Growth Kinetics Effects on Self-Assembled InAs/InP Quantum Dots
M. R. Gokhale
A systematic manipulation of the morphology and the optical emission properties of MOVPE %%@ grown ensembles of InAs/InP quantum dots is demonstrated by changing the growth kinetics %%@ parameters. Under non-equilibrium conditions of a comparatively higher growth rate and low %%@ growth temperature, the quantum dot density, their average size and hence the peak %%@ emission wavelength can be tuned by changing efficiency of the surface diffusion %%@ (determined by the growth temperature) relative to the growth flux. We further observe %%@ that the distribution of quantum dot heights, for samples grown under varying conditions, %%@ if normalized to the mean height, can be nearly collapsed onto a single Gaussian curve.
growthrate.TEX
\documentclass[twocolumn,showpacs,preprintnumbers,amsmath,amssymb]{revtex4}
\usepackage{graphicx}
\pagenumbering{}
\usepackage{dcolumn}
\renewcommand{\thefootnote}{\alph{footnote})}
\begin{document}
\title{Growth Kinetics Effects on Self-Assembled InAs/InP Quantum Dots}
\author{Bhavtosh Bansal\footnote{Email:bhavtosh@tifr.res.in}, M. R. Gokhale, Arnab %%@
Bhattacharya and B. M. Arora}
\affiliation{Department of Condensed Matter Physics and Materials Science, Tata Institute %%@
of Fundamental Research, 1 Homi Bhabha Road, Mumbai-400005, India.\\}
\date{\today}
\begin{abstract}
A systematic manipulation of the morphology and the optical emission properties of MOVPE %%@
grown ensembles of InAs/InP quantum dots is demonstrated by changing the growth kinetics %%@
parameters. Under non-equilibrium conditions of a comparatively higher growth rate and low %%@
growth temperature, the quantum dot density, their average size and hence the peak %%@
emission wavelength can be tuned by changing efficiency of the surface diffusion %%@
(determined by the growth temperature) relative to the growth flux. We further observe %%@
that the distribution of quantum dot heights, for samples grown under varying conditions, %%@
if normalized to the mean height, can be nearly collapsed onto a single Gaussian curve.      
\end{abstract}
\pacs{68.65.Hb, 78.67.Hc, 81.07.Ta, 68.37.Ps, 81.15.Gh}
\maketitle
Strained heteroepitaxy beyond the critical thickness can lead to spontaneous generation of %%@
three dimensional nanoclusters via the Stranski-Krastanov growth route \cite{stangl, %%@
sugawara}. The inherently statistical nature of this self-assembled growth process implies %%@
that quantum dots' areal density, average size and the dispersion in size around the %%@
average may be determined in subtle ways by the interplay of energetics and kinetics of %%@
the growth process. The morphological characteristics of the ensemble in turn determine %%@
the electronic density of states. Therefore understanding and experimentally controlling %%@
the size, density and the size dispersion of quantum dots has been a fundamental issue. 

In this letter, we have studied metal-organic vapor phase epitaxy (MOVPE) grown InAs/InP %%@
quantum dots. In a large number of previous studies on this system, the actual morphology %%@
and/or the emission properties of quantum dot ensembles have been found to be dependent on %%@
both the specific details of the material parameters and growth conditions (e. g., %%@
substrate miscut\cite{vicinal substrates}, long ranged surface stresses\cite{surface %%@
stress}, buffer morphology\cite{buffer layer morphology, buffer morphology}, the matrix %%@
material\cite{matrix material change1, matrix material change2}, material flux and partial %%@
pressures during growth\cite{3-5ratio}, annealing\cite{rta} and growth interruptions %%@
times\cite{growth interruption}) as well as on the generic growth parameters %%@
\cite{carlsson, marchand, ponchet_coverage} like the growth temperature, materials flux %%@
and coverage. Since the dependence of the quantum dots' properties on the latter set of %%@
growth kinetics parameters is expected to provide a more system independent insight into %%@
the problem of self-assembly, we have also followed this approach. Apart from the above %%@
mentioned references on the InAs/InP system, the approach also allows us to relate our %%@
work to other studies carried out in the same spirit but on different material systems. %%@
These include Monte Carlo simulations by Meixner, et al.\cite{meixner_kunert_scholl}, a %%@
rate equation based model for growth \cite{dobbs} and theoretical and experimental %%@
observations on InP/GaAs by Johansson and Seifert \cite{Johansson_Seifert1, %%@
Johansson_Seifert2} and many studies on the InAs/GaAs system, among which the one by %%@
Dubrovskii, et al.\cite{dubrovskii} is quite substantial. Furthermore, we demonstrate a %%@
very simple (phenomenological) scaling collapse of the {\em heights} distribution data %%@
onto a single Gaussian curve. The present study therefore attempts to demonstrate in a %%@
qualitative sense that the quantum dot density and the average size but also their size %%@
dispersion may be understood and therefore predicted on the basis of the three most basic %%@
growth parameters $-$coverage, growth rate and growth temperature$-$ provided the growth %%@
is carried out under far from equilibrium conditions.  

\begin{figure}[!th]
\begin{center}
\includegraphics[width=8.5cm,
  keepaspectratio,
  angle=0,
  origin=lB]{Fig1.EPS}
\caption{\label{fig:fig1}{\it (left column)$\sim 500nm \times 500nm$ AFM surface scan %%@
images, (middle column) heights histograms and (right column) the 25K PL spectra (on the %%@
corresponding capped samples) grown at different growth rates (GR) and growth temperatures %%@
(T) and growth durations (D). Growth rate $G_0$ corresponds to approximately 2.5 ML/s. %%@
Peaks around 1eV in (b), (c) and (f) are due to wetting layer. Notice that the morphology %%@
and PL (a) and (d), and in (e) and (g) are qualitatively similar.}}
\end{center}
\end{figure} 

MOVPE growth was carried out on n+ doped (001) InP substrates using trimethyl indium and %%@
arsine as group III and V sources in a horizontal reactor at a pressure of 100 torr with %%@
hydrogen as the carrier gas. InAs layers were grown at a relatively low temperature of %%@
430-450$^\circ$C. Prior to InAs deposition, an InP buffer layer was grown, first $\sim$500 %%@
\AA $\,$at 625$^\circ$C and then with temperature continuously ramped down to the InAs %%@
growth temperature and finally another 500 \AA$\,$ at the stable temperature. To avoid %%@
switching transients, the indium flux for the buffer, the InAs, and the cap layers was %%@
kept the same. For a given set of growth conditions, a pair of samples was grown with %%@
identically deposited InAs layer in two growth runs. In the first case, the sample was %%@
immediately cooled and taken out of the reactor after InAs deposition itself to enable a %%@
study of surface morphology and in the second case, an InP cap layer was grown for samples %%@
used for photoluminescence (PL) study. For these samples, about 50 \AA$\,$ InP cap was %%@
deposited at the InAs deposition temperature to minimise further ripening during the %%@
subsequent growth of the remainder of the cap at higher temperature. The uncapped dots %%@
were characterized by Nanoscope atomic force microscope in contact mode. PL spectra were %%@
recorded at $\sim$ 25K with a 0.67 meters McPherson grating monochromator and 325 nm %%@
helium-cadmium laser as the excitation source at a power density of $\sim$ 0.5W cm$^{-2}$. %%@
The measured spectra were corrected for the system response against a standard Oriel %%@
black-body source heated to 1350K.

Fig.\ref{fig:fig1} (a)-(g) summarizes the results of seven pairs of samples (uncapped for %%@
morphology and capped for PL measurements). The growth parameters (growth duration, %%@
approximate growth rate and growth temperature) for each case are given next to the %%@
figure. 
Six of the seven pairs of samples shown in the figure can be divided into two groups, %%@
where  the samples in Fig.\ref{fig:fig1}(a, b and d) and Fig.\ref{fig:fig1}(e, f and g) %%@
have nominally similar coverage but differing growth rates and growth temperatures. In the %%@
absence of in-situ thickness diagnostic tool for our MOVPE system, we have estimated the %%@
coverage as the trimethyl indium flux $\times$ growth duration, for a fixed group III %%@
source to group V ratio. This assumes that the growth rate scales linearly with the TMIn %%@
flux. The value of coverage was then inferred from the growth time. The growth rate was %%@
calibrated against the wetting layer PL peak\cite{wetting layer footnote} as described in %%@
a previous study\cite{our sk paper}. Since the primary confinement is along the growth %%@
direction, the peak and the dispersion in the heights histogram may be expected to %%@
proportionally show up in the low temperature (25K) PL spectrum of the corresponding %%@
capped sample, also depicted in Fig.\ref{fig:fig1} next to heights histogram. Despite the %%@
fact that overgrowth can substantially change the shape and composition of the dots and %%@
the areas sampled by PL and AFM are orders of magnitude different, there is a good %%@
qualitative agreement between the AFM data and the PL spectra. In particular, bimodally %%@
distributed dots show two PL peaks and the peak energy shifts with the average size of the %%@
dots. Possible reasons for a mismatch in the size dispersion with the PL linewidths are %%@
very briefly discussed later.

 From Fig. 1, it is evident that for similar coverage but by changing the growth rate and %%@
growth temperature, it is possible to change the quantum dots' density by over an order of %%@
magnitude. The corresponding peak PL emission wavelength is also seen to change from $\sim %%@
0.65 eV$ in Fig.\ref{fig:fig1}(f) to the more usual $\sim 0.8eV$ in Fig.\ref{fig:fig1}(a, %%@
d, e and g). At lower coverage, corresponding to intermediate stage of growth, we observe %%@
that the distribution is bimodal for comparatively smaller growth rates %%@
(Fig.\ref{fig:fig1}(b, c). This intermediate stage bimodality (Fig.\ref{fig:fig1}(b),(c)) %%@
is suppressed by making the growth more non-equilibrium, by either lowering the growth %%@
temperature as in Fig.\ref{fig:fig1}(a), or by increasing the growth flux as in %%@
Fig.\ref{fig:fig1}(d). This behavior has also been observed in previous studies on %%@
InAs/GaAs \cite{Saito} but also needs to be contrasted with the more complex trend %%@
observed for InP/GaAs samples \cite{Johansson_Seifert1}. 

Furthermore, we observe that Fig.\ref{fig:fig1}(a and d) and Fig.\ref{fig:fig1}(e and g) %%@
are qualitatively more similar to each other than they are to Fig.\ref{fig:fig1}(b) and %%@
Fig.\ref{fig:fig1}(f) respectively. This indicates that (1) a smaller growth rate (and an %%@
enhanced growth temperature) yields larger dots with a smaller areal density and (2) that %%@
the effect of a smaller growth rate can be compensated by a larger growth flux. %%@
Specifically,  our observation of point (2) is qualitatively very similar to the %%@
expectations in a recent growth simulation by Meixner, et al. (Fig. 7 in reference %%@
\cite{meixner_kunert_scholl}). The simplest models for self-assembled cluster %%@
growth\cite{dobbs, meixner_kunert_scholl} are developed in analogy with the submonolayer %%@
deposition\cite{barabasi} with the assumption that the later stage of self-assembly is %%@
largely dictated by the kinetic processes occurring at the surface. Then the average %%@
quantum dot density is dictated by how efficiently the preexisting material can diffuse %%@
and find an equilibrium site before more fresh material arrives on the surface. %%@
Quantitatively, this takes the form of a scaling relation\cite{barabasi, %%@
Johansson_Seifert2}, where the mean island density depends only on the ratio of the growth %%@
flux and surface diffusion efficiency. The largeness of this dimensionless ratio may also %%@
be taken to be the measure of departure from equilibrium.
\begin{figure}[!h]
\begin{center}
\resizebox{!}{7cm} {\includegraphics{collapse_inset.EPS}}
\caption{\label{fig:fig2}{\it Probability distribution function constructed from the %%@
respective histograms (Fig.\ref{fig:fig1}) scaled by the average height. Solid line shows %%@
a fit of the average of these data points to a Gaussian function. Inset shows the same %%@
histograms as in Fig.\ref{fig:fig1} except that the curve corresponding to Fig. \ref %%@
{fig:fig1} (a) is scaled down by a factor of three for clarity of comparison with other %%@
curves in the figure}}.
\end{center}
\end{figure} 

Although we have obtained quantum dots that, depending on the growth conditions, vastly %%@
vary in size and density, a striking feature of the height histograms in %%@
Fig.\ref{fig:fig1} (a, d, e, f and g) is that extent of size dispersion is proportional to %%@
the average height of the ensemble. Therefore we have re-plotted the heights histograms %%@
(for samples with a unimodal size distribution) in units of mean height\cite{collapse %%@
footnote} and normalized the area under the curve to unity in  Fig.\ref{fig:fig2}. Very %%@
approximately, we may describe the height dispersion by a single Gaussian curve centred %%@
around the mean ($h/ \langle h\rangle =0.98$) with a full width at half maximum of 0.43. %%@
These values provide a rough but very useful estimate of the expected size dispersion %%@
(since area $\propto$ height) in terms of the average size of dots. Since the average %%@
dot-sizes themselves may be written in terms of growth kinetic parameters, such a %%@
prescription can, {\em  in principle} lead toward a first principles prediction of the %%@
inhomogeneous broadening in terms of a few growth parameters, especially because the %%@
primary confinement occurs along the height of the quantum dots due to the large aspect %%@
ratios ($\sim 6-10$). 

While the peak energy and the modality of the size distribution can be correlated with the %%@
PL spectra, a direct correlation between the size dispersion and the low temperature PL %%@
emission linewidth is not always seen in the high density samples, Fig.\ref{fig:fig1}(a %%@
and e). This is presumably because of the strong interdot coupling effects. This may be %%@
understood as a combination of two effects (1) an overlap between the dots can lead to an %%@
excess `bandwidth' over and above the energy spread associated with quantum dots' size %%@
dispersion (2) despite a band formation (which would typically imply a narrower linewidth %%@
due to the transfer of carriers to the lowest available state in the density of states %%@
continuum), at low temperature, the strong potential fluctuations localize the excitons %%@
and they are not easily transferred to the lowest possible energy\cite{Runge}. A %%@
temperature dependent PL study that shows a qualitative difference between the temperature %%@
dependent emission properties of moderate and high density dots and which partially %%@
supports this hypothesis will be presented elsewhere. 

\noindent
{\em Conclusions:} MOVPE grown InAs/InP quantum dots ensembles grown at different growth %%@
rates and temperature were studied for their morphological and optical properties. We %%@
observed that the growth was largely kinetically determined with the surface diffusion %%@
being the most prominent process within the space of (deliberately highly non-equilibrium) %%@
growth parameters studied. The bimodality in quantum dots sizes and the PL emission peaks %%@
could be controlled by changing the growth conditions. It was also established, both in %%@
morphology and in optical properties, that the effect of lowering the growth temperature %%@
is qualitatively similar to the that of increasing the growth rate at a higher growth %%@
temperature. For dots with a unimodal distribution, the distribution of heights normalized %%@
by the average height were shown to be quite similar for samples with widely varying %%@
average heights (from 6nm to 12 nm). \\
\noindent
We thank J. John and Sandip Ghosh for their help with the AFM and PL measurements and %%@
Sandeep Krishna for his help with the development of the image processing software.  
{\small
\begin{references}
\bibitem{stangl}J. Stangl, V. Holy and G. Bauer, Rev. Mod. Phys. {\bf 76}, 725 (2004)
\bibitem{sugawara}M. Sugawara (Ed.) {\it Semiconductors and Semimetals}, vol 60, Academic %%@
Press, San Diego (1999).
\bibitem{vicinal substrates}O. Bierwagen and W. T. Masselink, Appl. Phys. Lett. 86, 113110 %%@
(2005).
\bibitem{surface stress}Zhi Jin, Benzhong Wang, Yuheng Peng, Fanghai Zhao, Weiyou Chen, %%@
Shiyong Liu and Chunxiao Gao, Surf. Sci. {\bf 423}, L211 (1999).
\bibitem{buffer morphology}C. A. C. Mendon�a, E. Laureto, M. J. S. P. Brasil, M. A. Cotta, %%@
M. M. G. Carvalho, and E. A. Meneses, Appl. Phys. Lett. {\bf 72}, 1015 (1998). 
\bibitem{buffer layer morphology}L. Gonz�lez, J. M. Garc�a, R. Garc�a, F. Briones, J. %%@
Mart�nez-Pastor, and C. Ballesteros, Appl. Phys. Lett. {\bf 76}, 1104 (2000).
\bibitem{matrix material change1}Q. Gong, R. No\"tzel, P. J. van Veldhoven, T. J. %%@
Eijkemans, and J. H. Wolter, Appl. Phys. Lett. {\bf 85}, 1404 (2004).
\bibitem{matrix material change2}V. M. Ustinov, E. R. Weber, S. Ruvimov, Z. %%@
Liliental-Weber, A. E. Zhukov, A. Yu. Egorov, A. R. Kovsh, A. F. Tsatsul'nikov, and P. S. %%@
Kop'ev, Appl. Phys. Lett. {\bf 72}, 362 (1998).
\bibitem{3-5ratio}K. Kawaguchi, M. Ekawa, A. Kuramata, T. Akiyama, H. Ebe, M. Sugawara, %%@
and Y. Arakawa, Appl. Phys. Lett. {\bf 85}, 4331 (2004).
\bibitem{rta}J. F. Girard, C. Dion, P. Desjardins, C. N� Allen, P. J. Poole, and S. %%@
Raymond,  
Appl. Phys. Lett. {\bf 84}, 3382 (2004).
\bibitem{growth interruption}S. Yoon, Y. Moon, T.-W. Lee, H. Hwang, E. Yoon, Y. D. Kim, U. %%@
H. Lee, D. Lee, H.-S. Kim, and J. Y. Lee, J Elec. Mat. {\bf 29}, 535 (2000).
\bibitem{carlsson}N. Carlsson, T. Junno, L. Montelius, M. -E. Pistol, L. Samuelson and W. %%@
Seifert, J. Cryst. Growth, {\bf 191}, 347 (1998).
\bibitem{marchand}H. Marchand, P. Desjardins, S. Guillon, J.-E. Paultre, Z. Bougrioua, %%@
R.Y.-F. Yip, and R.A. Masut, J. Elec. Mat. {\bf 26}, 1205 (1997).
\bibitem{ponchet_coverage}A. Ponchet, A. Le Corre, H. L'Haridon, B. Lambert, S. Sala�n, D. %%@
Alquier, D. Lacombe and L. Durand, Appl. Surf. Sci.,{\bf 123-124}, 751 (1998).
\bibitem{meixner_kunert_scholl}M. Meixner, R. Kunert, and E. Sch\"oll, Phys. Rev. B {\bf %%@
67}, 195301 (2003).
\bibitem{dobbs}H. T. Dobbs, D. D. Vvedensky, A. Zangwill, J. Johansson, N. Carlsson, and %%@
W. Seifert,  Phys. Rev. Lett. {\bf 79}, 897 (1997).
\bibitem{Johansson_Seifert1}J. Johansson and W. Seifert, Appl. Surf Sci. {\bf 148}, 86 %%@
(1999).
\bibitem{Johansson_Seifert2}J. Cryst. Growth {\bf 234}, 132 (2002), ibid. {\bf 234}, 139 %%@
(2002).
\bibitem{dubrovskii}V. G. Dubrovskii, G. E. Cirlin, Yu. G. Musikhin, Yu. B. Samsonenko, A. %%@
A. Tonkikh, N. K. Polyakov, V. A. Egorov, A. F. Tsatsul�nikov, N. A. Krizhanovskaya, V. M. %%@
Ustinov and P. Werner, J. Cryst. Grow. {\bf 267} 47 (2004). V. G. Dubrovskii, et al., %%@
Semiconductors {\bf 38}, 329 (2004).
\bibitem{wetting layer footnote}Interestingly, the wetting layer signature is visible in %%@
some samples right up to the late stage of growth (e.g., Fig.\ref{fig:fig1}(f)) whereas in %%@
some samples it was never observed. The reason for this is not clear to us. Literature on %%@
InAs/InP also suggests a similar anomaly. In particular many groups observe a wetting %%@
layer PL from samples with matured dots on (311) InP substrates. (For example, S. Hinooda, %%@
S. Loualiche, B. Lambert, N. Bertru, M. Paillard, X. Marie, and T. Amand, Appl. Phys. %%@
Lett. {\bf 78}, 3052 (2001)).
\bibitem{our sk paper}B. Bansal, M. R. Gokhale, A. Bhattacharya and B. M. Arora, %%@
arXiv:cond-mat/0505305.
\bibitem{Saito}H. Saito, K. Nishi, and S. Sugou, Appl. Phys. Lett. {\bf 74}, 1224 (1999).
\bibitem{barabasi}A-L. Barab�si, H. E. Stanley, {\it Fractal Concepts
in Surface Growth}, (Cambridge University Press, 1995).
\bibitem{collapse footnote}The island {\em heights} scaling attempted here is most similar %%@
to the  demonstration for InN/GaN by Y. G. Cao, M. H. Xie, Y. Liu, S. H. Xu, Y. F. Ng, H. %%@
S. Wu, and S. Y. Tong, Phys. Rev B {\bf 68}, 161304(R) (2003). For a detailed discussion %%@
on the related literature on growth models and experimental confirmation of  theoretically %%@
motivated scaling functions, see B. A. Joyce, D. D. Vvedensky, Mat. Sci. Eng. {\bf R 46}, %%@
127 (2004).
\bibitem{Runge} E. Runge, in {\it Solid State Physics}, edited by H. Ehrenreich and F. %%@
Spaepen, (Academic Press, San Diego, 2002), Vol. 57, p. 150, .
\end{references}
}
\end{document}

cond-mat0506648.extracted_bib
\bibitem{stangl}J. Stangl, V. Holy and G. Bauer, Rev. Mod. Phys. {\bf 76}, 725 (2004)

\bibitem{sugawara}M. Sugawara (Ed.) {\it Semiconductors and Semimetals}, vol 60, Academic %%@
Press, San Diego (1999).

\bibitem{vicinal substrates}O. Bierwagen and W. T. Masselink, Appl. Phys. Lett. 86, 113110 %%@
(2005).

\bibitem{surface stress}Zhi Jin, Benzhong Wang, Yuheng Peng, Fanghai Zhao, Weiyou Chen, %%@
Shiyong Liu and Chunxiao Gao, Surf. Sci. {\bf 423}, L211 (1999).

\bibitem{buffer morphology}C. A. C. Mendon�a, E. Laureto, M. J. S. P. Brasil, M. A. Cotta, %%@
M. M. G. Carvalho, and E. A. Meneses, Appl. Phys. Lett. {\bf 72}, 1015 (1998). 

\bibitem{buffer layer morphology}L. Gonz�lez, J. M. Garc�a, R. Garc�a, F. Briones, J. %%@
Mart�nez-Pastor, and C. Ballesteros, Appl. Phys. Lett. {\bf 76}, 1104 (2000).

\bibitem{matrix material change1}Q. Gong, R. No\"tzel, P. J. van Veldhoven, T. J. %%@
Eijkemans, and J. H. Wolter, Appl. Phys. Lett. {\bf 85}, 1404 (2004).

\bibitem{matrix material change2}V. M. Ustinov, E. R. Weber, S. Ruvimov, Z. %%@
Liliental-Weber, A. E. Zhukov, A. Yu. Egorov, A. R. Kovsh, A. F. Tsatsul'nikov, and P. S. %%@
Kop'ev, Appl. Phys. Lett. {\bf 72}, 362 (1998).

\bibitem{3-5ratio}K. Kawaguchi, M. Ekawa, A. Kuramata, T. Akiyama, H. Ebe, M. Sugawara, %%@
and Y. Arakawa, Appl. Phys. Lett. {\bf 85}, 4331 (2004).

\bibitem{rta}J. F. Girard, C. Dion, P. Desjardins, C. N� Allen, P. J. Poole, and S. %%@
Raymond,  
Appl. Phys. Lett. {\bf 84}, 3382 (2004).

\bibitem{growth interruption}S. Yoon, Y. Moon, T.-W. Lee, H. Hwang, E. Yoon, Y. D. Kim, U. %%@
H. Lee, D. Lee, H.-S. Kim, and J. Y. Lee, J Elec. Mat. {\bf 29}, 535 (2000).

\bibitem{carlsson}N. Carlsson, T. Junno, L. Montelius, M. -E. Pistol, L. Samuelson and W. %%@
Seifert, J. Cryst. Growth, {\bf 191}, 347 (1998).

\bibitem{marchand}H. Marchand, P. Desjardins, S. Guillon, J.-E. Paultre, Z. Bougrioua, %%@
R.Y.-F. Yip, and R.A. Masut, J. Elec. Mat. {\bf 26}, 1205 (1997).

\bibitem{ponchet_coverage}A. Ponchet, A. Le Corre, H. L'Haridon, B. Lambert, S. Sala�n, D. %%@
Alquier, D. Lacombe and L. Durand, Appl. Surf. Sci.,{\bf 123-124}, 751 (1998).

\bibitem{meixner_kunert_scholl}M. Meixner, R. Kunert, and E. Sch\"oll, Phys. Rev. B {\bf %%@
67}, 195301 (2003).

\bibitem{dobbs}H. T. Dobbs, D. D. Vvedensky, A. Zangwill, J. Johansson, N. Carlsson, and %%@
W. Seifert,  Phys. Rev. Lett. {\bf 79}, 897 (1997).

\bibitem{Johansson_Seifert1}J. Johansson and W. Seifert, Appl. Surf Sci. {\bf 148}, 86 %%@
(1999).

\bibitem{Johansson_Seifert2}J. Cryst. Growth {\bf 234}, 132 (2002), ibid. {\bf 234}, 139 %%@
(2002).

\bibitem{dubrovskii}V. G. Dubrovskii, G. E. Cirlin, Yu. G. Musikhin, Yu. B. Samsonenko, A. %%@
A. Tonkikh, N. K. Polyakov, V. A. Egorov, A. F. Tsatsul�nikov, N. A. Krizhanovskaya, V. M. %%@
Ustinov and P. Werner, J. Cryst. Grow. {\bf 267} 47 (2004). V. G. Dubrovskii, et al., %%@
Semiconductors {\bf 38}, 329 (2004).

\bibitem{wetting layer footnote}Interestingly, the wetting layer signature is visible in %%@
some samples right up to the late stage of growth (e.g., Fig.\ref{fig:fig1}(f)) whereas in %%@
some samples it was never observed. The reason for this is not clear to us. Literature on %%@
InAs/InP also suggests a similar anomaly. In particular many groups observe a wetting %%@
layer PL from samples with matured dots on (311) InP substrates. (For example, S. Hinooda, %%@
S. Loualiche, B. Lambert, N. Bertru, M. Paillard, X. Marie, and T. Amand, Appl. Phys. %%@
Lett. {\bf 78}, 3052 (2001)).

\bibitem{our sk paper}B. Bansal, M. R. Gokhale, A. Bhattacharya and B. M. Arora, %%@
arXiv:cond-mat/0505305.

\bibitem{Saito}H. Saito, K. Nishi, and S. Sugou, Appl. Phys. Lett. {\bf 74}, 1224 (1999).

\bibitem{barabasi}A-L. Barab�si, H. E. Stanley, {\it Fractal Concepts
in Surface Growth}, (Cambridge University Press, 1995).

\bibitem{collapse footnote}The island {\em heights} scaling attempted here is most similar %%@
to the  demonstration for InN/GaN by Y. G. Cao, M. H. Xie, Y. Liu, S. H. Xu, Y. F. Ng, H. %%@
S. Wu, and S. Y. Tong, Phys. Rev B {\bf 68}, 161304(R) (2003). For a detailed discussion %%@
on the related literature on growth models and experimental confirmation of  theoretically %%@
motivated scaling functions, see B. A. Joyce, D. D. Vvedensky, Mat. Sci. Eng. {\bf R 46}, %%@
127 (2004).

\bibitem{Runge} E. Runge, in {\it Solid State Physics}, edited by H. Ehrenreich and F. %%@
Spaepen, (Academic Press, San Diego, 2002), Vol. 57, p. 150, .
