%0 Book Section %1 statphys23_0916 %A Chatterji, A. %A Yang, N. %A Desai, R.C. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K alloys assembly asymmetric coupled deposition epitaxial films growth instabilities instability morphological nano-structures nitride self semiconductors. statphys23 thin topic-4 %T Epitaxial Growth in coherent, strained, asymmetric alloy films$^2$ %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=916 %X We examine the linear stability/ instability of an epitaxially grown coherent thin alloy film. Misfit stresses produce morphological instability in a dislocation-free thin film. The stability of the film's surface is affected by the coupling between the morphological and alloy segregation instabilities if the temperature and composition of the alloy is within the spinodal. An earlier$^3$ nonequilibrium continuum model is extended to nonsymmetric binary alloys. In the model, film- substrate misfit strain $\epsilon$, solute expansion coefficient $\eta$, growth velocity $V$ and growth temperature $T$ are important parameters that determine the film stability. The asymmetry of the binary alloy, as represented by the mean order parameter $\phi_o$ ($\phi_o = 2 c_o - 1$, $c_o$ is mean concentration) and the dependence of elastic moduli $E$ and $\mu$ on the fluctuations $\phi$ are also important. While $\phi(x, \tau)$ is a measure of the segregation instability, the morphological instability is monitored through the fluctuations of the film thickness $h(x, \tau)$ around its mean value $h(\tau) = V \tau$. We find that for $T < T_c$ where $T_c$ is the mean field critical temperature, the system is linearly unstable at all values of $\phi_0$ (for $GaAsN$ films grown on $GaAs$ substrate, $T=600K$ and $T_c=12990K$). The morphological instability is affected by the growth velocity even for small $\epsilon$ and the system remains linearly unstable as $\phi_0$ moves from the spinodal to the metastable region of the mean field phase diagram. For $=0$, the morphological instability is absent and high values of $V$ suppress compositional instability as a deposited layer is buried before the surface diffusion has a chance to segregate the two components. However for $0$, large $V$ enhances the coupled instability. The surface diffusion in solid alloy films is an activated process and the time scale for diffusion becomes exponentially large at lower temperatures. Since surface diffusion plays a central role in the coupled phase segregation and morphological instability, the time scales for the evolution of $\phi(x, \tau)$ and $h(x, \tau)$ can become very large in some systems, enabling an experimentalist to grow relatively flat films of uniform composition $\phi_0$ at low $T$. We determine the growth velcity $V_o (\phi_o)$ for which the coupled instability is minimised. For $V=V_o$ the phase segregation instability is just suppressed by the deposition. Our results in the multi-parameter space could provide some guidelines for growing flat films and also to exploit the coupled instability in the alloy film to form self assembled nano-structures. \\ $^2$~Supported by NSERC of Canada. \\ $^3$ F. Léonard and R. C. Desai, Phys. Rev. B57, 4805 (1998); Appl. Phys. Lett. 74, 40 (1999). Z.-F. Huang and R. C. Desai, Phys. Rev. B65, 195421 and 205419 (2002).

@incollection{statphys23_0916, abstract = {We examine the linear stability/ instability of an epitaxially grown coherent thin alloy film. Misfit stresses produce morphological instability in a dislocation-free thin film. The stability of the film's surface is affected by the coupling between the morphological and alloy segregation instabilities if the temperature and composition of the alloy is within the spinodal. An earlier$^3$ nonequilibrium continuum model is extended to nonsymmetric binary alloys. In the model, film- substrate misfit strain $\epsilon$, solute expansion coefficient $\eta$, growth velocity $V$ and growth temperature $T$ are important parameters that determine the film stability. The asymmetry of the binary alloy, as represented by the mean order parameter $\phi_o$ ($\phi_o = 2 c_o - 1$, $c_o$ is mean concentration) and the dependence of elastic moduli $E$ and $\mu$ on the fluctuations $\delta \phi$ are also important. While $\delta \phi(\vec{x}, \tau)$ is a measure of the segregation instability, the morphological instability is monitored through the fluctuations of the film thickness $\delta h(\vec{x}, \tau)$ around its mean value $\bar h(\tau) = V \tau$. We find that for $T < T_c$ where $T_c$ is the mean field critical temperature, the system is linearly unstable at all values of $\phi_0$ (for $GaAsN$ films grown on $GaAs$ substrate, $T=600K$ and $T_c=12990K$). The morphological instability is affected by the growth velocity even for small $\epsilon$ and the system remains linearly unstable as $\phi_0$ moves from the spinodal to the metastable region of the mean field phase diagram. For $\epsilon =0$, the morphological instability is absent and high values of $V$ suppress compositional instability as a deposited layer is buried before the surface diffusion has a chance to segregate the two components. However for $\epsilon \ne 0$, large $V$ enhances the coupled instability. The surface diffusion in solid alloy films is an activated process and the time scale for diffusion becomes exponentially large at lower temperatures. Since surface diffusion plays a central role in the coupled phase segregation and morphological instability, the time scales for the evolution of $\delta \phi(\vec{x}, \tau)$ and $\delta h({\vec x}, \tau)$ can become very large in some systems, enabling an experimentalist to grow relatively flat films of uniform composition $\phi_0$ at low $T$. We determine the growth velcity $V_o (\phi_o)$ for which the coupled instability is minimised. For $V=V_o$ the phase segregation instability is just suppressed by the deposition. Our results in the multi-parameter space could provide some guidelines for growing flat films and also to exploit the coupled instability in the alloy film to form self assembled nano-structures. \\ $^2$~Supported by NSERC of Canada. \\ $^3$ F. L\'{e}onard and R. C. Desai, Phys. Rev. B{\bf 57}, 4805 (1998); Appl. Phys. Lett. {\bf 74}, 40 (1999). Z.-F. Huang and R. C. Desai, Phys. Rev. B{\bf 65}, 195421 and 205419 (2002).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Chatterji, A. and Yang, N. and Desai, R.C.}, biburl = {https://www.bibsonomy.org/bibtex/24cbd87ff4096b8bf7cc161f65f06399d/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {01ef833e12997fe7d2eb0bb8984d0a86}, intrahash = {4cbd87ff4096b8bf7cc161f65f06399d}, keywords = {alloys assembly asymmetric coupled deposition epitaxial films growth instabilities instability morphological nano-structures nitride self semiconductors. statphys23 thin topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:34.000+0200}, title = {Epitaxial Growth in coherent, strained, asymmetric alloy films$^2$}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=916}, year = 2007 }