1. Introduction
GaInN/GaN/AlGaN quantum well structures are now at the heart of GaN-based LED’s and lasers, which are commercially available or soon to be commercialized Reference Nakamura, Senoh, Iwasa and Nagahama[1] Reference Nakamura, Senoh, Nagahama, Iwasa, Yamada, Matsushita, Kiyoku, Sugimoto, Kozaki, Umemoto, Sano and Chocho[2]. Nevertheless, the fundamental mechanisms of spontaneous and stimulated light emission are still subject to quite some debate. In particular, localization effects due to composition fluctuations and even quantum-dot-like structures due to phase separation in GaInN quantum wells have been invoked to explain some of the observations Reference Chichibu, Azuhata, Sota and Nakamura[3] Reference Narukawa, Kawakami, Fujita, Fujita and Nakamura[4].
Even more recently, it has been pointed out that many of the unusual optical properties of GaN-based heterostructures can be consistently explained by considering the piezoelectric properties of the III-nitrides Reference Takeuchi, Sota, Katsuragawa, Komori, Takeuchi, Amano and Akasaki[5] Reference Im, Kollmer, Off, Sohmer, Scholz and Hangleiter[6]. In fact, the importance of piezoelectric fields in III-V semiconductors has first been recognized for cubic zincblende heterostructures grown on a (111) plane Reference Smith[7]. The characteristics of such structures and some novel device applications have been discussed in detail Reference Cooper, Westwood and Blood[8] Reference Zhang, Chua, Xu, Chong and Onabe[9] Reference Ortiz, Pelekanos and Mula[10]. On the other hand, AlN has long been known as a strongly piezoelectric, though insulating material. For the semiconducting III-nitrides, piezoelectric effects have first been discussed in the context of heterostructure field effect transistors Reference Yu, Sullivan, Asbeck, Wang, Qiao and Lau[11] Reference Gaska, Yang, Osinsky, Bykhovski and Shur[12]. In such devices, the piezoelectric fields lead to a significant change of device characteristics and to new optimization strategies.
In this paper, we discuss the consequences of piezoelectric fields on the optical properties of GaN-based heterostructures and quantum wells. We demonstrate that the piezoelectric fields lead to a strong red-shift of the luminescence with respect to the bulk bandgap and the absorption edge, and to a dramatically reduced oscillator strength. Using specially designed test structures we determine the sign of the field and discuss its relation with the crystal orientation. We compare the photoluminescence with the stimulated emission and highlight the effects of screening of the piezoelectric field.
2. Piezoelectric fields
Non-centrosymmetric crystals, when subject to external stress, may generate so-called piezoelectric fields due to a stress-induced polarization. The electric polarization field is given by
where Pi is the electric polarization field, dik is the piezoelectric tensor, and σk is the stress tensor. We note that the polarization may also be related to the strain tensor εk by another piezoelectric tensor denoted by eik.
In the wurtzite structure typically occuring for the III-nitrides, biaxial strain in the (0001) plane results in a polarization field, which is most conveniently expressed by Reference Bykhovski, Gelmont and Shur[13]
where d31 is the piezoelectric constant, cij are the elastic constants, and εxx is the in-plane strain. Such a coherent in-plane strain is realized in case of pseudomorphically grown heterostructures with dissimilar lattice constants. The sign of the polarization of course depends on whether the strain is compressive or tensile.
3. Experimental
Our samples were grown on 0001-oriented sapphire substrates using low pressure metal-organic vapor phase epitaxy (LP-MOVPE) and employing an AlN nucleation layer. The GaInN layers were grown at temperatures at or below 800 °C with N2 as a carrier gas. GaInN/GaN, GaN/AlGaN, and GaN/GaInN/AlGaN double heterostructures (DH) as well as single quantum wells (SQW’s) of different thicknesses were investigated. The GaInN/GaN structures consisted of a 500 nm to 2 μm thick GaN buffer, a GaInN quantum well with varying In content, and a 50 nm GaN cap layer, whereas the GaN/AlGaN structures had a 500 nm AlGaN (≈15 % Al) buffer, a GaN well, and a 50 nm AlGaN cap layer.
Time-resolved spectroscopy with resonant excitation of the quantum wells was performed using a setup already described elsewhere Reference Im, Moritz, Steuber, Haerle, Scholz and Hangleiter[14]. The stimulated emission of the samples under high excitation conditions was studied utilizing the stripe excitation method as described earlier Reference Frankowsky, Steuber, Harle, Scholz and Hangleiter[15].
4. Oscillator strength in GaN/AlGaN and GaInN/GaN quantum wells
4.1 Basic observations
First, we have studied GaN/AlGaN and GaInN/GaN single quantum wells (SQW’s) with varying well thickness. For the GaN/AlGaN quantum wells, for example, time-integrated low-temperature luminescence spectra exhibited a fairly complex behavior. Besides the AlGaN emission at 3.75 eV, we observe two emission lines from thick quantum wells but only a single line from thin QW’s. As shown in Figure 1, thin quantum wells (1 nm and 2 nm) show a clear blue-shift of their emission due to size quantization. In thicker layers (5 nm and 10 nm) the higher energy emission line is about 70 meV above the GaN bandgap, whereas the lower energy line shifts to energies well below the GaN bandgap with increasing thickness.
Figure 1. Time-integrated photoluminescence spectra of a series of GaN/AlGaN quantum wells. The dashed line indicates the position of the GaN bandgap.
Measurements of the luminescence decay time ( Figure 2) reveal that both the single line in thin QW’s as well as the higher energy line in thicker layers have decay times of about 300 ps. The lower energy line in the thicker layers becomes extremely slow for the 10 nm sample, with a decay time of 3 μs. Time-resolved spectra of the lower energy line show that there is a red-shift of the emission peak of 27 meV for long delay times after pulsed excitation.
Figure 2. Double-logarithmic plot of the luminescence decay for a 2 nm, a 5 nm, and a 10 nm GaN/AlGaN quantum well. The thickest layer shows a decay on a microsecond timescale.
A very similar behavior was observed for several sets of GaInN/GaN QW’s, with the decay time of the lower energy line gradually increasing into the microsecond range with increasing well thickness.
4.2 Discussion and model
Basically, there are three possible explanations for the origin of the low-energy emission line found both in GaN/AlGaN and in GaInN/GaN structures.
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1. In GaInN/GaN MQW structures a red-shifting emission has already been attributed to localized excitons or quantum dots.
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2. The extremely slow luminescence decay could be an indication for spatially indirect donor-acceptor-like transitions.
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3. Piezoelectric fields due to mismatch-induced strain could lead to a Stark-shift of the emission and to a strong reduction of the oscillator strength.
Donor-acceptor-like impurity-related transitions can be excluded since it is hard to see how such transitions would shift to lower energy with increasing well width. Localization or quantum dots can not be the origin of this behavior for two reasons: i) for the GaN/AlGaN samples such transitions could not be below the bulk GaN bandgap; ii) the extremely slow decay in thick layers would require a localization to a radius of less than 1 Angstrom, which is clearly not feasible.
Let us now explore the case of piezoelectric fields in some detail. We have to recall that our sample design is such that the active quantum well is strained whereas the barriers are unstrained both for the GaInN/GaN and for the GaN/AlGaN structures. A qualitative picture with the energies and wavefunctions involved is shown in Figure 3. Due to the piezoelectric field, the energy levels of the quantum wells are red-shifted with increasing well width. At the same time, the electron and the hole wavefunction are more and more separated leading to a dramatic reduction in oscillator strength. We have performed a quantitative numerical calculation of the quantization energies, wavefunctions, and matrix elements for such a situation.
Figure 3. Schematic picture of the energies and wavefunctions of electrons and holes in a strained quantum well with a piezoelectric field.
A comparison of the calculated energies and oscillator strengths with the experimental data is shown in Figure 4 for GaN/AlGaN QW’r this figure, the energetic positions were taken from spectra at the longest possible delay time after excitation, i.e. with screening of the field being as small as possible. The calculated curves include only a single adjustable parameter (the band discontinuities were taken from the literature Reference Martin, Botchkarev, Rockett and Morkoc[16]), which is the magnitude of the piezoelectric field. In the present case, a field of 350 kV/cm consistently explains both the red-shift and the dramatic increase of the decay time with increasing well width.
Figure 4. Comparison of the measured energy positions (dots) and decay times (squares) of the low-energy lines in GaN/AlGaN SQW’s with a calculation based on piezoelectric fields. The triangles give the values for the respective higher-energy emission lines.
Moreover, Figure 4 also explains the origin of the higher energy line in the thick layers: It is due to spatially direct transitions in the strained GaN well layer. The dashed-dotted line was calculated on the basis of the known strain of about 0.4 % of the GaN layer and coincides almost perfectly with the measured position of the corresponding luminescence peaks.
Figure 5 summarizes our results for a series of GaInN/GaN single quantum wells. In this case, the analysis of the emission peaks yields a piezoelectric field of about 300 kV/cm. From x-ray diffraction data we estimate the strain to be of the order 0.3 %. Unlike the case of the GaN/AlGaN structures, the calculation of the decay times does not fit the experimental value for the largest well width. As we will show later on, this is related to the small conduction band discontinuity in the GaInN/GaN system, which leads to a rather weak electron confinement in such quantum wells.
Figure 5. Comparison of the measured energy positions (dots) and decay times (squares) of the low-energy lines in GaInN/GaN SQW’s with a calculation based on piezoelectric fields.
5. Carrier confinement and sign of the piezoelectric field
5.1 Results for asymmetric test samples
In order to study the effects of carrier confinement on piezoelectric field effects in nitride quantum wells in more detail, we have designed and fabricated a set of samples with asymmetric barriers, as shown in Figure 6a. Besides a control sample with a 7 nm GaInN quantum well sandwiched between GaN barriers, these samples had a 20 nm AlGaN barrier either “below” or “above” the quantum well.
Figure 6a. Layer sequence of the asymmetric GaN/GaInN/AlGaN test structures.
Figure 6b. Layer sequence of the asymmetric GaN/GaInN/AlGaN test structures.
The results of time-resolved photoluminescence measurements are shown in Figure 7. Very clearly, the luminescence decay is much faster (by almost 3 orders of magnitude) for the sample with the AlGaN barrier on top of the quantum well than for the one with the AlGaN barrier below the quantum well. In other words, the oscillator strength is much larger for the former sample than for the latter one. This indicates that carriers are much better confined in the first sample.
Figure 7. Comparison of the luminescence decay after pulsed excitation for the two test samples with an AlGaN barrier above or below the GaInN quantum well.
These results are compared to those obtained for samples with simple GaN barriers in Figure 8. One can see that the result for the control sample is in line with the data for the thickness series discussed earlier. On the other hand, the decay time is larger for the sample with the bottom AlGaN barrier, whereas it is smaller for the sample with the top AlGaN barrier. Interestingly, the latter result fits well with our calculation for the well width dependence of the decay time.
Figure 8. Comparison of the measured decay times for the test samples with those from symmetric GaInN/GaN quantum wells with the sample In mole fraction.
5.2 Carrier confinement and sign of the field
The origin of the different behavior of the asymmetric samples is explained in Figure 9 and Figure 10. Since the piezoelectric field introduces a natural asymmetry into the structures, it makes a big difference whether the AlGaN barrier is below or on top of the quantum well, depending on the direction of the piezoelectric field. In the latter case ( Figure 10), if the field points towards the substrate, electrons are strongly confined by the large GaInN/AlGaN heterobarrier towards the top surface. In the former case ( Figure 9), electrons are confined only by the small GaInN/GaN heterobarrier. Since the oscillator strength is directly related to the overlap of the electron and hole wavefunctions, the observed difference between the asymmetric samples is clearly related to the piezoelectric field.
Figure 9. Schematic view of the conduction band in the sample with an AlGaN barrier below the GaInN quantum well.
Figure 10. Schematic view of the conduction band in the sample with an AlGaN barrier on top of the GaInN quantum well.
Moreover, if the piezoelectric field had the opposite sign, the difference between the samples should be the other way round, i.e. the sample with the top AlGaN barrier should exhibit are smaller oscillator strength. Therefore, our results allow for an unambiguous determination of the sign of the piezoelectric field, which is shown to point towards the substrate.
5.3 Polarity of the layers and piezoelectric coefficient
It is interesting to discuss this result in the context of the polarity of the nitride layers. From hemispherically scanned x-ray photoelectron diffraction (HSXPD) and other data Reference Seelmann-Eggebert, Weyher, Obloh, Zimmermann, Rar and Bernardini Porowski[17], it seems to be well established that good MOVPE samples with smooth surfaces, grown on c-plane sapphire, are Ga-face, i.e. have a single Ga-N bond pointing towards the surface. On the other hand, theoretical calculations by Bernardini et al. Reference Fiorentini and Vanderbilt[18] predict a negative sign of the piezoelectric coefficient d31. In fact, our result is consistent with this prediction, assuming that our samples are Ga-face.
The piezoelectric coefficient derived from our data according to Equation 2 and using the elastic constants from Ref. Reference Schwarz, Khachaturyan and Weber[19] is d31 ≈−0.9 × 10−10 cm/V, both for the GaN/AlGaN and for the GaInN/GaN structures. Since the In content in the GaInN/GaN samples discussed here was low, we have used the GaN elastic constants for the GaInN as well.
6. High excitation, optical gain, and screening effects
Under strong pumping conditions, such as in a semiconductor laser, the quantum wells become populated with charge carriers, which screen the piezoelectric field. This becomes evident, for example, when looking at time-resolved photoluminescence spectra of quantum wells. As shown in Figure 11 for the sample with an AlGaN barrier below the quantum well, the luminescence peak shifts to lower energy by about 230 meV from immediately after the excitation pulse towards long delay times. This is due to the fact that the carrier population created by the excitation pulse decays, thus reducing the screening charge and increasing the effective field towards its equilibrium value.
Figure 11. Time-resolved photoluminescence spectra of the GaN/GaInN/AlGaN quantum well showing the effect of screening of the piezoelectric field by photogenerated carriers.
Under even higher excitation, as necessary to achieve inversion and optical gain the field becomes almost completely screened. In Figure 12 we compare the low-temperature photoluminescence spectra (pump power ≈ W/cm2) and room-temperature stimulated emission spectra (pump power ≈ MW/cm2) of GaInN/GaN quantum wells of different thicknesses, but almost identical In mole fraction. We note that there is a large energy shift of 150 meV and 290 meV, respectively, between the low-excitation photoluminescence peak and the high-excitation stimulated emission peak. The size of this energy shift strongly depends on well width, which confirms its origin as being due to the piezoelectric field. Moreover, the position of the stimulated emission peak does no longer depend significantly on pump power, which indicates that the field is almost completely screened under these conditions. The position of the stimulated emission peak is therefore a good measure of the real bandgap energy of the GaInN quantum well, without any Stark-shift.
Figure 12. Photoluminescence and stimulated emission spectra of GaInN/GaN quantum wells with 3 nm and 6 nm well thickness.
7. Discussion
Piezoelectric fields are now emerging as a dominant factor for the optical and electrical properties of nitride heterostructures. In fact, most of the observations previously attributed to localization effects Reference Chichibu, Azuhata, Sota and Nakamura[3] Reference Narukawa, Kawakami, Fujita, Fujita and Nakamura[4] can be easily explained:
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1. The large Stokes shift between emission and absorption in GaInN/GaN (and GaN/AlGaN) quantum wells is due to the fact that Stark-shifted states do dominate the luminescence, while they cannot efficiently absorb light due to their very small oscillator strength. Only highly excited states, which are close to the flatband bandgap, contribute significantly to the absorption.
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2. The large and energy-dependent decay time of the photoluminescence are due to the reduced oscillator strength and to the screening-induced red-shift of the luminescence peak towards long delay times.
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3. The blue-shift of the emission of quantum well LED’s for large forward currents is due to screening of the piezoelectric field.
Moreover, there are additional issues, which can not be easily explained by localization effects:
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1. The characteristic well width dependence of the peak positions and the decay times can not be accounted for by localization effects.
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2. Localization effects are unable to explain the extremely long decay times, well in the microsecond range, for thick quantum wells.
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3. The “negative” quantization energies for thick quantum wells (i.e. peak energies below the bulk bandgap), which are obvious at least for GaN/AlGaN quantum wells are not possible without piezoelectric fields.
Of course, there may still be localization of carriers due to well width fluctuations, composition fluctuations, or even phase separation of GaN and InN. The dominant effect, however, for the optical and electrical properties of nitride heterostructures appears to the piezoelectric fields rather than any localization effect.
8. Conclusion
In conclusion, we have shown that the optical properties of GaInN/GaN and GaN/AlGaN quantum wells are dominated by effects of the piezoelectric field due to the elastic strain built into these layers. Both the oscillator strength and the effective bandgap exhibit a characteristic well-width dependence. Compared to the piezoelectric effects, localization of carriers at composition fluctuations plays only a minor role. By introducing an AlGaN barrier either below or on top of a GaInN/GaN quantum well, the carrier confinement of the well can be manipulated. This allows us to determine the direction of the piezoelectric field to be towards the substrate in case of compressive in-plane strain. Under strong pumping conditions, such as in a laser diode, the piezoelectric field becomes almost completely screened.
