Size-dependent strain relaxation in InN islands grown on GaN by metalorganic chemical vapor deposition

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Size-dependent strain relaxation in InN islands grown on GaN by metalorganic

chemical vapor deposition

Wen-Che Tsai, Feng-Yi Lin, Wen-Cheng Ke, Shu-Kai Lu, Shun-Jen Cheng, Wu-Ching Chou, Wei-Kuo Chen,

Ming-Chih Lee, and Wen-Hao Chang

Citation: Applied Physics Letters 94, 063102 (2009); doi: 10.1063/1.3064166 View online: http://dx.doi.org/10.1063/1.3064166

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Size-dependent strain relaxation in InN islands grown on GaN

by metalorganic chemical vapor deposition

Wen-Che Tsai, Feng-Yi Lin, Wen-Cheng Ke, Shu-Kai Lu, Shun-Jen Cheng,

Wu-Ching Chou, Wei-Kuo Chen, Ming-Chih Lee, and Wen-Hao Changa兲

Department of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan

共Received 6 November 2008; accepted 12 December 2008; published online 9 February 2009兲 We report Raman measurements on InN islands grown on GaN by metalorganic chemical vapor deposition. The Raman frequency of the InN E2mode is found to decrease exponentially with the

island’s aspect ratio, indicating a size dependent strain relaxation during the island formation. Our results suggest that most of the strain at the InN–GaN interface have been released plastically during the initial stage of island formations. After that, the residual strain of only −3.5⫻10−3 _{is further}

relaxed elastically via surface islanding. The experimental data are in agreement with the strain relaxation predicted from a simplified model analysis as well as three-dimensional finite-element simulations. © 2009 American Institute of Physics. 关DOI:10.1063/1.3064166兴

Recently, the band gap energy of InN was found to be near 0.7 eV共Refs. 1–3兲 rather than the previously accepted value of about 1.9 eV. This finding makes the indium con-taining nitrides very appealing due to their potential applica-tions in the near infrared range. Beside the InN thin film growth, the fabrication of InN nanostructures also progress rapidly4–11 since the combination with GaN or AlN is ex-pected to form low-dimensional systems with large quantum confinement. However, the large lattice misfit共⬃10%–13%兲 between InN and GaN or AlN further complicated the epi-taxial growth of InN heterostructures. Many experimental evidences indicated that the strain of uncapped InN/GaN is-lands is almost fully relaxed by the formation of misfit dis-location共MD兲 networks at the InN–GaN interface.12,13 How-ever, it is less clear whether and how the residual strain further releases via surface islanding. In our previous works, we have demonstrated that InN islands with controlled size and density can be formed on GaN by using different pre-cursor injection schemes in metalorganic chemical vapor deposition 共MOCVD兲.7,8 Good optical quality has been achieved by growth optimizations.11A further understanding and subsequent control of strain relaxation in InN/GaN is-lands and the relationship with their size and shape become important subjects for the development of prospective InN-based photonic devices.

In this letter, we report Raman measurements on InN/ GaN islands of various sizes and shapes grown by MOCVD using different growth conditions. The Raman frequency is found to shift with the island size, indicating a size-dependent strain relaxation during the island formation. We show that the residual strain after plastic relaxation at the InN–GaN interface is further relieved elastically via surface islanding.

Samples were grown on 共0001兲 sapphire by MOCVD

using trimethylgallium, trimethylindium共TMIn兲, and ammo-nia 共NH3兲 as precursors. After the growth of a 2 ␮m GaN

buffer layer at 1120 ° C, the temperature was lowered to 625– 700 ° C for growing InN islands. Different gas-flow se-quences and growth temperatures were used to control the

InN island size. Two series of samples were prepared. The first series was grown by the so-called flow-rate modulation epitaxy 共FME兲 using alternately injected TMIn 关0.15 slm 共slm denotes standard liters per minute兲兴 and NH3 共18 slm兲

gas flows. A small NH3background flow共0.5 slm兲 was

sup-plied during the TMIn periods.8 Three FME samples were grown at 625, 650, and 700 ° C. Another series were grown by the same gas-flow sequence except that a high NH₃ back-ground flow 共10 slm兲 was used. Such a growth method is similar to the so-called pulsed mode 共PM兲, where the NH3

flow rate was kept high, but the TMIn was pulsed injected. Three PM samples have been grown at 700 ° C using differ-ent TMIn injection times tIn= 10, 15, and 20 s to control the

island size. The details of the gas flow sequence can be found in Refs. 7 and 8. Surface morphology was investigated by atomic force microscopy共AFM兲. Raman measurements were carried out at room temperature in backscattering geometry 共c-axis兲 using the 488 nm line of an Ar+ _{laser focused}

through a microscope objective into a spot of⬃2 ␮m. The scattering light was analyzed by a 1 m double monochro-mator with a spectral resolution of 0.9 cm−1 _{and a peak}

un-certainty of about ⫾0.2 cm−1_.

Figures1共a兲and1共b兲show the typical surface morphol-ogy of InN islands grown at 700 ° C by using the PM and the

a兲_{Author to whom correspondence should be addressed. Electronic mail:} [email protected]. 0 20 40 60 0 20 40 60 80 100 120 Height (nm) 0 200 400 600 0 20 40 60 80 Base (nm) 0.0 0.1 0.2 0.3 0 30 60 90 120 Aspect ratio 0 20 40 60 0 40 80 120 160 Height (nm) 0 200 400 600 0 20 40 60 80 100 120 Base (nm) 0.0 0.1 0.2 0.3 0 20 40 60 80 100 Aspect ratio

(a) PM

(b) FME

Nu mb e r of isla n d s Nu mb er o f is la nd s

FIG. 1. AFM images 共10⫻10␮m2_{兲 and dots size distribution of InN} is-lands grown by共a兲 the PM and 共b兲 the FME at 700 °C.

APPLIED PHYSICS LETTERS 94, 063102共2009兲

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FME methods, respectively. The island’s shape is hexagonal with a truncated flat top and steep faceted sidewalls. As shown in Fig. 1共a兲, the PM-grown islands have rather good size uniformity with flat shape and a typical aspect ratio 共height/base兲 less than 0.05, depending on the depositing time. However, for the FME-grown islands, the size distribu-tion is widespread. For the sample shown in Fig. 1共b兲, the island height共diameter兲 is from 6 to 60 nm 共50 to 500 nm兲, with an aspect ratio ranging from 0.02 to 0.26. Such a wide-spread size distribution allowed us to study InN islands of different sizes and shapes on the same wafer, so that the influence of growth conditions, particularly the growth tem-perature, on the strain state can be examined. In our Raman measurements, the laser illuminating spot covers a total of ⬃10–20 individual islands. In order to know the size distri-bution within the laser spot, we have fabricated an array of markers on the sample surface. This helped us to precisely control the position of laser spot with an accuracy better than 0.5 ␮m, so that the information about the island size can be obtained from AFM analysis. By inspecting different areas on the wafer, it is possible to locate some particular region where the island sizes are similar. Accordingly, Raman spec-tra for InN islands of different sizes were obtained.

In Fig.2, four representative Raman spectra for different island sizes grown either by the PM or the FME are dis-played, together with a spectrum obtained from a 300 nm InN thin film. Beside the sapphire peaks, the InN E2-high

mode near 490 cm−1 _{can be observed. The Raman}

frequen-cies of InN islands are higher than that of the InN film, indicating that islands are more compressively strained than the thin film. In particular, we found that the Raman fre-quency of the InN islands redshifts with the increasing island size, indicating a size-dependent strain relaxation in the InN islands.

Figure 3共a兲 shows the measured E₂-high-mode fre-quency of InN islands as a function of their aspect ratio共␥兲. A redshift in the Raman frequency with the increasing␥can be seen, regardless of how the InN islands were grown. In fact, we have also analyzed the Raman frequency as a function of island’s height or diameter,14 but the data are more scattered. This leads us to infer that the decreasing

E2-high-mode frequency with the island aspect ratio appears

to be a general trend.

The measured Raman shifts can be used to determine the in-plane strain ␧储 in the InN islands of different sizes. Here we adopt the values reported in Ref.15, where the strain-free Raman frequency and the slope coefficient ⌬␻/⌬␧储 of the InN E2-high mode was determined to be 490.1 cm−1 and

−1660⫾140 cm−1_{, respectively. As shown by the right scale}

of Fig. 3共a兲, the in-plane strain ␧储 of these InN islands is

compressive 共negative兲, decreasing from −3.1⫻10−3 _to

−0.6⫻10−3 _{with the increasing}_␥ _{from 0.026 to 0.26. It can}

be inferred that the in-plane strain would approach zero for

␥Ⰷ1, i.e., the limiting case of a columnlike structure. On the other hand, as ␥⬃0 共i.e., an infinite platelet structure兲, the measured in-plane strain would represent the initial strain␧_储0 at the InN–GaN interface. If we use the exponential function ␧储共␥兲=␧储0exp共−␭␥兲 with ␭ as a fitting parameter to approxi-mate the decreasing in-plane strain, the initial strain can be determined to be ␧储0= −3.5⫻10−3, with the parameter ␭ = 6.9. Since the theoretical lattice misfit for this heterosystem is f =共aGaN− aInN兲/aInN= −0.0971,13the deduced␧储0indicated that at least 96% of the interface strain has been released at the initial stage of island formations. This result is in good agreement with that deduced from the analysis of moiré fringes in high-resolution transmission electron microscopy images by Lozano et al.,12,13 where the degree of plastic relaxation was estimated to be 98% due to the formation of MD networks at the InN–GaN interface.

The decreasing in-plane strain with the island’s aspect ratio indicates that the residual strain共after the initial plastic relaxation兲 was further released elastically via surface island-ing. In order to know how the residual strain was released via the island’s free borders, we consider the ribbon model pro-posed by Kern and Muller.16Although this two-dimensional

420 440 460 480 500 520 Wavenumber ( cm-1) d c b Raman intensity ( a. u. ) Film InN E2 (high) Sapphire x5 a

FIG. 2.共Color online兲 Four representative Raman spectra for InN islands of different sizes grown by the FME 关共a兲 and 共b兲兴 and the PM 关共c兲 and 共d兲兴 methods. The average island height共base diameter兲 for 共a兲, 共b兲, 共c兲, and 共d兲 are 47共202兲, 38 共180兲, 22 共310兲, and 11 共320兲 nm, respectively. A spectrum taken from a 300 nm InN film is also included.

2D ribbon 3D disk

(a)

(b)

0.0 0.1 0.2 0.3 0.4 489 490 491 492 493 494 495 496 497 0.0 -0.1 -0.2 -0.3 -0.4 FME 700oC 650oC 600oC Raman frequency ( cm -1 ) Aspect ratio γ (h/b) PM ε || ( x10 -3 ) h 2D ribbon b 3D disk h b 0 +4 -4 -2 +2 (x10-3)

( , )

xx

y z

ε

300 nm 60 nm y z

FIG. 3. 共Color online兲共a兲 The measured Raman frequency as a function of aspect ratio. The solid共hollow and half-filled兲 symbols are data obtained from FME 共PM兲 samples grown at different temperatures. The hollow circles with error bars are from PM grown islands with tIn= 10, 15, and 20 s. The two half-filled circles are from different regions of the sample with

t_In= 10 s. The dotted line is the exponential fitting curve. The solid line is the average in-plane strain in disk-shaped islands calculated from 3D finite-element simulations.共b兲 Simulated distribution of ␧xxin the y-z plane of an uncapped disk-shape island.

063102-2 Tsai et al. Appl. Phys. Lett. 94, 063102共2009兲

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共2D兲 model is limited to elongated ribbons, it simplifies the problem considerably due to the availability of analytical expression, so that a good approximation for the relaxation of the topmost layers of the InN islands can be obtained.17In the model, the in-plane strain in an infinitely long ribbon of height h and base b is given by

␧储共␥,N兲 = ␧储0具M1典N−1, 共1兲具M1典 = 1 − 2␲␥ N +

冉

1 +

冑

2␲␥ N

冊

2 exp

冉

−

冑

2N ␥␲

冊

, 共2兲

where N is the number of monolayers and ␥= h/b is the aspect ratio. The equations illustrate that the relaxation de-pends on both ␥ and N, while our data 关Fig. 3共a兲兴 are a function of ␥ only. This means that the equations should be further simplified. For the islands sizes investigated here, i.e.,

0.02⬍␥⬍0.3 and Nⱖ28 共hⱖ8 nm兲, the exponential term

in 具M1典 is negligible, so that Eq. 共1兲 can be reduced to

␧储共␥, N兲=␧储0共1−2␲␥/N兲N−1. Numerically, as N⬎10, the ex-pression can be approximated by an exponential function,

␧储共␥兲 = ␧储0exp共− 2␲␥兲, 共3兲

which is a function of ␥ only and independent of N. This explains why the observed in-plane strain decreases expo-nentially with the aspect ratio. The fitted␭ value is also close to 2␲, consistent with this simplified model analysis.

The three-dimensional共3D兲 strain distribution in an un-capped island has also been calculated based on the finite-element method.18For simplicity, we consider a disk-shaped InN island formed on the GaN surface, with a residual strain of ␧储0= −3.5⫻10−3at the InN–GaN interface. The simulated strain distribution of ␧xx in the y-z plane is shown in Fig.

3共b兲, where a nonuniform distribution can be seen. By taking the average of the in-plane strain over the entire disk, the calculated results can be compared with the measured Raman data. As shown in Fig.3共a兲, the simulated result共solid line兲 agrees well with the experimental data, further confirming our assertion of size-dependent strain relaxations.

In summary, strain relaxation in uncapped InN/GaN is-lands of different sizes have been investigated by Raman measurements. A redshift in the Raman peak with the is-land’s aspect ratio was observed, regardless of how the InN islands were grown. Most of the strain at the InN–GaN in-terface was released plastically, with a relaxation degree up to⬎96%, during the initial stage of island formations. After

that, the residual strain of only −3.5⫻10−3 _{was further}

re-laxed elastically via the surface islanding. Based on a sim-plified 2D model analysis and full 3D simulations, we estab-lished the relationship of the strain relaxation in InN/GaN islands with their size and shape.

This work was supported in part by the project of MOE-ATU and the National Science Council of Taiwan under Grant Nos. NSC M-009-015-MY2, NSC 97-2112-M-009-018, NSC 96-2112-M-009-026-MY3, and NSC 95-2112-M-009-044-MY3.

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063102-3 Tsai et al. Appl. Phys. Lett. 94, 063102共2009兲