contrast to the concentration of the dopants the oxygen partial pressure p_O2 during the PLD process affects crucially the axial ZFS parameters D and ΔD. Fig. 5 illustrates the influence of p_O2 on the Mn²⁺ EPR spectra at B⃑ ⊥ c for two selected samples. Obviously, the line widths caused by the distribution in the ZFS parameters increase strongly for the film prepared at lower oxygen partial pressures (Fig. 4b) leading to less resolved outer fs transitions. The spectral simulation for both film orientations B⃑ ⊥ c and B⃑ ‖ c (spectra not shown) indicates clearly that this increase in line broadening is mainly caused by the distribution ΔD in the axial ZFS parameter D. There is also an effect of the oxygen partial pressures on the distribution ΔE of the rhombic fs parameter E but it appears to be less pronounced. In addition to the ΔD values, the absolute value of the axial ZFS parameter D depends likewise in a characteristic manner on p_O2. Overall it decreases with lower oxygen partial pressures. All ZFS parameters of the studied films as obtained from the spectral simulations are summarized in Table 1. In addition the ZFS parameters of Mn²⁺ impurities present in the homoepitaxial ZnO : Mn film sample (G4207) are presented in the table as well. For comparison its EPR spectrum is also displayed in Fig. 5a. It is worth noting that the ΔD parameter in the homoepitaxial ZnO : Mn film sample is substantially smaller (by a factor of four or more) than those of the heteroepitaxial film samples. In the case of the homoepitaxial sample we have to take into account that Mn²⁺ and Fe³⁺ ions are also present in the ZnO single crystal substrate as impurities for EPR spectroscopy appreciable concentrations, compare ref. 25. In contrast the sapphire substrates did not exhibit EPR signals from Mn²⁺ impurities. Only some minor Fe³⁺ signals were detected in the measured magnetic field range that did not interfere with the Mn²⁺ spectrum of the ZnO : Mn films. But the EPR spectra of the homoepitaxial sample do not allow us to distinguish between manganese ions incorporated in the thin film and the Mn²⁺ impurities of the ZnO substrate since only a single Mn²⁺ species is observed. Moreover, as the Mn²⁺ signal intensity for the sample G4207 is substantially higher than those for the heteroepitaxial ZnO : Mn films we assume that the Mn²⁺ EPR signal of the homoepitaxial ZnO : Mn film is mainly caused by manganese impurity ions in the ZnO single crystal substrate. Indeed the obtained spin Hamiltonian parameters of its Mn²⁺ ions (Table 1) are in agreement with those reported for Mn²⁺ impurities in low concentrations in ZnO single crystals.^17,18 Therefore we may refer to this sample as a ZnO single crystal in the following and consider it as a reference sample for Mn²⁺ substitution in undisturbed ZnO single crystals.

4. Discussion

The XRD data reveal an obvious relationship between the lattice axes parameters c and a and the oxygen partial pressure during the growth process. We suppose that the major reason for the observed dependence of this biaxial strain on p_O2 is the formation of oxygen vacancies at low p_O2 values. Pseudomorphic, i.e. in-plane lattice matched growth can be excluded for the heteroepitaxial ZnO films on sapphire. For films grown at p_O2 > 5 × 10⁻² mbar both lattice constants appear to be comparable to the single crystal values. However, the c-axis parameter increases strongly with decreasing pressure for pressures p_O2 < 5 × 10⁻² mbar, whereas the parameter a declines slightly. These opposing trends for c and a indicate that the volume of the unit cell of the ZnO films does not significantly change with oxygen partial pressure and stays comparable with that of the single crystal. This fact is illustrated by a comparison of the volume compression ratios ε_V for the various films with the single crystal value as displayed in Fig. 6.

Fig. 6 Volume compression ratio ε_V (solid squares) and axes compression ratios ε_a (open triangles) and ε_c (open circles) of the ZnO single crystal and ZnO thin film samples depending on oxygen partial pressures p_O2. Gray filled symbols indicate single crystal data.

The figure also includes the compression ratios for the c- and a-axes lattice parameters ε_c = c/c₀ − 1 and ε_a = a/a₀ − 1. The data suggest that the unit cell of the ZnO films shrink perpendicular to the crystallographic c-axis with increasing formation of oxygen vacancies at lower oxygen partial pressures and consequently the bond length between the Zn²⁺ ion and the three non-axial oxygen atoms in the ZnO₄ tetrahedra are becoming shorter. This, however, is related to an increase in the axial Zn–O bond length R₁(0) along the c-axis as the overall unit cell volume is conserved. For lower oxygen partial pressures and enhanced oxygen vacancy formation the strain in the films seems to increase as well as indicated by the widths of the diffraction peaks (Fig. 1c).

Supplementary to the XRD data the manganese ZFS parameters as determined from EPR spectroscopy provide a microscopic perspective at the changes of the ZnO₄ or more precisely the MnO₄ tetrahedra upon the enhanced formation of oxygen vacancies with decreasing oxygen partial pressures in the ZnO films. Indeed, we observe within the experimental accuracy almost linear correlations between the axial ZFS parameter D and the axis lattice parameter ratio c/a of the films and between distribution widths ΔD of the axial ZFS parameter and the widths of the diffraction peaks (Fig. 7). In that way a correlation can be established between the c/a ratio and the distortions of the metal ion–oxygen tetrahedra. The results confirm that the MnO₄ tetrahedra experience the same structural modification as the ZnO₄ units and the paramagnetic Mn²⁺ ions can be considered to be suitable probes to monitor the structural variations of the films on a local microscopic scale. However, the D parameter of the Mn²⁺ ions would not become zero even for an assumed case of an ideal wurtzite structure²² (c/a = (8/3)^1/2), see Fig. 7a. The reason is a small displacement δ of the Mn²⁺ ions with respect to the Zn²⁺ site along the c-axis in the metal–oxygen tetrahedron presumably due to minor differences in the ionic radii.^24,26 We have to note that the axial ZFS parameter D monitors the increase of the axial metal ion–oxygen bond length R₁ along the c-axis, which is related to an axial elongation of the unit cell and an increase in the lattice parameter c as observed in the XRD experiments. In addition, the determined distribution widths ΔD of the axial ZFS parameter point at some variance in the bond lengths R₁ and consequently at some structural distortions of the MnO₄ tetrahedra depending on oxygen growth pressure and the formation of oxygen vacancies in the films. Moreover, a small distribution ΔE of the rhombic ZFS parameter about E = 0 was likewise observed for all studied ZnO thin films (Table 1) indicating some deviation from the perfect C_3v symmetry of the tetrahedra. This might be caused either by slightly different non-axial metal ion–oxygen bond lengths or bond angles. Otherwise for the ZnO single crystal the EPR spectra reveal ΔE = 0 within the experimental accuracy. Therefore we suppose that the distortions of the C_3v symmetry of the tetrahedra indicate the presence of small strains in the films due to a misfit between the ZnO films and the a-sapphire substrates.

Fig. 7 Experimentally determined (a) ZFS parameter D depending on the ratio of the lattice parameters c and a and (b) ZFS distribution widths (filled squares) ΔD and (open circles) ΔE depending on FWHM of the ZnO(002) peak for ZnO thin film samples and the ZnO single crystal (gray filled symbols). The scaling 1.633 = (8/3)^1/2 in the c by a ratio takes into account the lattice parameter ratio c/a = (8/3)^1/2 of the ideal wurtzite structure.²² The solid lines are linear fits to the data points.

In the final step we want to rationalize why the absolute value of the ZFS parameter D decreases with increasing axial elongation of the metal ion–oxygen tetrahedra as indicated by the increase of the axis parameter c with decreasing p_O2 (Fig. 7a). Our analysis will further provide an interpretation of the experimentally obtained D parameters of the Mn²⁺ ions in terms of displacements of the metal ion in the oxygen tetrahedra depending on the axes lattice parameters c and a of the ZnO films.

Recently, Zi-Yuan²⁶ derived a local structure model of the MnO₄ tetrahedra from the D parameter of Mn²⁺ ions measured for lightly doped ZnO single crystals (D = −707 MHz) using the superposition model.²⁷ In the proposed model the structures of the MnO₄ tetrahedra differ slightly from those of the ZnO₄ tetrahedra in the parent ZnO material. The Mn²⁺ ion is displaced by δ = 0.03 Å with respect to the Zn²⁺ site along the c-axis towards the basal of the oxygen tetrahedra. Here, the displacement δ = 0.03 Å was taken from the average ionic radii of Mn²⁺ (0.8 Å) and Zn²⁺ (0.74 Å). Then, the D value was assumed to be related to a small deviation Δθ = 1° of the angle θ between c-axis and the bond directions of the three non-axial basal oxygen ions in the MnO₄ tetrahedra in comparison with the parent ZnO₄ tetrahedra. However, as only a single experimental D value with a single set of structural data, those from the single crystal, was used the validity of the structure model could not be tested.

By exploring the Mn doped ZnO thin films grown under different oxygen partial pressures we have a whole set of ZnO materials with different structural parameters and corresponding Mn²⁺D ZFS parameters available to identify the structure of the MnO₄ tetrahedra. In order to interpret the axial ZFS parameters we use high-order perturbation theory based on the spin–orbit coupling mechanism for S-state ions in a weak-field scheme^28,29 for the computation of the dependence of D on the structural parameters of the ZnO thin films. We postulate likewise that the Mn²⁺ ions are incorporated in the Zn²⁺ lattice sites but may be displaced by δ with respect to the zinc site along the c-axis towards the basal of the oxygen tetrahedra (Fig. 8) due to the slightly larger ionic radii of Mn²⁺versus Zn²⁺. However, we do not assume a fixed displacement but rather consider δ as a function of the lattice parameters c and a that depend on the oxygen partial pressure during the growth process.

Fig. 8 Schematic drawing of the structure of the MnO₄ tetrahedra in the ZnO : Mn films with the structural parameters θ, R₁, R₂, and δ.

The axial ZFS parameter D that depend on the crystal field parameters B₂₀, B₄₀, and B₄₃ in the case of trigonal symmetry has been calculated in the weak field scheme, where the total crystal field and the spin–orbit coupling are taken as perturbations, by Ju et al.²⁸ and Zheng et al.²⁹

D ≈ −P₁(B,C)⁻¹(3ξ_d²B₂₀² + 63ξ_d²B₂₀) − P₂(B,C)⁻¹(10ξ_d²B₄₀² − 7ξ_d²B₄₃²). (3)

The parameters

P₁(B,C) = 70(7B + 7C)²(17B + 5C) (4)

and

P₂(B,C) = 126(7B + 7C)²(10B + 5C) (5)

are solely determined by the Racah parameters B = 960 cm⁻¹ and C = 3352 cm⁻¹.²⁶ξ_d = 308 cm⁻¹ is the spin–orbit coupling constant of the Mn²⁺ ions. The dependencies of the crystal field parameters B₂₀, B₄₀, and B₄₃ on the bond lengths R₁ and R₂ between the Mn²⁺ ion and the axial and basal oxygen next neighbors (Fig. 8) are calculated using the approximation of the superposition model²⁷andwith the reference distance R₀ = 1.9813 Å, the exponents t₂ = 3 and t₄ = 5 and the two parameters A₄ = −27 Dq/16 and A₂ = 12 A₄, where Dq = −650 cm⁻¹ is the cubic crystal field splitting parameter.²⁶ The bond distances R₁ and R₂ as well as the angle θ between directions of bonds between the manganese ion with the basal and axial oxygen ions depend on the displacement δ (Fig. 8) and are given by

R₁(δ) = uc − δ (9)

with the parameter u = 0.3819 for ZnO.³⁰ Here, δ > 0 corresponds to displacements of the Mn²⁺ ions towards the axial oxygen ion with respect to the Zn²⁺ site whereas negative values of δ indicate a relative shift of the substitutional ion towards the basal oxygen ions.

The displacement δ of the Mn²⁺ ion along the c-axis with respect to the positions of the Zn²⁺ site can then be determined numerically for each set of film parameters c, a, and D by solving eqn (3)–(11). Two solutions δ₁ < 0 and δ₂ > 0 for the displacements are obtained for each parameter set and their absolute values are displayed to be dependent on the c-axis lattice parameter in Fig. 9a. The corresponding bond angles for the two solutions θ₁ = 107.7° and θ₁ = 109.5° vary by only ±0.1° within the obtained range of δ_1,2 values. Using eqn (9) two choices for the bond length between the Mn²⁺ ion and the axial oxygen ion, R₁(δ₁) and R₁(δ₂), can be calculated for the two solutions δ₁ and δ₂ (Fig. 9b).

Fig. 9 (a) Absolute values of calculated displacements (solid squares) δ₁ and (open circles) δ₂ of the Mn²⁺ ions along the c-axis in the MnO₄ tetrahedra and (b) corresponding bond lengths R₁ (solid squares for solutions δ₁, open circles for solutions δ₂) between the Mn²⁺ ions and the axial oxygen ion depending on the c-axis crystal parameter as obtained for ZnO thin film samples and the ZnO single crystal (gray filled symbols).

In the case of R₁(δ₁) the Mn²⁺ ion is displaced towards the axial oxygen ion along the c-axis with respect to the Zn²⁺ site whereas for R₁(δ₂) it is shifted towards the basal oxygen ions of the tetrahedron. In each situation the Mn–O bond distances increase with the increasing lattice axis parameter c and enhanced formation of oxygen vacancies with decreasing p_O2 during the growth of the ZnO films. The crystal field at the manganese ion becomes weaker with the increasing c-axis parameter. This explains why the absolute value of the axial ZFS parameter D decreases with increasing lattice axis parameter c although the axial distortion of the tetrahedron becomes larger. Fig. 10 illustrates the linear dependence of D on the absolute values of the computed displacement solutions δ₁ and δ₂.

Fig. 10 Correlation between experimentally determined axial ZFS parameter D and absolute values of displacements (a) δ₁ and (b) δ₂ of the Mn²⁺ ions along the c-axis in the MnO₄ tetrahedra as obtained for ZnO thin film samples and the ZnO single crystal (gray filled squares).

On the basis of our analysis of the D parameter we cannot safely rule out one of the two possible Mn²⁺ positions described by R₁(δ₁) and R₁(δ₂). We may only speculate that a displacement R₁(δ₁) towards the axial oxygen ion with respect to the Zn²⁺ position seems to be more likely as that such a shift has been observed for divalent manganese ions incorporated in the likewise axially distorted tetrahedral metal sites in GaN and AlN.^17,18,24 However, we can firmly rule out the above discussed model suggested by Zi-Yuan et al. where the axial ZFS splitting was assumed to be caused only by a variation in the angle θ between the MnO₄ and the host ZnO₄ tetrahedra.²⁶ Varying exclusively the angle θ in eqn (6)–(8) but keeping R₁ and R₂ constant, we have not been able to reproduce our experimental D parameters.

5. Experimental

ZnO : Mn thin films were grown by PLD using a KrF excimer laser from polycrystalline source targets mixed, pressed and sintered from ZnO and MnO powders (Alpha Aesar, 5N purity). As a substrate we used a-plane sapphire, or a c-plane O-face ZnO single crystal, both supplied by CrysTec GmbH. The growth temperature of the films was about 650 °C and 45 000 laser pulses were applied. The oxygen partial pressure was controlled in between 10⁻¹ and 6 × 10⁻⁵ mbar. Table 1 gives an overview of the samples (for identification of consecutively grown samples we maintain the original sample ID no.). For more details of our ZnO thin film growth activities see ref. 21 and references therein.

XRD rocking curves and reciprocal space maps were measured with a Philips X'pert diffractometer with Cu K_α1 point focus, a 4× Ge (220) Bartels primary monochromator, a 4-axis goniometer (Eulerian craddle), and either an open detector or a secondary monochromator (triple axis), respectively. XRD wide-angle 2θ − ω scans were measured with Cu K_α1/2 radiation and the focussing Bragg Brentano goniometer (Philips X'pert) with a graphite secondary monochromator for suppression of bremsstrahlung. For highly precise determination of out-of-plane (c) and in-plane (a) lattice constants of the heteroepitaxial films we used a PANalytical X'pert PRO MRD with a parabolic mirror and a Bartels monochromator as primary optics with Cu K_α1 line focus and the PIXcel^3D detector in 1D scanning mode with 255 channels. In order to precisely correct the goniometer height errors, we measured (002), (004), and if possible also (006) symmetric and (101) and (202) asymmetric peaks, and extrapolated the lattice constants from plots over cos²(θ). This method was recently proved to yield highly precise (5 × 10⁻⁴ and 5 × 10⁻⁵) lattice constants for heteroepitaxial ZnO films and single crystals, respectively, in agreement with independently determined values from X-ray multiple reflections.³¹

Proton induced X-ray emission (PIXE) and Rutherford backscattering spectrometry (RBS) were used for determination of Mn concentration, layer thickness, and for trace element analysis. A 1.2 MeV H⁺ beam of the Leipzig ion probe LIPSION with a beam diameter of 0.4 mm and a collected charge of 10 μC per measurement was used. PIXE and RBS spectra were fitted with the GeoPIXE II³² and RUMP³³ software, respectively.

The obtained Mn concentrations confirmed within the experimental uncertainty that the PLD target compositions were transferred almost unchanged into the ZnO : Mn thin films. The metal to oxygen ratio was 1.00 ± 0.02 for the samples grown at intermediate oxygen partial pressure. The ZnO : Mn film thickness of the heteroepitaxial samples was determined to be between 1.08 and 1.46 μm, depending on the growth conditions and using a mass density of 5.62 g cm⁻². These thickness values are in good agreement with the HR-XRD result of the homoepitaxial sample G4207, where around ZnO(002) Pendellösung oscillations could be observed (see Fig. 1d). The mean fringe period of 0.00653° yields a mean ZnO : Mn thickness of 1.41 ± 0.10 μm for this particular sample.

EPR experiments have been performed on an X-band Bruker ELEXSYS E580 spectrometer at room temperature using a cylindrical ER4119 HS cavity. The ZnO thin film samples (area size 2 mm × 4 mm) and the ZnO single crystal (with homoepitaxial ZnO : Mn film) were mounted on a quartz rod sample holder. The angle between the c-axis of the ZnO crystal and the direction of the applied magnetic field was controlled by a goniometer. Spectral simulations of the Mn²⁺ EPR spectra were done using the EasySpin EPR simulation package³⁴ which employs full matrix diagonalization of the complete Mn²⁺ spin Hamiltonian operator.

6. Summary and conclusions

The influence of the oxygen partial pressure during the PLD growth process on the structural properties was explored for manganese doped heteroepitaxial ZnO thin films by HR-XRD and EPR spectroscopy of Mn²⁺ ions substituting Zn²⁺ in the ZnO lattice. This combined approach allowed us to correlate the induced changes of the overall film structure with the local properties at the tetrahedral incorporation site of the divalent manganese ions. Our work reveals a significant expansion of the ZnO film structure along the c-axis combined with the a-axis compression with decreasing oxygen partial pressure that we ascribe to the enhanced formation of oxygen vacancies under oxygen deficient growth conditions. This increase of the c-axis lattice parameter translates into an increase of the bond distances between the metal ions and the axial oxygen ions along the c-axis in the metal ion–oxygen tetrahedra of the ZnO films. In the case of Mn²⁺ substituting Zn²⁺ this enlargement of the Mn–O bond distance is monitored by the axial Mn²⁺ ZFS parameter D. Using the superposition theory of crystal fields, the Mn–O bond distances could be calculated from the D parameter for the distinct oxygen partial pressures and related to the c-axis lattice parameters. In that way, linear relations have been obtained between the c-axis expansion and the ZFS parameter D as well as the axial Mn–O bond distance R₁. Although the D parameter decreases by about 120 MHz for the films grown under the lowest oxygen partial pressure (p_O2 = 3 × 10⁻⁴ mbar) used here in comparison with films grown at p_O2 = 1.6 × 10⁻¹ mbar or the ZnO single crystal, the corresponding increase in the axial Mn–O bond distance R₁ is only 0.013 Å that indicates the high sensitivity of the Mn²⁺ ZFS parameter with respect to small local structural distortions. We assume that the Mn²⁺ ion is slightly shifted towards the axial oxygen ion with respect to the Zn²⁺ site. In this case, the bond distance between the Mn²⁺ ion and the axial oxygen ion will increase with the increasing c-axis lattice parameter in comparison with the corresponding axial Zn–O bond length and the displacement of the Mn²⁺ ion from the Zn²⁺ site becomes smaller with an enhanced expansion of the ZnO lattice.

We would like to emphasize that the enhanced formation of oxygen vacancies at lower oxygen partial pressures also results in higher structural distortions of the films as indicated by the increase of the width of the HR-XRD rocking curves and, locally measured by the EPR of the Mn²⁺ ions, the larger distribution widths of the ZFS parameter D. The latter could again be interpreted in terms of increasing variation in the axial Mn–O bond distance R₁ at higher oxygen vacancy concentrations. The presented investigations may be extended to doped oxide thin films with low Mn²⁺ concentration as local probes for lattice distortions and bond lengths.

Acknowledgements

We thank Gabriele Ramm for PLD target preparation, Holger Hochmuth for PLD growth, Sascha Bader for technical support in the HR-XRD lattice constant determination. We gratefully acknowledge the financial support by the DFG within SFB 762 “Functionality of Oxide Interfaces” and the SPP 1601 “New Frontiers in Sensitivity for EPR Spectroscopy: From Biological Cells to Nano Materials”.

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Footnote

† Present address: Steinstr. 23, D-04275 Leipzig, Germany.

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