Multi-scale Fluid Flow Simulations
Wednesday 1st January 2003
WET
ETCH IS ONE OF THE MOST IMPORTANT PROCESSES FOR PRODUCING SEMICONDUCTOR
DEVICES. TO INCREASE COST AND WORK EFFICIENCY, WAFERS HAVE STEADILY
INCREASED IN SIZE, NOW REACHING 300MM IN DIAMETER. MEANWHILE, STRUCTURES
HAVE BEEN DECREASING. THEREFORE, ACCURACY OF WET ETCH HAS TO IMPROVE,
TOO. BERTRAM SCHOTT AND JAROSLAW KACZYNSKI OF CTR
AND ANDREAS BALDY OF SEZ GIVE AN OVERVIEW OF EFFORTS
TO IMPROVE THE QUALITY OF SINGLE-WAFER WET ETCHING EQUIPMENT THROUGH
COMPUTATIONAL FLUID DYNAMICS SIMULATIONS OF FLOWS AROUND THE WAFER
TO OPTIMISE GEOMETRIES AND PROCESSING PARAMETERS.
Untitled Document
Multi-scale
fluid flow simulations
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WET
ETCH IS ONE OF THE MOST IMPORTANT PROCESSES FOR PRODUCING SEMICONDUCTOR
DEVICES. TO INCREASE COST AND WORK EFFICIENCY, WAFERS HAVE STEADILY
INCREASED IN SIZE, NOW REACHING 300MM IN DIAMETER. MEANWHILE, STRUCTURES
HAVE BEEN DECREASING. THEREFORE, ACCURACY OF WET ETCH HAS TO IMPROVE,
TOO. BERTRAM SCHOTT AND JAROSLAW KACZYNSKI OF CTR
AND ANDREAS BALDY OF SEZ GIVE AN OVERVIEW OF EFFORTS
TO IMPROVE THE QUALITY OF SINGLE-WAFER WET ETCHING EQUIPMENT THROUGH
COMPUTATIONAL FLUID DYNAMICS SIMULATIONS OF FLOWS AROUND THE WAFER
TO OPTIMISE GEOMETRIES AND PROCESSING PARAMETERS.
|
Spin-process
technology has been developed over the past decade for the
wet chemical etching of single wafers such as by Austrian
semiconductor equipment company SEZ. This equipment includes
a rotating chuck inside the process chamber to carry the wafer.
The process chamber can have more than one vertically aligned
level to allow for different consecutive etching processes
within a single run. The wafer is placed on the chuck with
the side to be processed facing up and the etchant is supplied
from above (Figure 1). This particular design allows for high
uniformity and unmatched repeatability of etch process, while
the overall single process time can be significantly reduced,
compared to wet bench processes. However, despite the uniformity
of the etching process being very high at smaller wafer size,
etching can become non-uniform on the larger 300mm diameter
wafers.
When
examining equipment from the viewpoint of fluid dynamics,
we are dealing with multi-component flow in a partly rotating
coordinate system. The mathematical description of such a
complex problem based on the Navier-Stokes equation is complicated,
though well known. However, solving the governing partial
differential equations numerically is computationally very
expensive.
In
the following sections we will show, that numerical simulations
do allow for unprecedented insights into the fluid flow characteristics
involved in spin-process technology. Results can successfully
be applied to improve the design of equipment.
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Fig.1:
Overview of the equipment used in spin-processing. The
central parts are the rotating chuck and the surrounding
chamber with four different processing levels
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Spin-process
characteristics
The central point of the spin-process is
a fluid jet impinging on a solid rotating
disk in a gaseous atmosphere, resulting
in a two-phase flow.This situation has previously
been tackled in the context of the sputtering
of fluids impinging on rotating disks. The
fluid develops a thin velocity boundary
layer (BL) on the wafer’s surface.
The physical conditions in this BL govern
the etch rate and, therefore, the amount
of material being removed from the surface.
The
purpose of examining this model is to find
a suitable combination of fluid influx and
spin rate. If the spin rate is too low,
the etchant is not thrown off the wafer’s
edge by the centrifugal forces, but instead
can creep into the gap between wafer and
chuck, where it can cause damage. A high
spin rate helps avoiding this problem, but
can then cause other problems.
Consider
a rotating hydrophilic wafer with the fluid
applied along the axis of rotation.
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Fluid
particles sticking to the wafer move with
a tangential velocity v ö =R. Fluid
particles in contact with the surrounding
atmosphere move with a radial velocity v
r, too. The tangential velocity far exceeds
v r at a moderate angular velocity ù
, because of the large radius of the wafers
(up to 150mm for 300mm diameters). This
leads to the prediction that chemical reactants
from the etching process will not be adequately
removed from the wafer beyond a certain
radius, if the spin rate is high. Only the
centre of the wafer would be etched in such
circumstances.
A
good understanding of the fluid flow characteristics
is therefore a prerequisite for design optimisation.
In
this study, computational fluid dynamics
(CFD) models were applied to the spin process.
The partial differential equations governing
fluid flow - the Navier-Stokes equations
- were solved numerically by applying the
commercial CFD software FLUENT that uses
finite volume (FV) techniques.
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Fig.2:
Development of a thin fluid film on a
rotating wafer in an axisymmetric CFD model of two-phase flow
of water (red) in air (blue). The left vertical boundary is
the axis of rotation and gravity is pointing downwards.
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Fig.4:
Gas flow in the spin-processor visualised by streamlines
coloured due to velocity magnitude. Left is an existing
design with thin exhaust channels and therefore high flow
resistance. Right is a possible new design with wider exhaust
channels and lower flow resistance.
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Fine-scale
to mid-scale models-two-phase flow
The
structures to be resolved by the FV grid are tiny compared
with the model diameter of about 300mm. The fluid film
developing on the wafer is only about 0.1mm thick, requiring
a ten times finer FV grid. Because
of this large range of length-scales - almost five orders
of magnitude - it is necessary to split the model into
sub-models to keep the simulations efficient.
The
axisymmetric model of a fluid jet impinging at the centre
of a rotating wafer in a gaseous atmosphere is such
a typical sub-model (Fig 2). The rotating wafer is modelled
as a moving boundary condition (BC). The fluid is poured
from above. The flow is driven by gravity and rotation.
Key
parameters determining the thickness of the fluid film
developing on the rotating wafer are the fluid influx
and the wafer’s spin rate. Here, the influx was
3litres/min and the spin rate was 300 rotations a second,
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resulting
in an equilibrium fluid film thickness of about 0.05mm
in the outer part of the wafer (Figure 2). This model
result is consistent with the thickness derived by assuming
a force balance between the Coriolis and frictional
forces.
The
thin fluid film can break-up when the wafer’s surface
is changing from hydrophilic to hydrophobic during the
etch process. A too-thin fluid film could also evaporate
when the etch process is based on a highly exothermal
chemical reaction. Both effects would lead to an inhomogeneous
etch rate.
A
solution to these problems is to supply the etchant
away from the centre of the wafer. However, the model
has to be fully 3D in this case, and develops a complex
interaction between impinging jet and rotating fluid
layer. A hydraulic jump appears, which can be the source
of droplets emerging from its turbulent bulge, and the
central part of the wafer can dry up (Figure 3), depending
on the surface tension between
wafer and etchant.
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Large-scale
models: single-phase flow
A simulation of the “whole” spin-process chamber,
with the rotating chuck inside, includes all parts shown in
Figure 1, except wafer and fluid supplying boom. As a result,
the flow is restricted to the surrounding atmosphere and the
model can be simulated with reasonable effort.
Model
results show the gas flow in the process chamber. These results
are used to optimise the overall geometry for homogeneous
flow conditions. The design aims at a low flow resistance
to allow for a high “wind” speed inside the process
chamber.Figure 4 shows an example of an optimised geometry.
The first design, not based on CFD simulations (left), had
quite narrow exhaust channels and consequently a high flow
resistance. A design based on CFD simulations (right) has
wider exhaust channels with significantly reduced flow resistance.
These
results contrast with use experimental trial-and-error. Visualising
the flow inside the spin-process chamber through experiment
would be much too expensive. Hence, CFD simulations are becoming
more and more popular in industries such as semiconductor
production, which deal with fluid flows that need high levels
of control. However, the numerical models are limited by the
available computational power, which currently do not allow
for time dependent calculations of multi-phase flow.
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Fig.3:
Development of a thin fluid film on a rotating wafer in a three-dimensional
CFD model of two-phase flow of water (red) in air (blue). The
blue eye in the centre of the wafer indicates a hole in the
fluid film. A elevated water-air interface with fingering instabilities,
as shown on the right, would lead to the formation of drops |
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