Role of buried cracks in mitigating strain in crack free GaN grown on Si(111) employing AlN interlayer schemes

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Journal of Crystal Growth, 323, 1, pp. 413-417, 2010-11-18

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Role of buried cracks in mitigating strain in crack free GaN grown on

Si(111) employing AlN interlayer schemes

Tang, H.; Baribeau, J. -M.; Aers, G. C.; Fraser, J.; Rolfe, S.; Bardwell, J. A.

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Role of buried cracks in mitigating strain in crack free GaN grown on

Si (1 1 1) employing AlN interlayer schemes

H. Tang

n

, J.-M. Baribeau, G.C. Aers, J. Fraser, S. Rolfe, J.A. Bardwell

Institute for Microstructural Sciences, National Research Council Canada, Ottawa, Ontario, Canada K1A 0R6

a r t i c l e

i n f o

Available online 18 November 2010 Keywords:

A1. Molecular beam epitaxy B1. Gallium nitride B2. Strain relaxation B3. Buried cracks

a b s t r a c t

This paper investigates the effect of buried cracks in the AlN interlayer buffer on mitigation of the large, tensile, thermal expansion mismatch strain in the GaN/Si system, which is a key hurdle for achieving crack free GaN epitaxy on silicon. The thermally induced strain is determined by temperature-dependent, high-resolution X-ray diffraction measurements carried out from room temperature up to the growth temperature. It is found that in addition to the balancing effect of compressive lattice-mismatch strain induced by the AlN interlayers, buried cracks in the AlN interlayer region can also relax some of the thermal expansion mismatch strain through elastic distortion at crack edges. The degree of relaxation is dependent on the spacing-to-height aspect ratio of the buried cracks, consistent with prediction of crack-edge-induced relaxation models.

1. Introduction

Incentives to grow III-nitride devices on silicon wafers include low wafer cost, large wafer size, superior substrate quality, and compatibility to and potential integration with the silicon device technology. One major hurdle for GaN on silicon strategy is the large thermal expansion mismatch between GaN and Si, which yields GaN films under significant biaxial tensile stress and prone to cracking. Over the years, GaN epitaxy growers have investigated and developed various growth schemes to overcome the thermal strain hurdle in order to produce stable and crack free GaN epitaxial layers and devices on silicon wafers. The most widely investigated approach involves insertion of AlN interlayers (IL) during the growth of GaN on silicon wafers. There have been two major effective interlayer (IL) schemes reported in the literature. One scheme uses multiple relatively thin (in the order of 10 nm) AlN interlayers or AlN/GaN superlattices[1,2]. The other scheme uses a quite thick AlN/GaN bilayer stack as the strain balance buffer, with thickness typically of around 0.25

m

m for both layers in the stack

[3]. Both schemes are based on the same principles for achieving strain balance. Because the in-plane lattice constant of GaN is larger than that of AlN, the AlN interlayers induce compressive misfit strain in the GaN layer, which relaxes as a function of GaN layer thickness via generation of dislocations. Depending on growth conditions, the residual compressive strain can remain even in thick GaN layers, which balances off the tensile thermal mismatch strain after the wafer is cooled down to room temperature. In the

quest for stable, crack free GaN on silicon wafers, a large body of work has been devoted to optimization of growth schemes and conditions to maximize this compressive, residual, lattice-mis-match strain[4,5].

In the present article, we look into another less understood issue in the AlN IL schemes, which is the relaxation and cracking of the AlN interlayers, and the effect of the resulting buried cracks. AlN grown on GaN is under tensile misfit strain. The strain relaxes via generating dislocations as well as cracks. The cracks may propagate and be healed at top due to lateral overgrowth during subsequent growth, leading to networks of buried cracks[6,7]. The dimension and density of the buried cracks vary with different growth schemes and conditions. Crack-edge-induced relaxation of strain in thin films is a well known phenomenon. In the present paper, such buried cracks are revealed and characterized using various imaging techniques. In particular, the possible relaxation of the thermal mismatch strain by the buried cracks in the AlN interlayer structure has been studied by tempera-ture-dependent, high-resolution, X-ray diffraction strain measure-ments in the range of 25–750 1C. Such measuremeasure-ments simulate a playback of the strain state of the GaN layer at growth and during the cooling down procedure, thus allowing determination of thermally induced strain in different structures containing buried cracks. The degree of relaxation of the thermal expansion mismatch strain is experimentally determined and qualitatively interpreted with crack edge relaxation models.

2. Experimental

Crack free GaN layers employing the two types of AlN interlayer schemes were grown on 200_{Si (1 1 1) wafers by ammonia molecular}

Contents lists available atScienceDirect

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Journal of Crystal Growth

n

Corresponding author. Tel.: + 1 613 998 7636; fax: + 1 613 990 0202. E-mail address: Haipeng.Tang@nrc.ca (H. Tang).

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beam epitaxy (MBE) using an SVTA MBE system (model N35S). Prior to growth, the surface native oxide on Si (1 1 1) wafers was thermally removed in UHV of the growth chamber. For all samples, a 50 nm AlN nucleation layer was first deposited at 920 1C. For samples using the multi-thin AlN IL scheme, the interlayer buffer consists of 3 periods of 0.2

m

m GaN/10 nm AlN, both grown at 780 1C. Then a 1.5

m

m thick GaN layer was grown on this buffer structure also at 780 1C. For samples employing the thick AlN IL scheme, the buffer is a 0.2

m

m GaN/0.2

m

m AlN binary stack, where the GaN was grown at 780 1C, and AlN at much elevated tempera-ture of 920 1C. Again, on top of this buffer stack, a 1.5

m

m thick GaN layer was grown at 780 1C. For comparison purposes and as a reference sample, a plain GaN layer was grown on Si (1 1 1) at 780 1C without using any AlN interlayer buffer structure.

Secondary Electron Microscopy (SEM) as well as interference-contrast optical microscopy was used to reveal and image the buried cracks in the samples. Focused-ion-beam milling was used to prepare cross-sectional samples for SEM.

High-resolution X-ray diffraction (Bruker Discover D8) in the triple axis configuration was used to measure accurately the c lattice constant of the GaN layer, and thus the strain in the layer. The c lattice constant was calculated from the position of the center of gravity of the (0 0 0 2) diffraction spot in a reciprocal lattice map, using the position of (0 0 4) silicon substrate peak as a calibration reference. The variable temperature measurement was performed with a heating stage (Anton Paar DHS 900) filled with inert gas (nitrogen) in the range of 25–750 1C. The sample temperature was calibrated by matching measured and known silicon lattice con-stant as function of temperature.

3. Results and discussion

Fig. 1(a) shows a cross-sectional SEM image of a GaN sample grown with the multiple thin AlN IL scheme. The three thin AlN ILs, each 10 nm thick, are visible in the SEM image.Fig. 1(b) shows a magnified image of the interlayer region, providing clearer picture of the AlN ILs and the GaN layers between them. Although cracks cannot be observed from the cross-sectional SEM images, the AlN ILs are found to be cracked. This was found from plan-view SEM studies. In order to image the surface of the AlN interlayer, another sample was made containing only the multi-interlayer region with the last AlN layer on the surface.Fig. 1(c) shows the plan-view SEM image of the AlN surface, and clearly revealed the micro-cracks running in crystallographic directions. This means that the cracks are limited within the AlN ILs, and did not propagate into the GaN regions above or between them. The AlN layers are too thin for the cracks to be resolved in the cross-sectional images. Observation of micro-cracks in thin AlN ILs has been also been reported in literature[2,8].

Fig. 2(a) shows a cross-sectional SEM image of a GaN sample grown with the thick AlN interlayer scheme. The image clearly shows buried cracks mainly in the GaN buffer layer underneath the AlN layer, with some buried cracks remaining in the AlN layer. The dimension of the cracks runs through the whole thickness (0.2

m

m)

of the GaN buffer, with average spacing of about 1

m

m.Fig. 2(b) shows a plan-view optical micrograph of this sample, revealing a dense network of buried cracks running along crystallographic directions. The formation mechanism for the buried cracks in this interlayer scheme has been analyzed in previous work[6]. Unlike the thin AlN interlayer scheme, the thick AlN here is grown at a temperature (typically 900–930 1C) much higher than the GaN growth temperature (780 1C), and to a much greater thickness (typically 0.2–0.25

m

m). The AlN layer will start to crack within a few nanometers of growth. The cracks are along crystallographic directions and expose the GaN layer underneath along these crack

Fig. 1. (a) Cross-sectional SEM image of a GaN sample grown on Si (1 1 1) with multiple thin AlN IL structure; (b) magnified image of the AlN IL region of the same sample; and (c) plan-view SEM image of the surface of a thin AlN IL from another sample where the last AlN IL is the surface.

H. Tang et al. / Journal of Crystal Growth 323 (2011) 413–417 414

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directions. Since the AlN growth temperature ( 4900 1C) approaches or exceeds the GaN decomposition limit in vacuum, GaN evaporation and/or diffusion occurs along the crack openings in the AlN layer. This weakens the GaN mechanical toughness along the AlN crack regions. It has been reported that local strain field at a thin film crack edge can cause the crack to propagate downward into the layer underneath the crack[6,9]. As the AlN grows thicker, the crack openings are closed and healed due to lateral overgrowth. The continued diffusion of decomposed gallium into the AlN region to form AlGaN alloy also contributes to healing of cracks within the AlN layer, and formation of enlarged buried cracks in the GaN bottom layer[6].

The question that the present work aims to answer is whether the buried cracks region may act as a compliant buffer zone, and absorb part of the thermal expansion mismatch strain in the thick GaN layer grown on top.

For the thick GaN layer, if

e

_XX(RT) is the in-plane strain measured

at room temperature,

e

_XX(T_g) the strain at growth temperature,

then the thermal expansion caused strain is

e

_T¼

e

_XXðRTÞ

e

_XXðTgÞ ð1Þ

If written as

e

_XX(RT)¼

e

_XX(T_g)+

e

_T, we see that in order to achieve

low strain or compressive strain GaN at room temperature, i.e.

e

_XX(RT)r0, we have to increase the magnitude of

e

_XX(T_g; negative

value for compressive strain), and/or decrease the magnitude of

e

_T(positive value). Most works in the literature dealt with the issue

of enhancing the residual, compressive lattice-mismatch strain, i.e.

e

_XX(Tg). However, it has been rarely touched upon if the thermal

strain

e

_Tmay be reduced.

For ideal GaN on Si binary system grown without any interlayer buffer structure, the thermal expansion mismatch strain after cooling down is calculated as

e

0_T¼ Z RT

Tg

ð

a

_Si

a

_GaNÞdT ð2Þ

Based on the average thermal expansion coefficients in the temperature range (

a

_GaN¼ 5.6 10 6K 1

,

a

_Si¼ 3.2 10 6K 1

)

[10,11],

e

0_T¼ + 0.2% is obtained when temperature is cooling down

from 780 1C (growth temperature used here ) to RT.

For the GaN samples with interlayer schemes, if the measured

e

_T

is smaller than

e

0_T, the thermal mismatch strain is partially relaxed

by structural defects such as the buried cracks. The degree of relaxation is given by (

e

0_T

e

_TÞ=

e

0_T.

In this work, the strain in the GaN samples is determined by high-resolution X-ray diffraction measurement of the c-axis lattice constant using the (0 0 0 2) reflection. Since the thick GaN layer on top has the highest quality and constitute the dominant contribu-tion to the X-ray diffraccontribu-tion signal, the strain determined in this manner is considered to be the strain in the top GaN layer close to the surface. The strain in direction of the c-axis is determined by

e

_ZZ¼cc0 c0

ð3Þ where c and c0are the measured lattice constant and equilibrium

(strain free) lattice constant, respectively. The in-plane strain (

e

_XX)

perpendicular to c-axis is derived from

e

_ZZ¼

n

_c

e

_XX ð4Þ

where

n

_c¼ 2c13/c33 is the two-dimensional Poisson ratio for

c-plane strain, and

n

_c¼ 0.62 from Refs.[12,13] was used in the calculation.

Fig. 3(a) and (b) shows the measured c-axis lattice constants versus temperature for the GaN layers grown with the thick AlN/ GaN bilayer scheme, and those grown with the multiple thin AlN interlayers scheme. Data for strain free bulk GaN crystals and the plain GaN/Si reference sample are also shown in the graphs. The equilibrium lattice constant curve (solid curve without symbols) is obtained by fitting experimental data of GaN bulk crystals and powder pellets in the literature[12,14].

InFig. 3(a), the plain GaN/Si layer shows almost the equilibrium lattice constant at growth temperature (780 1C), but its tempera-ture dependence curve deviates the most from the equilibrium curve as the temperature decreases. This indicates that lattice misfit strain was completely relaxed during growth, and the largest thermal strain developed after cooling down. In comparison, the two samples with the thick AlN interlayer scheme show slightly larger c lattice constants than equilibrium, indicating in-plane compression to different degrees. The temperature dependence slopes are less steep, and deviate less from the equilibrium than the plain GaN/Si layer, which indicates smaller thermal strain devel-oped during cooling down. Though grown under nominally iden-tical conditions, the two samples with AlN ILs still show different strain levels at growth temperature, indicating that the residual lattice strain during growth is sensitive to growth details such as substrate treatment, nucleation procedure, and fluctuations in growth parameters. This has been investigated and discussed in Refs.[3,4].

In Fig. 3(b), the two samples with the multiple thin AlN IL scheme again show different degrees of strain at growth tempera-ture. However, their temperature dependence curves follow very closely the slope of the plain GaN/Si layer, and thus deviate from the

Fig. 2. (a) Cross-sectional SEM image of a GaN sample grown on Si (1 1 1) with thick AlN IL structure, showing a cross-sectional view of the buried cracks and (b) plan-view optical micrograph of the same sample revealing the dense network of buried cracks by focusing at about 2mm beneath the surface.

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equilibrium curve more sharply than the samples with the thick AlN IL scheme. This indicates higher thermally developed strain in these samples.

Using the data inFig. 3(a) and (b), values of

e

_XX(RT),

e

_XX(T_g), and

e

_Twere calculated for all the samples presented in the graphs, and

are given inTable 1. The measured thermally induced strain in the plain GaN/Si layer matches the full magnitude of the thermal expansion mismatch strain theoretically predicted for the binary system:

e

T¼

e

0_T¼ þ 0:20%. This indicates that the thermal strain

cannot be relaxed in such a sample structure. The samples with the thin AlN IL scheme show slightly reduced

e

_T(+ 0.17% and + 0.18%).

In contrast, the samples with the thick AlN IL scheme show significantly reduced

e

_T(+ 0.10% and +0.12%), which amounts to

nearly 50% relaxation of

e

0_T.

The buried cracks are considered to be channels for the observed partial relaxation of the thermal expansion mismatch strain. Crack-edge-induced strain relaxation in thin films has been modeled for

open cracks in literature[14]. However, no reference has been found on the models of buried cracks. The scope of the present article does not attempt quantitative modeling of strain relaxation by buried cracks. Instead, existing models on open cracks are used to provide approximate, qualitative interpretation of the experi-mental results.

Fig. 4shows an illustration of stress distribution in cracked thin film with crack height h, crack spacing 2L, and x axis for position. The stress distribution is derived by solving a self-consistent equation[15,16]:

s

ðx,LÞ ¼

s

₀2h

p

Z 2L 0 @

s

ðuÞ @u du xu ð5Þ

where

s

₀is the stress of the film in an uncracked state.

The average relative stress is then:

s

₌

s

₀¼ 1 2

s

0L

Z 2L 0

s

ðx,LÞdx ð6Þ

The degree of crack-edge-induced relaxation is thus 1

s

₌

s

₀.

This model finds that the degree of strain relaxation is a strong function of the spacing-to-height ratio L/h of the cracks[15].

For the samples with the thick AlN IL scheme inFig. 2(a), the average spacing of buried cracks is 2L 1

m

m, height is h¼0.25

m

m; thus L/h 2. According to the calculation in Ref.[15], a 40% strain relaxation is predicted for L/h¼2. The measured degree of relaxa-tion of the thermal strain is (0.2–0.1%)/0.2%¼50% for one sample, and is (0.2–0.12%)/0.2%¼40% for the other sample. Therefore, the crack model seems to agree approximately with the observed results.

For the sample with the thin AlN IL scheme inFig. 1, the average spacing is also 2L 1

m

m (seeFig. 1(c)); however, the height of crack

is only h¼10 nm¼ 0.01

m

m; thus L/h 50. The model in Ref.[15]

predicts only negligible 1% relaxation for such aspect ratio. The samples did show quite small degree of relaxation of the thermal strain, with (0.2–0.18%)/0.2%¼10% for one sample and (0.2–0.17%)/ 0.2%¼15% for the other.

Qualitatively, the crack model is consistent with the experi-mental result in that the crack induced strain relaxation becomes significant when the crack spacing-to-height ratio decreases to the

Fig. 3. c-axis lattice constant as a function of temperature for (a) two GaN layers grown on Si (1 1 1) using the thick AlN IL scheme (open circle and triangle symbols) and (b) two GaN layers using the multiple thin AlN IL scheme (open circle and square symbols). Data for equilibrium bulk GaN (solid curve without symbols) and for a plain GaN/Si (1 1 1) sample (filled square symbols) are also included in the graphs.

Table 1

Strain in samples determined from the measurement results inFig. 2.e_XX_(RT), e_XX_(T_g_{), and}e_T_{are the in-pane strain at room temperature, at growth temperature,}

and the thermally induced strain from sample cooling down, respectively.

Sample eXX(RT) eXX(Tg) eT(%)

Thick AlN IL scheme 8.7 10 4 _{1.5 10} 4 _0.10

Thick AlN IL scheme 5.6 10 4 _{6.2 10} 4 _0.12

Thin AlN IL scheme 1.7 10 3 ₀ _0.17

Thin AlN IL scheme 1.0 10 3 _{7.8 10} 4 _0.18

Plain GaN/Si 2.0 10 3 ₀ _0.20

Fig. 4. Illustrative distribution of the relative strain along the distance from the crack edge in a cracked thin film.s₀_{is the stress of the film in an uncracked state.} H. Tang et al. / Journal of Crystal Growth 323 (2011) 413–417

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order of unity, which is the case with the buried cracks in the thick AlN IL structure.

4. Conclusions

Buried cracks in AlN interlayer or interlayer region can relax some of the thermal expansion mismatch strain in GaN layers grown on silicon wafers employing AlN interlayer strain-mitigation schemes. The degree of relaxation is dependent on the spacing-to-height aspect ratio of the buried cracks, consistent with prediction of crack-edge-induced relaxation models. The thick AlN/GaN bilayer structure, with thick buried cracks and low spacing-to-height ratio, shows significant reduction in the thermally induced strain by around 50%. The thin multi-interlayer structure, with very thin buried cracks, and thus large spacing-to-height ratio, shows little impact on the magnitude of the thermally induced strain. The principal strain-mitigation mechanism for employing the AlN interlayer schemes is to induce a compressive lattice-mismatch strain at growth temperature, which offsets the tensile thermal mismatch strain built-up on cooling down to room temperature. However, this study finds that the thermally induced strain is additionally mitigated by the elastic distortion of the buried cracks.

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