Pressure induced increase of the exciton phonon interaction in ZnO/(ZnMg)O quantum wells Open Access

ZnO is a promising material for optoelectronic and electronic application. On the one hand this material possesses extremely high exciton binding energy which could be increased with the formation of quantum well (QW) structures. On the other hand, the main obstacle in wider applications of ZnO-based electronic is a lack of a stable p-type doping. ZnO based quantum wells can be achieved by using ternary alloys like (ZnMg)O or (CdMg)O. When ZnO crystalizes in wurtzite structure, the MgO and CdO are unstable in such crystallographic structure and crystalize in rock salt structure.¹ Generally, it is widely accepted that (ZnMg)O is stable in wurtzite structure up to about 40% of the magnesium concentration.² If wurtzite quantum structures are grown along c crystallographic direction they exhibit the quantum-confined Stark effect (QCSE) due to built-in electric fields, related to spontaneous and piezoelectric polarizations. These built-in electric fields separate electron and hole wave functions inside the QW reducing the external quantum efficiency and increasing of the emission lifetime. Such effects can be avoided by using nonpolar growth which could be for example performed on nonpolar bulk substrates or r-plane sapphire. The commonly used substrates for ZnO epitaxy are c-plane or a-plane sapphire. In both cases the grown structures are polar and they are the subject to the built-in electric field. The growth on the a-plane sapphire is this kind of epitaxy, when the symmetry of the grown layers does not follow the symmetry of the substrate and the epitaxy is referred to as “ uniaxial locked epitaxy“. In this letter we used samples grown in such a way.³ 

Despite recent achievement in physics and technology of zinc oxide and related materials the fundamental physical properties of these materials such as electron-phonon interaction and related physical parameters are less understood or completely unknown. These properties could also be interesting in the case of nitride materials and the similarities between both type of materials (nitrides and oxides) will be pointed out later. According to the report by Makino et al., exciton- LO phonon coupling constant of ZnO is much stronger than that of GaN.⁴ Generally there are various types of electron-phonon interactions: (a) the Fröhlich interactions – Coulomb interaction between electrons and electric field related to longitudinal optical (LO) phonons (b) deformation potential interaction related to optical and acoustic phonons (c) the piezoelectric interaction with acoustic phonons in both oxides and nitrides which are piezoelectric materials.⁵ 

One of the most common optical feature in ZnO/(ZnMg)O quantum wells is the appearance of LO-phonon sidebands at the low energy shoulder of the main emission from QWs. It is generally believed that the appearance of the LO-phonon sidebands are related to Fröhlich interaction which plays a dominant role due to strong ionic nature of ZnO. It is worth mentioning that similar behaviour was reported not only for oxide ZnO/(ZnMg)O QWs but also in nitride structures like GaN/(GaAl)N or (InGaN)/GaN.^6,7 The intensity of LO-phonon sidebands in relation to zero-phonon line (ZPL) emission from QWs can be described by the electron–phonon coupling parameter called Huang - Rhys (S) factor. It is widely known that the intensity of phonon replicas follows the Poisson-distribution:

where I_n is the intensity of the phonon replica, I₀ the main emission peak (ZPL), and n number n-th phonon satellite.⁵ 

As it was mentioned before, in ionic crystals or polar semiconductors, coupling between electron and phonon occurs mostly by a Fröhlich interaction. The strength of the interaction could be expressed by a dimensionless coupling constant α called Fröhlich constant:

where ε_∞ and ε₀ are the electronic and the static dielectric constants, respectively, m is the effective mass given by the band structure, and ω_LO is the LO phonon frequency. The value of this constant is equal to 0.85 for ZnO,⁸ while for GaN and for GaAs it is equal to 0.49 and 0.068, respectively.^9,10

As it was previously reported, the strength of the coupling between ZPL and phonon replicas is related to the QW thickness in ZnO/(ZnMg)O quantum wells.¹¹ Generally two factors influence the intensity of LO-phonon sidebands - the degree of exciton localization and the built-in electric field. However, the relative contributions of both factors are hard to separate from each other in a classical photoluminescence experiment. In this letter, we propose an efficient method which could be used for changing only one of these factors – built in electric fields. In order to observe a pronounced effect, in our experiment we used material (ZnO) with high value of the coupling constant α. This efficient method in our experiment was hydrostatic pressure.

The investigated sample was grown by plasma-assisted molecular beam epitaxy (PA-MBE) Riber Compact 21 on a-plane sapphire. The system was equipped with Addon RF plasma cell as a source of gas and standard effusion cells for the group II elements. The structures were fabricated on quarters of a 2 inch a-plane sapphire substrate. After chemical cleaning, the wafer pre-treatment process included an out-gassing step, which took a few hours, at 700 °C in a buffer chamber, and finally, a 30-minute oxidation in the growth chamber (700 °C). The growth was performed at 460 °C under nearly-stoichiometric conditions. The in-situ growth rate measured during epitaxy from optical reflectometry was at the level of 0.36µm/h. A streaky pattern from the sample surface was revealed during and after sample growth by reflection high-energy electron diffraction (RHEED). First, a 300 nm thick Zn_0.79Mg_0.21O layer was grown, then 8 nm quantum well and finally, the whole structure was covered by a 30 nm thick Zn_0.79Mg_0.21O cap layer.

The photoluminescence (PL) spectra of ZnO samples were obtained using a 275.4 nm (4.50 eV) line of argon 15 mW laser as the excitation source. The PL was measured with the use of a Horiba Jobin-Yvon FHR 1000 monochromator, and the signal was detected by means of a liquid nitrogen cooled charge coupled device (CCD) detector. The spectra were corrected for the quantum efficiency of the system. The high-pressure measurements were performed with use of a low-temperature diamond anvil cell (CryoDAC LT, easyLab Technologies Ltd) loaded with argon as a pressure-transmitting medium. The diamond anvil cell was mounted into an Oxford Optistat CF cryostat and measurements were performed at 11K. The R1-line ruby luminescence was used for pressure calibration. Polished samples of bulk ZnO crystals of thickness of about 30 μm were loaded into the cell along with a small piece of ruby.

At ambient pressure we observed emission from quantum well (ZPL - zero phonon line) followed by clearly seen phonon replicas. The high pressure experiment was performed up to 6 GPa which is a value below phase transition in zinc oxide. As can be seen from Fig. 1 a continuous increase of the relative intensity of the phonon replicas which followed emission from quantum well could be observed. This effect is accomplished by a slight shift of the quantum well emission towards higher energies and increase of the full width at half maximum (FWHM) of this emission. During the pressure experiment we observed a decrease of the intensity of successive spectra with increasing pressure. However, results in Fig. 1. are normalised to the intensity of the ZPL peak. The 1LO and 2LO phonon replicas are clearly seen in each pressure step.

The pressure coefficients related to emission from 8 nm quantum well – ZPL, together with pressure induced changes of the band gap in zinc oxide are plotted in Fig. 2. As can be seen in Fig. 2, pressure coefficient of the ZPL equal to 3 meV/GPa is much smaller than pressure induced change of the band gap in ZnO (20 meV/GPa).¹² Pressure induced increase of the full width at half maximum (FWHM) of the ZPL is shown in the insert of Fig. 2. Finally in Fig. 3 the calculated values of the Huang - Rhys (S) factors for subsequent pressures are presented. The calculations of this values were performed on the following way. We used a Voigt functions to fit our model to the experiments, and we established S parameter from the the 1LO and 2LO phonon replicas. The reason why we did not use the intensity of the ZPL was related to the fact that due to recently published results by Lange et al. to calculate the Huang-Rhys factor S correctly, only phonon replicas could be used.¹¹ That paper shows that QW emission possesses two components: one related to strong and the second to weak localized excitons. The authors suggested that only the strong localized excitons contribute to the phonon replicas whereas the weak localized excitons only contribute to the zero-phonon line. Taking into account that the intensity of the phonons replicas follow the Poisson-distribution, S factor can be established by using the following equation:

where I_n is the intensity of the n-th phonon satellites. In our case, in order to establish the S factor we use the 1LO and 2LO phonon replicas. As can be seen from these results we observe a pronounced increase of the Huang-Rhys factor S with increasing hydrostatic pressure.

Lack of the inversion symmetry in wurtzite crystal structure leads to high value of the built-in electric field, which is the result of piezoelectric and spontaneous polarization. The spontaneous polarization is related to the nature of the chemical bonds and charge distribution between cations and anions. The piezoelectric polarization is related to the strain existing due to the lattice mismatch in heterostructures and epitaxial layers. Both of these polarizations could be quite huge leading to high value of the built-in electric fields (up to 5 MV/cm in nitrides). In GaN/AlGaN structures it is believed that both polarizations play equivalent role in the total value of the built-in electric field. In ZnO/ZnMgO spontaneous polarization should be dominated due to relatively small lattice mismatch between ZnO and ZnMgO.

Generally, in most semiconductor systems pressure behaviour of the QWs is very similar to the pressure behaviour of the material which is used in a QWs region: this is for example a case in GaAs/AlGaAs. But there is a group of semiconductors where different pressure behaviour is observed. Probably the first observation of the lowering pressure coefficient with increasing thickness of the quantum well region, was reported on CdTe based materials.¹³ The authors explain these effects by using a model which includes such effects as pressure induced increase of the strain, nonlinear behaviour of the elastic constants, and pressure related nonlinearities of the piezoelectric coefficients. Similar behaviour was observed in nitrides where built-in electric fields are much higher. Pressure induced increase of the built-in electric field is actually well-grounded interpretation. This is strongly supported by such experiments as observation of an increase in the PL decay time or a direct comparison of the pressure properties of polar (with built-in electric field) and nonpolar (without built-in electric field) GaN/AlGaN quantum wells. Also in the case of InGaN/GaN quantum wells similar behaviour was observed.^14–16 Generally the increase of built-in electric field is explained by pressure induced increase of strain which leads to an increase of piezoelectric component of built-in electric field. Actually the experimental observations are explained by more sophisticated theories including nonlinear piezoelectric constants, pressure-induced changes of the exciton binding energy and nonlinear elastic stiffness coefficients.¹⁷ 

While pressure induced increase of the built-in electric field is a well-established experimental fact in nitrides, a similar experiment on ZnO/(ZnMg)O quantum wells was performed only by our group. For ZnO/(ZnMg)O QWs sample with magnesium concentration in quantum barriers equal to 20 % and different QW thicknesses we observed the pressure coefficient equal to 19.4 meV/GPa for 1.5 nm QW, where for 8 nm QW the pressure coefficient was equal to 8.9 meV/GPa only (Fig. 4). We also estimated that the built-in electric field to be equal to about 0.35 MV/cm at ambient pressure and increased with pressure with the “built-in electric field pressure coefficient” equal to 0.012 MV/(cm ⋅ GPa).

All of our experimental observations (i.e. lowering of the pressure coefficient of the ZPL and increase of the FWHM and Huang-Rhys factor S with pressure) could be explained by taking into account pressure induced increase of the built-in electric field.

The lowering of the pressure coefficient of the ZPL (emission from 8 nm quantum well) can be explained in the following way. With increasing pressure the value of the built-in electric field increases in the same way for thinner or thicker QWs. However, for thicker QWs due to QCSE the related red shift is more pronounced. When for thin QW the shift should with pressure as in bulk material (ZnO), The pressure coefficient of the thicker QW is in fact the sum of these two effects. One of them is associated with the increase of ZnO band gap (blue shift) and the second with an additional redshift (which increases with pressure) induced by the quantum confined Stark effect, that is related to an increase of the electric field. However, this additional redshift does not fully compensate for the blue shift related to pressure induced changes of the band gap, leading to pressure coefficient equal to 3 meV/GPa – much smaller than pressure induced change of the band gap in ZnO (20 meV/GPa). As previously mentioned, similar behaviour has been observed in the case of nitrides. For example, experimental confirmation of these effects was the comparison of two samples - polar and nonpolar GaN/AlGaN QWs grown on the same run. The important finding is derived from the fact that pressure coefficents of photoluminescence lines from all QWs grown along nonpolar crystallographic direction (without built-in electric field) are width independent.¹² This result reveals that for GaN/AlGaN QWs, the quantum confinement remains practically independent of the applied hydrostatic pressure. This also shows that in the GaN/AlGaN polar sample, the variation in pressure coefficients with the QW width is due to the pressure-induced increase in the built-in electric field. A more quantitative analysis performed by authors reveals built-in electric field increases with pressure with a rate of about 80 kV/(cm GPa).

The second experimental observation listed above is increase of the FWHM with pressure. In QW systems broadening of the spectral width of the emitting spectra mostly depend on the structural perfection and uniformity of barrier composition and abruptness of the interface. In ZnO/ZnMgO both of these factors are strongly magnified by huge built-in electric fields present in such structures. So pressure induced increasing of the built-in electric fields leads to spectral broadening of the QW ZPL emission. This effect is also observed in optical broadening of the phonon replicas.

Finally, the third experimental fact listed above is the increase of the coupling of LO phonons with hydrostatic pressure. We are able to shed some light on the problem, by following the work of S. Kalliakos et al. for InGaN/GaN quantum structure.¹⁸ He calculated that with increasing of the QW width, the Huang-Rhys factor increase, as expected due to the higher electron – hole separation. However, for larger QW thicknesses there is another factor that acts in the opposite direction, as electron – hole separation increases the binding energy of the exciton decreases, This should lead to the extension of the in-plane part of the excitonic wave-function and reduceing the Huang-Rhys parameter. Unfortunately, calculations performed by S. Kalliakos et al.¹⁸ did not agree with their experimental results i.e. increase of the Huang-Rhys factor with increasing QW thicknesses. The only way to overcome this problem was to fix the in-plane extension parameter which allowed them to receive good agreement between calculations and experiments. However, the analogy between this work and our experiments is not full. In the case of InGaN, which is a QW material in Ref. 18, the recombination occurs in the region where electrons and holes are localized at potential fluctuations. This could be a strong argument to fix the extension parameter of the in-plane part of the excitonic wave-function. In our case the QW region was built of binary compound, so there are no potential fluctuations in our case.

The paper where the coupling to LO phonons with ZnO/ZnMgO QWs were discussed is an article by M. Lange et al.¹¹ He used a model that includes weakly and strongly localized excitons to reproduce their experimental results. The authors assumed that whereas weakly localized excitons only contribute to the intensity of the zero-phonon line, strongly localized excitons contribute to the phonon replicas and follow the Poisson-distribution of the intensity. We try to reproduce these results by using Voigt function at ambient pressure. Unfortunately, we were unable to receive good agreement by using the model proposed by M. Lange.¹¹ In our opinion it is true that ZPL possesses two components but both of them contribute to the phonon replicas with different Huang-Rhys factors. In our case we also believe that both of them are influenced by pressure induced increase of the built-in electric field.

We could summarize the mechanism which leads to increase of the Huang-Rhys parameter in our case in the following way. By applying hydrostatic pressure in DAC, we increased strains in our system, which contributed to an increase of the piezoelectric component of the built-in electric fields. This increase electron – hole separation but without strong influence on the in-plane part of the excitonic wave-function (like in the InGaN/GaN case). We think that in our case the role of indium potential fluctuations could be played by dislocation, stacking faults, the interface roughness or finally potential fluctuations in the ZnMgO barriers due to different alloy composition. Finally, in this scenario, increased electron – hole charge density in the QW leads to the extension of the wave function in k-space which according to equation published by X. B. Zhang et al.⁵ results in increase of Huang-Rhys parameter.

To conclude, we have demonstrated that we are able to change electron–phonon interaction by using hydrostatic pressure. As we mentioned before, there are two factors which have a direct influence on intensity of LO-phonon sidebands: the degree of exciton localization inside the well and built-in electric field. Unfortunately, relationships between these factors are not easy to be separated without possibility of changes of one of the factor independently. Furthermore, these results open the way to study similar effects in nitrides, both in InGaN/GaN and GaN/AlGaN structures.