# Collimated Magnetron Sputter Deposition for Mirror Coatings

Authors: Anette Vickery; Carsten P. Jensen; Finn E. Christensen; Mads Peter Steenstrup; Troels  Schønfeldt
Journal: X-Ray Optics and Instrumentation
 (2008)

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## Abstract

At the Danish National Space Center (DNSC), a planar magnetron sputtering chamber has been established as a research and production coating facility for curved X-ray mirrors for hard X-ray optics for astronomical X-ray telescopes. In the following, we present experimental evidence that a collimation of the sputtered particles is an efficient way to suppress the interfacial roughness of the produced multilayer. We present two different types of collimation optimized for the production of low roughness curved mirrors and flat mirrors, respectively.


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## Body

## 1. Introduction

Multilayers
play an important role in X-ray optics and are used in a variety of
applications including synchrotron radiation, free electron lasers (FELs),
medical optics, and space-borne X-ray telescopes. The fabrication of
multilayers requires high precision of the layer thickness not only in the
growth direction but also laterally to obtain the desired uniformity or the
thickness gradient with respect to a given application. Further the specular
intensity reflectivity of the multilayer decreases exponentially with the sum
of the squared magnitude of the interface roughness and the interfacial
diffusion.At the Danish National Space Center (DNSC), a planar
DC-magnetron sputtering chamber has been established as a research and
production coating facility for curved X-ray mirrors for hard X-ray optics for
astronomical X-ray telescopes including the HEFT telescopes [1] and the forthcoming NuSTAR
telescopes [2, 3]. This means that this
sputtering facility has been dedicated solely to the production of laterally
homogeneous mirrors with radii of curvature in the range 60–120 mm. For this
reason, the production of long (≈200 mm) flat mirrors for, that is, synchrotron
radiation or FEL optics has not been an option at this facility. However by a
minor change of the coating setup, the sputtering facility has now been
qualified also for production of such mirrors. The first flat homogeneous mirrors
produced at DNSC are used in the focusing optics for the new compact light
source [4] to be
installed at Copenhagen University. The X-ray telescope mirrors typically have
several hundred bilayers with individual bilayer thicknesses as low as 1.5 nm.
Further it is proposed that the capabilities of DNSC are used for developing
X-ray optics for the European X-ray free electron laser (XFEL) which will be
built at the DESY site in Hamburg with first operation planned in 2013.In the following, we present experimental evidence
that a collimation of the sputtered particles is an efficient way to suppress
the interfacial roughness of the produced multilayer. We present two different
types of collimation optimized for the production of homogeneous curved mirrors
and flat mirrors, respectively.All multilayers presented in this paper has been
produced at DNSC using DC-magnetron sputtering. The substrates are commercially
available Si wafers with an rms roughness of about 2.5 Å. The rms
roughness of the multilayers has been determined by measurements of the
specular X-ray intensity reflectivity at CuKα radiation (8.05 keV).


## 2. The Sputtering Chamber

The coating facility at DNSC
is optimized to make multilayer coatings that meet strict quality requirements
for hard X-ray optics and on the same time have a high throughput: it is
possible to coat up to 0.8 m2 per run.Figure1 shows a photograph of the inside of the
magnetron sputtering chamber at DNSC and a top-view sketch of the coating
geometry. The facility is a bell-jar vacuum chamber with a diameter of 1 m and
it is 1.2 m tall. The 4 DC-magnetron sources (the targets) with shutters are
positioned inside the sample carrousel, facing out toward the substrates. On
the photography, two shutters are opened while the remaining two are closed.
The substrates are mounted vertically on the mounting plates of the big sample
carrousel so the coating geometry is cylindrical. There are a total of 18
mounting plates, each 800 mm tall and 125 mm wide and 3 open slots. The
presence of the open slots is to prevent sputtering the substrate when opening
and closing the shutters and accelerating the ring to the desired speed. The
coating rate is strongly dependent on the distance between the target and the
substrate. Therefore, to ensure a reproducible lateral homogeneity of the
produced multilayers, the alignment of the mounting plates is strictly
controlled: the bottom of the mounting plates are fixed by narrow slots on the
sample carousel while the top of the mounting plates are constrained by a steel
ring with the same diameter.(a) The sputtering chamber seen from above. (b) A top-view sketch of the coating geometry. In the horizontal plane the opening angle of each target is limited by achimney to approximately 102°.
(a)(b)During the coating, the targets remain stationary and
when a target shutter is open, material is deposited onto the substrates
passing by. When the coating parameters, Ar pressure, and applied power to the
cathodes have been decided upon, the thickness of each of the materials is
controlled by the rotation speed of the sample carrousel. When producing
multilayers comprised of two different materials normally three of the four
magnetron sources are in operation, so that two of three targets in operation
are equipped with the same material.


## 3. The Collimation of the Sputtered Particles

Here, we
present experimental evidence that for the DC-magnetron sputtering facility at
DNSC, the collimation of the sputtered material is essential in order to
suppress the interface roughness of the deposited multi-layers. We present two
different types of collimators, one which is suitable for the coating of strongly
curved mirrors (radii of curvature in the range 60–120 mm) and another one
suitable for the coating of flat mirrors. In the following, the types of
collimation are referred to as theseparator-plate collimation and the honeycomb collimation, respectively.


### 3.1. Separator-Plate Collimation

#### 3.1.1. Experimental Setup

Figure2(a) shows one curved substrate mounted on a mounting plate between two separator plates. The role of the separator plates is to provide a collimation of the sputtered particles, as explained in the sketch shown in
Figure 2(b). This is a side-view sketch of one target and a substrate during coating. The target is standing vertical and the arrows
symbolize the particles ejected from the target on their way to the substrate
shown to the right. The horizontal lines indicate the separator plates which
provide the collimation and prevent the material symbolized with the red arrows
from reaching the (flat) substrate. The degree of collimation in the vertical
direction is described by the opening angle β of the collimator. In the horizontal
direction, the total opening angle of the chimney around the target is ±51°.(a) Two separator plates and one
curved substrate. The width of the separator plate (S in the sketch below) is
50 mm. (b) For clarity, in this side-view sketch, the chimney around the target has been
left out. The dimensions of the sputtering chamber limits the maximum width of
the separator plates to S = 62 mm.
(a)(b)


#### 3.1.2. Experiment I

For 4 different
pressures of Ar in the chamber, sets of multilayers comprised of 10 bilayers of
W/Si have been produced with different separator plate distances (D in Figure 2(b)). All other parameters
are fixed. The bilayer thickness, the fraction of Si in the multilayer, and the
rms roughness have been determined from the measurements of the specular
intensity reflectivity at Cu Kα radiation. The results of the measurements are shown in Figure 3. From
these data, it can be seen that the coating rate of W is independent of the Ar
pressure and the degree of collimation. In contrast to this, the Si coating
rate decreases with increasing Ar pressure and with increasing degree of
collimation. We interpret this to be an effect of gas scattering: it is
expected that there will be some scattering of the sputtered material on the Ar
atoms. The mass of an Si atom amounts to only 70% of that of Ar, so the paths
of the Si atoms from the target to the substrate are likely to be affected by
scattering. This is in contrast to the W atom, the mass of which is more than 4
times that of the Ar atom. This theory is supported by the data presented in
Figure 3(c): a decrease of the Ar pressure leads to an increase of ΓSi,
that is, the scattering of the Si atoms on the Ar ions is less pronounced the
lower the Ar pressure. In [5], Rossnagel et al. report on similar results for the
deposition rate of collimated magnetron sputtering. Turning toward the
view-graph D, we see that for a given collimation the observed rms roughness
increases with increasing Ar pressure. Further it is clear that an increase of
the angle β also leads to an increase of the rms
roughness.Data from specular
reflectivity measurements of multilayers comprised of 10 bilayers of W/Si. The
substrates are commercially available Si wafers with an rms roughness of about
2.75 Å. For 4 different
pressures of Ar, the viewgraphs show (a) and (b)
the thickness of Si and W versus the opening angleβ. (c) The
fraction of Si ΓSi versus the opening angle β. (d) The
rms roughness versus the opening angle β.
(a)(b)(c)(d)For curved X-ray telescope mirrors, the collimation
has been successfully provided by theseparator plates [1]. The geometry of the
sputtering chamber limits the width of the separator plates to 62 mm, so for β=50° the maximum space between the separator plates
is D=147 mm. This in turn limits the length of the substrates in the vertical
direction and the cylindrical coating geometry limits the dimensions of the
substrates in the horizontal direction. However, regarding the coating of flat
multilayer mirrors, the most severe problem is that the separator plates induce
a strong variation of the coating rate along the length of the substrate (from
now on referred to as the shadowing effect): experiments with D=140 mm and S=50 mm have shown that 50 mm from the center of
the substrate (i.e., toward the ends of the substrate close to the
separator plates), the coating rate has decreased with 15%. It is worth noting that the shadowing effect is beneficial when coating curved samples: due to the cylindrical coating geomtry, the edges of one curved sample are closer to the target than the center of the sample. Therefore, without the shadowing effect, the thickness of the deposited layer would increase dramatically towards the edges of the sample, since the edges are relatively close to the
target [1].


### 3.2. The Honeycomb Collimation

#### 3.2.1. Experimental Setup

Figure4(left) shows a sketch of a
honeycomb mesh. Figures 4(a) and 4(b) show side- and top-view
sketches of one target and a substrate during coating. The target is standing
vertical and the arrows symbolize the particles ejected from the target on
their way to the substrate shown to the right. The dashed vertical line
indicates the honeycomb mesh which provides the collimation and prevents the
material symbolized with the red arrows from reaching the substrate. As shown
in the top-view sketch, the substrate may be mounted with an angle τ to the mounting plate. The degree of
collimation is described either by the solid angle spanned by the mesh or the
opening angle θMAX. θMAX is defined as follows: 99% of the particles
which reaches the substrate has been ejected from the target with a polar angle
smaller θMAX.
In the horizontal direction, the opening angle of the chimney around the target
is ±51°.
This method of collimation preserves the homogeneity defined by the target,
that is, there is no shadowing effect associated with these collimators. The
honeycomb mesh is mounted on the chimney of each target (rather than on the
mounting plates), hence there is no patterning of the substrate from the mesh.
Given the distance between the target and the mesh, the degree of collimation
is dependent on the honeycomb cell diameter and mesh thickness, see Table 1. The honeycomb is electrically floating and is placed between the plasma and the
substrate, so no sputtering of the honeycomb occurs.Table 1
The solid angle spanned by
the honeycomb mesh mounted the distanceℒH=48 mm from the target.
Mesh type123456Mesh thickness (mm)101010555Cell diameter (mm)6.49.612.86.49.612.8Solid angle (st.rad.)0.320.610.880.921.41.8θMAX(°), P(θ)=𝒞314148495864θMAX(°), P(θ) defined by (1), α=1.15314148485762Figure 4
(Left) Sketch of the honeycomb mesh. (a) A
top view of the coating geometry. Here, the flat substrate is mounted on a
wedge defined by the angleτ.
The wedges are designed so the distance between the target and substrate center
is independent of the value of τ. (b) A
side-view sketch of the coating geometry with τ=0.


#### 3.2.2. Experiment II

An experiment
has been performed to investigate the relationship between the angle of
incidence of the sputtered material and the rms roughness. At the DNSC
sputtering facility, substrates were coated with predefined anglesτ to the target, see Figure 4(a). The
angles were {0.0,3.7,6.3,16.3,23.7,26.3,33.7,36.3,43.7}∘.
The collimation of the sputtered material was provided by mesh type 1 (see
Table 1) in order to get as narrow an angular distribution of the particles
incident on the substrates. The substrates were coated with one layer of W on
an Si substrate, and the mean thickness of the coating was 244 Å. The coating
thickness is dependent on cosτ,
where the τ=0° coating has at thickness of 269Å and the τ=43.7° coating has a thickness of 220 Å. Figure 5 shows
that the rms roughness is fairly constant up to τ=30°.
For τ>30°,
the rms roughness is growing at an increasing rate. Similar experimental
results are reported on in [6].Figure 5
The rms roughness versus the tilt angleτ.


#### 3.2.3. Experiment III

The main purpose of this experiment is to identify which mesh is the optimal collimator for the sputtering facility at DNSC, that is, a collimator
which suppress the roughness and preserves an acceptable coating rate. Further
the coating rate associated with each mesh type has been determined and
compared to the mesh geometry in order to estimate an ejection law. We have
produced multilayers with 6 different honeycomb mesh collimators, see Table1.
The Si substrates were mounted with τ=0 and the multilayers are comprised of 10
bilayers of W/Si.The circular data points of Figure6 indicate the rms
roughness of the multilayers versus the solid angle spanned by the honeycomb
mesh collimators (lower x-axis) and θMAX (upper x-axis). The data shows that magnetron
sputtering with mesh types 1–4 as collimators results in multilayers with
similar low roughness. A collimation provided by the large solid angle mesh of
types 5-6 results in multilayers with a larger rms roughness.Figure 6
The mesh is mounted 48 mm from the target. The
circular data points show the rms roughnessσ of multilayers comprised of 10 bilayers of
W/Si; the dashed red line is a guide to the eye. The multilayers have been
produced with different degrees of collimation provided by honeycomb mesh of
types 1–6, see Table 1. The number next to each data point refers to the mesh
type in Table 1 and the gray dashed line indicates the rms roughness of a
[W/Si] multilayer mirror produced with no collimation at all. The lower x-axis indicates the total solid angle spanned
by the mesh while the upper x-axis indicates the value of θMAX (see text). The square data points indicate
the coating rate associated with each mesh.The square data
points indicate the coating rate associated with each of the 6 meshes. Not
surprisingly, there is a different coating rate associated with each mesh, that
is, a collimation with a more transparent mesh results in a bigger coating
rate. The collimation with a large solid angle (type 6) reduces the coating
rate to approximately 50% of the coating rate when there is no collimation at all.The data show
that an increase of the collimation beyond that provided by mesh type 4 will
not affect the rms roughness noteworthy. In order not to decrease the coating
rate unnecessarily the collimation provided by mesh type 4 is chosen as the
optimal collimator for flat mirrors in the current geometry.


#### 3.2.4. Estimation of the Angular Distribution of Particles
Ejected from the Target

Based on the
knowledge of the coating rate associated with each mesh and the mesh geometry,
anejection law, that is the angular distribution of particles ejected
from the target, is estimated. We follow the approach first presented in
[7]. From the ejection
law so derived, we calculate the intensity of sputtered particles which
arrive at the substrate versus the polar angle of ejection. In the
following, the angular distribution of particles incident on the substrate ℐ(θ) is estimated from a simple model which
neglects the scattering of the particles on, that is, the Ar ions/atoms. This
means that the particles ejected from the target are assumed to follow a linear
path to the substrate. This is a good approximation only for the W atoms.
Further, the model does not consider the effects of resputtering and
backscattering from the surface of the substrate. We adopt the model previously
suggested in [7, 8] for the angular distribution P(α,θ) of particles ejected from the target,
(1)P(α,θ)=2cos⁡αα2+(1−α2)cos⁡2θ.
Here, θ is the polar angle and the value of the
parameter α determines the angular width of P(α,θ).
As indicated in the insets of Figure 7, the expression for P(α,θ) is derived by considering an ellipse: the
parameter α is the ratio of the major to minor axis of the
ellipse, and P(α,θ) is the length of a vector with a direction
specified by θ. Ideally, the angular distribution of
particles ejected from each target should be considered independently. However,
following the approach adopted in [7], here is considered an efficient angular distribution
of the two materials (W and Si) together. In [7], a value of α=1 is estimated for the material combination Mo/Si.Figure 7
The angular distributionP(α,θ) of particles ejected from a point on the
target (1). The insets show two different top views of the target during
sputtering. The length of the vector with the direction specified by θ is a measure of the amount of material ejected
in that direction. In both cases shown, the intensity of ejected particles is
strongest in the forward direction toward the substrate and decreases with
increasing angle θ.First, the solid angleΦtot spanned by a honeycomb mesh is calculated. For
this calculation, it is convenient to define a coordinate-system oriented as
shown in Figure 8. Further it is convenient to define a function 𝒯(x,y,ℒH) which describes the transparency of a given
mesh which is placed the distance ℒH from the target. This function assumes the
value 1 if the mesh is transparent (corresponding to the green areas of Figure
8) and 0 otherwise.Figure 8
The view from the point(0,0) at the target through a honeycomb mesh. (see
text).For the remaining calculations, it is practical to
calculate the solid angle in the following way: the points(x,y) of a circle with the center at (0,0) are sharing the same polar angle θ,
that is, the dashed circle of Figure 8 corresponds to the polar angle θ0=arccos(ℒH/R02+ℒH2).
The number of particles ejected from the point (0,0) at the target which are transmitted with the
angle θ0 is then proportional to Φ(θ0),
where
(2)Φ(θ0)=∑(x,y)|x2+y2=R0T(x,y)Δx⁢Δy(ℒH/cos⁡θ0)2,and the total solid angle is
then calculated according to(3)Φtot=∑θΦ(θ).Note that Φ(θ) is defined with a point of origin at (0,0).
Since not only this point but all points (x,y) of the target contribute with ejected
particles, the number of particles per time ℐ(θ) transmitted through the mesh is calculated as
an average over all points of the target,(4)ℐ(θ)∝P(α,θ)〈Φ(θ)〉target.Within this model the coating
rate is proportional to(5)∑θℐ(θ)∝∑θP(α,θ)〈Φ(θ)〉target.The coating rate has been determined
experimentally for the 6 honeycomb mesh in question, and the functionΦ(θ) is determined (numerically) from the geometry
of each mesh according to (2). This means that we are now in a position to
estimate the ejection law P(α,θ) for the material combination W/Si by using α as a fitting parameter.It is worth
noting that if the angular distribution of particles ejected from the target
could be described byP(θ)=𝒞,
where 𝒞 is a constant, the coating rate associated
with one mesh would be directly proportional to the solid angle Φtot spanned by that mesh. The black squares of
Figure 9(a) show the coating rate versus the spanned solid angle Φtot (the lower X-axis). The dashed line is a
linear fit y to the data points Y.
Figure 9(b) compares the goodness of the fits (GOF) defined as(6)GOF=1−∑i(Yi−yi)2∑i(Yi−〈Y〉)2.Here, (Yi−yi) is the deviation of one data point Yi from the fit yi and (Yi−〈Y〉) is the deviation of one data point from a
horizontal line through mean value of all the data points. The dashed line
indicates the goodness of the linear fit to the coating rate versus Φtot,
and the solid line indicates GOF versus the parameter α.
The best fit is obtained with α=1.15.(a) The
coating rate increases with the total solid angle. The black square data points
indicate the coating rate versus the solid angle (lowerX-axis), and the black dashed
line is a linear fit assuming that P(θ)=𝒞 in (5). The red circles show the coating rate
versus the sum over theta of Φ(θ)P(α,θ) (5) with α=1.15 (upper X-axis). (b) The goodness of the linear fits (GOF) of the coating rate to (5) versus the
parameter α.
The dashed line indicates GOF for P(θ)=𝒞.
The red circle marks the maximum of GOF corresponding to the value α=1.15.
(a)(b)


#### 3.2.5. Estimation of the Transmitted Intensity versus Polar Angle

Figure10 shows the transmitted particle
intensity ℐ(θ) versus the polar angle θ as defined in (4). The view graphs compare ℐ(θ) calculated with the assumption of P(α=1.15,θ) with ℐ(θ) calculated with P(α,θ)=𝒞.
These curves have maximum between ∼15° (type 1) and ∼30° (type 6) and FWHM in the range from ∼22° (type 1) to ∼40° (type 6). The red regions mark the range of
angles which is excluded by the separator plate collimation when the distance
between the plates is 60 mm and the plates are 50 mm wide. From the six curves,
only the blue ones have tails inside the red areas which indicate the range θ>51°.
The curves indicate that the angular particle distribution of the DNSC system
is strongly dependent on the properties of the honeycomb collimator. As shown
in Figure 6, magnetron sputtering with a collimation provided by the mesh of
types 5 and 6 results in multilayers with a relatively large rms roughness
compared to that obtained with the mesh types 1–4.The number of sputtered particles transmitted through
the mesh versus the polar angleθ calculated according to (4). The green and
blue curves are calculated with P(α,θ) described by (1) with α=1.15.
The gray curves are calculated with P(θ)=𝒞.
(a)(b)(c)(d)(e)(f)Table1
compares the values of θMAX calculated with the two different models for
the angular distribution of particles ejected from the target, namely, P(α,θ)=𝒞 and P(α,θ) defined by (1) with α=1.15.
As expected from Figure 10, the two different models for P(θ) give similar results for θMAX.


## 3.1. Separator-Plate Collimation

### 3.1.1. Experimental Setup

Figure2(a) shows one curved substrate mounted on a mounting plate between two separator plates. The role of the separator plates is to provide a collimation of the sputtered particles, as explained in the sketch shown in
Figure 2(b). This is a side-view sketch of one target and a substrate during coating. The target is standing vertical and the arrows
symbolize the particles ejected from the target on their way to the substrate
shown to the right. The horizontal lines indicate the separator plates which
provide the collimation and prevent the material symbolized with the red arrows
from reaching the (flat) substrate. The degree of collimation in the vertical
direction is described by the opening angle β of the collimator. In the horizontal
direction, the total opening angle of the chimney around the target is ±51°.(a) Two separator plates and one
curved substrate. The width of the separator plate (S in the sketch below) is
50 mm. (b) For clarity, in this side-view sketch, the chimney around the target has been
left out. The dimensions of the sputtering chamber limits the maximum width of
the separator plates to S = 62 mm.
(a)(b)


### 3.1.2. Experiment I

For 4 different
pressures of Ar in the chamber, sets of multilayers comprised of 10 bilayers of
W/Si have been produced with different separator plate distances (D in Figure 2(b)). All other parameters
are fixed. The bilayer thickness, the fraction of Si in the multilayer, and the
rms roughness have been determined from the measurements of the specular
intensity reflectivity at Cu Kα radiation. The results of the measurements are shown in Figure 3. From
these data, it can be seen that the coating rate of W is independent of the Ar
pressure and the degree of collimation. In contrast to this, the Si coating
rate decreases with increasing Ar pressure and with increasing degree of
collimation. We interpret this to be an effect of gas scattering: it is
expected that there will be some scattering of the sputtered material on the Ar
atoms. The mass of an Si atom amounts to only 70% of that of Ar, so the paths
of the Si atoms from the target to the substrate are likely to be affected by
scattering. This is in contrast to the W atom, the mass of which is more than 4
times that of the Ar atom. This theory is supported by the data presented in
Figure 3(c): a decrease of the Ar pressure leads to an increase of ΓSi,
that is, the scattering of the Si atoms on the Ar ions is less pronounced the
lower the Ar pressure. In [5], Rossnagel et al. report on similar results for the
deposition rate of collimated magnetron sputtering. Turning toward the
view-graph D, we see that for a given collimation the observed rms roughness
increases with increasing Ar pressure. Further it is clear that an increase of
the angle β also leads to an increase of the rms
roughness.Data from specular
reflectivity measurements of multilayers comprised of 10 bilayers of W/Si. The
substrates are commercially available Si wafers with an rms roughness of about
2.75 Å. For 4 different
pressures of Ar, the viewgraphs show (a) and (b)
the thickness of Si and W versus the opening angleβ. (c) The
fraction of Si ΓSi versus the opening angle β. (d) The
rms roughness versus the opening angle β.
(a)(b)(c)(d)For curved X-ray telescope mirrors, the collimation
has been successfully provided by theseparator plates [1]. The geometry of the
sputtering chamber limits the width of the separator plates to 62 mm, so for β=50° the maximum space between the separator plates
is D=147 mm. This in turn limits the length of the substrates in the vertical
direction and the cylindrical coating geometry limits the dimensions of the
substrates in the horizontal direction. However, regarding the coating of flat
multilayer mirrors, the most severe problem is that the separator plates induce
a strong variation of the coating rate along the length of the substrate (from
now on referred to as the shadowing effect): experiments with D=140 mm and S=50 mm have shown that 50 mm from the center of
the substrate (i.e., toward the ends of the substrate close to the
separator plates), the coating rate has decreased with 15%. It is worth noting that the shadowing effect is beneficial when coating curved samples: due to the cylindrical coating geomtry, the edges of one curved sample are closer to the target than the center of the sample. Therefore, without the shadowing effect, the thickness of the deposited layer would increase dramatically towards the edges of the sample, since the edges are relatively close to the
target [1].


## 3.1.1. Experimental Setup

Figure2(a) shows one curved substrate mounted on a mounting plate between two separator plates. The role of the separator plates is to provide a collimation of the sputtered particles, as explained in the sketch shown in
Figure 2(b). This is a side-view sketch of one target and a substrate during coating. The target is standing vertical and the arrows
symbolize the particles ejected from the target on their way to the substrate
shown to the right. The horizontal lines indicate the separator plates which
provide the collimation and prevent the material symbolized with the red arrows
from reaching the (flat) substrate. The degree of collimation in the vertical
direction is described by the opening angle β of the collimator. In the horizontal
direction, the total opening angle of the chimney around the target is ±51°.(a) Two separator plates and one
curved substrate. The width of the separator plate (S in the sketch below) is
50 mm. (b) For clarity, in this side-view sketch, the chimney around the target has been
left out. The dimensions of the sputtering chamber limits the maximum width of
the separator plates to S = 62 mm.
(a)(b)


## 3.1.2. Experiment I

For 4 different
pressures of Ar in the chamber, sets of multilayers comprised of 10 bilayers of
W/Si have been produced with different separator plate distances (D in Figure 2(b)). All other parameters
are fixed. The bilayer thickness, the fraction of Si in the multilayer, and the
rms roughness have been determined from the measurements of the specular
intensity reflectivity at Cu Kα radiation. The results of the measurements are shown in Figure 3. From
these data, it can be seen that the coating rate of W is independent of the Ar
pressure and the degree of collimation. In contrast to this, the Si coating
rate decreases with increasing Ar pressure and with increasing degree of
collimation. We interpret this to be an effect of gas scattering: it is
expected that there will be some scattering of the sputtered material on the Ar
atoms. The mass of an Si atom amounts to only 70% of that of Ar, so the paths
of the Si atoms from the target to the substrate are likely to be affected by
scattering. This is in contrast to the W atom, the mass of which is more than 4
times that of the Ar atom. This theory is supported by the data presented in
Figure 3(c): a decrease of the Ar pressure leads to an increase of ΓSi,
that is, the scattering of the Si atoms on the Ar ions is less pronounced the
lower the Ar pressure. In [5], Rossnagel et al. report on similar results for the
deposition rate of collimated magnetron sputtering. Turning toward the
view-graph D, we see that for a given collimation the observed rms roughness
increases with increasing Ar pressure. Further it is clear that an increase of
the angle β also leads to an increase of the rms
roughness.Data from specular
reflectivity measurements of multilayers comprised of 10 bilayers of W/Si. The
substrates are commercially available Si wafers with an rms roughness of about
2.75 Å. For 4 different
pressures of Ar, the viewgraphs show (a) and (b)
the thickness of Si and W versus the opening angleβ. (c) The
fraction of Si ΓSi versus the opening angle β. (d) The
rms roughness versus the opening angle β.
(a)(b)(c)(d)For curved X-ray telescope mirrors, the collimation
has been successfully provided by theseparator plates [1]. The geometry of the
sputtering chamber limits the width of the separator plates to 62 mm, so for β=50° the maximum space between the separator plates
is D=147 mm. This in turn limits the length of the substrates in the vertical
direction and the cylindrical coating geometry limits the dimensions of the
substrates in the horizontal direction. However, regarding the coating of flat
multilayer mirrors, the most severe problem is that the separator plates induce
a strong variation of the coating rate along the length of the substrate (from
now on referred to as the shadowing effect): experiments with D=140 mm and S=50 mm have shown that 50 mm from the center of
the substrate (i.e., toward the ends of the substrate close to the
separator plates), the coating rate has decreased with 15%. It is worth noting that the shadowing effect is beneficial when coating curved samples: due to the cylindrical coating geomtry, the edges of one curved sample are closer to the target than the center of the sample. Therefore, without the shadowing effect, the thickness of the deposited layer would increase dramatically towards the edges of the sample, since the edges are relatively close to the
target [1].


## 3.2. The Honeycomb Collimation

### 3.2.1. Experimental Setup

Figure4(left) shows a sketch of a
honeycomb mesh. Figures 4(a) and 4(b) show side- and top-view
sketches of one target and a substrate during coating. The target is standing
vertical and the arrows symbolize the particles ejected from the target on
their way to the substrate shown to the right. The dashed vertical line
indicates the honeycomb mesh which provides the collimation and prevents the
material symbolized with the red arrows from reaching the substrate. As shown
in the top-view sketch, the substrate may be mounted with an angle τ to the mounting plate. The degree of
collimation is described either by the solid angle spanned by the mesh or the
opening angle θMAX. θMAX is defined as follows: 99% of the particles
which reaches the substrate has been ejected from the target with a polar angle
smaller θMAX.
In the horizontal direction, the opening angle of the chimney around the target
is ±51°.
This method of collimation preserves the homogeneity defined by the target,
that is, there is no shadowing effect associated with these collimators. The
honeycomb mesh is mounted on the chimney of each target (rather than on the
mounting plates), hence there is no patterning of the substrate from the mesh.
Given the distance between the target and the mesh, the degree of collimation
is dependent on the honeycomb cell diameter and mesh thickness, see Table 1. The honeycomb is electrically floating and is placed between the plasma and the
substrate, so no sputtering of the honeycomb occurs.Table 1
The solid angle spanned by
the honeycomb mesh mounted the distanceℒH=48 mm from the target.
Mesh type123456Mesh thickness (mm)101010555Cell diameter (mm)6.49.612.86.49.612.8Solid angle (st.rad.)0.320.610.880.921.41.8θMAX(°), P(θ)=𝒞314148495864θMAX(°), P(θ) defined by (1), α=1.15314148485762Figure 4
(Left) Sketch of the honeycomb mesh. (a) A
top view of the coating geometry. Here, the flat substrate is mounted on a
wedge defined by the angleτ.
The wedges are designed so the distance between the target and substrate center
is independent of the value of τ. (b) A
side-view sketch of the coating geometry with τ=0.


### 3.2.2. Experiment II

An experiment
has been performed to investigate the relationship between the angle of
incidence of the sputtered material and the rms roughness. At the DNSC
sputtering facility, substrates were coated with predefined anglesτ to the target, see Figure 4(a). The
angles were {0.0,3.7,6.3,16.3,23.7,26.3,33.7,36.3,43.7}∘.
The collimation of the sputtered material was provided by mesh type 1 (see
Table 1) in order to get as narrow an angular distribution of the particles
incident on the substrates. The substrates were coated with one layer of W on
an Si substrate, and the mean thickness of the coating was 244 Å. The coating
thickness is dependent on cosτ,
where the τ=0° coating has at thickness of 269Å and the τ=43.7° coating has a thickness of 220 Å. Figure 5 shows
that the rms roughness is fairly constant up to τ=30°.
For τ>30°,
the rms roughness is growing at an increasing rate. Similar experimental
results are reported on in [6].Figure 5
The rms roughness versus the tilt angleτ.


### 3.2.3. Experiment III

The main purpose of this experiment is to identify which mesh is the optimal collimator for the sputtering facility at DNSC, that is, a collimator
which suppress the roughness and preserves an acceptable coating rate. Further
the coating rate associated with each mesh type has been determined and
compared to the mesh geometry in order to estimate an ejection law. We have
produced multilayers with 6 different honeycomb mesh collimators, see Table1.
The Si substrates were mounted with τ=0 and the multilayers are comprised of 10
bilayers of W/Si.The circular data points of Figure6 indicate the rms
roughness of the multilayers versus the solid angle spanned by the honeycomb
mesh collimators (lower x-axis) and θMAX (upper x-axis). The data shows that magnetron
sputtering with mesh types 1–4 as collimators results in multilayers with
similar low roughness. A collimation provided by the large solid angle mesh of
types 5-6 results in multilayers with a larger rms roughness.Figure 6
The mesh is mounted 48 mm from the target. The
circular data points show the rms roughnessσ of multilayers comprised of 10 bilayers of
W/Si; the dashed red line is a guide to the eye. The multilayers have been
produced with different degrees of collimation provided by honeycomb mesh of
types 1–6, see Table 1. The number next to each data point refers to the mesh
type in Table 1 and the gray dashed line indicates the rms roughness of a
[W/Si] multilayer mirror produced with no collimation at all. The lower x-axis indicates the total solid angle spanned
by the mesh while the upper x-axis indicates the value of θMAX (see text). The square data points indicate
the coating rate associated with each mesh.The square data
points indicate the coating rate associated with each of the 6 meshes. Not
surprisingly, there is a different coating rate associated with each mesh, that
is, a collimation with a more transparent mesh results in a bigger coating
rate. The collimation with a large solid angle (type 6) reduces the coating
rate to approximately 50% of the coating rate when there is no collimation at all.The data show
that an increase of the collimation beyond that provided by mesh type 4 will
not affect the rms roughness noteworthy. In order not to decrease the coating
rate unnecessarily the collimation provided by mesh type 4 is chosen as the
optimal collimator for flat mirrors in the current geometry.


### 3.2.4. Estimation of the Angular Distribution of Particles
Ejected from the Target

Based on the
knowledge of the coating rate associated with each mesh and the mesh geometry,
anejection law, that is the angular distribution of particles ejected
from the target, is estimated. We follow the approach first presented in
[7]. From the ejection
law so derived, we calculate the intensity of sputtered particles which
arrive at the substrate versus the polar angle of ejection. In the
following, the angular distribution of particles incident on the substrate ℐ(θ) is estimated from a simple model which
neglects the scattering of the particles on, that is, the Ar ions/atoms. This
means that the particles ejected from the target are assumed to follow a linear
path to the substrate. This is a good approximation only for the W atoms.
Further, the model does not consider the effects of resputtering and
backscattering from the surface of the substrate. We adopt the model previously
suggested in [7, 8] for the angular distribution P(α,θ) of particles ejected from the target,
(1)P(α,θ)=2cos⁡αα2+(1−α2)cos⁡2θ.
Here, θ is the polar angle and the value of the
parameter α determines the angular width of P(α,θ).
As indicated in the insets of Figure 7, the expression for P(α,θ) is derived by considering an ellipse: the
parameter α is the ratio of the major to minor axis of the
ellipse, and P(α,θ) is the length of a vector with a direction
specified by θ. Ideally, the angular distribution of
particles ejected from each target should be considered independently. However,
following the approach adopted in [7], here is considered an efficient angular distribution
of the two materials (W and Si) together. In [7], a value of α=1 is estimated for the material combination Mo/Si.Figure 7
The angular distributionP(α,θ) of particles ejected from a point on the
target (1). The insets show two different top views of the target during
sputtering. The length of the vector with the direction specified by θ is a measure of the amount of material ejected
in that direction. In both cases shown, the intensity of ejected particles is
strongest in the forward direction toward the substrate and decreases with
increasing angle θ.First, the solid angleΦtot spanned by a honeycomb mesh is calculated. For
this calculation, it is convenient to define a coordinate-system oriented as
shown in Figure 8. Further it is convenient to define a function 𝒯(x,y,ℒH) which describes the transparency of a given
mesh which is placed the distance ℒH from the target. This function assumes the
value 1 if the mesh is transparent (corresponding to the green areas of Figure
8) and 0 otherwise.Figure 8
The view from the point(0,0) at the target through a honeycomb mesh. (see
text).For the remaining calculations, it is practical to
calculate the solid angle in the following way: the points(x,y) of a circle with the center at (0,0) are sharing the same polar angle θ,
that is, the dashed circle of Figure 8 corresponds to the polar angle θ0=arccos(ℒH/R02+ℒH2).
The number of particles ejected from the point (0,0) at the target which are transmitted with the
angle θ0 is then proportional to Φ(θ0),
where
(2)Φ(θ0)=∑(x,y)|x2+y2=R0T(x,y)Δx⁢Δy(ℒH/cos⁡θ0)2,and the total solid angle is
then calculated according to(3)Φtot=∑θΦ(θ).Note that Φ(θ) is defined with a point of origin at (0,0).
Since not only this point but all points (x,y) of the target contribute with ejected
particles, the number of particles per time ℐ(θ) transmitted through the mesh is calculated as
an average over all points of the target,(4)ℐ(θ)∝P(α,θ)〈Φ(θ)〉target.Within this model the coating
rate is proportional to(5)∑θℐ(θ)∝∑θP(α,θ)〈Φ(θ)〉target.The coating rate has been determined
experimentally for the 6 honeycomb mesh in question, and the functionΦ(θ) is determined (numerically) from the geometry
of each mesh according to (2). This means that we are now in a position to
estimate the ejection law P(α,θ) for the material combination W/Si by using α as a fitting parameter.It is worth
noting that if the angular distribution of particles ejected from the target
could be described byP(θ)=𝒞,
where 𝒞 is a constant, the coating rate associated
with one mesh would be directly proportional to the solid angle Φtot spanned by that mesh. The black squares of
Figure 9(a) show the coating rate versus the spanned solid angle Φtot (the lower X-axis). The dashed line is a
linear fit y to the data points Y.
Figure 9(b) compares the goodness of the fits (GOF) defined as(6)GOF=1−∑i(Yi−yi)2∑i(Yi−〈Y〉)2.Here, (Yi−yi) is the deviation of one data point Yi from the fit yi and (Yi−〈Y〉) is the deviation of one data point from a
horizontal line through mean value of all the data points. The dashed line
indicates the goodness of the linear fit to the coating rate versus Φtot,
and the solid line indicates GOF versus the parameter α.
The best fit is obtained with α=1.15.(a) The
coating rate increases with the total solid angle. The black square data points
indicate the coating rate versus the solid angle (lowerX-axis), and the black dashed
line is a linear fit assuming that P(θ)=𝒞 in (5). The red circles show the coating rate
versus the sum over theta of Φ(θ)P(α,θ) (5) with α=1.15 (upper X-axis). (b) The goodness of the linear fits (GOF) of the coating rate to (5) versus the
parameter α.
The dashed line indicates GOF for P(θ)=𝒞.
The red circle marks the maximum of GOF corresponding to the value α=1.15.
(a)(b)


### 3.2.5. Estimation of the Transmitted Intensity versus Polar Angle

Figure10 shows the transmitted particle
intensity ℐ(θ) versus the polar angle θ as defined in (4). The view graphs compare ℐ(θ) calculated with the assumption of P(α=1.15,θ) with ℐ(θ) calculated with P(α,θ)=𝒞.
These curves have maximum between ∼15° (type 1) and ∼30° (type 6) and FWHM in the range from ∼22° (type 1) to ∼40° (type 6). The red regions mark the range of
angles which is excluded by the separator plate collimation when the distance
between the plates is 60 mm and the plates are 50 mm wide. From the six curves,
only the blue ones have tails inside the red areas which indicate the range θ>51°.
The curves indicate that the angular particle distribution of the DNSC system
is strongly dependent on the properties of the honeycomb collimator. As shown
in Figure 6, magnetron sputtering with a collimation provided by the mesh of
types 5 and 6 results in multilayers with a relatively large rms roughness
compared to that obtained with the mesh types 1–4.The number of sputtered particles transmitted through
the mesh versus the polar angleθ calculated according to (4). The green and
blue curves are calculated with P(α,θ) described by (1) with α=1.15.
The gray curves are calculated with P(θ)=𝒞.
(a)(b)(c)(d)(e)(f)Table1
compares the values of θMAX calculated with the two different models for
the angular distribution of particles ejected from the target, namely, P(α,θ)=𝒞 and P(α,θ) defined by (1) with α=1.15.
As expected from Figure 10, the two different models for P(θ) give similar results for θMAX.


## 3.2.1. Experimental Setup

Figure4(left) shows a sketch of a
honeycomb mesh. Figures 4(a) and 4(b) show side- and top-view
sketches of one target and a substrate during coating. The target is standing
vertical and the arrows symbolize the particles ejected from the target on
their way to the substrate shown to the right. The dashed vertical line
indicates the honeycomb mesh which provides the collimation and prevents the
material symbolized with the red arrows from reaching the substrate. As shown
in the top-view sketch, the substrate may be mounted with an angle τ to the mounting plate. The degree of
collimation is described either by the solid angle spanned by the mesh or the
opening angle θMAX. θMAX is defined as follows: 99% of the particles
which reaches the substrate has been ejected from the target with a polar angle
smaller θMAX.
In the horizontal direction, the opening angle of the chimney around the target
is ±51°.
This method of collimation preserves the homogeneity defined by the target,
that is, there is no shadowing effect associated with these collimators. The
honeycomb mesh is mounted on the chimney of each target (rather than on the
mounting plates), hence there is no patterning of the substrate from the mesh.
Given the distance between the target and the mesh, the degree of collimation
is dependent on the honeycomb cell diameter and mesh thickness, see Table 1. The honeycomb is electrically floating and is placed between the plasma and the
substrate, so no sputtering of the honeycomb occurs.Table 1
The solid angle spanned by
the honeycomb mesh mounted the distanceℒH=48 mm from the target.
Mesh type123456Mesh thickness (mm)101010555Cell diameter (mm)6.49.612.86.49.612.8Solid angle (st.rad.)0.320.610.880.921.41.8θMAX(°), P(θ)=𝒞314148495864θMAX(°), P(θ) defined by (1), α=1.15314148485762Figure 4
(Left) Sketch of the honeycomb mesh. (a) A
top view of the coating geometry. Here, the flat substrate is mounted on a
wedge defined by the angleτ.
The wedges are designed so the distance between the target and substrate center
is independent of the value of τ. (b) A
side-view sketch of the coating geometry with τ=0.


## 3.2.2. Experiment II

An experiment
has been performed to investigate the relationship between the angle of
incidence of the sputtered material and the rms roughness. At the DNSC
sputtering facility, substrates were coated with predefined anglesτ to the target, see Figure 4(a). The
angles were {0.0,3.7,6.3,16.3,23.7,26.3,33.7,36.3,43.7}∘.
The collimation of the sputtered material was provided by mesh type 1 (see
Table 1) in order to get as narrow an angular distribution of the particles
incident on the substrates. The substrates were coated with one layer of W on
an Si substrate, and the mean thickness of the coating was 244 Å. The coating
thickness is dependent on cosτ,
where the τ=0° coating has at thickness of 269Å and the τ=43.7° coating has a thickness of 220 Å. Figure 5 shows
that the rms roughness is fairly constant up to τ=30°.
For τ>30°,
the rms roughness is growing at an increasing rate. Similar experimental
results are reported on in [6].Figure 5
The rms roughness versus the tilt angleτ.


## 3.2.3. Experiment III

The main purpose of this experiment is to identify which mesh is the optimal collimator for the sputtering facility at DNSC, that is, a collimator
which suppress the roughness and preserves an acceptable coating rate. Further
the coating rate associated with each mesh type has been determined and
compared to the mesh geometry in order to estimate an ejection law. We have
produced multilayers with 6 different honeycomb mesh collimators, see Table1.
The Si substrates were mounted with τ=0 and the multilayers are comprised of 10
bilayers of W/Si.The circular data points of Figure6 indicate the rms
roughness of the multilayers versus the solid angle spanned by the honeycomb
mesh collimators (lower x-axis) and θMAX (upper x-axis). The data shows that magnetron
sputtering with mesh types 1–4 as collimators results in multilayers with
similar low roughness. A collimation provided by the large solid angle mesh of
types 5-6 results in multilayers with a larger rms roughness.Figure 6
The mesh is mounted 48 mm from the target. The
circular data points show the rms roughnessσ of multilayers comprised of 10 bilayers of
W/Si; the dashed red line is a guide to the eye. The multilayers have been
produced with different degrees of collimation provided by honeycomb mesh of
types 1–6, see Table 1. The number next to each data point refers to the mesh
type in Table 1 and the gray dashed line indicates the rms roughness of a
[W/Si] multilayer mirror produced with no collimation at all. The lower x-axis indicates the total solid angle spanned
by the mesh while the upper x-axis indicates the value of θMAX (see text). The square data points indicate
the coating rate associated with each mesh.The square data
points indicate the coating rate associated with each of the 6 meshes. Not
surprisingly, there is a different coating rate associated with each mesh, that
is, a collimation with a more transparent mesh results in a bigger coating
rate. The collimation with a large solid angle (type 6) reduces the coating
rate to approximately 50% of the coating rate when there is no collimation at all.The data show
that an increase of the collimation beyond that provided by mesh type 4 will
not affect the rms roughness noteworthy. In order not to decrease the coating
rate unnecessarily the collimation provided by mesh type 4 is chosen as the
optimal collimator for flat mirrors in the current geometry.


## 3.2.4. Estimation of the Angular Distribution of Particles
Ejected from the Target

Based on the
knowledge of the coating rate associated with each mesh and the mesh geometry,
anejection law, that is the angular distribution of particles ejected
from the target, is estimated. We follow the approach first presented in
[7]. From the ejection
law so derived, we calculate the intensity of sputtered particles which
arrive at the substrate versus the polar angle of ejection. In the
following, the angular distribution of particles incident on the substrate ℐ(θ) is estimated from a simple model which
neglects the scattering of the particles on, that is, the Ar ions/atoms. This
means that the particles ejected from the target are assumed to follow a linear
path to the substrate. This is a good approximation only for the W atoms.
Further, the model does not consider the effects of resputtering and
backscattering from the surface of the substrate. We adopt the model previously
suggested in [7, 8] for the angular distribution P(α,θ) of particles ejected from the target,
(1)P(α,θ)=2cos⁡αα2+(1−α2)cos⁡2θ.
Here, θ is the polar angle and the value of the
parameter α determines the angular width of P(α,θ).
As indicated in the insets of Figure 7, the expression for P(α,θ) is derived by considering an ellipse: the
parameter α is the ratio of the major to minor axis of the
ellipse, and P(α,θ) is the length of a vector with a direction
specified by θ. Ideally, the angular distribution of
particles ejected from each target should be considered independently. However,
following the approach adopted in [7], here is considered an efficient angular distribution
of the two materials (W and Si) together. In [7], a value of α=1 is estimated for the material combination Mo/Si.Figure 7
The angular distributionP(α,θ) of particles ejected from a point on the
target (1). The insets show two different top views of the target during
sputtering. The length of the vector with the direction specified by θ is a measure of the amount of material ejected
in that direction. In both cases shown, the intensity of ejected particles is
strongest in the forward direction toward the substrate and decreases with
increasing angle θ.First, the solid angleΦtot spanned by a honeycomb mesh is calculated. For
this calculation, it is convenient to define a coordinate-system oriented as
shown in Figure 8. Further it is convenient to define a function 𝒯(x,y,ℒH) which describes the transparency of a given
mesh which is placed the distance ℒH from the target. This function assumes the
value 1 if the mesh is transparent (corresponding to the green areas of Figure
8) and 0 otherwise.Figure 8
The view from the point(0,0) at the target through a honeycomb mesh. (see
text).For the remaining calculations, it is practical to
calculate the solid angle in the following way: the points(x,y) of a circle with the center at (0,0) are sharing the same polar angle θ,
that is, the dashed circle of Figure 8 corresponds to the polar angle θ0=arccos(ℒH/R02+ℒH2).
The number of particles ejected from the point (0,0) at the target which are transmitted with the
angle θ0 is then proportional to Φ(θ0),
where
(2)Φ(θ0)=∑(x,y)|x2+y2=R0T(x,y)Δx⁢Δy(ℒH/cos⁡θ0)2,and the total solid angle is
then calculated according to(3)Φtot=∑θΦ(θ).Note that Φ(θ) is defined with a point of origin at (0,0).
Since not only this point but all points (x,y) of the target contribute with ejected
particles, the number of particles per time ℐ(θ) transmitted through the mesh is calculated as
an average over all points of the target,(4)ℐ(θ)∝P(α,θ)〈Φ(θ)〉target.Within this model the coating
rate is proportional to(5)∑θℐ(θ)∝∑θP(α,θ)〈Φ(θ)〉target.The coating rate has been determined
experimentally for the 6 honeycomb mesh in question, and the functionΦ(θ) is determined (numerically) from the geometry
of each mesh according to (2). This means that we are now in a position to
estimate the ejection law P(α,θ) for the material combination W/Si by using α as a fitting parameter.It is worth
noting that if the angular distribution of particles ejected from the target
could be described byP(θ)=𝒞,
where 𝒞 is a constant, the coating rate associated
with one mesh would be directly proportional to the solid angle Φtot spanned by that mesh. The black squares of
Figure 9(a) show the coating rate versus the spanned solid angle Φtot (the lower X-axis). The dashed line is a
linear fit y to the data points Y.
Figure 9(b) compares the goodness of the fits (GOF) defined as(6)GOF=1−∑i(Yi−yi)2∑i(Yi−〈Y〉)2.Here, (Yi−yi) is the deviation of one data point Yi from the fit yi and (Yi−〈Y〉) is the deviation of one data point from a
horizontal line through mean value of all the data points. The dashed line
indicates the goodness of the linear fit to the coating rate versus Φtot,
and the solid line indicates GOF versus the parameter α.
The best fit is obtained with α=1.15.(a) The
coating rate increases with the total solid angle. The black square data points
indicate the coating rate versus the solid angle (lowerX-axis), and the black dashed
line is a linear fit assuming that P(θ)=𝒞 in (5). The red circles show the coating rate
versus the sum over theta of Φ(θ)P(α,θ) (5) with α=1.15 (upper X-axis). (b) The goodness of the linear fits (GOF) of the coating rate to (5) versus the
parameter α.
The dashed line indicates GOF for P(θ)=𝒞.
The red circle marks the maximum of GOF corresponding to the value α=1.15.
(a)(b)


## 3.2.5. Estimation of the Transmitted Intensity versus Polar Angle

Figure10 shows the transmitted particle
intensity ℐ(θ) versus the polar angle θ as defined in (4). The view graphs compare ℐ(θ) calculated with the assumption of P(α=1.15,θ) with ℐ(θ) calculated with P(α,θ)=𝒞.
These curves have maximum between ∼15° (type 1) and ∼30° (type 6) and FWHM in the range from ∼22° (type 1) to ∼40° (type 6). The red regions mark the range of
angles which is excluded by the separator plate collimation when the distance
between the plates is 60 mm and the plates are 50 mm wide. From the six curves,
only the blue ones have tails inside the red areas which indicate the range θ>51°.
The curves indicate that the angular particle distribution of the DNSC system
is strongly dependent on the properties of the honeycomb collimator. As shown
in Figure 6, magnetron sputtering with a collimation provided by the mesh of
types 5 and 6 results in multilayers with a relatively large rms roughness
compared to that obtained with the mesh types 1–4.The number of sputtered particles transmitted through
the mesh versus the polar angleθ calculated according to (4). The green and
blue curves are calculated with P(α,θ) described by (1) with α=1.15.
The gray curves are calculated with P(θ)=𝒞.
(a)(b)(c)(d)(e)(f)Table1
compares the values of θMAX calculated with the two different models for
the angular distribution of particles ejected from the target, namely, P(α,θ)=𝒞 and P(α,θ) defined by (1) with α=1.15.
As expected from Figure 10, the two different models for P(θ) give similar results for θMAX.


## 4. Summary

At the
sputtering facility of DNSC, it has been shown that the collimation of the
sputtered particles plays an important role in the production of W/Si
multilayers with low rms roughness. Two methods of collimation have been
presented, they are referred to as the separator plate collimation and the
honeycomb mesh collimation, respectively.In experiments I and III [W/Si] multilayers were produced
by DC-magnetron sputtering with different degrees of collimation of the
sputtered particles. In experiment I we used the separator plate collimation,
whereas the honeycomb mesh collimation was used in experiment III. In both
experiments we saw that the multilayers produced with collimators opaque for
sputtered particles with polar angles exceeding∼50° have similar low (3.5 Å  rms) interface
roughness. When particles with polar angles above ∼50° are allowed to pass on to the substrate, a
strong increase of the interface roughness is observed. Regarding the honeycomb
mesh collimation, for each mesh the particle flux versus the polar angle has
been estimated from the mesh geometry. For the sputtering facility at DNSC, the
mesh of type 4 is the optimal collimator, since this mesh suppresses the
roughness and has the highest coating rate.In experiment II single layers of W were deposited on
Si substrates. Here, the sputtered particles were collimated by mesh type 1,
which is the mesh spanning the smallest solid angle and hence providing the most
narrow particle flux distribution versus the polar angle. The substrates were
mounted on wedges defining the angleτ to the target. It is important to note that
the angle of incidence of the particles on the substrate is not defined by τ alone: the particle flux allowed by mesh type
1 is centered around 15° and has a width of approximately 22°.
We observed a strong increase of the roughness for τ>∼35°.
Taking into account that the maximum particle flux is at a polar angle of 15°, this is in correspondence with the results
of experiments I and III.The honeycomb mesh collimators qualify the
sputtering chamber for the coating of low-roughness multilayer mirrors. The
length of the substrates which can be coated at DNSC is now limited only by the
length of the targets. By utilizing this new type of collimators, DNSC has
produced the multilayer mirrors for an optical element [9] for the next generation
X-ray source, the compact light source [4].



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*Source: 792540-2008-06-15.xml*