Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

Abstract

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A pseudo-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of ~10 4 monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.The Kardar-Parisi-Zhang (KPZ) equationoriginally describes interface motion under conditions of no bulk conservation and exponentially fast relaxation 2 . The height field h(x, t) is measured from a d s -dimensional substrate at location x, with x ∈  d s at time t ≥ 0. ν, λ and D are phenomenological parameters, physically representing the surface tension, the excess of velocity in the growth, and the amplitude of a space-time white noise η, respectively.Although posed 30 years ago, outstanding advances on the understanding of the KPZ class have been made quite recently. Following seminal works on multiple-meaning stochastic models 3, 4 , long-awaited analytical solutions 2,5 , experiments 6, 7 and numerical simulations 7-9 came out to confirm that asymptotic 1D-KPZ height distributions (HDs) are related to statistics of the largest eigenvalues of random matrices 10 , while spatial covariances are dictated by the time-correlation of Airy processes 11 . Noteworthy, both HDs and covariances exhibit sensibility to initial conditions (ICs) 4, 11 , splitting the KPZ class into subclasses according to the ICs. This unanticipated feature was recently observed also in models for nonlinear molecular beam epitaxy class 12 . Similar scenario has been found for the 2D-KPZ case, based on numerical simulations [13][14][15] , although no analytical result is known for 2D-KPZ HDs and covariances and the existing theoretical approaches 16,17 for the scaling exponents disagree with numerical outcomes. In such arid landscape, the rare reliable experimental evidences of 2D-KPZ universality [18][19][20][21] turns to be precious achievements.The short-time roughening of systems exhibiting asymptotic KPZ scaling is also rich in behavior. For example, a transient scaling in the Edwards-Wilkinson 22 (EW) class, might appear whenev...

Growth stages of nano-structured mixed-phase titania thin films and effect on photocatalytic activity

“…who identified two regimes during CdTe growth with films that were untextured in early growth and developed a texture in late stage growth [34]. Theory predicts a maximum growth exponent of unity in a single phase material, and the late stage exponent here is larger than that.…”

Roughness and Correlations in the Transition from Island to Film Growth: Simulations and Application to CdTe Deposition

“…In Ref. [45], the global roughness of films deposited on Kapton fluctuate between 15 nm and 25 nm for thicknesses between 300 nm and 3 µm. In films thicker than 5 µm, it increases as W ∼ d 0.24 , which is the scaling of the KPZ class.…”

“…Although our model qualitatively explains the transition from island to film formation, it cannot be used for a quantitative description of the island morphology because it is built on a simple cubic lattice. The model is also not suitable for a quantitative description of the polycrystalline structures of thick CdTe films [45,57]. Despite these limitations, the compatibility with negligible ES barriers and the estimate of the diffusion coefficient on Kapton may be important for future quantitative modeling of vapour deposited CdTe films.…”

The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

“…In this way, the KPZ equation, Eq. 2, is a general nonlinear stochastic differential equation, which can characterize the growth dynamics of many different systems [4][5][6][7][8][9]; [16][17][18][19]. As a consequence, most of these stochastic systems are interconnected.…”