The kinetics of In and Ga incorporation into wurtzite InxGa1−xN nanorods, grown by plasma-assisted MBE under N-rich conditions at a moderate temperature, has been systematically investigated with Ga-flux set as a growth parameter at three distinct values while varying In-flux. The interplay of Ga and In fluxes in their contributions to the incorporation was found to disagree with the empirical Böttcher's formula, of which the reliability is based on the assumption of preeminent Ga incorporation. The competition between Ga and In for incorporations involves, we believe, the displacement of In from the weaker In-N bonds by Ga to form the Ga-N bonds at high In and Ga fluxes.

Structured arrays of self-assembled nanorods hold the promise for practical applications in optoelectronic devices due to their high radiative efficiency contributed by the reduced strain and thus significantly-lower defect densities.1,2 For this reason, there have been many attempts to construct semiconductor devices based on such nanostructures, among which those made of InxGa1-xN with tunable bandgap in the green–yellow regions have received the highest attention.3 However, the large difference in lattice constants between GaN and InN and the inherent tendency to decomposition by pseudo-binary phase separation make growth of InxGa1-xN of uniform stoichiometry a formidable task.

Reports on the growth of InxGa1-xN nanorods have been largely centered around use of molecular beam epitaxy, metal organic chemical vapor deposition and hydride vapour-phase epitaxy. The latter two methods are more adaptable to large scale fabrications, but have yet to overcome various difficulties in producing high-In-content InxGa1-xN (x>0.25) either because proper growth must take place at high temperature, or hydrogen would retard the indium incorporation.4,5 Yang et al. has recently reported the synthesis of InxGa1-xN nanorods across the full stoichiometric range using halide chemical vapor deposition.6 However, the non-uniform In profile or compromised crystal quality for those on the high In-content side was assessed by the broad full width at half maximum (FWHM) of the photoluminescence (PL) spectral peaks. The method of rf-plasma assisted molecular beam epitaxy (rf-PAMBE), on the other hand, has been able to produce nanorods of reasonable quality with high-In-content, overcoming the existing issue faced by other methods.7–10 However, few reports in this regard have attempted at systematic investigations concerning the adsorption and desorption of In or Ga, and their incorporation to form the InxGa1−xN nanorod alloys. It is worthwhile to mention here that the structural configuration of nanorod is ideal to study the incorporation kinetics because strain effect is naturally ruled out.

In this work, (0001) oriented InxGa1−xN nanorods were grown on p-type Si (111) substrates without any foreign catalyst. We had three sets of samples containing InxGa1-xN nanorods produced under an N-rich condition at 2.2 × 10−5 Torr of beam equivalent pressure (BEP), a unit used to quantify the flux here. For the first set, the BEP of In-flux, In-BEP, was set at a series of values varying from 1.31 × 10−7 to 2.22 × 10−7 Torr while keeping Ga-BEP as a parameter fixed at 1.1 × 10−7 Torr. The other set with varying In-BEP was prepared with different values of Ga-BEP of 0.95 × 10−7 and 1.2 × 10−7 Torr, intended for the sake of comparison. The growth temperature was always at 575°C throughout this work, which was calibrated by pyrometer. Meanwhile, the rf-plasma source was operated at 350 W, with which the much-dreaded phase separation issues seem all shunned.11 

The In-content of the nanorods was characterized at room temperature using photoluminescence spectroscopy (RT-PL) based on the assumption that the relevant PL-peaks manifest the true bandgaps of InxGa1−xN and thus their compositions. The samples were excited by a 150-W white-light source of Xe lamp, monochromatically filtered to give 0.1 W/cm2 power density at 320 nm and 0.5 W/cm2 at 435 nm. Equipped with these two distinct wavelengths, we have two different probing depths at disposal since 90% of the light would be absorbed over 136 nm for λ = 320 nm, and 171 nm for λ = 435 nm, according to the established data of dispersive optical absorption coefficients α().12 

Fig. 1 shows the scanning electron microscope (SEM) images and RT-PL data of the samples grown with In-BEP varying from 1.31 × 10−7 to 2.22 × 10−7 Torr accompanied by a constant Ga-BEP of 1.1 × 10−7 Torr, giving a range of V/III ratios between 67 and 91. Fig. 1(a) is for those obtained with the lowest and highest In-fluxes. The diameters of the nanorods falls between 40 nm and 120 nm while the lengths between 347 and 387 nm, correspond to a range of density increasing from 4.5 × 109 to 6.0 × 109 /cm2 when the In-BEP increases from 1.31 × 10−7 to 2.22 × 10−7 Torr. Further increases of In-flux would eventually lead to formation of nanopillars, about 35∼40 nm in diameter, atop of the nanorods. At 2.22 × 10−7 Torr, for example, the average density of the nanopillars is about 2.5 × 109 /cm2 and average height about 25 nm. Within this range of variations of the In-flux, there is a subtlety in the incorporation of In into the alloy. As revealed by the PL data for samples under 325-nm UV illumination, shown in Fig. 1(b), the luminescence peaks shift from 527 nm to 552 nm when the In-BEP increases from 1.31 × 10−7 Torr to 2.01 × 10−7 Torr. However, in continuing to 2.22 × 10−7 Torr, this trend was reversed as a slight blue shift of the PL peak took place. The FWHMs of the PL peaks range from 63 nm to 72 nm, but its interpretation will be provided later.

By changing the light source to 435 nm (Fig. 1(c)), a similar trend was found, except for a slight difference when compared to what was observed using the 320-nm illumination, at least for samples obtained with high In-flux. For In-BEP >1.77 × 10−7 Torr, a non-uniform profile of In would develop throughout the depth. For In-BEP = 2.22 × 10−7 Torr, illumination with λ = 435-nm and that with λ = 320-nm give an equivalent difference of about 0.4% in the In-content.

Relevant results were also obtained with Ga-BEP set as parameter at a few different values for comparison, i.e., 0.95 × 10−7, 1.10 × 10−7 and 1.20 × 10−7 Torr. The In-content for the InxGa1-xN nanorods in relation to the In- and Ga-fluxes were then estimated, again according to the RT-PL peak positions, as afore-presented. The results from the 320-nm illumination were summarized in Fig. 2, where we see the In-content tends to increase monotonically with the In-flux in the low-flux region. This is not surprising in view of metal limited growth for the N-rich case.13 The slope of Fig. 2, indicative of increase rate of the In-content with respect to In-flux, is proportional to the sticking coefficient of In. For In-fluxes beyond this range, the In-content would reach saturation. This means the incorporation of In cannot be further controlled by the In/Ga flux ratio. Above saturation, a slight decrease in In-content was observed. For this we suspect that an In-wetted layer might have formed atop the nanorods surface under high flux of In.14 In light of this, there might be a kinetic competition between taking In into InxGa1-xN and mere wetting the advancing surface with it. In case of wetting, it would then act as a trap for the ensuing influx of In, thus leading to a reduction in the In-content of the InxGa1-xN nanorods.15,16

When Ga BEP was decreased from 1.2 × 10−7, 1.1 × 10−7 to 9.5 × 10−8 Torr, the saturation levels of the In-content were increased, in correspondence, to 33.2 %, 34.5% and 35.5%. Here, the error bars should fall within ± 0.1%. The flux of Ga, in any case, does indeed put a limit on the incorporation of In. However, the trend does not follow the empirical Böttcher's formula cited in the literature,13 

\begin{equation}x_{\max } = 1 - \frac{{F_{Ga} }}{{F_N }}\end{equation}
xmax=1FGaFN
(1)

where F is the incident flux, assuming that the incorporation of Ga is preeminent.

To better understand the incorporation process of Ga and In, we took a kinetic model that has been successfully applied to GaAs systems.17,18 The Ga, In and N surface coverage (Θ) in relation to the sticking coefficient (s), incident fluxes (F), desorption rate constant (k), and incorporation rate (G) can be written as follows.

\begin{equation}\frac{{d\Theta _{Ga + In} }}{{dt}} = s_{Ga} F_{Ga} + s_{In} F_{In} - k_{Ga} \Theta _{Ga} - k_{In} \Theta _{In} - G_{InGaN}\end{equation}
dΘGa+Indt=sGaFGa+sInFInkGaΘGakInΘInGInGaN
(2)
\begin{equation}\frac{{d\Theta _N }}{{dt}} = s_N F_N - mk_N \Theta _N{}^m - G_{InGaN}\end{equation}
dΘNdt=sNFNmkNΘNmGInGaN
(3)

Here, sF represents the adsorption rate, while the desorption rate. Meanwhile, m reflects the kinetic order of desorption, that is, m = 0 suggests zero desorption, while m = 1 means atomic desorption and m = 2 molecular recombinative desorption. It is known that desorption of N from GaN follows the 1st order kinetics at moderate temperatures.19 Within those regions of static Ga, In, and N coverages, the left side of Eqs. (2) and (3) would be zero and, consequently, the In-content x can be expressed as

\begin{equation}x = \frac{{s_{In} F_{In} - k_{In} \Theta _{In} }}{{s_{Ga} F_{Ga} - k_{Ga} \Theta _{Ga} + s_{In} F_{In} - k_{In} \Theta _{In} }} = \frac{{s_{In} F_{In} - k_{In} \Theta _{In} }}{{G_{InGaN} }} = 1 - \frac{{s_{Ga} F_{Ga} - k_{Ga} \Theta _{Ga} }}{{G_{InGaN} }}\end{equation}
x=sInFInkInΘInsGaFGakGaΘGa+sInFInkInΘIn=sInFInkInΘInGInGaN=1sGaFGakGaΘGaGInGaN
(4)

If the Ga incorporation is unity and the desorption of reactive N is negligible, Eq. (4) would asymptotically approach Bottcher's empirical expression of Eq. (1), which gives the maximal value of In-content xmax.

\begin{eqnarray}x\xrightarrow{S_{Ga} = 1,k_{Ga} = 0}\left[ 1 - \frac{F_{Ga}}{G_{InGaN}} \right]\xrightarrow{{(2) = 0;G_{InGaN} = s_N F_N - mk_N \Theta _N{} ^m ,m = 1}}\nonumber \\\left[1 - \frac{F_{Ga}}{s_N F_N - k_N \Theta _N} \right]\xrightarrow{{S_N = 1,\Theta _N = 0ork_N = 0}}\left[1 - \frac{F_{Ga}}{F_N} \right]\end{eqnarray}
xSGa=1,kGa=01FGaGInGaN(2)=0;GInGaN=sNFNmkNΘNm,m=11FGasNFNkNΘNSN=1,ΘN=0orkN=01FGaFN
(5)

What has been assumed in deriving the Bottcher's equation should carry some clues to the deviation of xmax from our finding. First of all, the N desorption, if any at all, should be insignificant, as there is no evidence of N diffusion on the nitride surface so far. The N-atoms are chemically absorbed without detectable time delay upon arrival at growing surface, as the desorption of N from InxGa1-xN is included in the term GInGaN. Therefore, it is reasonable to pay an attention to the argument about full incorporation of Ga.

Considering InxGa1-xN as a pseudo-binary alloy of (InN)x and (GaN)1-x, we have investigated the rate of incorporation of GaN as a whole, which is, in turn, proportional to the Ga-incorporation rate. From Eq. (4), we can calculate the rate of GaN incorporations in relation to the growth rate of InxGa1-xN alloy and the In-content x as follows.

\begin{equation}G_{GaN} = G_{InGaN} (1 - x).\end{equation}
GGaN=GInGaN(1x).
(6)

Fig. 3 shows the GaN incorporation rate as a function of In-flux within the region where In-content increases linearly with In-flux (henceforth uniform In depth-profile) and.|$\frac{{d\Theta _{Ga} }}{{dt}} = \frac{{d\Theta _{In} }}{{dt}} = 0$|dΘGadt=dΘIndt=0. The rate of InxGa1-xN formation (GInGaN), and In content x used for the calculation are summarized in Table I.

We observed that GGaN is not constant with respect to the In-flux when Ga BEP is higher than 0.95 × 10−7 Torr and that GGaN increases with increasing In-content. Meanwhile, the slope of the GGaN plotted with respect to In-flux, serving as a quantitative measure of In-incorporation, tends to be reduced as the Ga-flux is lowered. With Ga BEP at 0.95 × 10−7 Torr, the GGaN is nearly constant. It is commonly believed that, under an N-rich condition and at moderate growth temperatures, as in our case of 575°C growth temperature, the incorporation of Ga is almost unity. However, we have demonstrated that the incorporation of Ga can be manipulated by altering the incident In-flux.

Kinetically at a steady state, GInGaN can be equated with the decomposition rate; that is,

\begin{equation}G_{InGaN} = \gamma {\kern 1pt} \Theta _{In + Ga} \Theta _N - k_{InGaN} (1 - \Theta _N),\end{equation}
GInGaN=γΘIn+GaΘNkInGaN(1ΘN),
(7)

where γ is the adsorption rate and kInGaN is the decomposition rate of InxGa1-xN. R. Averbeck et al.20 have suggested that the probability for InN to decompose from the InxGa1-xN structure could be actually enhanced by increasing the In-flux. The consequence of this is in the significant loss of In from the alloy by breaking up the In-N bonds. Since the activation energy of such decomposition also slightly decreases with an increasing In-content, the tendency to decompose suggests the weakness of the In-N bonds. That the exchange reaction of In with Ga on the growing surface would be energetically favorable can be argued as due to the different bonding energies of In-N and Ga-N.21 In the context of this model, the In-Ga exchange would be augmented by increasing the In-flux due to increased number of exchange sites. The eventual rate of incorporation of GaN as a whole should thus increase with the In-flux.

Finally, we point out yet another relevant observation regarding the existence of window of In-content as measured by the minimal FWHM of the RT- PL peaks, as seen from Fig. 4. Regardless of the set Ga-flux, the PL peaks of the InxGa1-xN nanorods are the narrowest when the In-content is around 33%, which corresponds to a Ga-In ratio of 2 : 1. In light of this simple ratio, enhanced ordering may have occurred, although speculative at best, when the Ga to In -ratio is an integer.

In summary, single-crystalline InxGa1-xN (0001) nanorods have been grown directly on p-type Si (111) substrates by rf-PAMBE methods under N-rich conditions. We have demonstrated the effects of In and Ga-fluxes on both the In and Ga incorporation rates into the InxGa1-xN nanorod alloys. We conclude that the incorporation of Ga is affected by that of In even at a moderate temperature of 575 °C. The empirical Bottcher's equation has been carefully re-considered based on a kinetic model of balance between adsorption and desorption. We conclude that the Ga-incorporation rate during the growth of InxGa1-xN is not unity even at the moderate temperatures, contrary to previous reports.13,22

This work was supported in part by National Science Foundation under grant number EPS-1003970, and in part by the NASA through grant number NNX09AW22A. Assistance in SEM characterizations by the Nanotechnology Center, University of Arkansas at Little Rock, and useful discussions with Mr. Emad Badraddin are kindly acknowledged. Work at NSYSU was supported in part by the National Science Council, Taiwan, under grant number 99-2112-M-110-012-MY2 and in part by the Southern Taiwan Science Park Administration (STSPA), Taiwan, R.O.C. under contract number 99RC05 through Enli Technology, Kaohsiung, Taiwan.

1.
F.
Limbach
,
C.
Hauswald
,
J.
Lähnemann
,
M.
Wölz
,
O.
Brandt
,
A.
Trampert
,
M.
Hanke
,
U.
Jahn
,
R.
Calarco
,
L.
Geelhaar
and
H.
Riechert
,
Nanotechnology
23
,
465301
(
2010
).
2.
H. W.
Seo
,
Q. Y.
Chen
,
M. N.
Iliev
,
L. W.
Tu
,
C. L.
Hsiao
,
J. K.
Meen
, and
W. K.
Chu
,
Appl. Phys. Lett.
88
,
135124
(
2006
).
3.
W.
Guo
,
M.
Zhang
,
A.
Banerjee
, and
P.
Bhattacharya
,
Nanoletter
10
,
3355
(
2010
); references therein.
4.
J.
Bai
,
Q.
Wang
, and
T.
Wang
,
J. Appl. Phys.
111
,
113103
(
2003
).
5.
H. M.
Kim
,
W. C.
Lee
,
T. W.
Kang
,
K. S.
Chung
,
C. S.
Yoon
, and
C. K.
Kim
,
Chem. Phys. Lett.
380
,
181
(
2003
).
6.
C.
Hahn
,
Z.
Zhang
,
A.
Fu
,
C. Hao
Wu
,
Y. J.
Hwang
,
D. J.
Gargas
, and
P.
Yang
,
ACS nano
5
,
3970
(
1999
).
7.
T.
Tabata
,
J.
Paek
,
Y.
Honda
,
M.
Yamaguchi
, and
H.
Amano
,
Phys. Stat. Soli. C
9
,
646
(
2010
).
8.
K.
Wu
,
T.
Han
,
K.
Shen
,
B.
Li
,
T.
Peng
,
Y.
Pan
,
H.
Sun
, and
C.
Liu
,
J. Nanosci. Nanotechnol.
10
,
8139
(
2010
).
9.
A. P.
Vajpeyi
,
A. O.
Ajagunna
,
K.
Tsagaraki
,
M.
Androulidaki
, and
A.
Georgakilas
,
Nanotechnology
20
,
325605
(
2009
).
11.
H. W.
Seo
,
S. M.
Hamad
,
D. P.
Norman
, and
F.
Keles
,
J. Crystal Growth
(submitted,
2013
).
12.
O. K.
Jani
, Develpment of wide-band gap InGaN solar cells for high-efficiency phtovoltacis (GIT,
2008
).
13.
T.
Böttcher
,
S.
Einfeldt
,
V.
Kirchner
,
S.
Figge
,
H.
Heinke
,
D.
Hommel
,
H.
Selke
, and
P. L.
Ryder
,
Appl. Phys. Lett.
73
,
3232
(
1999
).
14.
J. E.
Northrup
and
C. G.
Van de Walle
,
Appl. Phys. Lett.
84
,
4322
(
2004
).
15.
E.
Calleja
,
J.
Ristić
,
S.
Fernández-Garrid
,
L.
Cerutti
,
M. A.
Sánchez-García
,
J.
Grandal
,
A.
Trampert
,
U.
Jahn
,
G.
Sánchez
,
A.
Griol
, and
B.
Sánchez
,
phys. stat. sol. (b)
244
,
2816
(
2007
).
16.
M. A. L.
Johnson
,
W. C.
Hughes
,
W. H.
Rowland
, Jr.
,
J. W.
Cook
, Jr.
,
J. F.
Schetzina
,
M.
Leonard
,
H. S.
Kong
,
J. A.
Edmond
, and
J.
Zavada
,
Journal of Crystal Growth
,
175–176
,
72
(
1997
).
17.
S. Yu.
Karpov
and
M. A.
Maiorov
,
Surf. Sci.
393
,
108
(
1997
).
18.
D. D.
Koleske
,
A. E.
Wickenden
,
R. L.
Henry
,
W. J.
DeSisto
, and
R. J.
Gorman
,
J. Appl. Phys.
84
,
1998
(
1998
).
19.
O.
Brandt
,
H.
Yang
, and
K. H.
Ploog
,
Phys. Rev. B
54
,
4432
(
1996
).
20.
21.
E.
Iliopoulos
and
T. D.
Moustakas
,
Appl. Phys. Lett.
81
,
295
(
2002
).
22.
D. F.
Strom
,
J. Appl. Phys.
89
,
2452
(
2001
).