Spin Speed vs Film Thickness: How to Build and Use a Spin Curve

At what speed does this ink give the thickness I need? Theory gives the shape of the answer, thickness falling roughly as the inverse square root of spin speed, but not the number for your ink. That comes from a spin curve: films coated at several speeds with everything else fixed, then measured and fitted. This guide shows how to plan the series, fit it without overstating what the points show, choose a speed, and decide when to change the ink instead. A spin curve fitter for your own data is built in.

In one paragraph: coat at least four distinct speeds across the range you expect to use, with repeat films and a mixed run order, and fit log(thickness) against log(speed). Fewer speeds support less: one point only scales the ideal curve, two fix a line, three give a preliminary fit. Choose speeds only inside the measured range; beyond it, measure further or change the ink.

1.  The short answer: thickness vs rpm

For most solution-based inks, spin coating thickness vs rpm follows a simple pattern: a faster final speed gives a thinner dry film, and the dependence is weak. In the ideal model, doubling the speed reduces the thickness by a factor of about 1.4, and quadrupling it halves the thickness.¹⁸ Measured exponents close to −1/2 have been reported for several polymer solutions,⁴⁵ but the exponent belongs to a particular ink and process, not to nature. The practical consequences are:

• Speed is a fine adjustment within a given process window. In the ideal evaporation-controlled model, thickness scales as the inverse square root of speed. Across a tenfold speed range, that model predicts a thickness change by a factor of about 3.2. The measured response of a real ink can differ.
• The ink sets much of the curve’s scale. Solids content, viscosity and solvent volatility affect the final thickness and drying behaviour. Their effects are formulation-dependent and should be measured.
• The curve must be measured. A literature exponent or model gives a starting expectation; your own controlled series shows how your ink and process actually behave.

The physics behind this, including the four stages of spin coating and the Emslie–Bonner–Peck and Meyerhofer models, is covered in Spin Coating Explained: Stages, Physics and Film Thickness. If you are still deciding whether spin coating is the right method at all, start with the guide to choosing spin, dip, slot-die or blade coating.

2.  Why thickness falls with speed (theory)

This section explains why a power law is a reasonable shape to fit, not what exponent your ink will have. In the Emslie–Bonner–Peck model, a Newtonian liquid without evaporation keeps thinning for as long as the disc spins; the model has no final thickness.² Meyerhofer added solvent evaporation. Thinning by outflow slows as the film gets thinner, evaporation continues at a roughly steady rate, and the film sets when the two become comparable. His result for the final thickness is:¹

The −1/2 exponent therefore rests on an assumption: that evaporation grows as the square root of speed. Lawrence reached the same exponent by a different route, a diffusion boundary layer near the free surface, with final thickness proportional to the initial concentration and evaporation proportional to speed.³ So a measured slope near −1/2 is consistent with these models but does not prove that either describes your ink, and a different slope is not an error in itself: evaporation that departs from the assumed speed dependence, shear-thinning, very volatile solvents, skin formation, or a run that stops before the film has set can all change it.⁶⁷⁸

The same reasoning limits the fit: a power law describes the range you measured; outside it, the mechanism that sets the thickness, and the exponent with it, may change.

3.  How to build a spin curve

Fix everything except the final speed

A spin curve is only meaningful if the final speed is the only thing that changes. Before the first film, write down and freeze:

• Ink: one batch and concentration, filtered the same way, used within a defined time.
• Substrate: the same type, size, cleaning and chuck.
• Program: the same dispense and volume, spread step, acceleration and time at the final speed. Choose a time long enough for the film to set at the slowest speed; if a run stops while the film is still thinning, thickness also depends on spin time.⁸
• Environment: the same lid position, exhaust and atmosphere, and similar temperature and humidity.
• After coating: the same bake, instrument, method and measurement positions.

Choose the speeds

• Use at least four distinct final speeds that cover the intended operating range. Where practical, include measured points on both sides of the target range so that the target does not sit at the edge of the data. Space the speeds approximately evenly on a logarithmic scale—for example, 1,000, 1,500, 2,000, 3,000 and 4,000 rpm. Do not use the fitted curve to recommend a speed outside the measured range.
• Coat at least two films per speed, so that film-to-film scatter is measured, not assumed.
• Mix the run order instead of coating from slow to fast, so that drift in the atmosphere or the ink does not look like a speed effect. After the coater has stood idle, one or two dummy substrates can help the solvent atmosphere settle.⁸

Measure the right film

Measure the dry film in the state in which you will use it. Photoresist films, for example, continue to lose residual solvent after spinning, and the thickness measured immediately after coating differs from the thickness after the soft bake.⁸ Use the same instrument and positions on every substrate, keep clear of the edge, and record each position, not only an average. If one number cannot describe the film, fix the uniformity first. If the instrument or method has uncertainty comparable to the thickness differences between speeds, quantify that uncertainty before interpreting the fitted slope; otherwise, measurement noise can be mistaken for a process trend.

4.  Fitting the curve: one to many points

Take logarithms of both sides of h = k·ω^α:

How much the fit can tell you depends on how many distinct speeds you have.

One measured point: scale the ideal curve, do not fit

One point cannot measure an exponent. You can fix α at the ideal −1/2 and calibrate only k. Worked example (assumed values): a single film of 440 nm at 2,000 rpm gives an estimate of 440 × √(2,000/3,000) ≈ 359 nm at 3,000 rpm. Label such a number as an ideal-exponent estimate, not a fit. A single point cannot estimate the exponent or residual scatter, so it cannot provide a data-based confidence interval or prediction interval. Measurement uncertainty in the input thickness still exists, and the assumed exponent adds model uncertainty that this one-point calculation does not quantify.

Two points: a line, but no scatter

Two speeds determine the line exactly, leaving no residuals from which to estimate scatter. Worked example (assumed values): 612 nm at 1,000 rpm and 318 nm at 4,000 rpm give α = ln(318/612) / ln(4) ≈ −0.47. If each thickness could be off by 3 % in opposite directions, the exponent could lie anywhere from about −0.43 to −0.52, and the two points cannot tell you which. Use the line as a first look, not a calibrated curve.

Three points: a preliminary fit

With three distinct speeds a least-squares fit has one residual degree of freedom. It can give a standard error for the exponent, but that standard error is itself very uncertain, and a band for predicting new films is not yet reliable. Treat the result as preliminary and add speeds or repeats before setting a recipe.

Four or more distinct speeds, with repeats: a fit that can be evaluated

With four or more distinct speeds and repeat films, a log–log fit can estimate the exponent and residual variation. Whether the fit is useful depends on the residual pattern, the spread between repeat films, the number and distribution of speeds, and whether the process remained stable. Treat the result as a candidate process model, not as automatic validation of a single power law.

Worked example (assumed values, not measurements): ten films, two at each of five speeds.

Assumed values chosen to illustrate the calculation. They are not results from any ink, coater or Levon™ instrument.

An ordinary least-squares fit of ln h against ln ω for these ten films gives:

• Exponent: α = −0.468, standard error 0.008; 95 % confidence interval about −0.486 to −0.449 (8 residual degrees of freedom).
• Prefactor: k ≈ 1.54 × 10⁴ nm with ω in rpm (k depends on the units).
• Scatter: the residual standard deviation is about 1.3 % of thickness.

Two checks belong with every fit. Plot the residuals against speed: a curved pattern means a single power law does not fit the whole range, which should be narrowed or split. And compare the scatter between repeats with the scatter about the line: if the line misses the repeats by much more than they differ from each other, something other than random variation is at work.

Fit your own data: spin curve fitter

The fitter below applies these rules to your own films: enter each film’s final speed and dry thickness. It states what the number of speeds supports, runs the curvature and repeat checks, and gives a speed for a target thickness only inside the measured range. It opens with the worked example, labelled as example values, not measured data, and runs in your browser without sending anything.

5.  Using the curve to choose a speed

Invert the fitted line to find the speed for a target thickness:

In the worked example above (assumed values), a target of 350 nm gives about 3,250 rpm, inside the measured range of 1,000–4,000 rpm. Two different uncertainties apply:

• Fit uncertainty: how well the average thickness at 3,250 rpm is known. For the example data, the 95 % interval for the fitted line is about 346–354 nm.
• Prediction uncertainty: where a single new film coated at 3,250 rpm is likely to land, including film-to-film scatter. For the example data, the 95 % prediction interval is about 339–361 nm, roughly two and a half times wider.

For a recipe, the prediction interval usually matters more. It assumes similar scatter at every speed, independent films and a process that has not drifted since the curve was measured; with few speeds or no repeats, report the speed without one.

Rules for using a curve

• Stay inside the measured range. If the target needs a speed outside it, coat films at the new speeds and refit; do not extend the line.
• Do not use a curve that does not fall with speed, or one whose uncertainty is too large to separate the speeds you are choosing between. Find the cause first.
• The coater's maximum speed is a hardware limit, often specified without load. It does not tell you the thinnest film an ink can reach.
• Check the result at the chosen speed before committing the recipe.

When to change the ink instead of the speed

Because thickness changes slowly with speed, a distant target often lies outside the window in which your process is reproducible. For photoresists, MicroChemicals recommends choosing a resist that reaches the target thickness with conventional spin profiles, about 2,000–4,000 rpm for 20–30 s, for reasons of reproducibility.⁸ For other inks, the usual levers include solids content, solvent and viscosity. Changing any of them can alter the curve’s scale, slope, wetting, drying and film morphology. Lawrence’s model predicts a concentration dependence under its own assumptions, but that result is not a universal correction factor.³ Rebuild and measure the curve after changing the formulation.

6.  What invalidates a spin curve

Rebuild or recheck a spin curve when any of these change:

7.  Spin coater specifications for a spin curve

The following Levon™ configurations illustrate the specifications most relevant to building a spin curve: speed range, speed resolution, acceleration and program storage. This is a selected comparison, not a complete catalogue of every available configuration. Values belong to the model or configuration named and are not interchangeable.

Values from the Levon™ product pages as listed on 22 October 2026, in the pages' own wording (“1 rpm” or “±1 rpm”). “No load” values are hardware limits, not process results. The full range is on the Levon™ spin coaters page.

How the specifications map to a spin curve

• Speed range limits where you can place points, not the thickness you can reach. Plan the curve inside the range in which your ink coats reproducibly, usually much narrower than the hardware range.
• Speed resolution is rarely the limiting factor. In the ideal model, a 1 rpm change at 3,000 rpm changes the predicted thickness by about 0.02 % (theory, ideal exponent). Compare that with the scatter between your own repeat films. A stated speed resolution describes the size of the selectable or reported increment; it does not by itself establish actual speed accuracy or stability under load. Those properties should be confirmed separately if they matter to the experiment.
• Acceleration is one of the fixed conditions: recheck the curve if the ramp changes.
• Program storage recalls the same steps for every film in the series. The EZ4-S stores 5 programs of 5 steps and the EZ6-S 10 × 10; the AC100-S, AC200-S-PP, AC200-SE and AC200-PE store 100 recipes of up to 100 steps; the AC200-SE-PLUS and AC300-S-CTM pages do not state a recipe count.
• Atmosphere: a curve measured in air does not transfer to a glovebox. The EZ4-S page describes it as suitable for glovebox setups, and all four AC200 configurations can be recessed into a glovebox; the EZ6-S, AC100-S and AC300-S-CTM pages do not mention glovebox use.
• Heated spin tables: the IC5000-S (spin table RT to 150 °C) and IC8000-S (RT to 200 °C) add table temperature as a process variable; build a separate curve at each temperature you use.

What the published uniformity data can and cannot tell you

Several Levon™ pages publish film uniformity results for named photoresists and thicknesses. They do not state the spin speed behind each result, so the values cannot serve as points on a thickness–speed curve; your curve still has to be measured with your ink.

Before you request a quote

• Speed window: the intended final-speed range, any low-speed spread step, and the acceleration and spin-time requirements.
• Substrates: material, shape, dimensions, thickness, and the chuck or carrier required.
• Environment and temperature: air or glovebox operation, solvent-vapour or exhaust conditions, and whether a heated spin table is required.
• Recipe control: the number of programs and steps to store, required timing resolution, and whether the same program must be recalled across repeated runs.
• Measurement: the target dry-film thickness, measurement method, measurement locations, and acceptable run-to-run variation.

Send these through the contact form or the Get Quote request on the product page.

8.  Keep Exploring the Spin Coating Knowledge Hub

Part of the spin coating section of the ACS Material thin-film library. The other articles in the series are listed below. A related article outside the series, How to Measure Thin Film Thickness: Profilometry, Ellipsometry and Interference (coming soon), is also in preparation.

More in this series

• Pillar guide: Solution-Processed Thin Films: Choosing Spin, Dip, Slot-Die or Blade Coating
• #01: Spin Coating Explained: Stages, Physics and Film Thickness
• #03: Spin Coating Acceleration and Multi-Step Recipes: What the Ramp Actually Does
• #04: Static vs Dynamic Dispense in Spin Coating: Volume, Coverage and Material Waste
• #05: Spin Coating Defects: Comets, Striations, Pinholes and Edge Beads Diagnosed
• #06: Spin Coating Small, Square and Fragment Substrates: Chucks, Vacuum and Corners
• #07: Heated Spin Coating: How Substrate Temperature Changes Evaporation and Thickness
• #08: How to Choose a Lab Spin Coater: Speed, Acceleration, Substrate Size and Glovebox Fit

Spin coating equipment

• Levon™ spin coaters — compact, programmable, servo and heated spin coaters.
• EZ4-S compact spin coater, EZ6-S benchtop spin coater and AC100-S programmable spin coater — spin curves on small pieces and wafers in research labs.
• AC200 programmable servo spin coater and AC300-S-CTM servo spin coater — servo-driven coaters for larger wafers.

9.  FAQ

10.  References