Spin Coating: A Guide to Film Thickness


Written by Emma Spooner, a PhD student in Fullerene-Free Photovoltaic Devices at the University of Sheffield  in collaboration with Ossila Ltd.

Spin coating is a deposition technique used to coat thin films of materials from a liquid solution. Due to the simplicity of this technique, you will be able to produce great films even without a deep understanding of the background physics involved. Having an understanding of the mechanisms at work is a bonus, and will give you better insight into how solution properties can affect deposited films.

This guide covers the theory of spin coating, and the physical factors that are important for eventual film thickness. For a comprehensive overview of the qualitative aspects of spin coating, such as what speed/duration/method to use, along with common defects and how to prevent them, check out Ossila’s Spin Coating: A Guide to Theory and Techniques.


Basic Steps of Spin Coating

Spin coating involves depositing a liquid solution onto a spinning substrate in order to produce a thin film of solid material, such as a polymer. This can be broadly divided into 4 main steps:

  1. Deposition. The initial step of casting the solution onto the substrate, typically using a pipette. If the substrate is already spinning (dynamic spin coating) or is spun after deposition (static spin coating), the centrifugal motion will spread the solution across the substrate. 
  2. Spin up. The substrate reaches the desired rotation speed – either immediately or following a lower-speed spreading step. At this stage, most of the solution is expelled from the substrate. Initially, the fluid may be spinning at a different rate than the substrate, but eventually the rotation speeds will match up when drag balances rotational accelerations – leading to the fluid becoming level. 
  1. Spin off. The fluid now begins to thin, as it is dominated by viscous forces. As the fluid is flung off, often the film will change colour due to interference effects. When the colour stops changing, this will indicate that the film is mostly dry. Edge effects are sometimes seen because the fluid must form droplets at the edge to be thrown off
  2. Evaporation. Fluid outflow stops, and thinning is dominated by evaporation of the solvent. The rate of solvent evaporation will depend the solvent volatility, vapour pressure, and ambient conditions. Non-uniformities in evaporation rate, such at the edge of a substrate, will cause corresponding non-uniformities in the film.


Interference effects are sometimes seen during the spin off stage of spin coating, when films change color as fluid is thrown off and thickness changes


Emslie, Bonner, and Peck Model

Many researchers will use a simple proportionality rule (related to spin speed) to describe the final film thickness from spin coating, as expressed in Equation 1.

Equation to calculate approximate film thickness from spin coating, related to spin speed
Equation 1: A simple relationship used to approximate film thickness

Where ω is angular velocity/spin speed and hf is final film thickness. However, this rule does not always apply and does not allow for predictions of film thickness without experimental data. There have also been several attempts to describe the process in a more rigorous manner. The earliest (and simplest) of these was by Emslie, Bonner, and Peck in 1958.1 This analysis made several approximations, including ignoring the effects of evaporation (the validity of which will depend on how volatile the solvent is) and ignoring the possibility of non-Newtonian behaviour. This means it is assumed that the viscosity of the fluid used will not be changed by stress. For a non-volatile, viscous fluid on an infinite rotating disk, Emslie’s model can be seen in Equation 2.

Equation by Emslie, Bonner, and Peck for fluid dynamics in spin coating
Equation 2: Emslie, Bonner, and Peck’s model for fluid dynamics during spin coating

Where t is time since the start of the process, ω is angular velocity, r is the distance from the centre of rotation, ρ is the density, η is the viscosity and h is thickness of the fluid layer, (rather than the dry thin film). Here, ∂h/∂t represents the rate of change of thickness, and ∂h/∂r the rate of spreading.

Approximation of rotating disk with horizontal rotation plane (Emslie, Bonner, & Peck)
Figure 1: The approximation of a rotating disk used by Emslie, Bonner and Peck, where the rotational plane is horizontal

If the film is considered initially uniform, this leads to a description of the fluid film thickness as seen in Equation 3.

Final fluid film thickness equation by Emslie, Bonner, & Peck
Equation 3: Emslie, Bonner and Peck’s equation for final fluid film thickness

Here h0 represents the uniform thickness of the film at the start of the process (i.e. t=0). As this model does not account for evaporation, it cannot be used to calculate the exact thickness of the final dry film. An approximate dry thickness can be calculated from fluid film thickness by using the concentration of solute and solution density. To get an accurate value, including the impact of solvent viscosity and surface tension, a more detailed model is needed.

Spin Coater - Price and Specification

Meyerhofer Model

The first attempt to include evaporation effects was published by Meyerhofer in 1978,2 who modified the equations of Emslie, Bonner, and Peck (seen earlier in Equation 2) with the inclusion of a solvent evaporation rate:

Spin coating fluid dynamics equation by Meyerhofer
Equation 4: Meyerhofer’s equation for fluid dynamics during spin coating

Here E is the uniform solvent evaporation rate, in units of solvent volume evaporated per unit area per unit time.

Meyerhofer proposed that early in the spin coating process, flow dominates the thinning process of the film (spin off); whereas later in the process (when the film is thinner and flow is slow), thinning is mainly due to evaporation. Meyerhofer also established that if the transition from fluid thinning to evaporation thinning is abrupt, then the film thickness can be estimated analytically – where it is assumed that the film is thin enough to ensure solvent concentration remains uniform through the depth of the film. This transition point will clearly be the point at which thinning by flow is equal to thinning by evaporation:

Equation for transition point between fluid thinning to evaporative thinning
Equation 5: The transition point between fluid thinning to evaporative thinning

Where C is the volume fraction of solute in the film and h0 is the film thickness at the transition between the two film-thinning regimes. 

Representation of the different thinning regimes in spin coating used by Meyerhofer
Figure 2: A representation of the different thinning regimes in spin coating, as used by Meyerhofer

This gives the final film thickness as:

Equation for final dry film thickness from
Equation 6: Meyerhofer’s equation for final dry film thickness from evaporation rate

Where C0 is the initial concentration of solute, and η0 equates to η(C0). The concentration of solute is assumed to remain at C0 until the transition of evaporation-driven thinning begins. Final spin coating film thickness can also be calculated without the solvent evaporation rate. This can be done by making several assumptions, including the assumption that air flow remains laminar during the process. This gives an overall equation as:

Equation for final dry film thickness (without evaporation rate) by Meyerhofer
Equation 7: Meyerhofer’s equation for final dry film thickness without evaporation rate

Where k is a constant specific to the coating solvent and for typical spin coating solvents k ≈ 1(-5)cm/s(-1/2). Readers will then recognise that this can be expressed as hf∝ ω(-1/2) which is equivalent to Equation 1, showing that the proportionality constant is a product of several other terms, including solution density, viscosity and concentration, and the properties of the solvent.


Beyond Meyerhofer

Despite what is shown in Equation 7, final film thickness from spin coating is not always proportional to ω(-1/2).This equation is dependent on numerous assumptions, and where these are not correct, the dependency will fail.

An example of this is when the transition between the two thinning regimes is not abrupt. This has occurred in some cases in research,3 where the spin coating process is terminated early. This means the cross-over to evaporative thinning doesn’t occur, and thickness and spin speed have a different relationship. If a longer spin time was used in these cases, it is possible that Equation 7 would have proven correct. Systems may also deviate from expected behaviour where non-Newtonian fluids do not cross over to a Newtonian flow before being immobilised by evaporative thinning. This mostly occurs in colloidal solutions or solutions close to the gelation point.

In many cases, it is most straightforward to establish the relationship for a given solution by using a ‘spin curve’. This can be done by spin coating a solution at varying spin speeds and then measuring the film thickness. In literature, there has also been success using semi-empirical models, as a combination of Meyerhofer’s equation and experimental data.4

Spin Coater - Price and Specification

Further Reading

For more information on the different aspects of spin coating, please refer to Ossila’s Spin Coating: A Guide to Theory and Techniques. Further information and details on the models used in this post can be found below.

Journal Article: Dynamic, crystallization and structures in colloid spin coating, M. Pichumani et al., Soft Matter (9), 3220-3229 (2013); 10.1039/C3SM27455A.

Book: Liquid Film Coating. R. G. Larson and T. J. Rehg, ed. S. F. Kitsler and P. M. Schweizer, Chapman & Hall, 1st edn, 1997, ch. 14, pp. 709-734.

References

  1. Flow of a Viscous Liquid on a Rotating Disk, E. G. Alfred et al., J. Appl. Phys. (29), 858–862 (1958).
  2. Characteristics of resist films produced by spinning, D. Meyerhofer, J. Appl. Phys. (49), 3993–3997 (1978).
  3. An Investigation of the Thickness Variation of Spun-on Thin Films Commonly Associated wtih the Semiconductor Industry, J. W. Daughton, J. Electrochem. Soc. (129), 173–179 (1982).
  4. Dynamics of polymer film formation during spin coating, Y. Mouhamad, J. Appl. Phys. (116), 123513 (2014).