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Brief Description of Spin Coating Process:The Key Stages in Spin CoatingAlthough different authors sometimes count things
differently, there are four distinct stages to the spin coating process. Stage 3
(flow controlled) and Stage 4 (evaporation controlled) are the two stages that
have the most impact on final coating thickness.  Stage
One: The first stage is the deposition of the coating
fluid onto the wafer or substrate.
It can be done using a nozzle that pours the coating solution out, or it could be sprayed onto the surface, etc. Usually this dispense stage provides a substantial excess of coating solution compared to the amount that will ultimately be required in the final coating thickness. For many solutions it is often beneficial to dispense through a sub micron sized filter to eliminate particles that could lead to flaws. Another potentially important issue is whether the solution wets the surface completely during this dispense stage. If not, then incomplete coverage can result.
 Stage
Two: The second stage is when the substrate is
accelerated up to its final, desired, rotation speed.
This stage is usually characterized by aggressive fluid expulsion from the wafer surface by the rotational motion. Because of the initial depth of fluid on the wafer surface, spiral vortices may briefly be present during this stage; these would form as a result of the twisting motion caused by the inertia that the top of the fluid layer exerts while the wafer below rotates faster and faster. Eventually, the fluid is thin enough to be completely co-rotating with the wafer and any evidence of fluid thickness differences is gone. Ultimately, the wafer reaches its desired speed and the fluid is thin enough that the viscous shear drag exactly balances the rotational accelerations.
 Stage
Three: The third stage is when the substrate is
spinning at a constant rate and fluid viscous forces dominate fluid
thinning behavior.
This stage is characterized by gradual fluid thinning. Fluid thinning is generally quite uniform, though with solutions containing volatile solvents, it is often possible to see interference colors "spinning off", and doing so progressively more slowly as the coating thickness is reduced. Edge effects are often seen because the fluid flows uniformly outward, but must form droplets at the edge to be flung off. Thus, depending on the surface tension, viscosity, rotation rate, etc., there may be a small bead of coating thickness difference around the rim of the final wafer. Mathematical treatments of the flow behavior show that if the liquid exhibits Newtonian viscosity (i.e. is linear) and if the fluid thickness is initially uniform across the wafer (albeit rather thick), then the fluid thickness profile at any following time will also be uniform --- leading to a uniform final coating (under ideal circumstances).
 Stage
Four: The fourth stage is when the substrate is
spinning at a constant rate and solvent evaporation dominates the coating
thinning behavior.
As the prior stage advances, the fluid thickness reaches a point where the viscosity effects yield only rather minor net fluid flow. At this point, the evaporation of any volatile solvent species will become the dominant process occurring in the coating. In fact, at this point the coating effectively "gels" because as these solvents are removed the viscosity of the remaining solution will likely rise -- effectively freezing the coating in place. (This behavior was used in the seminal work of Meyerhofer (J. Appl. Phys. 49 (1978) 3993) where he quantified the coating thickness dependence on spin speed and viscosity and its relationship to the evaporation rate.) After spinning is stopped many applications require that heat treatment or "firing" of the coating be performed (as for "spin-on-glass" or sol-gel coatings). On the other hand, photoresists usually undergo other processes, depending on the desired application/use. Clearly stages 3 and 4 describe two processes that must be occurring simultaneously throughout all times (viscous flow and evaporation). However, at an engineering level the viscous flow effects dominate early on while the evaporation processes dominate later. Brief Theory:Fluid Flow Basics (Ideal Case)The starting point for much of the spin coating modeling was published by Emslie, Bonner, and Peck [J. Appl. Phys. 29 (1958) 858-862] (hereafter referred to as EBP). Their seminal treatment is based on assuming that flow has reached a stable condition where the centrifugal and viscous forces are just in balance (this is also the basis for most other modeling work - note that this does NOT apply to the first stage of spin-up and excess solvent explusion). When the centrifugal and viscous forces are in balance, this equation must be satisfied:      Instead of solving this equation explicitly, Meyerhofer assumed that early stages were entirely flow dominated, while later stages would be entirely evaporation dominated. He set the transition point at the condition where the evaporation rate and the viscous flow rate became equal. This can be thought of as the fluid-dynamical "set" point of the coating process. When these assumptions are made, the final coating thickness, hf, is predicted to be:   Fluid Flow Complications The flow behavior described above ignores several effects that are important for many coating solutions. As noted above, the evaporation step is critical in defining what the final coating thickness will be. But, evaporation occur -- by necessity -- from the top surface, and only some of the solution components are volatile enough to evaporate to any substantial degree. Thus, there will necessarily be an enrichment of the non-volatile components in the surface layer of the coating solution during the spinning process.  The
figure at right illustrates that concept. One of the key consequences is that
this surface layer will very likely have a higher viscosity than the unmodified
starting solution (this may simply be due to the higher concentration, but might
also occur because of cross-linking effects, etc). With a higher viscosity, it
will then impede the flow characteristics set out above, making it a difficult
differential equation to solve directly. And, this surface layer may have the
secondary result of reducing the evaporation rate. So both the evaporation and
flow processes are coupled through the behavior of the "skin" that develops on
the top of the outwardly flowing solution during spin coating. Another important effect is that some solutions are not "Newtonian" in their viscosity/shear-rate relationships. Some solutions change viscosity depending on what shear rate is used, thus depending on distance from the center, the shear rate will be different and thus the flow behavior. This can give radial thickness variation that varies rather smoothly in a radial sense, as pointed out by Britten and Thomas [J. Appl. Phys. 71 (1992) 972-979]. Air Flow Effects Important for Spin CoatingAir Flow Basics (Ideal Case) Air Flow Complications 
The steady flow field described above is limited to cases where the flow is
laminar and where it is "steady". In fact, except for very large wafers, most
spinning conditions DO satisfy the constraint of having laminar flow. However,
there can be un-steady oscillating instabilities in the boundary layer near the
surface of the wafer. These form spiral shaped waves or rolls that are called "Ekman"
spirals. Wahal, et al [Applied Physics Letters 62 (1993) 2584-6]
have experimentally observed Ekman spirals (shown in the figure at right) for
nominally laminar conditions in spin coating. They claim that these
instabilities can lead to coating thickness variations, but have not explained
WHY that would be the case.
Common Defects Found When Spin Coating This is by no means an exhaustive list, but I try to
highlight a number of defects/features that are characteristic of spin coated
films. Comets: These usually
occur when relatively large solid particles impede the normal flow patterns of
the solution on the spinning wafer. Except during "spin up", the flow is
normally smooth and radial in nature (having a gradient in radial velocity
governed by the applicable force balances and viscosity constraints The
presence of comets can be reduced or eliminated by working in cleaner
environments and by filtering coating solutions as part of the dispense process.
Striations:Striations
are radially oriented lines of thickness variation in the as-coated film.
Usually they are quite smoothly varying thickness variations with a spacing or
periodicity in the 50-200 micron range, or so. Their orientation corresponds the
direction of major fluid flow (which is running horizontally in 2 of the 3
the optical micrographs shown below). Their occurance is thought to arise
because of evaporation driven surface tension effects. The early evaporation of
light solvents can cause an enrichment of water and/or other less volatile
species in the surface layer. IF, the surface tension of this layer is larger
than the starting solution (and what still exists at deeper levels), then an
instability exists where the higher surface tension actually draws material in
at regular intervals and the spaces in-between are more able to evaporate, and
surface relief develops. This is essentially due to the Marangoni effect which
governs the development of structures in the drainage patterns of wine down the
sides of a wine glass: ethanol evaporates first leaving an ethanol-depleted wine
layer that gathers into rivulets and drains down the glass wall.
Evaporation driven surface tension effects can create
striations the following way:
Environmental Sensitivity: When making coatings in the ambient environment, it is possible for the surroundings to have an influence on the coating quality. One critical variable is the humidity of the surrounding air. For many solutions, water can play an important role in the chemistry of the solution itself, so when varying amounts of water are present in the surroundings then varying coating quality can result. This can manifest itself as coating roughness, microcracking of the coating upon further drying, exaggerated striation formation in the coating, etc. Obviously, close control of the environment around the spin coater is crucial. Wafer Edge Effects: The edges of the substrate will always be areas of concern. If better uniformity can be maintained out to the edges then more area can be used for device fabrication. The edges are problems for several reasons. First, surface tension effects make it difficult for solution that is flowing radially outward to detach from the wafer. Thus a small "bead" of liquid can stay attached around the entire perimeter and result in thicker coatings in this rim zone. In addition, if substrates are not exactly round and especially if they are square or rectangular, then the air flow over the protruding parts (corners) will be perturbed. Although the flow may still be laminar, it will have different flow history and will usually result in non-uniformity in coating thickness in these corner areas.
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The image at the right, from Millsaps and Pohlhausen, [J.
Aeronautical Sci., (1952) 120-126] shows a schematic of the
ideal airflow field above an infinitely large spinning disk. At the surface of
the disk there is a "no-slip" condition so the contacting air must be exactly
co-rotating --- hence the flow vectors pointing essentially tangentially to any
point at a given radius (and proportional to the distance from the center). At
moderate distances from the surface a centripetal acceleration must be provided
by the viscous effects; this condition is thus maintained only when some outward
radial air flow is also occurring. This outward flow is balanced by some minor
downdraft over the entire wafer. This is a steady state configuration and does
not include inertial effects included in the "spin-up" stages. This air flow
pattern also only hold true so long as the flow is laminar. A "boundary layer"
of uniform thickness thus exists over the entire surface area of the spinning
wafer: it is through this boundary layer that evaporating solvent must diffuse.
Because the boundary layer is constant in thickness over the wafer then the
evaporation rate as a function of position is predicted to also be constant.
Chuck
Marks: These patterns can
be created by thermal "communication" between the solution on top of the wafer
and the metal vacuum chuck on the back side of the wafer . Thus, the thermal
conductivity of the substrate material is very important as is the thermal
driving force (mainly evaporative cooling, but could also be due to temperature
differences between solution and substrate and chuck....). The figure at
right has a single layer sol-gel-derived coating on a glass substrate.Silicon
wafers, because of their higher thermal conductivity, will usually have smaller
thickness differences compared to glass or plastic. 
