Impact of Mg content on native point defects in Mg_xZn_1−xO (0 ≤ x ≤ 0.56)

ZnO is a prime candidate for next generation opto- and microelectronics with a large exciton binding energy that permits efficient light emission at room temperature.^1–3 The 3.37 eV band gap of ZnO can be tuned by incorporating either Mg or Cd⁴ to enable complex heterostructures that can enhance transport properties in ZnO based transistors^5,6 and optoelectronic efficiency of UV lasers,⁷ light emitting diodes, and solar blind detectors.⁸ The ZnO band gap increases with Mg alloying and Mg can be incorporated into ZnO at low concentrations without significantly disrupting the wurtzite structure.⁷ Thus, (Mg,Zn)O layers can be stacked on ZnO layers with only a small lattice mismatch allowing for high quality heterostructures and devices.^9–11 However, ZnO occurs naturally in a zincblende or wurtzite structure, while MgO occurs naturally in a rocksalt structure, and little study has been directed at the detection and characterization of defects in the (Mg,Zn)O alloys, especially with high quality, isostructural single crystals across a wide alloy range.

The two most thermodynamically stable defects in ZnO are oxygen vacancies (V _O) and zinc vacancies (V _Zn), particularly under our Zn-rich growth conditions.¹² (Details of our growth conditions and defect thermodynamic stability are reported in Ref. 13.). These native point defects can be electrically charged and can contribute to free carrier densities.^14–17 Thus, V _Zn defects act as acceptors to partially compensate degenerate carrier densities in Ga-doped ZnO.¹⁸ Similarly, defect complexes associated with V _O can be associated with increased n-type doping in ZnO.¹⁹ These vacancies appear to be mobile since depth-resolved cathodoluminescence spectroscopy (DRCLS) reveals pronounced segregation of V _O^20,21 and cation vacancies V _C, either V _Zn or V _Mg (this paper). Besides doping, defect levels deep within the band gap of ZnO and (Mg,Zn)O represent traps that increase “non-radiative” recombination of free carriers for transport and optoelectronic applications as well as introduce interface states that affect Schottky barrier heights. Indeed, while (Mg,Zn)O alloys are envisioned as lattice-matched confinement layers for ZnO quantum well lasers, deep level defects would degrade such lasing as well as alter the heterojunction band offsets that determine quantum well depths. Here, we describe the spatial distributions, densities, and energy levels of V _C and V _O defects and their dependence on Mg alloy composition. These defects produce energy levels deep within the (Mg,Zn)O band gap that produce nearly all midgap luminescence intensity, reflecting their recombination velocities relative to band-to-band recombination and, in turn, the impact of these native point defects on transport and light emission efficiency.

We performed these studies using a wide (0 ≤ x ≤ 0.56) range of single crystal Mg_xZn_1−xO alloy compositions grown on r-plane sapphire by molecular beam epitaxy (MBE). This wide range is particularly useful in identifying electronic trends that would not be evident over a more limited range. Furthermore, X-ray diffraction (XRD) shows these a-face (Mg,Zn)O alloys are isostructural and single-phase over this range,²² notwithstanding the Mg-rich lattice transformation from wurtzite to cubic rocksalt crystal symmetry. The depth dependence of defect densities measured for these alloys provided additional advantages: (1) the magnitude of defect segregation to the free surface vs. alloy composition and (2) the bulk defect densities independent of that surface segregation. A combination of depth-dependent and lattice structural techniques over this extended alloy series revealed that native defect densities rather than piezoelectric fields play a role in their near-surface segregation, that Mg in ZnO dramatically reduces native defect densities, that these defect densities depend sensitively on variations in (Mg,Zn)O alloy lattice dimensions, and that the electrostatic energy associated with surfaces and lattice unit cell dimensions can be a key factor in carrier transport and doping of these oxide semiconductors.

We grew five 1 μm thick Mg_xZn_1−xO films with varying Mg concentration on r-plane sapphire. Alloy compositions measured directly from Rutherford backscattering spectrometry (RBS) were x = 0, 0.31, 0.44, 0.52, and 0.56. Using ion channeling experiments (RBS/C), we determined that ∼93% of all Mg incorporated homogeneously in the epilayers occupied Zn sites in the wurtzite structure. XRD showed these films to be single phase, high quality, all with the wurtzite structure and with no cubic inclusions.²² Atomic force microscopy (AFM) showed these surfaces to be smooth on a nanometer scale with no surface asperities. We performed DRCLS measurements using incident electron beam energies E_B = 0.1–5 keV from a glancing electron gun in an ultrahigh vacuum (UHV) system with an optical train consisting of a CaF₂ focusing lens, a sapphire viewport, and f-number matcher coupled to an Oriel monochromator and a CCD detector. DRCL spectra in this energy range display near band edge (NBE) and band-to-defect level transitions with nanometer depth resolution.^23–25 Depth dependence of electron-hole excitation was modeled using Monte Carlo simulations.²⁶ For E_B = 1, 2, 3, 4, and 5 keV, excitation peaks at depths U₀ = 7, 18, 32, 50, and 72 nm, respectively, with Bohr-Bethe maximum range R_B ∼ 3x longer.¹³ Surface photovoltage spectroscopy (SPS) features display the onsets of photostimulated population and depopulation transitions into and out of states within the semiconductor band gap.^27–29 The increase or decrease in work function measured using an atomic force microscope in Kelvin Probe Force Microscopy (KPFM) mode¹³ indicates the valence (E_V) or conduction (E_C) band nature, respectively, of such transitions and hence their energy level position within the bandgap. All these measurements were compared with deep level optical spectroscopy (DLOS), current-voltage (I-V), Schottky barrier, and steady state photo-capacitance (SSPC) measurements obtained previously on the same specimens.³⁰ 

Figures 1(a)–1(e) show representative DRCL spectra for all five Mg concentration samples. In each spectrum, the NBE peaks at ≥3.33 eV are the dominant features, increasing in energy with increasing Mg%. Below the NBE are emissions corresponding to defect levels within the band gaps. We subtracted out the second-order replicas of the NBE peak to avoid overlap with defect features. Deep level emission intensities are normalized by NBE intensity to factor out possible variations in collection efficiency. Normalized spectra of Figure 1 display orders-of-magnitude change in defect intensity versus Mg content. Comparison of the ZnO deep level emission to the NBE emission intensities in Fig. 1(a) shows that the 1.77 eV V _Zn intensity is approximately 10x lower than the NBE peak intensity. V _Zn clustering broadens this energy from 1.7 to 2.0 eV with increasing cluster size.^31,32 With the addition of 31% Mg in Fig. 1(b), this V _C intensity drops by nearly an order of magnitude. Similarly, V _O intensity decreases to 0.01x of the NBE intensity. Both reach minima for 44% Mg (Fig. 1(c)), then rise gradually for 52% (Fig. 1(d)) and 56% (Fig. 1(e)). Similar defect intensity decreases are evident in MgZnO grown by vapor transport but over a much smaller alloy range.^33,34 NBE energies in Fig. 1 increase linearly with Mg content up to x = 0.52, consistent with theory³⁵ and other reports,^36–38 deviating upward for x = 0.56, near the crossover from wurtzite to rocksalt structure.¹³ Figure 1(f) presents characteristic V _C and V _O intensity profiles with depth showing strong defect segregation toward the surface over tens of nanometers with a minimum at 44% Mg (inset).

SPS spectra provided defect level positions in the bandgap for each of the alloys. The contact potential (cpd), i.e., work function difference between the reference AFM probe tip and the (Mg,Zn)O surface, indicates how the Fermi level E_F varies with photo-induced population or depopulation of states and thereby band bending within the surface space charge region. For a representative x = 0.31 spectrum in Figure 2, onsets of photostimulated depopulation (n-type positive slope change) from a gap state to E_C are evident at 1.85 and 2.5 eV, as with the 3.6–4 eV NBE transition, above which additional free carriers decrease band bending. Population transitions from E_V into a gap state (n-type negative slope change) are evident at 2.05 and 2.25 eV. Since their sum nearly equals the bandgap, the 1.85 and 2.05 eV features correspond, respectively, to photo-depopulation and population of the same gap state. Slope changes at 3.6 and 3.86 eV indicate two additional states. Five similar features are evident for all samples, in reasonable agreement with the transition energies of five DLOS trap states reported previously.³⁰ 

Figure 3 shows band gap position of the dominant defect transitions. Here, the ZnO E_C is taken as 4.6 eV below the vacuum level, consistent with the electron affinity of the ZnO (⁠$10 1 ̄ 0$⁠) surface,³⁹ and E_C (E_V) increases (decreases) with Mg% following a 2/3-1/3 rule. As Mg content varies, the defect associated with the 2.3 eV ZnO V _O level moves nearly parallel with E_V, while the 1.77 eV V _C level in ZnO tracks with E_C. These movements are consistent with their orbital—derived character, i.e., the O 2p-derived E_V maximum and the Zn 4s-derived E_C minimum.

Figure 4 shows defect densities vs. composition and comparison with lattice constant variation. In Fig. 4(a), both V _C and V _O defect intensities I(V _C) and I(V _O) are normalized to the NBE intensity I(NBE) vs. Mg alloy content. We used DRCL spectra at 2 keV in order to avoid the near-surface segregated defects, which could increase defect intensities by more than an order of magnitude. Both I(V _C)/I(NBE) and I(V _O)/I(NBE) exhibit clear minima at x ∼ 0.44. I(V _C)/I(NBE) decreases by >100x, while I(V _O)/I(NBE) decreases by >30x. Intensity differences measured from two points on the same surface correspond to <10% for x = 0 and <1% for x>0. Trap state densities measured by t-SPS correlate with DRCLS intensities and display relatively good agreement⁴⁰ with Gür et al. DLOS results,³⁰ as expected from previous DLOS/t-SPS comparisons.^41,42 Total DLOS deep level concentrations for x = 0%, 31%, 44%, 52%, and 56% of 50.6, 6.1, 6.8, 7.8, and 5.4 × 10¹⁶ cm⁻³, respectively,³⁰ also correlate with Figure 4(a). The bulk I(V _C)/I(NBE) values for ZnO are consistent with positron annihilation spectroscopy (PAS) calibration values corresponding to ∼0.08 × 10¹⁷ cm⁻³ in the bulk and 0.25 × 10¹⁷ cm⁻³ at the surface.³¹ Previous electrical measurements on these samples also displayed pronounced Schottky barrier decreases and sheet resistance increases above this Mg%,³⁰ consistent with additional donors. Figure 4(b) shows the XRD-measured variation in (Mg,Zn)O lattice parameter vs. Mg content measured by RBS. Both a-lattice and c-lattice parameters exhibit pronounced minima at x ∼ 0.52.⁹ A smaller range of alloy composition would not have revealed these XRD and DRCLS minima.

Both electrostatic and thermodynamic factors may contribute to the decrease in V _C and V _O defect densities with unit cell volume. Electrostatic repulsion may contribute to the free energy associated with defect formation. Thus, V _O sites in ZnO result in neighboring Zn atoms with extra charge that would otherwise lead to lattice expansion. Reduction of the unit cell dimension should increase the energy required to form such defects, lowering their density. Analogous effects are reported for native point defects in complex oxides.^43,44 The strong decrease in V _C density with Mg content may also be thermodynamically driven given the higher bond strength of MgO vs. ZnO, i.e., −ΔH₂₉₈ (kJ/mol) = 601.6 (MgO) vs. 350.5 (ZnO). Since Mg is energetically more favorable than Zn in filling vacant Zn sites during growth, increasing Mg content would promote decreasing V _C density. Density functional theory calculations based on the pressure dependence of defect formation energies are also consistent with the defect density variations in Figure 4(a).⁴⁵ 

These results show that Mg in MBE-grown a-plane ZnO strongly reduces V _Zn and V _O native point defects, which are mid-gap defects that dominate recombination and follow band edges. Nearly, the same minima of V _Zn and V _O defect densities in (Mg,Zn)O coincide with minima of their unit cell volumes. This correlation is consistent with the effect of these Zn and O vacancies to increase lattice electrostatic repulsion, thereby increasing formation energies and decreasing their densities. This work reveals a coupling between electronic defect and lattice structural changes and shows that the free energy associated with surfaces, interfaces, and lattice unit cell dimension can be a major factor in carrier transport and doping of these oxide semiconductors.

The authors gratefully acknowledge National Science Foundation, Grant No. DMR-1305193 (Charles Ying and Haiyan Wang), for support of this work. W.W. acknowledges partial funding from the Center for Emergent Materials, an NSF MRSEC (DMR 1420451) and AFOSR, Award # FA9550-14-1-0322. A.R.-C. acknowledges Juan de la Cierva program under Contract No. JCI-2012-14509 (Spain).