Spin Coating Case Study

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Table of Contents
1. Introduction 2
1.1. What is spin coating? 2
1.2. Schematics and design 2
1.3. Factors on which Spin Coating depends 2
1.4. Industrial uses 4
2. Model 4
2.1. Governing Equations 4
2.2. Modified Governing Equations 4
2.3. Radial and Axial Velocities 5
2.4. Volumetric Flow Rate 6
2.5. Variation of Height with time 6
2.5.1. Case A: No Evaporation of Solvent 6
2.5.2. Case B: Evaporation of Solvent 7
3. Future Work 9
4. Appendix 10

Introduction

Spin coating is a predominant technique in modern science and engineering to produce thin uniform coatings of organic materials onto a substrate. This report deals with the modelling of spin coating to develop a relationship between film thickness, spinning time and speed of coater.
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as RPM increases, height decreases. Experimentally it has been shown that,

h=〖Cω〗^(-a) (1)

Where h – Final Film Thickness, ω – Spin Speed and C & a are some constants. In this report,

Polymer Concentration:
The film thickness is inversely proportional to viscosity. Also viscosity is directly proportional to solute concentration. Hence, as the concentration decreases, final film thickness decreases.

Concentration of solvent in overhead gas phase:
Thinning of film due to evaporation depends upon the solvent concentration in the overhead gas phase as it is a mass transfer process. Evaporation rate of solvent decreases, if the vapour pressure of solvent increases in overhead gas phase.

Industrial uses

Spin coating has been accepted as one of the best coating methods for obtaining films over a wide range of thicknesses typically 10 to 1000 nm.

Some technologies that depend heavily on high quality spin coated layers are: Photoresist for defining patterns in microcircuit
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Radial and Axial Velocities

Calculation of Radial Velocity 〖[u〗_r=f(r,z)]
Integrating the modified Navier Stokes Equation, with the boundary conditions as stated below, No Slip Condition: u_r=0 at the disk surface of z = 0 Zero Shear Stress: ∂/∂z (u_r )=0 at z = h

u_r =ρ/μ [ -ω^2 rz^2 + 2ω^2 rzh ] (5)
Calculation of Axial Velocity 〖[u〗_z=f(z)]
For calculation of u_z the continuity equation has to be considered. Though u_z is small as compared to u_r, ∂/∂z (u_z ) cannot be neglected.

1/r ∂/∂r (rρu_r )+(∂〖(ρu〗_z))/∂z=0 (6)

By integrating the modified Continuity Equation, with the boundary condition:
No Slip Condition: u_z=0 at the disk surface of z = 0

u_z =(2ρω^2)/μ [ z^3/3- hz^2 ] (7)

Volumetric Flow Rate

The volumetric flow in the radial direction can be written as

Q=∫_0^h▒〖u_r (2πRdz) 〗 or Q = (4πR^2 ω^2 h^3 ρ)/3μ (8) Variation of Height with time

Case A: No Evaporation of Solvent

Due to splashing of solution, height of the film decreases with time. Considering the mass balance, the volumetric flow rate in the radial direction is same as the instantaneous rate change of volume with

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