Spin coating is a process by which thin and uniform layers of liquids are formed on substrates by rotation of the substrate at high speed. Production of these thin liquid layers, specifically using liquids called photoresists, is essential for photolithography in semiconductor and microelectronics processing whereby patterns are transferred and ultimately formed in layers on the substrate. With the surge in interest for increased domestic semiconductor processing capabilities, it makes sense that students in physics and engineering are provided with more knowledge of these processing techniques and how they rely on, among other things, traditional course work, and topics. Spin coating provides an excellent example to connect fluid dynamics with microfabrication. We present detailed experiments that can be performed in a college-level undergraduate laboratory, wherein students can explore both the variables appearing in a known model for spin coating in addition to investigating several of the variables related key assumptions used in the derivation of the model but which do not appear in the resulting equation.

The recent global pandemic exposed the fragility of the supply chain for microelectronic and semiconductor devices and the over reliance of the US on foreign production facilities for these products.1,2 As a direct response, there has been strong interest in growing domestic microfabrication capabilities through government-sponsored actions like The CHIPS and Science Act.3,4 A necessary part of these plans involves workforce development and training efforts.5 In addition, it is essential to stimulate and nurture physics and engineering students' interest in this field.

To introduce our students to the field of microfabrication, which at commercial production scale uses large and very expensive equipment and materials, we are developing manageable theoretical and small-scale experimental educational modules that apply existing knowledge from traditional courses to a microfabrication-related application. Here, we present the relevant theory and describe low-barrier-to-implement experiments involving spin coating that can be shared with an undergraduate student audience.6 What follows is an outline of that content which can be used to build connections between fluid dynamics and microfabrication. Similar opportunities exist within other disciplines of physics and engineering.7 

Photolithography is essential for the bulk processing that makes low-cost microelectronic devices possible. In this process, patterns for desired surface features are transferred from a mask onto a photo-sensitive chemical commonly known as a photoresist.8 The mask controls which regions of the photoresist are exposed to light. Photoresists are liquid combinations of solvent, resin, and a photoactive compound (PAC).9 The chemistry of the PAC determines whether the resist is positive or negative (that is, whether the unexposed or exposed region is more soluble in a chemical developer). The solvent and resin concentrations determine important liquid properties, such as density and viscosity. Because of the nature of the chemical constituents, photoresists are non-Newtonian liquids,10 meaning that their viscosity varies depending on the applied stress.

For acceptable pattern transfer at the length scales necessary for microfabricated components, thin and uniform layers of photoresist must be applied to substrates with extremely low thickness variation.9 These layers are on the order of 1 μ m for traditional resists used in photolithography for semiconductor device processing,11 but they can be 100 μ m or more using thick-film resists in a technique known as “soft lithography,”12 which is used for the production of microfluidic devices. Whether the photoresist film is thin or thick, the uniform layer is achieved by a process known as spin coating. During spin coating, an initial volume of photoresist, V i, is dispensed onto the substrate (e.g., a silicon wafer). This can be accomplished statically, with the substrate not rotating, or dynamically, with rotation.13 Although spin coating recipes can be quite complicated and involve many changes in speed, time, and acceleration, they fundamentally involve: (1) a “spread cycle” in which the initial volume of resist is dispersed from the starting size and shape across the substrate and (2) a “spin cycle” where the photoresist liquid layer is thinned over time by the higher rotational speed. A large angular acceleration is used between steps.9 We can envision an ideal spin coating process as one in which the initial volume is transformed into a thick uniform layer h 0 by the low-speed spread cycle (where h 0 V i / A, A being the area of the substrate), followed by thinning of the uniform film over time, h(t), as centrifugal forces cause the photoresist to flow off of the substrate. These steps are captured in the schematic of Fig. 1.

Fig. 1.

Schematic diagram showing the basic spin coating process involving (a) static dispense of photoresist, (b) the spread cycle where low speed rotation is intended to create a thick and uniform film with thickness h 0, and (c) the spin cycle in which the film thickness is decreased over time by a faster rotational speed.

Fig. 1.

Schematic diagram showing the basic spin coating process involving (a) static dispense of photoresist, (b) the spread cycle where low speed rotation is intended to create a thick and uniform film with thickness h 0, and (c) the spin cycle in which the film thickness is decreased over time by a faster rotational speed.

Close modal

The fluid dynamic theory of spin coating, in which a model for the film thickness h(t) is desired, was initially developed in the work of Emslie et al.,14 and then further refined in more detailed theoretical and experimental studies.15,16 These early models of Newtonian liquids have been expanded to include non-Newtonian behavior.17 Of particular concern, complicated changes in liquid properties can occur during the coating process due to rapid solvent evaporation from thin films.18,19 In addition, because of the need for high yield rates in processing, important work has also been published that contains studies of fluid instabilities, which can lead to coating defects.20,21

While the consideration of non-Newtonian liquids and instabilities is important to more advanced studies, in this introduction for undergraduates, we focus our attention on the theory of Newtonian liquids, which captures the important features of spin coating of photoresists while remaining simple enough to provide an appealing introduction. We develop a model that predicts how (and whether) h depends on these experimental parameters: liquid density ρ, viscosity μ, spin speed ω, spin time t, substrate diameter D, and substrate roughness ϵ. Note that we consider only the speed ( ω = ω spin) and time associated with the spin cycle as we treat the spread cycle to have created the film of thickness h 0 from dispensed volume V i. Our final result will demonstrate which, if any, of these variables are important to the final film thickness.

We use an approach that should be familiar to an undergraduate student who has learned about both control volume analysis and differential analysis methods in fluid dynamics problem solving. The technique here follows derivations provided in many sources14,18,22 and we include only the most important results. Ultimately, a classroom example, homework problem, or project would involve the student showing all of the steps in the derivation.

We restrict our attention to the spin cycle and assume that the spread cycle has already created a uniform film of thickness h 0 that completely covers a substrate of diameter D. Given the geometry, we use a cylindrical coordinate system with an origin aligned with the axis of rotation and the surface of substrate (see Fig. 2). Using a control volume that surrounds the liquid on the substrate at all times during the spread cycle (see the dashed rectangle in Fig. 2 which has a top area of π D 2 / 4 and sidewall area of π D h), the conservation of mass equation can be written as
d h d t = 4 D 0 h v r ( r = D / 2 ) d z ,
(1)
assuming incompressible axisymmetric flow at speed v r ( r ), in addition to neglecting the interfacial fluid dynamics at the edge of the substrate in which surface tension plays a role in allowing the liquid to flow off of the substrate (this will be explored later). We can see that Eq. (1) assumes that the outward flow of liquid off of the wafer is directly responsible for the thinning of the film.
Fig. 2.

Schematic diagram for the fluid-dynamic modeling of the spin coating process. The film is considered to be uniform throughout and a circular substrate creates an axisymmetric problem about the z-axis which is aligned with the axis of rotation.

Fig. 2.

Schematic diagram for the fluid-dynamic modeling of the spin coating process. The film is considered to be uniform throughout and a circular substrate creates an axisymmetric problem about the z-axis which is aligned with the axis of rotation.

Close modal
It is now necessary to derive an expression for vr and then evaluate it at r = D / 2, which can be accomplished using the radial component of the Navier–Stokes equations. Although the substrate rotates at high speed, the thinness of the film and its high viscosity guarantee a low Reynolds number laminar flow with negligible acceleration. In addition, the velocity component vz is present—the film thickness does decrease—but is very small in comparison to vr and v θ = ω r. Again, because of the nature of the thin film where h D, gradients of vr in the z direction (across the film) are much larger than gradients of vr in the r direction (in the direction of flow). The result of all of these assumptions is that the radial velocity in the film is governed by
2 v r z 2 = ρ μ ω 2 r ,
(2)
which when integrated twice and using the no-slip boundary condition at z = 0 and the no-shear boundary condition at z = h, yields the velocity at any h to be
v r ( r , z , h ) = ρ μ ω 2 r [ h z z 2 2 ] ,
(3)
where, as a reminder, h is a function of time. As we will see later, the no-shear boundary condition is acceptable since for our least viscous liquid μ air / μ oil 10 7. We also neglect substrate roughness for now, i.e., considering the substrate smooth and/or roughness-independent, as this is often the case for laminar flows such as in the pressure-driven flow in a pipe. However, we recognize that spin conditions may allow the thickness h to approach the roughness ϵ (i.e., h ϵ), and, in that case, the thickness will influence the radial speed.

We can interpret Eq. (2) as a balance between viscous forces and the apparent centrifugal forces driving flow outward in the radial direction. The result provided in Eq. (3) makes intuitive sense that as ρ or ω increases, the centrifugal force increases and give rise to a larger radial velocity, but as μ increases, velocity is reduced owing to increased viscous forces opposing the flow. The profile of Eq. (3) at any radial location r is nothing more than a half-parabola between the no-slip condition at z = 0 and the no-shear condition at z = h. This profile is similar to other 1D thin-film results such as flow of a viscous flow down an incline and flow up a moving belt presented in undergraduate fluid mechanics texts.23,24

By substituting Eq. (3) into Eq. (1), integrating the profile across the film and then solving the resulting differential equation for dh/dt using the initial condition that h ( t = 0 ) = h 0, a result for h(t) is obtained
1 h ( t ) 2 1 h 0 2 = 4 ρ ω 2 t 3 μ .
(4)
Given that the initial dispensed volume creates a thick film after the spread cycle, h 0 h, Eq. (4) can be simplified to yield
h ( t ) = 3 μ 4 ρ ω 2 t ,
(5)
which is the classic result for the spin coating of Newtonian liquids (a more complete derivation of this result can be found in the text of Middleman and Hochberg22) In particular, it predicts that h ω 1 and h t 1 / 2, whereas non-Newtonian liquids and photoresists where solvent evaporation effects play a role have different exponents. For example, photoresists have been shown to produce films consistent with a h ω 1 / 2 dependence.18,19

Notice that Eq. (5) does not contain h 0, D, or ϵ, which we had originally thought might affect the thickness. Thus, we have an opportunity to explore the validity of Eq. (5), through experiments by varying parameters that do and do not appear in our theoretical result. By exploring both, we can further understand the nature of spin coating and understand the rationale for certain choices made in actual spin coating processes. Section III describes a set of accessible experiments for undergraduate students.

Experiments were designed and performed so that students can assess the validity of Eq. (5), including the variables that do not appear to play a role. We chose to guide our experiments by seeking options for students that are accessible (i.e., inexpensive and readily available), provided a range of conditions, and are safe to work with. In this section, we describe our choice of liquids, substrates, method of measuring film thickness, and procedures.

Although the theme of this study is to introduce students to the spin coating process in order to better understand aspects of the microfabrication industry, using traditional photoresist chemicals is ill advised because of (1) safety concerns (toxic and hazardous chemicals that require a ventilated space and personal protective equipment), (2) cost (photoresist often costs $1k/l), and (3) complexity of fluid properties, i.e., because a photoresist is a complex mixture of resin and solvents, the behavior is non-Newtonian and can even vary during spin coating due to solvent evaporation. We chose to explore liquids that would satisfy the requirements of safety, low-cost, and simple properties and so focused our attention on food-grade and safe-to-ingest Newtonian liquids that are available at most local grocery or pharmacy stores. In addition, we sought liquids that would provide a large range of liquid viscosity values.

After testing a variety of options including various oils (cooking and pharmaceutical), syrups (corn and chocolate), and glycerin-water mixtures, we found that three liquids were ideal for use in experiments: (a) olive oil, (b) castor oil, and (c) Karo® “dark” corn syrup. All of these liquids can be procured at a cost of $10/l or less. As Eq. (5) contains ρ and μ, we needed measurements of these properties for each liquid, in addition to confirming that each exhibited Newtonian fluid behavior.

To measure the density of each liquid, we used a gravimetric technique measuring the mass of liquid samples contained in nominal ∼ 5 ml plastic cuvettes, whose volume was determined through mass measurements with water. Density values are provided in Table I. The statistical uncertainty from five measurements of each liquid density is reported with the nominal values. Other techniques exist for obtaining liquid density values, e.g., measuring mass of liquid poured into a graduated cylinder, and instructors are encouraged to use whatever method is most convenient.

Table I.

Measured liquid properties for spin coating liquids used in experiments. Uncertainty of viscosity is estimated using the standard deviation of values calculated during viscosity measurements.

Density Viscosity
ρ μ
Liquid (g/cm3) (mPa s)
Olive oil  0.91 ± 0.01  77 ± 0.3 
Castor oil  0.95 ± 0.01  760 ± 7 
Karo® dark corn syrup  1.38 ± 0.01  6070 ± 200 
Density Viscosity
ρ μ
Liquid (g/cm3) (mPa s)
Olive oil  0.91 ± 0.01  77 ± 0.3 
Castor oil  0.95 ± 0.01  760 ± 7 
Karo® dark corn syrup  1.38 ± 0.01  6070 ± 200 

The three liquids provide a wide range of viscosity values to probe in experiments. This can be qualitatively seen by the withdrawal of a glass rod from a beaker of the liquid and observing the quantity of liquid that remains (see Fig. 3). To demonstrate that the liquids exhibited Newtonian behavior and in order to measure values of viscosity, we used a rheometer (TA Instruments Discovery HR2) with a temperature-controlled cone-and-plate fixture.

Fig. 3.

Qualitative evidence of viscosity differences is provided by photographs of the samples after a 6 mm glass rod is withdrawn from a beaker of liquid.

Fig. 3.

Qualitative evidence of viscosity differences is provided by photographs of the samples after a 6 mm glass rod is withdrawn from a beaker of liquid.

Close modal

The viscosity of our liquid samples were measured over a range of shear rates from 1 1000 s 1 maintaining the liquids at a temperature of 21 ° C. This temperature was selected as to be consistent with the range of temperatures in our lab space measured over several days ( 20 22 ° C). The near-constant value of viscosity with variation in shear rate, as shown in Fig. 4, strongly suggests Newtonian fluid behavior as does the linearity of the shear stress vs shear rate as is shown in the inset of Fig. 4 (data for castor oil is provided as an example). Values of liquid viscosity are provided in Table I. The reported uncertainty of viscosity is estimated as the standard deviation of viscosity values computed by the rheometer during the shear rate sweep, i.e., based on the 16 measurements for each liquid in Fig. 4. Students with limited equipment resources can still perform measurements to determine liquid density; however, if no access to a viscometer exists, students can be directed to use the viscosity values provided here but should be reminded that there can be variations between manufacturers of these liquids and viscosity is a temperature-dependent property.25 If resources are limited but students are still interested in estimating viscosity values of their own liquid samples, they might find success employing a “falling ball viscometer” approach. Numerous published sources can provide insight into this technique for an undergraduate laboratory audience.26,27

Fig. 4.

Viscosity measurements for the three liquids selected for spin coating experiments. All liquids exhibit Newtonian behavior. (Inset) stress vs shear rate plot for castor oil.

Fig. 4.

Viscosity measurements for the three liquids selected for spin coating experiments. All liquids exhibit Newtonian behavior. (Inset) stress vs shear rate plot for castor oil.

Close modal

With regard to our highest-viscosity liquid, care should be taken when using a corn syrup product as over time water evaporates from the liquid and it will become more viscous than if used straight from the bottle within 1 2 min. This drying of the film prohibits spin coating for long times. We found that it was still a suitable liquid for short spin time experiments, such as up to ∼100 s.

In semiconductor and microelectronic processing, a variety of substrate materials are employed with the most common being polished silicon wafers. However, these wafers are cost prohibitive for student experiments (∼$10–$100 per wafer depending on size) and can be easily broken if handled carelessly. We sought an alternative to silicon that was inexpensive, not easily broken, would be wetted by the liquids discussed, and available in a variety of sizes. Acrylic sheet was found to meet all of these criteria; however, students interested in spin coating glycerin–water mixtures will find that the hydrophobic nature of the material makes it impossible unless some kind of surface treatment is used (although for these liquids, glass substrates, e.g., common microscope slides cut into squares, would likely be an excellent alternative). Acrylic sheet of 1.6 mm thickness was purchased from McMaster-Carr and was laser cut to form substrates ranging from 25 152 mm diameter with a cost of ∼$0.10–$1.00 per piece depending on size. Commercially available pre-cut acrylic disks are also an option. We will refer to these substrates as our wafers for the remainder of the paper. There are certainly many other substrate materials that can be employed which all depend on the budget allowed for experiments. In addition, for liquid–substrate combinations not discussed in this work, it is recommended that the chemical compatibility between liquid and substrate be examined prior to use.

To increase substrate roughness explore substrate roughness, we sanded wafers using 400-grit and 100-grit wet/dry sandpaper. We label these as S 1 (as supplied), S 2 (400 grit), and S 3 (100 grit). The grit size of the paper correlates with roughness; however, the grit size does not necessarily dictate the exact magnitude of the roughness features. We used an Ambios XP 1 stylus profilometer to measure roughness of our wafer samples (three 5 mm long scans for each wafer type). An example of the results is presented visually in Fig. 5 and quantified in Table II. Given the nature of the single-direction scans, the average roughness is reported and is defined using
R a = 1 L 0 L | z ( x ) | d x
(6)
with L = 5 mm. We provide these for students who do not have access to tools with which to measure roughness.
Fig. 5.

Sample photographs (top) showing roughness of surface for substrates S 1 (un-sanded acrylic), S 2 ( 400-grit sanding), and S 3 ( 100-grit sanding), and sample profilometer scans with roughness measurements (bottom).

Fig. 5.

Sample photographs (top) showing roughness of surface for substrates S 1 (un-sanded acrylic), S 2 ( 400-grit sanding), and S 3 ( 100-grit sanding), and sample profilometer scans with roughness measurements (bottom).

Close modal
Table II.

Substrate roughness measurements performed using an Ambios XP 1 stylus profilometer. Absolute average roughness has been chosen to quantity profilometer scan data as a simple quantitative comparison between substrate roughness is needed. Note that root-mean-square roughness, Rq, values are 25 % higher and 35 % higher for the S 3 and S 2 substrates, respectively.

Ra R ¯ a
Substrate (μm) (μm)
S 1 (no sanding)  0 (smooth)  0 (smooth) 
S 2 ( 400-grit)  0.62 , 0.80 , 0.74  0.72 
S 3 ( 100-grit)  3.31 , 2.73 , 3.74  3.26 
Ra R ¯ a
Substrate (μm) (μm)
S 1 (no sanding)  0 (smooth)  0 (smooth) 
S 2 ( 400-grit)  0.62 , 0.80 , 0.74  0.72 
S 3 ( 100-grit)  3.31 , 2.73 , 3.74  3.26 

As a further test of surface roughness, we used a polished silicon wafer, but this is not essential for students who don't have access to this material. It was determined that most experiments should be performed using the 400-grit sanded wafers with the reason being that cleaning with soapy water and sponges and regular handling would inevitably introduce scratches and defects on the wafers and it would be better to perform most measurements with a less-than-pristine surface. In addition, sanding substrate surfaces has been shown to improve wettability in coating experiments.28 

To make these measurements, one needs to have the ability to control the spin speed and time of their samples and to measure—directly or indirectly—film thickness. We had access to a commercially manufactured spin coater that we used for our experimental study (Laurell WS 400 8 N / L), which had a range of spin speeds between 0 6100 rpm. The spin coater had a capacity to accommodate wafers in the range of 25 154 mm). Students designed and fabricated plastic 3D printed parts for properly centering the wafers on the vacuum chuck in addition to creating an easily assembled catch tray for liquids wasted as a result of the spin coating process (cf. Fig. 6). In particular, the 3D printed catch tray is invaluable so as to keep the workspace clean. If students do not have access to a commercially available spin coater, for example, if one cannot be borrowed or budget constraints prohibit even the purchase of an older inexpensive used model, then there are online resources that can be used to construct one which should be sufficient for the goals of this experiment.29,30

Fig. 6.

Photography showing 3D printed catch tray (a) fabricated in two halves to clip around the spin coater vacuum chuck (the prominent black circle is an O-ring on the chuck). In this photo, a 3D printed centering tool (b) is used with a 100 mm diameter plastic wafer (c) which is handled with wafer tongs (d).

Fig. 6.

Photography showing 3D printed catch tray (a) fabricated in two halves to clip around the spin coater vacuum chuck (the prominent black circle is an O-ring on the chuck). In this photo, a 3D printed centering tool (b) is used with a 100 mm diameter plastic wafer (c) which is handled with wafer tongs (d).

Close modal
Spin coated film thicknesses are generally in the range of 1 100 μ m depending on the type of photoresist used for processing. For the lower end of that range, optical tools such as spectral reflectometry are often employed.13 For the upper end of that range, stylus profilometers can be used for baked (hardened) resists. Both options provide only single-point measurements of thickness, and neither are readily available to a general audience of undergraduate students. Instead of using these tools, we can more simply measure the mass of the spin-coated liquid film, m exp, and then from this and knowing the area of the substrate A and the density of the liquid, we can use this to indirectly measure the average experimental film thickness,
h ¯ exp = 4 m exp / ( π ρ D 2 ) .
(7)
Note that this same idea was used earlier to determine h 0 from V i. If the spin coated liquid films are uniform over the surface of the wafer, then this average film thickness is no different than any single value of film thickness at any location. Theoretically, films that are spin coated will be uniform, and this has been demonstrated experimentally in the literature,15,18 therefore justifying the use of Eq. (7) as a way of determining film thickness. Additional discussion and proof of film uniformity are provided in the  Appendix. It is worth mentioning that similar gravimetric approaches for indirectly measuring average liquid film thickness have been employed in the literature for other coating techniques, e.g., drag-out coating of flat plates.28 

For measuring mass, we selected several inexpensive digital balances that cost $ 100 $ 300 and had resolutions 0.01 , 0.001 , and 0.0001 gm. Obviously higher resolution balances will be needed for very thin films created from low-viscosity liquids, long times, and high rotation speeds. Additionally, higher resolution balances will be needed to achieve acceptable uncertainties in film thickness if small substrate sizes are used owing to the decrease in measured film mass. It was found that for our experimental conditions, the 0.001 gm resolution scale was more than adequate and that was used exclusively for the measurements reported in this work. Calibration was performed only using the internal option on each balance—no precision standards were employed as these would not typically be available for an undergraduate class project.

To simplify the experimental procedure, we employed the same spread cycle parameters for all tests. Specifically, we used a 10 s spread cycle with a final speed of 500 rpm accelerating from rest at a rate of 492 rpm/s. This was shown from observations to spread the most viscous liquid across a 100 mm wafer within the 10 s window. Spin cycles used a fixed acceleration of 1066 rpm/s (note that the specific accelerations provided are from a limited number of pre-programmed options in the spin coater controller).

For each experiment, a clean wafer was picked up with wafer tongs or tweezers, swiped several times with an anti-static brush, and placed on a balance to record the initial wafer weight. Liquid was dispensed using a syringe to a pre-determined target weight, which was recorded. The size of the dispensing syringe was based on the target weight and liquid density so that no refilling was required for a single dispense (hence, syringes of 1–10 ml were used in our experiments). The spin coating process (spread and spin cycles) was performed with pre-programmed spin speed and time. Within several seconds, the wafer was then removed and placed on the balance to determine the final weight of the wafer and the liquid. Transfer and measurement were accomplished quickly in an attempt to minimize time for liquid evaporation to affect the measured mass. No variations in mass during the measurement window were noticed during the experiments, and this is consistent with the low volatility of the liquids used. All handling was performed with wafer tongs or tweezers to minimize contact and unwanted removal of liquid mass from the substrates which could also introduce error into the determination of film thickness. Given the size of the potential contact area for the wafer tongs, we estimate this to be no more than 1 % of the total mass for the smaller sized substrates, which is a negligible error for the experiments. After a single use, each wafer was wiped clean with paper towels and then washed with warm water and dishwashing detergent. Wafers were then allowed to air dry before their next use.

The variety of results presented here demonstrates the possible range of experiments that could be performed by undergraduate students within a typical laboratory timeframe. We leave it to the instructor to determine what is most appropriate for their specific conditions and equipment availability.

It turns out that the variables that do not appear directly in Eq. (5) are some of the most important to explore so that relationships between h, ω, and t can be conclusively determined.

1. Initial thickness h0

Let us start by assessing the influence of the initial amount of liquid on the wafer, h 0. Recall that Eq. (5) is obtained by treating h h 0; however, no formal ratio was used. Figure 7 shows the results of experiments in which various dispensed masses were added to 100 mm diameter S 2 wafers. Five unique spin coating tests were performed for each nominal dispensed mass.

Fig. 7.

Results of experiments to understand the influence of dispensed mass on overall film thickness resulting from the spin coating process. All experiments used 100 mm S 2 wafers with castor oil. Speed and time were fixed at 2000 rpm and 30 s, respectively.

Fig. 7.

Results of experiments to understand the influence of dispensed mass on overall film thickness resulting from the spin coating process. All experiments used 100 mm S 2 wafers with castor oil. Speed and time were fixed at 2000 rpm and 30 s, respectively.

Close modal

The inset of Fig. 7 shows that as the dispensed mass m i increases, the ratio of the final mass m f to the initial mass decreases and stabilizes at “large” values. In other words, a greater fraction of the initial mass is lost in the spin coating process as the dispensed mass increases. For the conditions of this set of experiments, the final m f / m i value approaches 4 % which highlights how incredibly wasteful the spin coating process is (i.e., over 95 % of all liquid dispensed on the wafer is wasted to produce the thin film). The inset also shows that the region of constant m f / m i coincides with ∼1 ml of initial volume per 25 mm of substrate diameter. This is in line with suggestions (i.e., baseline processing recommendations) for photoresists often provided in technical data sheets.31,32 When viewed in a non-dimensional form, we see that low values of h 0 / h theory lead to h ¯ exp / h theory < 1 indicating films either thinner than expected or incomplete coverage. For conditions in which h 0 / h theory > 10, the resulting film thickness is larger than theory by 6 %; however, no further changes in h occur with increases in dispensed mass. Thus, from a practical standpoint, this highlights how a minimal acceptable amount of dispensed mass can be determined for a spin coating process—which would be needed in a production scenario to reduce expenses. If we average the last 20 measurements which correspond to nearly constant film thickness, i.e., h 0 / h theory > 10, we can use the statistical variation to suggest that with 95 % confidence, any one single measurement will predict the true value within ± 6 %. A conservative conclusion for undergraduate experiments would be that given the variety of non-ideal conditions that exist for spin coating of thin liquid films outside of a cleanroom environment, we should expect an uncertainty in measurements O ( ± 10 % ), which end up being much larger than individual uncertainties associated with substrate diameter and displayed balance resolution error (which was only as large as 3 % for the thinnest olive oil films but below 1 % for nearly all other conditions explored in experiments).

As for as what causes h ¯ exp / h theory < 1 for small dispensed masses, using photographs taken before and after the spin coating process, we can see that too little dispensed mass leads to incomplete coverage and not a thinner-than-predicted uniform film. Figure 8 shows that the spread cycle is unable to achieve a uniform coating and instead the edge of the initial volume does not grow large enough for the critical radius of the fingering instability to exceed the wafer radius. Thus, fingers develop at the edge of the dispensed volume and flow is preferentially channeled through those fingers.20,21 To eliminate any issues with incomplete coverage, all other experiments used a conservative 1.25 ml / 25 mm ratio of volume to substrate diameter.

Fig. 8.

Images of initial liquid puddles and final films on 100 mm diameter wafers using castor oil. (a) 0.5, (b) 1, (c) 2, and (d) 3 ( 1 gm / ml). Each panel is a superposition of two images—one taken after the liquid is dispensed and the wafer has been loaded onto the spin-coater vacuum chuck and one taken after the spin coating process. The thin white line helps show the edge of the dispensed liquid mass prior to rotation. The white arrow in (c) shows defects along the edge, presumably from the fingering instability, which do not appear for larger dispensed volumes (e.g., they are not visible in (d)).

Fig. 8.

Images of initial liquid puddles and final films on 100 mm diameter wafers using castor oil. (a) 0.5, (b) 1, (c) 2, and (d) 3 ( 1 gm / ml). Each panel is a superposition of two images—one taken after the liquid is dispensed and the wafer has been loaded onto the spin-coater vacuum chuck and one taken after the spin coating process. The thin white line helps show the edge of the dispensed liquid mass prior to rotation. The white arrow in (c) shows defects along the edge, presumably from the fingering instability, which do not appear for larger dispensed volumes (e.g., they are not visible in (d)).

Close modal

2. Substrate roughness ϵ

Because of the laminar flow assumption used in the derivation of Eq. (5), the substrate roughness was not considered. However, is there an influence that we can measure experimentally? To explore this, we used wafers with un-sanded and sanded acrylic substrates (i.e., S 1 , S 2, and S 3) in addition to a limited number of experiments using single-sided-polished silicon wafers. For these experiments, all other parameters were held fixed (e.g., D = 100 mm , ω = 2000 rpm , t = 30 s, and only castor oil was used). Figure 9 captures the results of these experiments, presented in a dimensionless form, where open symbols are average values of five measurements for each substrate and the zero of the graph is not displayed so that the range of data can be more easily observed. We can see that there is almost no meaningful variation in film thickness with changing roughness for surface roughness less than approximately 16 % of the film thickness. However, we still see a larger-than-expected film thickness measured in our experiments as compared to the theoretical prediction (i.e., h ¯ exp / h theory 1.1) as was observed in Fig. 7.

Fig. 9.

The data from experiments with varying substrate roughness suggest limited influence for the range tested. Values of average substrate roughness, R ¯ a, are provided in Table II.

Fig. 9.

The data from experiments with varying substrate roughness suggest limited influence for the range tested. Values of average substrate roughness, R ¯ a, are provided in Table II.

Close modal

3. Substrate diameter D

The remaining variable that was eliminated in the derivation of Eq. (5) was the substrate diameter D. In other words, the spin coating theory is diameter-independent so long as a sufficient initial volume is dispensed onto the wafer so that h 0 h. However, is this actually the case or is there some change that can be observed with changes to wafer diameter? This is rather easily explored with acrylic wafers that can be cut to any desired size. The results shown in Fig. 10, obtained from experiments using acrylic wafers with a factor of six increase in diameter, present a picture of the influence of substrate diameter on the resulting film thickness.

Fig. 10.

Diameter dependence of the height and mass using S 2 substrates of diameters ranging from 25 154 mm. All experiments were performed using castor oil at 2000 rpm for 30 s. Wafer diameters are normalized to the diameter of the smallest wafers tested, 25 mm. Gray symbols are all data points, whereas open symbols are average values (with error bars representing the statistical uncertainty of each sample). The solid line is a prediction made by accounting for the additional mass within the edge bead using σ = 40 mN / m.

Fig. 10.

Diameter dependence of the height and mass using S 2 substrates of diameters ranging from 25 154 mm. All experiments were performed using castor oil at 2000 rpm for 30 s. Wafer diameters are normalized to the diameter of the smallest wafers tested, 25 mm. Gray symbols are all data points, whereas open symbols are average values (with error bars representing the statistical uncertainty of each sample). The solid line is a prediction made by accounting for the additional mass within the edge bead using σ = 40 mN / m.

Close modal

The inset of Fig. 10 shows what we would expect to see: as substrate diameter is increased (recall that we add sufficient initial volume so as to ensure complete coverage) the resulting film mass increases—and without a more careful inspection we may think there is agreement between the theory and experiment. However, when we compare the experimental film thickness to the theoretical film thickness a different picture emerges. Figure 10 shows a striking increase in average film thickness as diameter decreases.

It turns out that the “edge bead” is responsible for this effect [a sample photo is provided in Fig. 11(a)]. In the derivation of Eq. (5), we mentioned that we model the flow of liquid off of the wafer neglecting all interfacial fluid dynamic phenomenon including the influence of surface tension σ. However, for a real wafer with an edge, surface tension forces resist the flow of liquid off of the edge. The region near the edge where surface tension forces are involved is called the edge bead and this is a region of increased film thickness with a length scale similar in magnitude to the capillary length L c σ / ( ρ g O ( 1 mm ). This is similar to the Plateau border that is present when soap films are formed using wire frames.33 We can estimate the mass of liquid contained in the edge bead by balancing surface tension forces with the apparent centrifugal force F σ F c, as illustrated in Fig. 11(b),
M b D 2 ω 2 σ π D .
(8)
Fig. 11.

The thickness of the film near the edge of the wafer is larger than that near the center of the film. This region is often called the “edge bead” and is not considered in the spin coating theory presented in Sec. II B. (a) images of the edge bead from experiments with castor oil and a 50 mm wafer. The inset shows more detail and an approximate dimension of the edge bead region. (b) A side-view schematic of the edge bead region showing relevant length scales and forces.

Fig. 11.

The thickness of the film near the edge of the wafer is larger than that near the center of the film. This region is often called the “edge bead” and is not considered in the spin coating theory presented in Sec. II B. (a) images of the edge bead from experiments with castor oil and a 50 mm wafer. The inset shows more detail and an approximate dimension of the edge bead region. (b) A side-view schematic of the edge bead region showing relevant length scales and forces.

Close modal

When the mass of the edge bead M b is added to the mass of the film, we get m f , total = M b + m f , exp and this total mass is used to predict h ¯ exp, the experimental results end up being in good agreement both qualitatively and quantitatively with the theory (cf. solid line in Fig. 10). We conclude that our experimental film thicknesses will tend to exceed the theoretical predictions in part because of the edge bead that will always be present on a wafer.

A more traditional approach to investigating the validity of the spin coating model, i.e., Eq. (5), would be to investigate the variables that appear directly in the equation. This type of analysis and comparison can be found in existing literature, but it is still useful for students to perform their own experiments. Given that we have three liquids with nearly a factor of 10 difference in μ between each, and that a spin coater allows for variations in spin speed and time, it is quite straight-forward to do this.

In Fig. 12, we present results that capture the influence of both liquid viscosity (really kinematic viscosity ν = μ / ρ as we cannot decouple the liquid viscosity and density) and spin speed. As expected, film thickness increases with increasing viscosity and decreases with increasing speed. Results are shown using log-log axes to highlight the power-law nature of the h ω a relationship, where curve fits yield values of a =  1.09 , 0.99, and 0.94 for olive oil, castor oil, and Karo dark corn syrup, respectively (with an average value of a =  1.03 for all three liquids which is excellent agreement with a =  1 as predicted by Eq. (5)). We can also report that h ¯ exp / h theory are, on average, 1.03 , 1.11, and 1.14 for these liquids. This is not altogether surprising and given our knowledge of the influence of the edge bead and the conservative estimate of the uncertainty of individual measurements, and we can conclude that there is acceptable quantitative agreement in magnitude of film thickness values as compared to theory.

Fig. 12.

Results from spin coating experiments using all three liquids for variable spin speed. Each data point represents a single measurement, and all experiments use S 2 substrates ( 100 mm diameter) with castor oil and a 30 s spin time. The solid lines represent theoretical predictions from Eq. (5).

Fig. 12.

Results from spin coating experiments using all three liquids for variable spin speed. Each data point represents a single measurement, and all experiments use S 2 substrates ( 100 mm diameter) with castor oil and a 30 s spin time. The solid lines represent theoretical predictions from Eq. (5).

Close modal

Holding spin speed fixed and varying spin time yields the data presented in Fig. 13. Again, the influence of viscosity is also observed, and trends follow those suggested by Eq. (5). More specifically, we can see the h t b relationship, where curve fits yield values of b =  0.50 , 0.52, and 0.47 for olive oil, castor oil, and Karo dark corn syrup, respectively (with an average value of b =  0.50 for all three liquids which is indistinguishable from b =  0.5 predicted in Eq. (5)). We can also report that h ¯ exp / h theory are, on average, 1.16 , 1.08, and 1.06 for these liquids. Again, these are reasonable from what we can anticipate from experiments such as these.

Fig. 13.

Results from spin coating experiments using all three liquids for variable spin time. Each data point represents a single measurement, and all experiments use S 2 substrates ( 100 mm diameter) with castor oil and a 2000 rpm spin speed. The solid lines represent theoretical predictions from Eq. (5).

Fig. 13.

Results from spin coating experiments using all three liquids for variable spin time. Each data point represents a single measurement, and all experiments use S 2 substrates ( 100 mm diameter) with castor oil and a 2000 rpm spin speed. The solid lines represent theoretical predictions from Eq. (5).

Close modal

A final way to capture the results of both Figs. 12 and 13 together is to present the results in a form where h is plotted vs ( 1 / ω ) μ / ( ρ t ). When this is done, the result is Fig. 14, and our results are similar to those found in the literature for experiments that used silicone oils of various viscosity22 where experimental coating thickness was found to be 10 % higher than theoretical predictions.

Fig. 14.

Results from spin coating experiments using all three liquids for various spin times and spin speeds (i.e., the data from Figs. 12 and 13). The solid line represents Eq. (5).

Fig. 14.

Results from spin coating experiments using all three liquids for various spin times and spin speeds (i.e., the data from Figs. 12 and 13). The solid line represents Eq. (5).

Close modal

Guided by classical spin coating theory, we have presented the detailed results of experiments designed to introduce undergraduate physics and engineering students to the topic of spin coating—and thereby connect them via application to the field of microfabrication. It was found that three safe-to-handle, inexpensive, and readily available Newtonian liquids provide a wide range of viscosity for testing. These liquids work well with laser-cut acrylic wafers, and average film thickness covering a range of 1 100 μ m can be measured gravimetrically using a digital balances with resolution of 0.001 gm. Variables that appear directly in the spin coating model for film thickness (i.e., μ, ρ, ω, and t) can be evaluated to show agreement with the model. In addition, variables that might be thought to play a role but that do not appear in the model (i.e., h 0, ϵ, and D) are also explored and connected to practical spin coating guidelines and rules-of-thumb (e.g., to ensure complete coverage) or interesting features (e.g., the edge bead).

The authors acknowledge the financial support provided from the Cal Poly SLO Office of the University Diversity and Inclusivity OUDI BEACoN program for student researchers. In addition, the authors recognize the Cal Poly SLO ME Department Constant J. and Dorothy K. Chrones Endowment for financial assistance in purchasing equipment, materials, and supplies for this project. Author H.C.M. thanks Professor Russ Westphal (Cal Poly SLO Mechanical Engineering) for the use of the extended light source for interference fringe measurement experiments and Professor John Sharpe (Cal Poly SLO Physics Department) for assistance with the interpretation and analysis of fringes patterns essential to the film uniformity study.

The authors have no conflicts to disclose.

1. Rationale and experimental options

Comparing the theoretically predicted film thickness to that obtained experimentally using the mass of the liquid deposited on the substrate (i.e., Eq. (7)) assumes that the thickness of the film is uniform across the surface of the wafer. We can refer to this as the “global” uniformity of the film in contrast to the “local” uniformity that might vary within a small region if there is a microstructure on the substrate surface, e.g., if there are underlying features on the wafer that has been coated or if there are small-scale defects caused by dust or bubbles in the film. The literature confirms that global uniformity is achieved by spin coating.14,15,18 This is supported by the prevalence of the technique in the semiconductor processing industry, where uniformity is essential for successful photolithography of very small scale features. Aside from the known change in thickness that occurs within the edge bead, our experiments using mass measurements also confirm the uniformity of the film given the agreement with the theory. However, there is value in confirming global uniformity of our spin coated films through additional experimental means in order to satisfy any lingering doubts as to the efficacy of the thickness through mass approach that has been described in detail.

Two experimental techniques have been used to assess the global uniformity of spin coated films: (A) spectral reflectometry for quantitative film thickness measurements at many single locations which can be combined to build a map of thickness and (B) interpreting interference fringe patterns over the entire wafer surface. We performed one experiment using each technique for the purposes of confirming uniformity. In both cases, spin coated films were produced with castor oil on silicon wafers (chosen due to their high reflectivity) and with a spin speed and time of 2000 rpm and 30 s, respectively, as these were conditions in the middle of the ranges previously reported for liquid viscosity, spin speed, and spin time.

2. Option A: Spectral reflectometry

Spectral reflectometry is an industry-standard approach for measuring spin coated film thickness (in addition to other films produced by microfabrication techniques, e.g., silicon dioxide layers grown during thermal oxidation). Measurements are made at individual locations on the surface of a wafer and by comparing these measurements the global uniformity of the film can be determined. To perform these measurements, we used a Filmetrics F20 instrument running FILMeasure software. The instrument, whose measurement stage is shown in Fig. 15, directs white light down to the substrate and film through a fiber-optic cable (i). This light is reflected from a small region (on the order of a few millimeters in diameter) at both the air–liquid surface and from the substrate–liquid surface (ii). The reflected light at normal incidence angle is passed through an additional fiber-optic cable to a spectrometer where it is analyzed. In order to assess film uniformity, we needed to measure film thickness at a number of known locations. To do this in a rapid manner, a 3D printed wafer fixture, (iii) and (iv) in Fig. 15, was constructed so that the wafers could be rotated manually to achieve measurements at angular increments of 45°. Radial positioning was controlled by a lettered part that shifted and held fixed the distance between the center of the wafer and the measurement location.

Fig. 15.

Photograph of 3D printed wafer fixture for the Filmetrics F20 spectral reflectometry instrument. White light is directed top-down toward a substrate from a fiber optic cable housed in (i). Light reflected from the film and substrate at (ii) is passed into an overhead fiber optic cable (also housed in (i)) and sent to a spectrometer within the instrument (this part of the instrument not shown). A 3D printed fixture was used to locate a 100 mm diameter silicon wafer and to index it to set radial and angular locations. Part (iii) holds the wafer and has features on the edge to indicate angle increments of 45°. Part (iv) positions the center of the wafer away from the measurement location by a set radial distance and allows for part (iii) to rotate against it. Five different (iv) parts allowed for five unique radial positions to be measured.

Fig. 15.

Photograph of 3D printed wafer fixture for the Filmetrics F20 spectral reflectometry instrument. White light is directed top-down toward a substrate from a fiber optic cable housed in (i). Light reflected from the film and substrate at (ii) is passed into an overhead fiber optic cable (also housed in (i)) and sent to a spectrometer within the instrument (this part of the instrument not shown). A 3D printed fixture was used to locate a 100 mm diameter silicon wafer and to index it to set radial and angular locations. Part (iii) holds the wafer and has features on the edge to indicate angle increments of 45°. Part (iv) positions the center of the wafer away from the measurement location by a set radial distance and allows for part (iii) to rotate against it. Five different (iv) parts allowed for five unique radial positions to be measured.

Close modal

The thickness of the film is determined through software by comparing the pattern of constructive and destructive reflectance values across the visible spectrum to predictions of this pattern using known optical properties of the film and a sweep of film thicknesses. The film thickness from the calculated pattern that produces the best agreement with the measured pattern is considered the film thickness, which we denote as h exp , I. An example of this comparison is shown in Fig. 16. Since details of the refractive index of our particular castor oil were not known, we used a single value of n f = 1.47 and used only a 100 nm range of wavelength to determine a fit. Given the limited accuracy of the fit, we chose to report film thickness measurements to the nearest 0.1 μ m. This is sufficient for our purposes.

Fig. 16.

Representative figure showing data from the Filmetrics F20 instrument and FILMeasure software. The inset plot shows the reflectance values measured over a range of wavelength from 400 850 nm. The main plot shows a region of detail in addition to showing a comparison between the measured reflectance and the calculated reflectance that gives the best fit over the 700 800 nm range using a refractive index of n f = 1.47. The calculated reflectance is based on a film thickness, and the best fit film thickness is considered the measured thickness of the film.

Fig. 16.

Representative figure showing data from the Filmetrics F20 instrument and FILMeasure software. The inset plot shows the reflectance values measured over a range of wavelength from 400 850 nm. The main plot shows a region of detail in addition to showing a comparison between the measured reflectance and the calculated reflectance that gives the best fit over the 700 800 nm range using a refractive index of n f = 1.47. The calculated reflectance is based on a film thickness, and the best fit film thickness is considered the measured thickness of the film.

Close modal

Results from measurements of h exp , I, made for a single castor oil film for radial positions of r = 0 , 10 , 20 , 30 , and 40 mm, and for angular positions of θ = 0 ° 315 ° in 45 ° increments, are shown in Fig. 17. Because castor oil does not readily wet silicon, and therefore dust in the room contributes to defects in the film where the film wants to de-wet, if a measurement coincided with a defect, the wafer was moved a few millimeters to obtain a meaningful measurement. Measurements were taken a few seconds apart—as quickly as we could locate a new position and acquire a measurement through the software. In Fig. 17, we can see that because there are no significant trends in film thickness vs either r or θ we can conclude that the film thickness is uniform across the wafer (with the exception of the region near the wafer edge, r > 45 mm). Note that measurements using the spectral reflectometer instrument, the average of the 33 measurements yielding h ¯ exp , I = 22.6 μ m, agreeing with those from the corresponding mass measurement ( h ¯ exp , m = 24.2 μ m), and that both agree reasonably well with the theoretical prediction ( h theory = 21.1 μ m).

Fig. 17.

Comparison of film thickness measurements using the spectral reflectometer, h exp , I, across a single wafer suggests that the film is globally uniform. A total of 33 unique measurements are shown. We have chosen to group measurements for fixed values of θ and to show these sets as functions of radial position r. No apparent trend exists, which is consistent with a uniform film. In addition, the optical measurements agree with the prediction from the measured mass of the film, h exp , m, and the theoretical prediction, h theory.

Fig. 17.

Comparison of film thickness measurements using the spectral reflectometer, h exp , I, across a single wafer suggests that the film is globally uniform. A total of 33 unique measurements are shown. We have chosen to group measurements for fixed values of θ and to show these sets as functions of radial position r. No apparent trend exists, which is consistent with a uniform film. In addition, the optical measurements agree with the prediction from the measured mass of the film, h exp , m, and the theoretical prediction, h theory.

Close modal

Thus, we can reasonably conclude from measurements using Option A that the films produced via spin coating are globally uniform. However, it should be noted that they are susceptible to local variations in thickness especially in a normal laboratory environment where particulates landing on the surface can cause defects in the film (these particulates are removed by air handling and filtration systems in a cleanroom facility). While Option A provides direct thickness measurements, building a picture of uniformity from multiple measurements can be laborious and is only as detailed as the number of individual measurements that can be gathered.

3. Option B: Interference fringe patterns

The use of interference fringes have long been used to study the surfaces of thin films and in precision measurements.34 Examples include the use of Fizeau fringes (i.e., fringes of constant thickness35) for determining the flatness of machined surfaces,36 fringe patterns in wedge-shaped oil films used to measure surface shear stress in aerodynamics applications,37 and local uniformity measurements for films spin coated over substrate features.38 Since our goal is to assess the global uniformity of spin coated films, over flat and bare substrates without patterned features (i.e., films that are expected to be uniform), we chose an illumination technique that would yield Haidinger fringes (i.e., fringes of constant inclination35) This technique turns out to be quite simple to implement and can be incorporated to enhance the undergraduate spin coating experiments previously described.

The experimental setup to view Haidinger fringes during spin coating is shown in the schematic diagram of Fig. 18(a). The liquid film of thickness h, where h(t), and refractive index nf, is illuminated by an extended monochromatic light source placed directly over the wafer. In our case this is a “Unilamp” green light source with a wavelength of λ = 545 nm (confirmed by measurement with an Ocean Optics USB-4000 fiber optic spectrometer). A cell phone camera mounted on a tripod is used to image the light reflected from the film and wafer. The camera is mounted to view the wafer at an angle of θ i 20 ° and the lens-to-wafer distance is estimated to be L 37 cm. The distance from the center of the wafer to directly below the camera lens is computed to be 12 cm from θi and L. Not shown in Fig. 18(a) is the spin coater and transparent lid formed from a piece of cast acrylic that allows for viewing of fringes during the spin coating process.

Fig. 18.

Experimental setup to observe Haidinger fringes during spin coating. (a) A side view shows the arrangement of a camera, wafer with film, and extended monochromatic light source. (b) If a large uniform film is viewed directly from above, Haidinger fringes would appear as a series of concentric rings (Ref. 39). However, the film in question on the wafer is isolated to just a limited region (the wafer—shown as a dotted circle) and viewed at some angle. Thus, we expect to see fringes that appear as parallel arcs of radius R at the middle of the wafer. The number of fringes N, counting both dark and light as fringes (in this case, N = 4), corresponds to the thickness of the film where N increases as film thickness h increases.

Fig. 18.

Experimental setup to observe Haidinger fringes during spin coating. (a) A side view shows the arrangement of a camera, wafer with film, and extended monochromatic light source. (b) If a large uniform film is viewed directly from above, Haidinger fringes would appear as a series of concentric rings (Ref. 39). However, the film in question on the wafer is isolated to just a limited region (the wafer—shown as a dotted circle) and viewed at some angle. Thus, we expect to see fringes that appear as parallel arcs of radius R at the middle of the wafer. The number of fringes N, counting both dark and light as fringes (in this case, N = 4), corresponds to the thickness of the film where N increases as film thickness h increases.

Close modal

To view fringes resulting from the illuminated film, the normal spin coating process is followed (e.g., weighing wafer, dispensing and weighing wafer and oil, spin coating, weighing after spin coating). The only difference is that the cell phone camera is used in a fixed location to record the process. Once the spin coating experiment has been performed, frames from the cell phone camera movie can be extracted at known times in the process. An example of a selection of cell phone movie frames is shown in Fig. 19. Here, we can see (a) the very thick initial volume of liquid dispensed prior to rotation, (b) numerous fringes begin to appear as the film thins during the spread cycle, but the film thickness is still much larger than the final film thickness, and then in (c) and (d), clearly discernible fringes with different numbers, indicating different thickness, that appear over time during the spread cycle. Because of the low frame rate compared to the rate of rotation, each image is blurry (smearing many rotations in one image); however, this does not prevent viewing the “average” of the fringes that form. In fact, this smearing helps to avoid seeing local defects in the film and gives us a picture of the most important fringes related to global uniformity. Note the similarity between the fringes diagrammed in Fig. 18(b) and those observed experimentally in Figs. 19(c) and 19(d).

Fig. 19.

Images of fringes observed during a representative spin coating experiment (castor oil 5 ml, 100 mm polished silicon wafer substrate, 10 s spread, 30 s spin at 2000 rpm). (a) Initial mass deposited (no rotation), (b) 5 s into the spread cycle, (c) 10 s into spin cycle (i.e., t = 10 s), and (d) 30 s into spin cycle (i.e., t = 30 s). The radius measured from the fringe at the center of the wafer in (d) was R = 12.7 cm which is similar to the expected value of R = 12 cm based on the dimensions of the experiment setup.

Fig. 19.

Images of fringes observed during a representative spin coating experiment (castor oil 5 ml, 100 mm polished silicon wafer substrate, 10 s spread, 30 s spin at 2000 rpm). (a) Initial mass deposited (no rotation), (b) 5 s into the spread cycle, (c) 10 s into spin cycle (i.e., t = 10 s), and (d) 30 s into spin cycle (i.e., t = 30 s). The radius measured from the fringe at the center of the wafer in (d) was R = 12.7 cm which is similar to the expected value of R = 12 cm based on the dimensions of the experiment setup.

Close modal

Without knowledge of how the thin liquid films are formed, a picture of fringes as seen in Fig. 19 can lead to the question: Are these Haidinger fringes or Fizeau fringes? The answer to this question is important since both types of fringe patterns can be formed from the illumination scheme presented. Haidinger fringes will form in the pattern as observed if the film is of uniform thickness. Fizeau fringes will appear in a similar pattern but under different film conditions. First, Fizeau fringes would appear as parallel bands if the film had a thickness variation representative of a wedge (i.e., front-to-back change in thickness). Second, the parallel bands from Fizeau fringes may have a radius to them if, superimposed on the front-to-back wedge shape, the film is bowed about an axis from front-to-back (e.g., this type of pattern can be seen with an optical flat placed on a rod but with a wedge created along the axial length of the rod36) Now if we bring in the knowledge that the films are formed during spin coating, then we expect that any non-uniformity in the films will present itself in an axisymmetric way. Thus, logically, we can conclude that these must be Haidinger fringes as there is no way for the spin coating process to produce a wedge-shaped film that remains fixed in orientation with respect to the camera as the substrate spins. Knowing that we are observing Haidinger fringes, we can immediately conclude (albeit qualitatively) from the circularity of the fringes that the film produced during spin coating are globally uniform throughout most of the spin cycle, and thus Option B supports the results of Option A in assessing the global uniformity of spin coated films.

As an added result of collecting images of Haidinger fringes, we can use the theory of these fringes to quantify film thickness based on fringe number. Traditionally, optics textbooks35,39 provide information about Haidinger fringes (i.e., fringes of equal inclination) produced using extended light sources from the standpoint of changes in fringes that would be observed at fixed angle if film thickness were varied. Consider a film of uniform thickness h of refractive index nf, sitting atop a substrate of higher index material. This film is covered on top with a material of lower index, and this is the case when we have a liquid film spin coated onto a silicon wafer in air. For these interference fringes, the conditions to observe constructive and destructive interference corresponding to a given inclination angle θi (where this is related to the transmitted angle through the film, θt, by Snell's law, sin θ t = sin θ i / n f) are given by
h cos θ t = ( 2 m + 1 ) λ 4 n f
(A1)
for maxima and
h cos θ t = ( 2 m ) λ 4 n f
(A2)
for minima, where m = 0,1,2,… Given our fixed camera angle θi, we can use these equations and the observed spacing between sequential maxima and minima to estimate the film thickness. In other words, for the same value of h, what change in θt satisfies both Eqs. (A1) and (A2)? By this we mean that for Eq. (A1) there is some θ t , max, and that for Eq. (A2) there is some θ t , min, which are related via Snell's law to θi and θ i + Δ θ, where Δ θ is the angular distance between sequential maxima and minima. This angular distance can be estimated as Δ θ θ D / N, where N is the number of fringes counted manually from a cell phone movie image and θD is the angle shown in Fig. 18 which is based trigonometrically on the camera inclination angle θi, the distance L, and the wafer diameter D. And so, by combining Eqs. (A1) and (A2) and using m = 0, we arrive at
h = λ 4 n f ( cos θ t , min cos θ t , max ) .
(A3)
While not directly apparent in Eq. (A3), as N increases and Δ θ decreases, h increases. In other words, observable fringes only appear for thin films, and as film thickness decreases the number of fringes decrease as well—this is a qualitative observation from cell phone movies.

We can also use Eq. (A3) to theoretically predict the number of observable fringes N from a given input of film thickness h (this requires an iterative solution for Δ θ within the equation—accomplished using the GoalSeek feature in Excel for our case). Since our cell phone movie images allow us to observe and measure N(t), we can compare these measurements to a “theoretical” prediction driven by the input of the theoretical prediction of h(t) (i.e., Eq. (5)) which describes the thinning of the spin coated film for the spin cycle only). Using the experimental test conditions described in Fig. 18 to predict h(t), and then using Eq. (A3) to predict N(t), the resulting theoretical prediction is shown as the solid curve in Fig. 20. We have also chosen to create theoretical uncertainty bands by varying θi by ± 2.5 ° and these are plotted as well. As expected, N(t) decreases as time increases (driven by a decrease in h). Numbers of fringes were manually counted from a selection of cell phone movie frames spanning the length of the spin cycle. These measured fringe numbers are also reported in Fig. 20. When measurements of N(t) are compared to theoretical predictions, we see very good agreement between both the trends and the magnitudes. This is further confirmation that Option B shows globally uniform films and suggest that in future experiments, Haidinger fringes can be used to monitor detailed and quantitative h(t) behavior of thin spin coated films.

Fig. 20.

Measured fringe number N vs time t acquired from cell phone movie images of a spin coated castor oil film. Good agreements between trends and magnitudes are observed when comparing predicted fringe number to measurements. This agreement confirms that fringes can also be used to quantify film thickness and allows for an additional method to track h(t) for thin films in an undergraduate setting.

Fig. 20.

Measured fringe number N vs time t acquired from cell phone movie images of a spin coated castor oil film. Good agreements between trends and magnitudes are observed when comparing predicted fringe number to measurements. This agreement confirms that fringes can also be used to quantify film thickness and allows for an additional method to track h(t) for thin films in an undergraduate setting.

Close modal
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