Investigation of strain effect in InGaN/GaN multi-quantum wells

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1 Indian Journal of Pure & Applied Physics Vol. 51, January 2013, pp Investigation of strain effect in In/ multi-quantum wells Ya-Fen Wu Department of Electronic Engineering, Ming Chi University of Technology, New Taipei City 24301, Taiwan Received 23 August 2012; revised 28 September 2012; accepted 12 October 2012 The strain effect of In/ multi-quantum wells with different indium contents has been studied in the present paper. The high-resolution X-ray diffraction (HRXRD) curves of the samples have been measured and analyzed by a theoretical model. Based on the model, it is found that sample with higher indium content exhibits a stronger internal strain. To further investigate the calculated results, the injection-current dependent electroluminescence (EL) spectra have been carried out for the samples. An evident blueshift of EL peak energy with increasing current is observed for the sample with higher indium content, implying a stronger quantum-confined-stark effect and internal strain of it. The inference obtained from the HRXRD line profile analysis is confirmed by the experimental results. The HRXRD can be used as an effective tool to investigate the internal strain of In/ MQW heterosystems. Keywords: High-resolution X-ray diffraction, Quantum-confined-Stark effect, Electroluminescence, Internal strain 1 Introduction The wide band-gap materials and In are very suitable for the fabrication of light-emitting devices, as have been extensively demonstrated in recent years 1-3. The wavelength of radiation emitted from In can be tuned over a wide range from visible red (~610 nm) to ultraviolet (~365 nm) by changing the alloy composition and forming heterostructures such as quantum wells. This property makes the growth of -based semiconductors and their heterostructures being an important issue because of the broad applications to the light-emitting diodes (LEDs), laser diodes (LDs), solar cells and photodetectors 1-5. Much interest has been focused on In/ multiquantum wells (MQWs) because of their utility as the active layer in high brightness III-nitride LED and cw blue-green LDs. Understanding the structural property of In/ MQWs is important for the fabrication of light-emitting devices. Because of the large lattice mismatch (11%) between InN and, the growth of In/ MQWs is strongly related to the strain distributions of their well and barrier layers. The built-in macroscopic polarization field consists of the spontaneous polarization field due to interface charge accumulations and the strain-induced piezoelectric polarization field 6-8. The strain between In and causes the presence of a large piezoelectric field in the wells, leading to the quantum-confined-stark effect (QCSE), which has been considered to act as an important role in the emission mechanisms of In/ heterostructures. Therefore, classification of the internal strain is essential for the development and application of In/ MQW devices. In the present paper, we report a study on the strain effect of In/ MQW heterostructures which composed of In/ multiple quantum barriers (MQBs) with different indium contents. The highresolution X-ray diffraction (HRXRD) was measured from the samples. The HRXRD line profile is analyzed by theoretical model and represents a wellestablished technique for determining the internal strain of the samples. From the calculation, stronger internal strain is found for the sample with higher indium content. To further investigate the calculated results, electroluminescence (EL) spectra of the samples were measured in the driving-current range from 1 to 100 ma. An evident QCSE is obtained for the higher-indium-content MQW sample, implying a stronger internal strain of it, coinciding with the inference investigated from the HRXRD line profile analysis. 2 Experimental Details The sample investigated in this study was grown by metal-organic vapour phase epitaxy (MOVPE) on c-plane sapphire substrate. A 20-nm-thick buffer layer was deposited for all the samples, followed by a 3- m-thick Si-doped n-type layer, an undoped layer possessing five periods of In 0.15 Ga 0.85 N MQWs, and a 100-nm-thick Mg-doped p-type layer. The MQW heterostructures of the samples were

2 40 INDIAN J PURE & APPL PHYS, VOL 51, JANUARY 2013 composed five In well layers separated by six sets of multi-quantum barriers (MQBs). The thickness of every In well is 2 nm and every set of MQB is formed by five 1-nm-thick In x Ga 1-x N layers separated, respectively, by six 1-nm-thick layers. The values of x of the In x Ga 1-x N/ MQBs were 0.005, 0.01, and 0.02 for sample A, sample B, and sample C, respectively. After growth, the epilayer of the MQWs were characterized by HRXRD. Rocking curves of the (002) reflection were produced using the Bede D1 system. From the rocking curves, the splitting due to lattice mismatch and the indium content between In and were deduced. The chips were fabricated over a broad area ( m 2 ) using standard photolithography processes. Ti/Al/Ti/Au and Ni/Au were employed for the n-and p-type electrodes, respectively. The temperature dependent EL measurements were carried out by mounting the sample in a closed cycle helium cryostat where the temperature (T) was varied from 20 to 300 K and using a current source operated from 1 to 100 ma. The photoluminescence (PL) spectra were measured using a He-Cd laser operating at a wavelength of 325 nm and the average excitation intensity was in the range 5-35 mw. The samples were mounted on a Cu cold stage where the temperature was 20 K. The luminescence signal was dispersed through a 0.5 m monochromator and detected using a silicon photodiode by standard lock-in amplification technique. 3 Results and Discussion The normalized EL spectra of the In/ MQWs with low (sample A), medium (sample B), and high (sample C) indium content barriers under injection current 20 ma at 20 and 300 K are shown in Fig. 1(a and b), respectively. At 20 K, we observed In-related main emissions with peak wavelengths 422.8, 424.5, and nm for sample A, sample B, and sample C, respectively. It is apparent from the plots that the observed EL peak wavelength increased with increasing InN molar fraction of the In/ barrier structures. Fig. 2 shows the (002) reflection HRXRD /2 scans measured from the samples, from which the In/ MQWs with low, medium, and high indium content barriers can be qualitatively analyzed. The major peak at zero arc sec corresponds to the thick layer. The zeroth-, first-, and secondorder superlattice satellite peaks emerging from the In thin layer, which implying the indium incorporation in the barriers, are clearly seen in the Fig. 2 (marked as, and, respectively). Fig. 1 Electroluminescence spectra from sample A, sample B and sample C with low, medium and high indium contents, respectively, at (a) 20 K, and (b) 300 K. The driving-current is 20 ma X-ray Intensity (a.u.) FWHM (arcsec) sample A sample B sample C sample A sample B sample C ω / 2 2θ (arcsec) Fig. 2 High-resolution X-ray diffraction /2 scan spectra for sample A, sample B and sample C, respectively. The variation in the FWHM of the higher-order superlattice satellite peaks for the samples is shown in the inset

3 WU: STRAIN EFFECT IN In/ MULTI-QUANTUM WELLS 41 The superlattice peaks appear as a low angle shoulder on the peaks, representing the average indium composition in the MQW pairs. Since the (002) diffraction peak reflects the lattice constant in the growth direction, the largest splitting between the and the peak of sample C means the highest indium content. The inset of Fig. 2 depicts the variation in the full width at half maximum (FWHM) of the superlattice satellite peaks for the samples. The smallest linewidth of the peak was observed for sample A, implying that this sample has the best structural quality among the samples. With increasing indium content, the FWHMs of the superlattice satellite peaks are broadened. Thanks to the large lattice mismatch and low miscibility between the InN and compounds, the broadening of the XRD FWHMs indicates crystalline randomization, the intermixing, and/or interface roughness in In/ heterostructures 9. The angular separation between the satellite peaks can be expressed 10 as : ( ) 2D sinθ sin θ = ± nλ (1) n 0 where D is the period of the MQW pairs (equal to the combined thickness of one In 0.15 Ga 0.85 N well layer and one set of In x Ga 1 x N/ MQB layers). From the positions of the satellite peaks of the samples, the periodicity of the MQW pairs for sample A, sample B and sample C is determined to be 130.5, and Å, respectively. The values are very close to the designed values. The variation in thickness comes from the different indium contents of the samples. Fig. 3 shows the map of reciprocal space mapping (RSM) in the (102) plane of the samples. It was found that the intensity maximum of the underlying layer and superlattice peaks of the MQW heterosystem are aligned along the line =, confirming that the MQWs have grown on axis to the underlying layers. Additionally, the RSM scan reveals that the superlattices are coherently strained to the base layer 11. The In/ MQWs studied in our work can be regarded as a partially disordered structure since the nanostructures resulting from the indium-rich clusters are observed due to the large lattice and thermal expansion coefficient mismatches between the sapphire substrate and the epitaxial layers 12. The dynamical diffraction theory of perfect crystal predicts the existence of very sharp XRD lines with some small inherent breadth. Lattice mismatch between heteroepitaxial thin films is common with some lattice imperfections, and will show some additional broadening effects on the measured XRD. Therefore, the shape and breadth of the experimental XRD are the mixture of different effects 13. The basis for X-ray line profile analysis is Warren-Averbach analysis. According to the method, the Fourier coefficients for intrinsic physical line profile are the product of size and strain broadening coefficients Information on the distribution of nanostructure sizes and internal strains can be derived by calculating the diffracted intensity of X-ray beam in Fourier space. In the present model, the material is considered in terms of columns of unit cells perpendicular to the reflecting planes. The column length L is given by L=n a, where n are integers and a is the lattice constant normal to the reflecting plane. The Fourier coefficients of the X-ray line profile are the product of size and strain broadening coefficients as: size strain ( ) ( ) ( ) A L = A L A L, (2) where A is the Fourier coefficient computed from the X-ray line profile, A size the size broadening coefficient, and A strain is the strain broadening coefficient given by: ( ) = exp 2π ε ( ) strain A L L L l, (3) where l is the diffraction vector and 2 (L) is the mean square strain. The effects from size broadening Fig. 3 Reciprocal θ space mapping for sample A, sample B, and sample C, respectively

4 42 INDIAN J PURE & APPL PHYS, VOL 51, JANUARY 2013 and strain broadening can be separated because the strain coefficient is dependent on the order of reflection, while the size coefficient is independent on the order From Eqs (2 and 3), we have: size strain ( ) = ( ) + ( ) = ln ( ) 2π ε ( ) ln A L ln A L ln A L A L L L l size (4) Plot ln A versus l 2 for different (00l) reflection, the intercept of this line gives ln A size (L) and the slope gives the argument of the exponential in Eq. (3). The strain broadening coefficient A strain and the mean square strain 2 (L) are then derived. Fig. 4 shows the strain coefficient A strain versus L for the samples. The first-order peak is treated as a (00l eff ) reflection. The calculated results of the variation of mean square strain of the samples according to the method mentioned are shown in Fig. 5. It is clear that stronger internal strain exists in the sample with higher indium content which we attribute to the larger lattice mismatch between In and of the sample. To further investigate the internal strain of the samples, the injection-current dependent EL was performed. In In/ MQW heterostructures, the piezoelectric field arises from the strain caused by the lattice mismatch of the barrier and In well material, and the built-in field induces the QCSE. Generally, the strain-induced polarization field tilts the potential profile, which results in a red shift of the emission wavelength 17. As the carriers are injected into the samples, the piezoelectric fields in the strained well layer are screened by the carriers and the QCSE is weakened 18. With increasing injectioncurrent, the emission wavelength blueshifts because of the further weakened QCSE. From the magnitude of the blueshift of emission wavelength, one can estimate the QCSE of the samples. The injectioncurrent induced blueshifts of peak wavelength ( blue ), relative to their original values measured at 1 ma ( 1mA ), are expressed as: λ blue = λ 1mA λ i ma (5) where i ma is the emission wavelength at injectioncurrent i ma. The values of blue at 20 K for the samples are shown in Fig. 6(a). Observing the Fig. 4 Strain coefficients determined from the real part of the Fourier transform for sample A, sample B and sample C, respectively Fig. 5 Variation of the mean square of strains 2 (L) determined from the Fourier coefficients of the diffraction peaks for sample A, sample B, and sample C, respectively Fig. 6 Dependence of the peak wavelength blueshift on (a) injection current, and (b) incident power of sample A, sample B, and sample C at 20 K, respectively

5 WU: STRAIN EFFECT IN In/ MULTI-QUANTUM WELLS 43 calculated results as the injection current increases from 1 ma to about 50 ma, the emission peak wavelength of sample A is almost independent on the driving current. In the contrast, sample B and sample C exhibit a blueshift of peak wavelength. As the current is higher than 50 ma, a redshift of the emission wavelength is observed for all of the samples because the blueshift is compensated and overcome by the redshift of peak wavelength due to the temperature shrinkage of bandgap energy. Referring to the amounts of blueshift of emission wavelength of the samples from injection-current 1 to 50 ma, the driving-current independence of peak wavelength for sample A indicating a small QCSE of it. On the other hand, the blueshift of peak wavelength for sample B and sample C are 0.88 and 1.3 nm, respectively. The more apparent blueshift of sample C implies that stronger piezoelectric field and larger QCSE existing in this sample. A similar calculation for the incidentpower induced blueshifts of PL peak wavelength at 20 K is carried out for the samples, as shown in Fig. 6(b). The blueshift of PL peak wavelength for sample C is more distinct than the other samples. It is obvious that sample C exhibits evident QCSE, coinciding with the results obtained from the current dependent EL spectra. The deduction obtained from the analysis of XRD line profile is confirmed by the measurements of current dependent EL spectra and power dependent PL spectra. 4 Conclusions In the present paper, the strain effect of In/ MQW samples with different indium content has been investigated. Analyzing the HRXRD line profiles measured from the samples by the Warren-Averbach model, it is found that sample with higher indium content exhibits a stronger internal strain due to the lattice mismatch between In and. The driving-current-dependent EL spectra of the samples were measured to demonstrate the strain effect. The higher-indium-content sample exhibits an evident blueshift of EL peak wavelength with increasing driving currents, implying stronger QCSE and internal strain of it. It indicates that the HRXRD lineshape analysis is confirmed by the experimental result obtained from the EL spectra. Conclusively, the HRXRD lineshape analysis can be used as an effective tool to determine the internal strain of In/ MQW heterostructures. References 1 Nakamura S & Fasol G, The Blue Laser Diode (Springer, Berlin) Matsushita T, Narimatsu H & Nakamura S, Jpn J Appl Phys, 37 (1998) L Gaikwad S A, Samuel E P, Patil D S & Gautam D K, Indian J Pure & Appl Phy, 45 (2007) Nakamura S, Senoh M, Nagahama S, Iwasa N, Yamada T, Matsushita T, Kiyoku H, Sugimoto Y, Kozaki T, Umemoto H, Sano M & Chocho K, Appl Phys Lett, 72 (1998) Schubert E F & Kim J K, Science, 308 (2005) Akasaka T, Gotoh H, Saito T & Makimoto T, Appl Phys Lett, 85 (2004) Johnson M C, Bourret-Courchesne E D, Wu J, Liliental- Weber Z, Zakharov D N, Jorgenson R J, Ng T B, McCready D E & Williams J R, J Appl Phys, 96 (2004) Lü W, Li D B, Li C R, Shen F & Zhang Z, J Appl Phys, 95 (2004) Nee T E, Shen H T, Wang J C & Lin R M, J Cryst Growth, 287 (2006) Kim I H, Park H S, Park Y J & Kim T, Appl Phys Lett, 73 (1998) Shiao W Y, Huang C F, Tang T Y, Huang J J, Lu Y C, Chen C Y, Chen Y S & Yang C C, J Appl Phys, 101 (2007) Nee T E, Shen H T, Wang J C & Wu Y F, J Appl Phys, 101 (2007) Lee J C, Wu Y F, Nee T E & Wang J C, IEEE T Nanotechnol, 10 (2011) Warren B E & Averbach B L, J Appl Phys, 21 (1950) Klug H P & Alexander L E, X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials (Wiley, New York) Warren B E, X-ray diffraction (Dover) Berkowicz E, Gershoni D, Bahir G, Lakin E, Shilo D, Zolotoyabko E, Abare A C, Denbaars S P & Coldren L A, Phys Rev B, 61 (2000) Bai J, Wang T & Sakai S, J Appl Phys, 90 (2001) 1740.