Homoepitaxy of non-polar ZnO/(Zn,Mg)O multi-quantum wells: From a precise growth control to the observation of intersubband transitions

Zinc oxide (ZnO) is a direct wide bandgap semiconductor (3.31 eV) which can be used to fabricate optoelectronic devices in the UV range.¹ The large exciton binding energy (60 meV in bulk ZnO^2,3) allows the design of room temperature (RT) excitonic devices such as polariton lasers.^4,5 Despite significant advances on the reproducibility and the stability of the p-doping of ZnO,^6–8 it remains a huge challenge, which strongly limits the development of this wide bandgap oxide semiconductor for bipolar electrical devices. Still, it may be possible to use ZnO-based heterostructures for unipolar devices (with only n-type doping) such as resonant tunneling diodes (RTDs⁸) and quantum well infrared photodetectors or quantum cascade detectors or lasers (QCDs or QCLs^9,10). Another remarkable property of ZnO is its large optical phonon energy compared to those of conventional III-V semiconductors (36 meV and 72 meV for GaAs and ZnO, respectively). This feature should facilitate the population inversion for ISBTs with an energy well below the optical phonon energy. In the THz regime, QCLs based on ZnO heterostructures are thus expected to be able to work at room temperature,¹² while QCLs based on conventional semiconductors are operated at low temperature.¹¹ To achieve this goal, high quality heterostructures should be grown including (i) multi-layers with controlled thicknesses over several periods, (ii) abrupt interfaces without interdiffusion between quantum wells (QWs) and barriers, and (iii) a homogeneous alloy in the barrier and no plastic relaxation. Due to these strong requirements, only two groups have been able to observe ISBTs in ZnO based heterostructures.^13,14 ISBTs have already been studied in the mid infrared (MIR) and the terahertz range in other wide bandgap semiconductor materials such as GaN based heterostructures¹⁵ or II–VI semiconductors.¹⁶ For ZnO, the reports focused on the MIR range and dealt with heterostructures grown on c-$0001$ polar oriented substrates. Along this orientation, QWs exhibit a strong internal electric field as a result of the polarization discontinuity between ZnO and ZnMgO, leading to the Quantum Confined Stark Effect (QCSE).¹⁷ As a consequence, the QW potential becomes asymmetric, which in general makes the design of ISBT devices more difficult. This effect can be suppressed when the layers are grown in a non-polar orientation.¹⁸ Recently, the commercial development of non-polar ZnO substrates has led to a drastic reduction of the structural defect density, leading to an improvement of the optical quality of non-polar ZnO-based heterostructures.¹⁹ Here, we demonstrate that it is possible to observe the ISBTs in non-polar ZnO-based multi-quantum wells (MQWs). In the absence of the internal electric field, we show that the ISBT energies can be accurately calculated when many body effects are taken into account.

Samples were grown on 10 × 20 mm m-oriented ZnO substrates (Crystec). The substrates were annealed at 1065 °C under an oxygen (O) atmosphere to reveal atomic steps. The layers were grown in a molecular beam epitaxy system (RIBER, Epineat) equipped with zinc (Zn) and magnesium (Mg) cells and one gallium (Ga) cell for n-type doping. The atomic O was provided by a plasma cell operating at 420 W, and the O flow was set to 0.3  sccm. The substrate temperature was set to 420 °C. The Zn and O fluxes were adjusted to be close to stoichiometry to limit defect concentrations with a growth rate of 170 nm/h.²⁰ The structures consisted of a 100 nm ZnO buffer layer followed by a 50 nm (Zn,Mg)O buffer. Then, 20 periods ZnO/(Zn,Mg)O MQW were grown with a constant Mg content (30%) for all samples. In addition, for the ISBT observations, the QWs were doped to n ∼1× 10¹⁹ cm⁻³ and the QW thickness was varied from 2.2 nm to 4.0 nm, while the barrier thickness was kept constant (15.0 nm). The Mg content and the total (Zn,Mg)O thicknesses were chosen to avoid strain relaxation which is highly anisotropic in non-polar orientations.^21,22

The c axis (or $[0001]$ direction) has a six-fold symmetry in a wurtzite crystal such as ZnO. In the case of the $m−(101¯0)$ plane, which is one of the non-polar orientations, the c axis lies in the growth plane. Figure 1(a) displays a model of such a growth plane. Although the surface contains the same density of O and Zn atoms, it is strongly anisotropic and exhibits a rectangular symmetry, leading to two different in-plane lattice parameters (c and a, 0.52 nm and 0.325 nm, respectively). The monolayer (ML) along the m orientation is 0.281 nm thick. Figure 1(b) shows a typical atomic force microscopy (AFM) picture of a MQW for ISBTs. The surface is flat with an RMS roughness of 0.3 nm and a maximum peak-to-valley height of 2.5 nm. The surface morphology is characteristic of a non-polar orientation, i.e., with elongated stripes along the c axis. Note that this morphology does not evolve during the growth and is not related to the (Zn,Mg)O/ZnO mismatch strain for the 30% Mg content in the barriers.²³ This anisotropy results more from the different diffusion lengths of the adatoms along the in-plane c axis and a axis during the growth.²⁴ 

Samples were investigated by X-ray reflectivity (XRR) in order to precisely measure the layer thicknesses and to probe the interface properties. Some spectra were fitted with the GenX software.²⁵ An RTD structure was investigated as a test structure. The RTD consists of a 4.0 nm QW sandwiched between 2.0 nm thick Zn_0.7Mg_0.3O barriers. Figure 2 displays the experimental and the simulated XRR spectra (green line in Fig. 2). Several parameters can be deduced from this simulation: the layer thicknesses, the surface roughness, and the refractive index of both ZnO and (Zn,Mg)O, which depends on the electronic density of the materials and, in turn, on the alloy composition. Owing to the numerous fitting parameters of the XRR simulation, it is necessary to correlate the XRR with other characterization techniques. The roughness deduced from XRR was compared with the one measured by AFM. Both values are in agreement (RMS roughness, ∼0.6 and 0.7 nm in XRR and AFM, respectively, see Fig. 2). In order to verify independently the QW and barrier thicknesses, the growth rates of ZnO and (Zn,Mg)O were measured by cross-sectional scanning electron microscopy on thick calibration layers. Figure 3 shows XRR spectra taken from ISBT MQWs with different QW thicknesses. Sharp peaks are observed due to the highly periodic structure. The peaks are shifted from one sample to the other, while the roughness (related to the overall damping of the spectrum) is very similar in every sample. The shift is an evidence of the QW thickness variation.

The presence of these sharp interference peaks is a clear evidence of the interface abruptness between ZnO and (Zn,Mg)O and with the same roughness from one interface to another. In other words, the interface roughness is coherent along the growth direction, which means that the thickness remains constant. This was recently demonstrated using atomic probe tomography.²³ In addition, the X-Ray Diffraction (XRD) spectrum shows a very sharp diffraction peak surrounded by thickness related peaks and Pendellösung fringes (supplementary material, Fig. S1), which is an evidence of the good material and interface reproducibility and quality. Taken together, the methods allow us to estimate the layer thickness with one monolayer (ML) resolution, which is a prerequisite for ISBT determination in QWs.

The samples were investigated by photoluminescence (PL) spectroscopy at low temperature (10 K) and at RT. Doped and undoped samples were measured by PL, while only doped samples could be measured by infrared absorption spectroscopy. Figure 4 illustrates the evolution of the PL energy of the QWs as a function of the QW thickness for all samples. The PL spectra taken from the doped samples only are shown in the inset. The RT PL spectra exhibit two main peaks. The more intense peak is related to the excitonic emission from the ZnO QWs. Its energy is higher than that of bulk ZnO and is shifted towards higher energies as the QW thickness decreases because the quantum confinement increases. Note that the low temperature PL spectrum exhibits sharp excitonic peaks with phonon replica (supplementary material, Fig. S2). No luminescent band in the visible is observed, which is a sign of good material quality. The second peak observed in Fig. 4 is related to the emission of the exciton recombination in the barrier. The excitonic transitions are shifted towards higher energies with the increasing Mg content. The Mg content x can be estimated following the relation²² 

where $EZn1−xMgxO$⁠, $EZnO,$ and $x$ are the (Zn,Mg)O bandgap, the ZnO bandgap, and the Mg composition (in %), respectively. The dependence of the (Zn,Mg)O bandgap can be found spanning from 20 meV to 25 meV per % of Mg as a function of the measurement techniques and the strain states.^26–28 While the exact excitonic bandgap can be measured by deep UV ellipsometry,²⁹ the PL measurement gives access to the radiative recombination of the localized excitons in the (Zn,Mg)O potential fluctuations, which exist even at RT. The localization of the exciton decreases the transition energy with respect to the mean bandgap of the alloy and the localization increases with the Mg concentration.³⁰ In addition, the exciton binding energy increases with the Mg content,²⁹ which also contributes to reduce the transition energy. Thus, the localized excitonic transition exhibits a slower evolution with the Mg content compared to that of the (Zn,Mg)O bandgap. In Fig. 4, excitonic transitions from many QWs and MQWs are plotted as a function of the QW width for a Mg content of 30%. The samples designed for the ISBT experiments are highlighted in red full circles. In the same figure (red open squares), we also show results of a calculation which includes the confinement effects on the electron and hole levels in the QW and the assumption of the absence of a Quantum Stark Effect in these non-polar oriented layers. The confinement energies of electrons and holes in the QWs were calculated in the effective mass approximation with electron and hole masses m_e = 0.24 m₀ and m_h = 0.78 m₀, respectively.³¹ The conduction band to valence band offset ratio was set to ΔEc/ΔEv = 0.675.^13,32 The increase in the exciton binding energy as the QW thickness decreases was approximated following the Leavitt-Little model.³³ The maximum deviation between our calculations and the experimental data reaches 8 meV for the thinnest QW (2.2 nm), which is lower than the FWHM of the PL peak at 10 K. Thus, the calculated data describe very satisfactorily our PL experiments.

The samples from the ISBT series were doped with Ga (n ∼ 1 × 10¹⁹ cm⁻³) to populate the first level leaving the second level mostly unpopulated. They were prepared as 45° multi-pass waveguides, with the beveled edges and the backside of the substrate polished to optical quality, so that the light propagates in a plane perpendicular to the c axis. ISBTs follow a transverse magnetic polarization selection rule: only the light fully or partially polarized perpendicular to the plane of the QWs can be absorbed.³⁴ Absorbance spectra were taken for s and p polarized light. For s polarized light, the electric field is parallel to the c axis, whereas for p polarized light, the electric field is perpendicular to the c axis and has a component perpendicular to the QW planes. Figure 5(a) displays the p/s absorbance ratio for the three investigated samples. Note that no absorption was detected from the 2.2 nm wide MQW because the second electronic level lies in the continuum. Absorption peaks are visible from 2100 cm⁻¹ to 2800 cm⁻¹ with a FWHM of about 800 cm⁻¹. Note that the spectra do not show neat Lorentzian shapes. These spectra are taken on pieces of sample prepared as multipass waveguides which are 5 to 6 mm long. In this configuration, the light travels through more than 5 mm of substrate. Therefore, the samples are essentially opaque for wavenumbers below 1000–1500 cm⁻¹ due to multiphonon and free electron absorption.³⁵ The ratio of these spectra (whose transmittance is close to zero in that range) yields a very noisy spectra for wavenumbers below 1500 cm⁻¹. In addition, the doping level is not very high in this work. Then, the noisy baseline is maintained in the peak profile. If the doping is increased, the peaks become more intense and the Lorentzian shape of the peaks emerges.³⁵ The Schrödinger-Poisson equations with the exchange-correlation effects were self-consistently solved to calculate the transitions in order to take into account the modifications of the potential profile due to the inhomogeneous carrier distribution within the QW. The QW and barrier thicknesses deduced above were used for the calculation. The effective masses and the conduction band offset were taken identical to those used for the calculations of the interband transitions above. The calculated transitions are strongly red-shifted [open circles in Fig. 5(b)] with respect to the experimental observation due to the depolarization shift resulting from the interaction between the external radiation and the electron plasma.³⁶ This leads to a collective motion of the carriers, inducing an increase in the transition energy. To account for this, a model has been developed for non-polar ZnO by building a non-isotropic dielectric function, including the interaction of light with the lattice, the in-plane free electrons, and the off-plane ISBT.³⁵ Using this model as a function of the QW thickness, the calculated transitions describe satisfactorily the observed ones [open green squares in Fig. 5(b)]. The error bars were obtained by considering a +/−1 ML variation on the QW thickness. The effect is very large in the ZnO QW due to the very dense two-dimensional electron gas achieved here (5 × 10¹² cm⁻²) and the large difference between the static and high-frequency dielectric constants in ZnO.

As a conclusion, we have demonstrated that non-polar ZnO/(Zn,Mg)O MQWs grown by MBE fulfil the requirements for ISBT-based devices in terms of structural and optical quality. The layers show flat surfaces with a roughness below 0.5 nm. The thicknesses are controlled with a precision of one ML or below by means of XRR experiments. With such heterostructures, we report the observation of ISBTs in the IR domain at RT in non-polar QWs. The transition energies can be well predicted if a large depolarization shift is taken into account. These results offer perspectives for the realization of unipolar ISBT devices based on m-plane ZnO/(Zn,Mg)O heterostructures in the MIR and the THz range.

See supplementary material for additional evidences of the material quality based on structural characterization (X-Ray diffraction of the multiple quantum well) and optical characterization (low temperature photoluminescence, which exhibits no visible band due to defects).

This work was funded by EU commission under the H2020 FET-OPEN program: project “ZOTERAC” FET-OPEN 6655107. We thank J.-Y. Duboz and M. Leroux for critical reading of the manuscript and M. Nemoz, and A. Courville for the X-Ray and AFM experiments.