Molecular-beam epitaxial growth and surface diffusion

In silico testing of the universality of epithelial tissue growth

The universality of interfacial roughness in growing epithelial tissue has remained a controversial issue. Kardar-Parisi-Zhang (KPZ) and molecular beam epitaxy (MBE) universality classes have been reported among other behaviors including a total lack of universality. Here, we simulate tissues using the cellsim3d kinetic division model for deformable cells to investigate cell-colony scaling. With seemingly minor model changes, it can reproduce both KPZ- and MBE-like scaling in configurations that mimic the respective experiments. Tissue growth with strong cell-cell adhesion in a linear geometry is KPZ like, while weakly adhesive tissues in a radial geometry are MBE like. This result neutralizes the apparent scaling controversy.

A comprehensive picture of roughness evolution in organic crystalline growth: the role of molecular aspect ratio

Exploiting the capabilities of organic semiconductors for applications ranging from light-emitting diodes to photovoltaics to lasers relies on the creation of ordered, smooth layers for optimal charge carrier mobilities and exciton diffusion. This, in turn, creates a demand for organic small molecules that can form smooth thin film crystals via homoepitaxy. We have studied a set of small-molecule organic semiconductors that serve as templates for homoepitaxy. The surface roughness of these materials is measured as a function of adlayer film thickness from which the growth exponent (β) is extracted. Notably, we find that three-dimensional molecules that have low molecular aspect ratios (AR) tend to remain smooth as thickness increases (small β). This is in contrast to planar or rod-like molecules with high AR that quickly roughen (large β). Molecular dynamics simulations find that the Ehrlich-Schwöbel barrier (E_ES) alone is unable to fully explain this trend. We further investigated the mobility of ad-molecules on the crystalline surface to categorize their diffusion behaviors and the effects of aggregation to account for the different degrees of roughness that we observed. Our results suggest that low AR molecules have low molecular mobility and moderate E_ES which creates a downward funneling effect leading to smooth crystal growth.

Evolution of Roughness on InP Layers Observed by Scanning Force Microscopy

The evolution of surface roughness with increasing thickness of (100) InP layersgrown by metalorganic molecular beam epitaxy has been observed by scanningforce microscopy. The process of roughening gives rise to periodic elongatedfeatures on the surface aligned in the [011] direction, reflecting the surfaceanisotropy. The morphology eventually evolves to a grain-like surface. Theroughening is dependent on both the group III and V flux, and the growthtemperature, indicating that this phenomenon is kinetically controlled by surfacediffusion activation. For each set of parameters chosen for the growth, there is aminimum temperature where smooth, two-dimensional growth can be obtained.Below that temperature the roughening shows two distinct power law regimesdependent on the epitaxial layer thickness.

The effect of pressure on the growth of tumour cell colonies

This paper describes some experiments on the manner in which external pressure affects cell colony growth in general, and tumour growth in particular. More precisely, our results show that cell colony borders growing under high-pressure conditions have geometrical and dynamical properties that are markedly different from those corresponding to growth under homeostatic, normal pressure conditions. These behaviours are characterized by means of the so-called dynamical exponents of each type of growth. These are shown to correspond to statistical properties of solutions of some stochastic partial differential equations that account for the evolution of the interface between the expanding colony and the surrounding medium.

The universal dynamics of tumor growth

Scaling techniques were used to analyze the fractal nature of colonies of 15 cell lines growing in vitro as well as of 16 types of tumor developing in vivo. All cell colonies were found to exhibit exactly the same growth dynamics-which correspond to the molecular beam epitaxy (MBE) universality class. MBE dynamics are characterized by 1), a linear growth rate, 2), the constraint of cell proliferation to the colony/tumor border, and 3), surface diffusion of cells at the growing edge. These characteristics were experimentally verified in the studied colonies. That these should show MBE dynamics is in strong contrast with the currently established concept of tumor growth: the kinetics of this type of proliferation rules out exponential or Gompertzian growth. Rather, a clear linear growth regime is followed. The importance of new cell movements-cell diffusion at the tumor border-lies in the fact that tumor growth must be conceived as a competition for space between the tumor and the host, and not for nutrients or other factors. Strong experimental evidence is presented for 16 types of tumor, the growth of which cell surface diffusion may be the main mechanism responsible in vivo. These results explain most of the clinical and biological features of colonies and tumors, offer new theoretical frameworks, and challenge the wisdom of some current clinical strategies.

Self-consistent expansion results for the nonlocal Kardar-Parisi-Zhang equation

In this paper various predictions for the scaling exponents of the nonlocal Kardar-Parisi-Zhang (NKPZ) equation are discussed. I use the self-consistent expansion (SCE), and obtain results that are quite different from the result obtained in the past, using dynamic renormalization-group analysis, a scaling approach, and a self-consistent mode-coupling approach. It is shown that the results obtained using SCE recover an exact result for a subfamily of the NKPZ models in one dimension, while all the other methods fail to do so. It is also shown that the SCE result is the only one that is compatible with simple observations on the dependence of the dynamic exponent z in the NKPZ model on the exponent rho characterizing the decay of the nonlinear interaction. The reasons for the failure of other methods to deal with NKPZ are also discussed.

Self-consistent expansion for the molecular beam epitaxy equation

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-r('),t-t('))=2D(0)[r-->-r(')](2rho-d)delta(t-t(')). I find a lower critical dimension d(c)(rho)=4+2rho, above which the linear MBE solution appears. Below the lower critical dimension a rho-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.