Generalized Model for Photoinduced Surface Structure in Amorphous Thin Films Chao Lu, 1 Daniel Recht, 2 and Craig Arnold 1, * 1 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA 2 School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA (Received 22 April 2013; revised manuscript received 2 August 2013; published 5 September 2013) We present a generalized model to explain the spatial and temporal evolution of photoinduced surface structure in photosensitive amorphous thin films. The model describes these films as an incompressible viscous fluid driven by a photoinduced pressure originating from dipole rearrangement. This derivation requires only the polarizability, viscosity and surface tension of the system. Using values of these physical parameters, we check the validity of the model by fitting to experimental data of As 2 S 3 and demonstrating good agreement. DOI: 10.1103/PhysRevLett.111.105503 PACS numbers: 81.65.b, 66.30.h, 68.35.Fx, 78.66.Jg Introduction.—Photoinduced surface relief structures are generated in a variety of materials including azobenzene-containing polymers, chalcogenide glasses (like As 2 S 3 , AsSe, and GeAsSe), and other amorphous materials [1–5]. Macroscopic surface structures can be inscribed by illumination with a laser field having spatially varying intensity or polarization [6]. This phenomenon is potentially useful for technologies such as rewritable opti- cal data storage, active optical devices, nanofabrication, and optical actuators [7]. However, to date a complete description of the underlying microscopic mechanism has not been produced. Much experimental and theoretical work has been performed to clarify the mechanism of this phenomenon. Models have been proposed to describe the formation of surface relief [3,8], where volumetric internal pressure, interaction among dipoles, anisotropic diffusion, or optical gradient forces were considered as the driving force for deformation [9–11]. These efforts have not led to a unified model that captures all experimental observations. Here we model surface relief formation as arising from viscous flow driven by the opposition of surface tension and an optically induced pressure which provides a driving force for mass transport that depends on both intensity and polarization. Accommodating both of these dependencies in a single model formulation is the main innovation of this work. Simulations using our model agree well with literature data on the temporal and spatial dependence of optically induced surface relief in As 2 S 3 . The model.—For simplicity and correspondence with past experiments we model a film of chalcogenide glass exposed to normal-incidence, time-independent, near- band-gap illumination that varies in one direction along its surface (the x axis) but is uniform along the other surface axis (y). At near-band-gap wavelengths films with thicknesses of order 1 micron or less are optically thin and so we take illumination to be uniform in the direction normal to the film’s surface (z)[12]. Figure 1 illustrates this coordinate system. We assume that the vis- cosity remains high enough to justify the low-Reynolds number lubrication approximation to the Navier-Stokes equations [13]. We further posit that surface tension and the optically induced pressure are the dominant forces. The above assumptions bring surface relief formation within the scope of the Navier-Stokes equation simplified into a two-dimensional boundary layer equation in x and z [14] (see Fig. 1). @v x @t þ v x @v x @x þ v z @v x @z ¼ 1  @P @x þ  @ 2 v x @z 2 þ f; (1) where the v i ’s are components of the velocity vector,  is the mass density, P is the total pressure, f is the body force, and  is the kinematic viscosity. Deriving the stan- dard high-surface-tension lubrication equation in the pres- ence of a pressure and absence of any body force yields @h @t  @ @x  h 3 3  @PðxÞ @x  s @ 3 h @x 3  ; (2) in which hðx; tÞ is the film thickness,  is the dynamic viscosity, s is the curvature coefficient of the surface tension, and PðxÞ is the optically induced pressure, which is assumed to vary only in x because that is the only FIG. 1. Schematic of the typical experimental setup used to generate surface structure. Two beams, W1 and W2, interfere on the surface of a thin film of amorphous, light-sensitive material, leading to the pictured definitions of the coordinate system and polarization directions. PRL 111, 105503 (2013) PHYSICAL REVIEW LETTERS week ending 6 SEPTEMBER 2013 0031-9007= 13=111(10)=105503(5) 105503-1 Ó 2013 American Physical Society