Spin Coating - Yizhuo Chen

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CHEM-ENG 590E: Microfluidics and Microscale Analysis in Materials and Biology

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Introduction to Spin Coating

One of the most commonly used techniques to create thin films of controlled thickness on substrate is spin coating. Spin coating could easily and quickly create a very uniform film in a specific thickness range from only several nanometers to hundreds of microns. Spin coating is widely used in a variety of industrial and researching areas. The industrial application of spin coating is famous in electronics, nanotechnology and microfluidics.

Method

Figure 1. Spinner in Professor Sun Lab, University of Massachusetts Amherst
Figure 2. Schematic graph of Spin coating (Hellstrom 2007)[1]

Spin coating is a commonly used procedure to uniformly make thin-layer films to flat the substrates. On the center of the substrate, certain amount of the coating material is placed on a flat substrate. Spin coater, also referred to as a ‘spinner’, then rotates the substrate to generate a centrifugal force and define the film. A typical spin coating procedure involves the following steps: (1) The substrate should be rotated at a low speed spinning in order to spread the coating material well-covered on the entire substrate or be placed without spinning at all until the coating material naturally well-covered on the entire substrate. One alternative method is to only begin spinning after the material has covered the entire surface, if the material is a low viscous material. (2) The substrate should be rotated at a relatively high speed in order to spread the coating material by centrifugal force. (3) The spinner keeps rotating. At the same time, the coating material is flung off of the edges of the substrate. The thickness of the coating material on the membrane is getting thinner and thinner until the film reaches to the expected thickness.

Film Thickness as a Function of Spin Speed

The coating layer thickness (h) depends on the time (t) spent on the rotation, fluid viscosity (μ), angular velocity of the turntable (ω) and fluid density (ρ). In order to understand this correlations, a fluid dynamic equation is required to solve the spin coating process. A model developed by Emslie et al. is used for the process. Based on the common experiments in the lab, photoresist coating and silicon oil coating, we assume the fluid is Newtonian because normally photoresist and silicon oil we use in the lab are in a low viscosity. But in industrial application, deriving a equation for the specific fluid viscosity is very necessary because the fluids such as polymer solution are not Newtonian.

In the model of Emsile et al., the flow of the fluid is also assumed to be unidirectional in the radical direction. So only the radial component of the fluid velocity is not zero. What’s more, the fluid is assumed to be rotated together all the time with the substrate. So, the angular velocity of the fluid is:

Equation 1. Angular velocity of the fluid [2].






So the equation of the fluid velocity in the cylindrical coordinate is:

Equation 2. Continuity equation for the fluid velocity. [2]







Then the Navier-Stokes equations are:

Equation 3. Navier-Stokes equation. [2]
Equation 4. Navier-Stokes equation. [2]
Equation 5. Navier-Stokes equation. [2]

















Another assumption is that the height of the liquid on turnable is much smaller than the radius. So the rescaled coordinate could be introduced:

Screen Shot 2019-05-13 at 5.43.15 PM.png







So the Equation 3 is transformed into the equation below:

Equation 6. Transformed Equation. [2]








After simplification, we obtain the equation:

Equation 7. Transformed Equation. [2]







The boundary conditions of the fluid velocity determined by:

(1) the no-slip condition at the substrate surface,

Equation 8. Boundary condition 1. [2]






(2)The free surface condition between the fluid and the vaccuum

Equation 9. Boundary condition 2. [2]






h(r,t) represents the height of the liquid and we got the following equation after integrating Equation 7 twice under the boundary conditions:


Equation 10. Simplified equation. [2]







Equation 10 is used to describe the radial velocity correlated with the height h(r,t) of the film. The height of the film should be always much smaller than the radius. What's more, it may vary sometimes, which help us to neglect the correlation of the height on the position r and come up h(t) from the mass balance of radial direction.


Equation 11. Derivative equation. [2]
Equation 12. Integral equation. [2]











So, after substituting Equation 12 into the mass balance equation, the following equations could be obtained:



Equation 13 [2]
Equation 14 [2]









Next step is to solve Equation 13, we get:


Equation 15 [2]








At h0 = h(t=0), we assume that:


Equation 16 [2]








So, Equation 15 comes up with the relation of the film thickness vs time and rotational velocity:


Equation 17 [2]

Spin coating during the soft lithography process

PDMS

Figure 2. PDMS Sylgard® 184, Dow Corning Corporation

Polydimethylsiloxane (PDMS), in other terms as dimethylpolysiloxane and dimethicone, is in the group of polymeric organosilicon compounds. Polymeric organosilicon compounds are always named as silicones in trademark [3]. PDMS is one of the most widespread organic silicon-based polymer. It is especially famous for its special rheological, chemical and mechanical properties. PDMS is inert, bio-compatible, non-toxic, non-flammable and optically transparent polymer. Polydimethylsiloxane is one of polymerized siloxane, which is a type of silicone oil [4]. The application of PDMS is huge. PDMS could be the material of contact lenses and could be the elastomer of medical device. It is also the addition in shampoo as slippery gradient, antifoaming agent in food industry and main component in lubricants.

Film Thickness vs. Spin Speed

The final thickness of PDMS membrane on the substrate (silicon wafer) mainly depends on both spin speed and spinning period. Other significant properties to get reproducible thickness of PDMS layer are type of PDMS, ratio between curing agent and elastomer, time spent in mixing of curing agent and elastomer, and temperature in environment [5][6][7]. PDMS elastomer and PDMS curing agent (Sylgard 184, Dow Corning) are mixed in a 10:1 weight to weight ratio and then are stirred for 2 minutes. After that, the PDMS was placed in vacuum chamber for degassing for 10 to 13 minutes [5].

Figure 3. Dependence of the PDMS layer thickness as a function of spin speed for a rotation time of 5 min (left) and as a function of rotation time (right).https://www.elveflow.com/microfluidic/PDMS%20thickness%20VS%20spin%20speed.pdf

References

[1] Hellstrom, S.L. (2007), Published course work for physics 210, Stanford University, Autumn 2007.

[2] A. G. Emslie, F. T. Bonner, and L. G. Peck, “Flow of a Viscous Liquid on a Rotating Disk”, J. Appl. Phys. 29, 858-862 (1958)

[3] Mata, A., Fleischman, A.J. & Roy, S. Biomed Microdevices (2005) 7: 281. https://doi.org/10.1007/s10544-005-6070-2

[4] "Linear Polydimethylsiloxanes" Joint Assessment of Commodity Chemicals, September 1994 (Report No. 26) ISSN 0773-6339-26.http://www.ecetoc.org/wp-content/uploads/2014/08/JACC-055-Linear-Polydimethylsiloxanes-CAS-No.-63148-62-9-Second-Edition.pdf

[5] Koschwanez, J. H., Carlson, R. H. & Meldrum, D. R. Thin PDMS Films Using Long Spin Times or Tert-Butyl Alcohol as a Solvent. PLoS ONE 4, e4572 (2009).https://doi.org/10.1371/journal.pone.0004572.

[6] F. K. Balagadde, L. You, C. L. Hansen, F. H. Arnold, S. R. Quake, Science 309:5731, 137‐140 (2005) https://doi.org/10.1063/1.4789751

[7] Zhang, W. Y., Ferguson, G. S. & Tatic-Lucic, S. Elastomer-supported cold welding for room temperature wafer-level bonding. in Micro Electro Mechanical Systems, 2004. 17th IEEE International Conference on. (MEMS) 741–744 (2004). https://doi:10.1109/MEMS.2004.1290691