Related Experiment Video
Updated: Jan 1, 2026
10:18
Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
Published on: January 27, 2017
14.9K
Slope selection in unstable multilayer growth in 1+1 dimensions: Step flow models with downward funneling
Ian Johnson1, Christian Ratsch2, Frederic Gibou3
1Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. E
|December 25, 2019
Summary
This study investigates crystal growth dynamics, focusing on how step edges influence surface morphology. We found that downward funneling and step interactions lead to eventual slope selection in homoepitaxial growth.
Area of Science:
- Surface science
- Materials science
- Condensed matter physics
Background:
- Homoepitaxial crystal growth involves the deposition of material onto a crystal substrate, leading to the formation of terraces and steps.
- The dynamics of these steps are crucial for determining the final surface morphology and quality of the grown crystal.
- Understanding step dynamics is essential for controlling crystal growth and developing advanced materials.
Purpose of the Study:
- To analytically and numerically investigate the dynamics of slope selection in one-dimensional models of homoepitaxial crystal growth.
- To examine the influence of kinetic processes, including adatom diffusion, attachment/detachment kinetics, and downward funneling, on slope selection.
- To analyze the effects of boundary conditions and step-step interactions on the step flow dynamics and slope selection.
Main Methods:
- Analytical treatment using perturbation theory to characterize time-periodic solutions for slope-selected profiles.
- Numerical simulations of step flow dynamics for straight step geometries.
- Modeling of kinetic processes: adatom diffusion, Ehrlich-Schwoebel barriers, material deposition, and downward funneling (DF).
Main Results:
- Numerical simulations demonstrate that slope selection eventually occurs in the studied system.
- Perturbation theory successfully characterizes time-periodic solutions of step flow for slope-selected profiles.
- A simplified step flow theory incorporating constant probabilities for adatom motion effectively models slope selection in the presence of DF.
Conclusions:
- Slope selection is a key phenomenon in homoepitaxial crystal growth, influenced by various kinetic and interaction parameters.
- Downward funneling and repulsive step-step interactions play significant roles in achieving slope selection.
- The findings provide a framework for understanding and controlling surface morphology during crystal growth, with potential applications in materials science.
More Related Videos
Related Concept Videos
01:23Steady, Laminar Flow in Circular Tubes
944
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
944
01:30Bernoulli's Equation for Flow Along a Streamline
1.4K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.4K
01:29Gradually Varying Flow
350
Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
350
01:18Uniform Depth Channel Flow: Problem Solving
401
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
401
01:30Typical Model Studies
579
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
579
01:17Steady, Laminar Flow Between Parallel Plates
728
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
728