Strong evidence for diffusion of point defects in GaInN/GaN quantum well structures

The internal quantum efficiency (IQE) of light emitters, in our case GaInN/GaN quantum wells (QWs), is governed by the competition of radiative and non-radiative recombination processes. Defects such as dislocations¹ and point defects² can act as non-radiative recombination centers. The higher the defect density, the shorter the non-radiative lifetime. Therefore, one way to enhance the IQE is to reduce the defect density or suppress its activity in the QW. The dislocation density can be substantially lowered by using pseudo bulk GaN substrates for growth.³ In cases of heteroepitaxial growth, like on sapphire substrates, one option is to take advantage of the V-pit formation⁴ for screening threading dislocations, which prevent carriers from recombining non-radiatively at the cores.⁵ However, point defects, including native defects, such as Ga and N vacancies, or impurities, like C and O, and their complexes, may also contribute to non-radiative recombination processes. Point defect formation energies, transition levels, and other properties in III-V semiconductors have been studied theoretically.^6–8 Among the point defects, Ga and N vacancies and their complexes are found to be the main cause of non-radiative recombination processes in the QW.^8–11 There are two great challenges to be overcome: the identification of which point defect is affecting the QW luminescence and the reduction of point defect density in the QW.

So-called underlayers (ULs), i.e., the layer(s) grown before the QW, have been widely used for improving the IQE of GaInN/GaN QWs. In-containing ULs have been extensively used.^12–18 It was argued that mostly nitrogen vacancies are formed on the surface during high temperature GaN growth.⁹ Then, they are thought to be trapped by In atoms, preventing their propagation into the QW.¹³ Although the IQE improvement has been attributed to a reduction of the point defect density in the QW, the mechanism causing this lower defect density is not fully understood yet.

Usually, if the UL contains In,^12–18 it requires growth at low temperatures¹⁹ with nitrogen as a carrier gas^20,21 and a high V/III ratio in the gas phase.^22–25 We find that GaN UL without indium under the same conditions likewise strongly increases the non-radiative lifetime in GaInN/GaN SQW, and that growth at low temperatures is the main cause for this. Subsequently, we show strong evidence that point defects diffuse and that their density in the QW can be reduced by choosing proper UL growth conditions.

Our samples were grown on c-plane sapphire substrates via metal-organic vapor-phase epitaxy (MOVPE) in a horizontal AIX 200RF reactor. They differ only in the thickness, composition, and growth temperature of the UL. The growth started with a low temperature nucleation layer, followed by a 1.8 µm thick GaN buffer layer grown at a nominal 1180 °C, using hydrogen as a carrier gas, trimethylgallium (TMG) as a precursor, and a total pressure of 100 mbar. The last 1/5 of the buffer layer was n-doped with diluted silane, expecting a doping level of about 2 × 10¹⁸ cm⁻³. For the buffer layer growth, an ammonia flux of 2000 sccm and a TMG flux of 17 sccm were used. Then, under the same conditions but at a nominal 855 °C and a reduced silane flow (by 1/7), a pit-inducing layer^4,26–28 of about 100 nm was grown. After that, the UL was grown using nitrogen as a carrier gas, triethylgallium (TEG) as a precursor, and a total pressure of 200 mbar. Three series of undoped GaN ULs were grown: one with a fixed temperature of 734 °C but varying the thicknesses (0.3–31 nm), another with 31 nm thickness, grown at 692 °C, and adding molecular hydrogen to the carrier gas at different phases of the UL growth, but closing the supply between 2 and 15 nm before the QW growth, preventing indium etching,²¹ and the last one with a fixed total UL thickness of 31 nm and varying the growth temperature in a range of 692–746 °C. For the GaInN UL, two samples were prepared with a total UL thickness of 31 nm without intentional doping: GaInN (746 °C, 10 nm, 14.5% ± 0.4% In)/u-GaN (692 °C, 21 nm) labeled (A), and GaInN (785 °C, 29 nm, 7.0% ± 0.6% In)/u-GaN (692 °C, 2 nm) labeled (B). Subsequently, a GaInN single quantum well (SQW) with nominally 2.3 nm thickness and ≈ 23% In was grown using nitrogen as a carrier gas, TEG, and trimethylindium (TMI) as precursors, and a pressure of 200 mbar. For the UL and the QW, the fluxes of ammonia, TEG, and TMI were 2580, 8, and 47 sccm, respectively. Finally, a GaN barrier of 21 nm was deposited under similar conditions as the QW, and a GaN cladding layer was grown at 900 °C with TMG and a mixture of nitrogen:hydrogen with a ratio of 3500:500 as carrier gas. The temperatures are measured by a thermocouple within the susceptor, which is offset by the real surface temperatures. The surface temperatures of the ULs are corrected by comparing the In incorporation in AlInN reference samples.²⁹ These temperatures are important for determining the activation energy, as discussed below.

The samples were characterized by high-resolution x-ray diffractometry and scanning electron microscopy (SEM). From the analysis, the In content, thickness, and relaxation state of the In-containing UL were determined. Furthermore, the cap layer thickness (average of all samples of 140.5 ± 0.5 nm) and buffer epilayer lattice constants were determined. By determining the pit density using SEM, the threading dislocation density is derived, which is comparable for all samples with an average value of 2.0 ± 0.1 × 10⁹ cm⁻².

The samples were optically characterized with time-resolved photoluminescence (TRPL). The second harmonic of a 35 fs Ti:sapphire laser (Coherent Vitara-S) was used for resonantly exciting the samples with a 405 nm wavelength at an excitation energy density of <10 μJ/cm². The laser pulse repetition rate of 4 MHz was set with a pulse picker. For temperature-dependent measurements, the samples were mounted in a continuous flow cryostat with a range of 5–300 K. With this setup, the effective lifetime and the absolute IQE of the GaInN/GaN SQWs were evaluated. The evaluation methods of both are explained in Ref. 30.

The IQE is a ratio of the radiative and total recombination rates. It can be determined on an absolute scale.³⁰ This method allows the extraction of the temperature-dependent non-radiative lifetime since the effective lifetime and IQE are known.³¹ Whenever the effective lifetime is dominated only by radiative recombination at low temperatures, this is verified by observing a synchronous rise of the effective lifetime together with the radiative lifetime at low temperatures.³⁰ This observation can be seen in Fig. 1(a). The case where, even at low temperatures, the effective lifetime has a high contribution from non-radiative recombination is demonstrated in Fig. 1(b).

As an auxiliary method, with a standard sample that has unity LT IQE and the same layer structure and emission wavelength as the other samples, the absolute IQE at low and room temperature can also be estimated from an intensity comparison between samples by measuring them side by side.³² This was performed using the same TRPL setup but in a confocal configuration and measuring each sample in various spots. This second method can assist in defining the radiative lifetime for samples that do not have unity LT IQE, thus later helping the synchronous fitting procedure described in Ref. 30.

As described by the model of Shockley and Read³³ and Hall³⁴ (SRH), considering a low injection regime and carriers captured by the defect levels in the forbidden gap, the non-radiative lifetime is inversely proportional to the defect density. Furthermore, although at room temperature (RT) the recombination is dominated by non-radiative processes,³³ the non-radiative lifetime could only be higher than the effective lifetime, depending on the IQE of the QW. The RT non-radiative lifetime is higher than the effective lifetime for a high RT IQE sample, as shown in Fig. 1(a). Meanwhile, the RT non-radiative lifetime is equivalent to the effective lifetime for a low RT IQE sample, as demonstrated in Fig. 1(b). Our research is primarily concerned with the defects in the QW; hence, the non-radiative lifetime is the correlated variable, and those methods are indispensable for its precise determination. Since the threading dislocations are screened, variations in the non-radiative lifetime are most likely due to point defects in the QW.

A comparison of the non-radiative lifetimes (τ_nonrad) at room temperature (RT) of SQWs grown on different ULs is shown in Fig. 2. First, regarding the u-GaN UL samples grown at a fixed temperature of 734 °C (average emission wavelength of 482 ± 9 nm), the non-radiative lifetime increases by two orders of magnitude with UL thickness from 0.3 to 31 nm.

Comparing u-GaN and u-GaInN UL samples, with nominally identical QWs and total UL thickness, similar non-radiative lifetimes were observed, as shown in Fig. 2. The XRD analysis suggests that the GaInN UL samples have somewhat lower UL thickness as represented in Fig. 2. Now comparing to the GaInN UL from literature data,¹³ the same qualitative trend and magnitude of improvement with the UL thickness can be observed, although Ref. 13 reports effective carrier lifetimes rather than non-radiative lifetime. Hence, this observation is independent of whether an In-free or an In-containing UL is used. The quantitative resemblance is only coincidence, since our QWs do have different thicknesses and In contents compared to those from the literature.¹³ 

The non-radiative lifetime is inversely proportional to the defect density.^33,34 As the density of dislocations is very similar for all samples, point defects should be responsible for the observed variation of the non-radiative lifetime. Obviously, an increasing thickness of the UL, with or without indium, reduces the density of point defects in the quantum well. This dependence suggests a point defect distribution profile over distance (between the high temperature GaN buffer layer and the QW), which is natural from the diffusion equation.³⁵ 

In order to further investigate the role of the underlayer, we have varied the UL growth temperature. Those samples have an average emission wavelength of 505 ± 14 nm. As shown in Fig. 3, the non-radiative lifetime at room temperature increases significantly with decreasing UL growth temperature. In this Arrhenius plot, the straight line fit constitutes an activation energy of 3.9 ± 0.9 eV, which means that the diffusion of point defects into the quantum well during growth is a thermally activated process. The combination of this and the previous result related to the UL thickness provides strong evidence that point defect diffusion is a key mechanism governing the defect density in the quantum well.

The dependence of the non-radiative lifetime on the UL thickness, as shown in Fig. 2, suggests that the point defects diffusing into the QW are likely formed during the growth of the buffer layer rather than the UL growth. Otherwise, the effective lifetime would be independent of the UL thickness. Consequently, during the UL growth, the already existing defects, i.e., likely vacancies, diffuse through the UL, assuming that it has a much lower or negligible point defect density than the buffer layer. This is supported by accurately modeling our results with a simple solution to the diffusion equation. Furthermore, the result also suggests that independent of whether the ULs are In-free or In-containing, a thickness dependency is observed, which means that the hypothesis of indium atoms trapping vacancies¹³ is unlikely. Therefore, the determined activation energy likely represents the point defect migration energy.

In the literature, the nitrogen vacancy (V_N) is theoretically considered the major point defect in GaN⁴¹ as a consequence of its lowest formation energy among other native defects.^6,41–43 The V_N migration energy varies depending on the model, diffusion path, charge state, and Fermi level. Its value is predicted between 2.0 and 4.3 eV, which is the highest migration barrier among the native defects.^6,41–44 Experimentally, for n-type Si-doped GaN layers, nitrogen self-diffusion has been measured within a temperature range of 770 and 970 °C, with a migration energy of 4.1 ± 0.4 eV.³⁸ For p-type Mg-doped GaN layers, a nitrogen vacancy migration energy of 2.5 ± 0.3 eV was determined (thermal annealed between 500 and 800 °C).⁴⁵ For the gallium vacancy (V_Ga), its migration energy is in the range of 1.5–2.68 eV.^41–44 Just to point out the complexity, vacancies can also form complexes with oxygen, hydrogen, another vacancy, and impurities.^11,45–47 Therefore, considering the experimental uncertainty, our activation energy is in the range expected for nitrogen vacancies in n-type GaN.

The proposed point defect diffusion model has the following three assumptions: (1) due to the high temperature GaN layer growth, the desorption of nitrogen is high;^38,48 therefore, the buffer layer has a high vacancy density, i.e., most likely nitrogen vacancy; (2) such defects are non-radiative recombination centers;^8–11,40 (3) point defects, e.g., vacancies, can diffuse.^36,38,40 We observe experimentally that the non-radiative lifetime increases with increasing UL thickness and exponentially with decreasing UL growth temperature. Both results are in agreement with the assumptions, as diffusion both leads to complementary error function profiles and is subject to thermal activation.

According to our model, the effect of layer(s) grown after the QW^49–62 and of post-growth annealing^63–66 can be explained by the diffusion of point defects. In the present work, the cladding layer and its growth conditions are the same for all samples; therefore, this layer cannot be responsible for any of our observations regarding the UL thickness dependence or the UL temperature dependence.

Assuming the validity of the diffusion based model, other results could also be explained, e.g., the observation regarding the drop in the effective lifetime of SQWs at RT while increasing the GaN buffer growth temperature and the interlayer growth temperature and thickness,⁹ the growth temperature of the GaN spacer layer,¹³ and the GaInN UL growth temperature.⁶⁷ For the case of a GaN spacer layer,¹³ an activation energy of 3.6 eV was derived, and the authors interpreted it as the decomposition energy of GaN. However, if the temperature during the growth of that layer is raised, diffusion of point defects also becomes more likely, including diffusion through the GaInN UL underneath, where the activation energy would represent a migration barrier. A second GaInN UL grown afterward (as in the supplementary material of Ref. 13) would just reduce the point defect density like the first one, due to slower diffusion at its lower growth temperature.

Generally, it is argued that higher GaN growth temperatures lead to higher defect densities.⁹ However, as is usually the case, a high temperature GaN buffer layer is used in homo or heteroepitaxial growth; hence, not only are defects created and may have a high density, but they are also diffusing toward the QW. Therefore, a layer between the buffer and the QW (i.e., UL, spacer, interlayer, or superlattice) can influence the point defect density in the QW, whereas its thickness (growth time times growth rate) and growth temperature are the control parameters.

In the literature, previous studies conclude that In-containing UL is far superior to In-free UL. This statement disagrees with our observations about the In-containing UL. In order to get a clear picture of the observation, we can apply the proposed diffusion model, considering two aspects, namely, the total thickness of the lower temperature layers grown after the high temperature (usually, ≥1000 °C) GaN buffer layer and prior to the QW, and their growth conditions.

If the composition of ULs is to be compared, then, firstly, the total layer thickness should be the same. Secondly, the growth conditions should be as similar as possible. Additionally, we have to consider point defect diffusion, as discussed in this work. The results related to the In-containing UL shown in Refs. 12, 13, 14, and 17 can be explained by a difference between the total lower temperature layer(s) thickness and the layer(s) growth temperature, emphasizing not only the importance of the UL growth conditions rather than the presence of In, but also the significant effect of point defect diffusion. In Ref. 13, there was an attempt to grow QWs on pure GaN UL, which showed a much lower effective lifetime compared to the ones grown on GaInN UL. This result contradicts our findings but may be explained by undocumented differences in growth conditions.

In summary, this work reports on the reduction of the point defect density in GaInN/GaN quantum wells. It demonstrates that the presence of a low temperature UL strongly decreases the point defect density in GaInN/GaN SQWs. The non-radiative lifetime depends on the UL growth temperature and thickness. This dependency is consistent with the equation derived from a diffusion model. Therefore, the results provide strong evidence for the decisive role of point defect diffusion. Additionally, the observations suggest that the high temperature GaN buffer layer is the source of the point defects, e.g., vacancies. Therefore, in our case, the activation energy represents the defect migration barrier. Furthermore, the defect diffusion coefficient is determined. The UL thus represents one way to reduce the diffusion of point defects into the quantum well by choosing proper growth conditions.