Crystallographic tilt in GaN-on-Si (111) heterostructures grownby metal–organic chemical vapor deposition

H. F. Liu • L. Zhang • S. J. Chua • D. Z. Chi

Received: 18 November 2013 / Accepted: 8 January 2014 / Published online: 22 January 2014

� Springer Science+Business Media New York 2014

Abstract We report on the studies of crystallographic tilt

induced by miscut of the Si (111) substrate in GaN-on-Si

(111) heterostructures grown by metal–organic chemical

vapor deposition. By employing high-resolution X-ray

diffraction, we found that the onset of crystallographic tilt

occurred at the interface between the AlN nucleation layer

and the Si (111) substrate. The orientation of the GaN

overlayer always follows that of the AlN nucleation layer

irrespective of its quality and miscut of the substrates. The

resultant GaN [0002] is tilted toward GaN (11-20) and

(10-10) atomic planes for the miscuts of Si (111) toward

Si [1-10] and [11-2], respectively. In both cases, the

misorientation of GaN (0002), i.e., the tilt of GaN [0002]

from the surface normal direction, is in the same direction

of the miscut of Si (111). The misorientation angle of the

GaN epilayer is generally smaller than the miscut angle of

the substrate. However, the crystallographic tilt, i.e., the

angle formed between GaN [0002] and Si [111], is always

much larger than the Nagai tilt. These observations are

attributable to misfit dislocations that are anisotropically

generated at the AlN/Si (111) interface. This mechanism is

discussed based on recent microscopic observations of in-

plane misfit dislocations at the interface near the atomic

step edges.

Introduction

The epitaxial growth of GaN-on-Si (111) has long been

studied, probably as early as that of GaN-on-Sapphire which

currently dominates the GaN-based light-emitting diodes

(LED) market. However, its development lagged far behind

that of GaN-on-Sapphire due to the large thermal expansion

coefficient mismatch, besides the large lattice constant

mismatch, between III-nitrides and Si [1]. In the last few

years, driven by the pressure to reduce cost of GaN-based

devices, the epitaxial growth of GaN-on-Si (111) with a large

diameter substrate has attracted increased research interest

[2, 3]. One of the main attractive features is that high quality

single crystalline Si (111) wafers, when compared with

sapphire wafers, are readily available in large sizes at lower

cost.

From the crystal epitaxy point of view, AlN-on-Si, when

compared to GaN-on-Si, has a smaller mismatch in thermal

expansion coefficient; meanwhile, the chemical reactions

between Al and Si at elevated temperatures are much more

difficult than those between Ga and Si. These features

make AlN the most reliable intermediate layer for nucle-

ation in the epitaxial growth of GaN-on-Si. As a conse-

quence, the crystal quality and the crystallographic

orientation of the AlN nucleation layer play an important

role in the subsequent growth of GaN [3–5]. The Si (111)

substrate, on which AlN is nucleated, has the same rotation

symmetry as that of wurtzite Al(Ga)N (0002); however, the

large lattice mismatch between AlN and Si leads to the

island growth mode at the initial AlN/Si (111) interface. As

the growth progresses, the AlN islands grow in size and

coalesce laterally with adjacent neighbors, leading to the

generation of threading dislocations [6]. At the same time,

generation of misfit dislocations, typically pure edge dis-

locations, in the individual islands takes place at the AlN/Si

H. F. Liu (&) � S. J. Chua � D. Z. Chi

Institute of Materials Research and Engineering (IMRE),

A*STAR (Agency for Science, Technology and Research),

3 Research Link, Singapore 117602, Singapore

e-mail: liuhf@imre.a-star.edu.sg

L. Zhang

NUS Graduate School for Integrative Sciences and Engineering,

National University of Singapore, Singapore 117597, Singapore

123

J Mater Sci (2014) 49:3305–3313

DOI 10.1007/s10853-014-8025-6

(111) interface to release the lattice strain that accumulates

with the growth of islands due to the large lattice

mismatch.

The misfit dislocations generated at the AlN/Si (111)

interface, when having components of Burgers vector in

the direction perpendicular to the interface plane (b\), will

result in a crystallographic tilt of the growing plane [7, 8],

i.e., the AlN (0002) atomic plane tilts away from Si (111).

The tilt direction is perpendicular to the dislocation line

and the amount of tilt (dMD) is proportional to the dislo-

cation density (qMD), i.e., dMD = qMDb\. In fact, some of

the misfit dislocations may bend up to form threading

dislocations making the tilt analysis more complex [9].

Furthermore, the miscut of the substrate, both unintentional

and intentional ones, and the surface atomic step bunching

of Si (111) play important roles in the nucleation of AlN as

well as in determining the orientation and distribution of

misfit dislocations, which in turn affect the crystallographic

tilt of the resultant GaN-on-Si (111) heterostructures.

Unfortunately, there is much less studies in the literature

about crystallographic tilt in GaN-on-Si heterostructures

grown on flat/vicinal substrates as compared with those of

GaN-on-SiC and GaN-on-Sapphire [3, 10, 11]. In the latter

cases, the observed results were explained by the Nagai

model and the extended Nagai model, respectively [10–

12]. In this work, we attempt to shed some light on the

crystallographic tilt in GaN-on-Si (111) heterostructures

grown by metal–organic chemical vapor deposition

(MOCVD). For this purpose, we have employed high-res-

olution X-ray diffraction (HRXRD), scanning electron

microscopy (SEM), and atomic-force microscopy (AFM).

The results obtained reveal that the crystallographic ori-

entation of the GaN overlayer always follows that of the

AlN nucleation layer regardless of the angle and direction

of the miscut of the Si (111) substrates. This relationship is

not dependent on the crystal quality of the AlN nucleation

layer. Moreover, the crystallographic tilts found in the

GaN-on-Si (111) heterostructures studied, in contrast to

those in the GaN-on-SiC and GaN-on-Sapphire hetero-

structures [10, 11], cannot be explained by either the Nagai

model or the extended Nagai model.

Samples and experiment

A series of GaN-on-Si heterostructures, including AlGaN/

GaN high electron mobility transistor (HEMT) using step-

graded AlGaN buffer layers (sample A) [13], GaN tem-

plates using multiple low temperature (LT) grown AlN

interlayers (samples B and C), and GaN layer grown on

AlInN buffer layer (sample D), received from different

sources were studied in this work. All the heterostructures

were grown by MOCVD and verified by transmission

electron microscopy (TEM, images not shown). For the

sake of brevity, we present in Table 1 the GaN-on-Si het-

erostructure samples A-D together with the comparisons of

crystal quality indicated by the full width at half maximum

(FWHM) of the HRXRD rocking curves.

For the HRXRD characterizations, a Philips X’Pert-

MRD X-ray (Cu-Ka1) diffractometer equipped with a

hybrid monochromator (4-bounce) in the incident beam

and a channel-cut Ge (220) analyzer in the diffraction beam

is employed. To study the crystallographic tilt between

GaN (0002) and Si (111) atomic planes, x–2h scans,

ranging from 13� to 19�, were measured for the four 90�-

rotated azimuths [8]. This scanning range covers Si (111)

diffractions at about x = 14.22�, GaN (0002) diffractions

at about x = 17.28�, and AlN (0002) diffractions at about

x = 18.02�. GaN (0002) diffractions were used as the

optimization reference in each scan. However, to determine

the relationship with a high degree of accuracy between the

miscut of the substrate and the misorientation of the epi-

layer [which is referred to as the angle between GaN

(0002) and the surface normal], we have employed the

rotation and fitting method [14]. With this method the

crystallographic tilt [referred to as the angle between GaN

(0002) and Si (111)] can thus be accurately determined.

The principle of this method is schematically shown Fig. 1,

where the orientation of the height of the cylinder repre-

sents the surface normal of the sample; it is the common

surface normal of the substrate and the epilayer. To detect

the highest diffraction intensity at a certain rotated azimuth

angle /, the sample surface has to be tilted in x (the angle

between the incident X-ray beam and the sample surface

plane) to compensate the offset a (angle difference between

2h/2 and x). The tilt angle a0 of the target lattice plane

(i.e., either the miscut of the substrate or the misorientation

of the epilayer) can be derived by recording a as a function

of / from 0� to 360� via the equation

tan aþ c1ð Þ ¼ cos /þ c2ð Þ � tanða0Þ: ð1ÞHere, c1 and c2 are fitting parameters, corresponding to

the mounting tilt and orientation, respectively, of the

sample on the sample stage of the HRXRD system.

Table 1 Summary and comparisons of the GaN-on-Si heterostruc-

ture samples targeting at the HRXRD rocking curves from the

Al(In)N nucleation layer and the GaN overlayer

Sample Nucleation and

buffer

FWHM (�)

Al(In)N

(0002)

GaN

(0002)

GaN

(20-21)

A AlN/Triple AlxGa1-xN 0.50 0.11 0.19

B AlN/multi-LT-AlN 0.24 0.10 0.22

C AlN/multi-LT-AlN 0.72 0.27 0.89

D AlInN 1.92 0.88 –

3306 J Mater Sci (2014) 49:3305–3313

123

Obviously, the difference in c2 between GaN (0002) and Si

(111) of a certain GaN-on-Si (111) heterostructure strongly

correlates with the misorientation of the GaN epilayer with

respect to the miscut direction of the Si (111) substrate.

Results and discussion

Figure 2a shows the HRXRD x–2h scans collected from

sample A ranging from GaN (0002) to AlN (0002). The

corresponding scan range of Si (111) is shown in Fig. 2b.

The X-ray scans were collected from the four 90�-rotated

azimuths using GaN (0002) diffractions as the optimization

reference. It is seen in Fig. 2a that the four X-ray scans do

not exhibit any distinguishable difference in the range from

GaN (0002) to AlN (0002). This result indicates that the

GaN (0002) atomic planes are parallel to those of AlN

(0002), i.e., there is no crystallographic tilt between the

GaN (0002) and the AlN (0002) atomic planes in sample A.

However, a significant difference in the Si (111) diffraction

peaks is observed in Fig. 2b, where the diffraction inten-

sities are much lower in the X-ray scans collected at /= 0� and 180� than those collected at / = 90� and 270�.

Since the scans were optimized according to the GaN

(0002) diffractions, the remarkable variation in Si (111)

diffraction intensities at different azimuth angles provides

evidence that the Si (111) atomic planes are not parallel to

those of GaN (0002), i.e., there is an epitaxial crystallo-

graphic tilt between GaN (0002) and Si (111) atomic

planes.

It is also seen in Fig. 2b that the scans of Si (111) col-

lected at / = 90� and 270� (having much higher diffrac-

tion intensities than those collected at / = 0� and 180�) are

exactly the same in both peak position and peak intensity.

These results indicate that the crystallographic tilt between

the GaN (0002) and Si (111) atomic planes occurred in the

direction of / = 0� or 180�. To measure the tilt angle, the

sample must be tilted in the direction of / = 0� or 180� to

introduce a certain offset a between x and h (i.e., half of

Fig. 1 (color online) Schematic geometry for measuring the misori-

entation, i.e., the tilt between the surface atomic plane and the surface

plane, of a crystal. The tilt angle a0 can be derived by fitting a as a

function of / using tan (a ? c1) = cos (/ ? c2) 9 tan (a0) with c1

and c2 as the fitting parameters

Fig. 2 (color online) HRXRD

x–2h diffraction patterns

collected from GaN-on-Si (111)

heterostructure in the four 90�-

rotated azimuths: a sample A in

the range from GaN (0002) to

AlN (0002), b sample A in the

range of Si (111), c, d samples

B and C in the range from GaN

(0002) to AlN (0002),

respectively. GaN (0002)

diffractions were used as the

optimization reference in the

pattern collections. The insets

are the corresponding scans

collected with sample tilted to

introduce a certain offset

between x–h, so that Si (111)

diffractions can be detected

J Mater Sci (2014) 49:3305–3313 3307

123

2h), so that the highest Si (111) x–2h diffraction peak can

be detected; the results are shown in the inset of Fig. 2b. A

comparison between these results and the scans (/ = 0� or

180�) in Fig. 2b, where the GaN (0002) diffractions were

taken as the optimization reference, shows that the Si (111)

peak intensity is reached when the sample is tilted about

0.19� and -0.2� in the scans collected at / = 0� and 180�,

respectively. As a result, the tilt angle between GaN (0002)

and Si (111) of sample A is half of the peak separation in

the inset of Fig. 2b [8], which is 0.193�.

Likewise, the HRXRD results of samples B and C are

shown in Fig. 2c, d, respectively. These results, together

with Fig. 2a, b, clearly indicate that there is a crystallo-

graphic tilt between the GaN (0002) and the Si (111)

atomic planes, which is numerically equal to half of the

angle separating the Si (111) peaks shown in the insets of

Fig. 2b–d. The tilts are 0.193�, 0.222�, and 0.799� for

samples A, B, and C, respectively. One can also see that the

orientation of GaN (0002) always follows that of AlN

(0002) regardless of the crystal quality of the AlN nucle-

ation layer, the buffer layer, and the GaN overlayer (see the

comparisons of samples A–C in Table 1). In this regard, we

may conclude that the crystal orientation of nitride over-

layers in the GaN-on-Si heterostructure always follows that

of the nitride nucleation layer. In other words, the onset of

crystallographic tilt in the growth of GaN-on-Si structure

generally occurred at the interface between AlN and Si.

To further support this conclusion, we have grown and

measured the orientation of a GaN film on an AlInN-buf-

fered Si (001) substrate, i.e., sample D. The AlInN buffer

layer with the thickness of 150 nm (see Fig. 3b) was grown

by magnetron sputtering at 700 �C [15, 16], which has an

even worse crystal quality (see Table 1) due to the mis-

match in rotation symmetry between AlInN (0002) and Si

(001). Figure 3a, b present the SEM images recorded from

sample D in the top view and cross-sectional configura-

tions, respectively. It is seen that *2.0 lm thick GaN layer

with an average in-plane grain size larger than 500 nm was

grown on the AlInN buffer layer. The rough surface of the

GaN layer was mainly caused by the limited lateral growth

rate. Nevertheless, clear and smooth interfaces of GaN/

AlInN and AlInN/Si, together with a uniform thickness of

the AlInN buffer layer along the interface, are observed in

Fig. 3b. The inset in Fig. 3a shows the X-ray pole figure

measured from the GaN (10-11) atomic planes of sample

D. The ring structure is formed due to high diffraction

intensities at about u = 60� (i.e., in the radial direction

with origin at the center and 90� at the edge), corre-

sponding to the angle between the GaN (10-11) and

(0002) atomic planes. One sees that there is no preferential

distribution at all in / (i.e., the rotation direction). This

result reveals that the GaN layer consists of columnar

grains with c-axis parallel to each other and perpendicular

to the surface of the substrate; however, the in-plane ori-

entations of the columnar grains are randomly distributed.

This structure, the so-called fiber texture [17], is the same

as those of AlInN thin films grown by magnetron sputtering

on Si (001) substrates [15, 16]. It is formed mainly due to

the mismatch in rotation symmetries between Ga(/AlIn)N

(0002) and Si (001) (see, e.g., Ref. [1] and references

therein).

It is shown in Table 1 that the FWHM of the GaN

(0002) rocking curve of sample D is quite large (0.88�).

The broad rocking curve, together with the randomly dis-

tributed in-plane orientations (see above discussion),

makes the tilt-angle measurement via the x–2h scans from

the four 90�-rotated azimuths inaccurate for sample D.

Instead, HRXRD maps aiming at the GaN (0004) and Si

(004) atomic planes were carried out for the directions of

/ = 0� and 90�, from which the crystallographic tilt can be

Fig. 3 (color online) SEM images recorded from the GaN thin film

of sample D grown by MOCVD on Si (001) substrate employing an

ex-situ AlInN buffer: a top view and b cross-sectional view. The inset

shows the pole figure measured by X-ray diffractions from the GaN

(10-11) atomic planes of sample D, the ring-like distribution is

located at about u = 60� in the radial direction (origin at the center

and 90� at the edge)

3308 J Mater Sci (2014) 49:3305–3313

123

derived with a higher accuracy. Figure 4a, b present the

HRXRD maps around the GaN (0004) and Si (004) dif-

fractions collected from sample D at / = 0� and 90�,

respectively, the corresponding map around AlInN (0002)

and Si (004) collected at / = 0� is presented in Fig. 4c.

The insets in the left and right in Fig. 4c are the enlarged

maps of AlInN (0002) and Si (004), respectively. The

straight dashed and solid lines are linear functions of

x = (2h)/2 ? Da; where Da is the angle offset between xand h in the mapping. It is clearly seen in Fig. 4a that if

GaN (0004) is taken as the reference, the sample must be

tilted to meet an x–h offset of 1.1� to reach the Si (004)

diffraction peak. However, the map in Fig. 4b, where the

sample is 90� rotated, shows that the Si (004) peak can be

observed without any x–h offset. These results clearly

indicate that there is a tilt of *1.1� between the GaN

(0004) and Si (004) atomic planes in sample D and the tilt

is in the direction of / = 0�. Likewise, a tilt angle of about

1.0� between the AlInN (0002) and Si (004) atomic planes

is observed in Fig. 4c collected from the same azimuth (/= 0�) as that shown in Fig. 4a. These observations provide

clear-cut evidence that both the angle and direction of the

crystallographic tilt between GaN (0004) and Si (004) are

nearly the same as those of the tilt between AlInN (0002)

and Si (004) regardless of the low crystal quality of the

AlInN buffer. This evidence supports the conclusion that

the orientation of the GaN overlayer always follows that of

the nucleation layer regardless of its crystal orientation and

crystal quality.

To measure the crystallographic tilts in the GaN-on-Si

(111) heterostructures with a higher accuracy as well as to

determine the tilt direction with respect to GaN crystal

axis, we have employed the rotation and fitting method

described in ‘‘Samples and experiment’’ section. A typical

example is shown in Fig. 5a, where a is plotted as a

function of / ranging from 0 to 360� for both the Si (111)

and the GaN (0002) atomic planes of sample B. The AlN

nucleation layer has a much better crystal quality in sample

B than those in samples A and C (see the comparisons in

Table 1). The best curve fitting using Eq. (1) reveals that

the miscut of the Si (111) is 0.43�, while the misorientation

of GaN (0002) is 0.21�, both tilted to the same azimuth

without any significant phase shift (i.e., difference in /).

This relationship is schematically shown as the inset of

Fig. 5a. Figure 5b shows the HRXRD / scans collected

from the Si (220) and GaN (10-15) atomic planes without

changing the sample setup as that used for the a mea-

surements in Fig. 5a. The alignment in the / scans around

Fig. 4 (color online) HRXRD

reciprocal space mappings

collected from the GaN thin film

of sample D grown by MOCVD

on Si (001) substrate employing

an ex-situ AlInN buffer:

a aiming at GaN (0004) and Si

(004) collected at / = 0�,

b aiming at GaN (0004) and Si

(004) collected at / = 90�, and

c aiming at AlInN (0002) and Si

(004) collected at / = 0�. The

insets in c are the enlarged maps

of AlInN (0002) and Si (004)

diffractions. The inclined

straight dashed and solid lines

are linear functions of x = 2h/

2 ? Da(see the text for details)

J Mater Sci (2014) 49:3305–3313 3309

123

GaN (10-15) and Si (220) shown in Fig. 5b confirms the

in-plane epitaxial orientation of GaN [10-10]//Si [-112]

and GaN [11-20]//Si [1-10]. Meanwhile, the alignment

between Fig. 5a, b reveals that the miscut of Si (111) is

toward Si [1-10], while the misorientation of GaN (0002)

is toward GaN [11-20], both are in the same azimuth. The

dots in Fig. 5b are the differences in a between Si (111)

and GaN (0002), their fitting using Eq. (1) shows that the

crystallographic tilt between GaN (0002) and Si (111) is

0.22�. This tilt is also in the azimuth of GaN [11-20]//Si

[1-10] as indicated by the vertical arrow in Fig. 5a, b.

In the same way, we have measured the miscut of Si

(111), the misorientation of GaN (0002), and the crystal-

lographic tilt between GaN (0002) and Si (111), as well as

their directions, for samples A and C. The experimental

data and their fittings using Eq. (1) are presented in Fig. 6.

The results, together with those of sample B obtained from

Fig. 5, are summarized and compared in Table 2. The

vertical arrows in Fig. 6a, b show that there is an apparent

phase shift in the orientations of the GaN (0002) and Si

(111) of sample A, which has an unintentional Si (111)

miscut toward Si [11-2] direction (see Table 2). The

resultant misorientation of GaN (0002) is toward GaN

[10-10], which is also in the same azimuth as that of Si

[11-2]. However, the crystallographic tilt, i.e., the largest

angle between GaN (0002) and Si (111), occurred in the

GaN [11-20] direction, which is 30� rotated from the

miscut direction of the Si (111) substrate (see Fig. 6a, b).

Finally, for sample C, the situation is quite similar to that

of sample B except for the larger angle of miscut and its

induced GaN (0002) misorientation and tilt (see Table 2).

In Table 2, one can see that the misorientation direction of

GaN (0002) generally follows the miscut direction of Si

(111) and the misorientation angle of GaN (0002) is always

smaller than the miscut angle of the Si (111) substrate (see

the inset of Fig. 5a). It is worth mentioning that this

accurate crystallographic tilt measurement method is also

useful in other epitaxial heterostructures and/or device

fabrications, e.g., polarized GaN-LED [18], where the

orientation of surface polarizer with respect to the crys-

tallographic tilt may have important consequences affect-

ing the light polarization properties.

In epitaxial growth of heterostructures with small lattice

mismatches, a miscut of the substrate, a0S, generally gives

rise to a misorientation of the epilayer, a0E. This is because

the surface of the vicinal substrate contains many atomic

steps with the step height corresponding to the out-of-plane

lattice constant. The lattice mismatch in the growth direc-

tion near the step edges introduces elastic strain into the

heterostructures. The elastic strain decreases with increas-

ing distance away from the step edges, so that the growing

plane is tilted with respect to the substrate in the direction

perpendicular to the surface atomic steps. This phenome-

non was first observed by Nagai in the epitaxial growth of

InGaAs/GaAs heterostructures and can be modeled as [12]

tan aE0

� �¼ �d� tan aS

0

� �; ð2Þ

where d = (cE - cS)/cS, while cE and cS are the out-of-

plane lattice constants (i.e., monolayer thickness) of the

epilayer and the substrate, respectively. a0S is the miscut

angle of the substrate and a0E is the crystallographic tilt

angle, also named as Nagai tilt. Obviously, in this model,

the miscut, the misorientation, and the Nagai tilt are toward

the same direction, which is perpendicular to the surface

atomic steps.

For the GaN-on-Si (111) heterostructures studied here,

the misorientation direction of GaN (0002) summarized in

Table 2 indeed follows that of the miscut direction of Si

(111) in all the samples. However, the crystallographic tilt

direction of sample A is 30� rotated. On the other hand, the

vertical lattice mismatch at the interface of AlN/Si (111) is

-d = 0.2055; in terms of the Nagai model, the miscut

Fig. 5 (color online) a Orientation tilts of GaN (0002) and Si (111)

of the GaN-on-Si (111) heterostructure (sample B) measured by

HRXRD as a function of sample rotations, b differences in the

orientation tilts between Si (111) and GaN (0002) and their alignment

to the /-scan collected from the GaN (10-15) and Si (220) atomic

planes. The solid lines are the best fittings to the experimental data by

using Eq. (1)

3310 J Mater Sci (2014) 49:3305–3313

123

induced Nagai tilt is about a0E & 0.21a0

S. In this regard, the

Nagai tilts of samples A, B, and C should be 0.10�, 0.09�,

and 0.62�, respectively. In fact, we found that these values

are much smaller than those of 0.19�, 0.23�, and 0.79�measured by HRXRD for samples A, B, and C, respec-

tively (see Table 2). Besides, the extended Nagai model for

the case of GaN-on-Si (111), having -d = -0.1917 [11,

19] when compared to the Nagai model (-d = 0.2055),

tends to induce a larger rather than the smaller misorien-

tation angle of the resultant GaN (0002) than the miscut

angle of the Si (111) substrate (see Table 2). Based on the

misorientation directions and the tilt angles discussed

above, we can draw a conclusion that there must be other

factors in the GaN-on-Si (111) heterostructures that con-

tributed to the extra crystallographic tilts and the tilt rota-

tion (typically observed in sample A, see Table 2). As

mentioned above, those misfit dislocations having Burgers

vector components in the direction perpendicular to the

AlN/Si (111) interface must be the main concerns.

It has been reported by Huang et al. [20] that the surface

atomic steps on vicinal substrate of the AlN/SiC hetero-

structure have an important role in relaxing the interfacial

mismatch strain via unpaired partial misfit dislocations. By

employing high-resolution TEM, Litvinov et al. [21]

recently observed misfit dislocations with Burgers vector

parallel to the growth direction at the AlN/Si (111) inter-

face located at the area of Si atomic steps. Such misfit

dislocations, when arranged in a certain direction [22, 23],

e.g., due to atomic step bunching on the surface of vicinal

substrates, [24, 25] will cause significant crystallographic

tilts in the heteroepitaxial growth of GaN-on-Si (111). In

this regard, the rotated tilt (e.g., see sample A shown in

Fig. 6a, b and Table 2) is readily associated with the

anisotropy of dislocation nucleation and/or glide in the

initial growth stage controlled by the bunched atomic steps

on the surface of the vicinal Si (111) substrate. Step bun-

ches and large step-free regions are further confirmed by

AFM on the surface of the GaN-on-Si (111)

heterostructures.

Figure 7a shows the AFM image taken from sample C.

In this sample, the Si (111) substrate has an intentional

miscut of *3� toward Si [1-10] direction. Cross-sectional

TEM revealed that the thickness of the GaN overlayer is

about 1.6 lm, which was grown on an AlN nucleation

layer, separated into 400, 450, 450, and 300 nm sublayers

by three 10 nm thick LT-AlN interlayers. It is clearly seen

Fig. 6 (color online) a,

c Orientation tilts of GaN

(0002) and Si (111) in GaN-on-

Si (111) heterostructures

measured by HRXRD as a

function of sample rotations:

a sample A and c sample C,

b and d differences in the

orientation tilts between Si

(111) and GaN (0002) and their

alignments to the /-scan

collected from the GaN (10-

15) and Si (220) atomic planes:

b sample A and d sample C.

The solid lines are the best

fittings to the experimental data

by using Eq. (1). Rotated tilt is

observed in sample A rather

than sample C as indicated by

the straight arrows

Table 2 Summary and comparisons of the GaN-on-Si (111) hetero-

structure samples aiming at the miscut of the substrate, the misori-

entation of the GaN overlayer, the crystallographic tilt between the

overlayer and the substrate, as well as their directions

Sample Si (111) miscut GaN (0002)

misorientation

Crystallographic

tilt indicated by

GaN

Angle

(�)

Toward Angle

(�)

Toward Angle

(�)

Toward

A 0.46 [11-2] 0.29 [10-10] 0.19 [11-20]

B 0.43 [1-10] 0.21 [11-20] 0.23 [11-20]

C 2.96 [1-10] 2.16 [11-20] 0.79 [11-20]

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in Fig. 7a that the GaN surface structures step down from

top right to bottom left in the AFM image. A section

analysis from the locations indicated by the straight line in

Fig. 7a is shown in Fig. 7b, which clearly reveals flat ter-

races and inclined multiple steps periodically arranged one

after another, i.e., step bunches. The step bunched structure

of the GaN surface is schematically shown in the inset of

Fig. 7b. Following the AFM section analysis in Fig. 7b,

when moving every 1.5 lm along the horizontal axis, the

surface structures increase *50 nm in height. As a result,

the inclined angle between GaN [0001] axis and the surface

normal direction is about 1.9�. Obviously, this AFM

measurement is localized in microscale. The accuracy in

the measured tilt angles is largely depended on the uni-

formity of surface morphology and roughness. In contrast,

the tilt angle measured by HRXRD discussed above is from

an area of 2 9 2 mm2 (defined by the X-ray beam size on

the sample surface). In this light, the tilt angle of sample C

measured by AFM (i.e., 1.9�) is relatively consistent with

the HRXRD result (i.e., 2.16�, see Table 2). The observed

atomic step-bunching effect is believed to affect the

nucleation and/or glide of misfit dislocations that in turn

contributed to the crystallographic tilt and its rotation in the

epitaxial growth of GaN-on-Si (111) heterostructures.

Conclusion

In conclusion, crystallographic tilts have been studied in

various GaN-on-Si (111) heterostructures grown by

MOCVD on unintentional and intentional miscut Si (111)

substrates. It is found that the misorientation direction of the

GaN (0002) atomic planes always follows the miscut

direction of the Si (111) substrate, i.e., perpendicular to the

surface atomic steps. However, the crystallographic tilt, i.e.,

the angle formed between GaN (0002) and Si (111), is

always larger than those derived from the Nagai model and

extended Nagai model. A 30�-rotated tilt is also observed

when the miscut direction of the Si (111) substrate is toward

Si [11-2]. These observations are attributed to the surface

atomic step bunching, which tends to anisotropically locate/

distribute the nucleation and/or glide of misfit dislocations

in the initial growth stage that in turn contributed to the

crystallographic tilt as well as its rotation. Atomic step

bunching on the surface of GaN overlayer has been con-

firmed by AFM in a GaN-on-Si (111) heterostructure with

the Si (111) miscut of *3�; meanwhile, a tilt angle of 1.9�between GaN (0002) and the surface normal direction (i.e.,

misorientation) is derived from the AFM image via section

analysis, which is relatively consistent with the value of

2.16� obtained by HRXRD. We also found that the crystal

orientation of the GaN overlayer always follows that of the

AlN nucleation layer regardless of the crystal qualities of

the nucleation layer, the materials and structures of the

buffer layer, and the angles and directions of the miscut.

Acknowledgements The authors would like to thank C. B. Soh, S.

Tripathy, and K. Y. Zang for sharing the GaN-on-Si (111) hetero-

structure samples.

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Fig. 7 (color online) a AFM image (5.7 lm 9 5.7 lm) recorded

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