phases. The grating equation showsthat a single grating with spacing dcauses scatter into the angle, σ,according to: sin σ = λ/d where λ is
the wavelength of light. d can beconsidered as one spatial wavelength
present on the surface, or accordingly,
f = 1/d as one spatial frequency. At arandomly rough surface (such as ourthin film component), many different
spatial frequencies are present. This isquantitatively expressed by the PowerSpectral Density (PSD), giving therelative strength of each roughness
component of a surface microstructure
as a function of spatial frequency.3
The red curve in Figure 2a shows thePSD of the thin film of Figure 1. Inorder to cover an extended range ofspatial frequencies, we combined thePSD curves from 1µm x 1µm and10µm x 10µm scans. Also given inFigure 2a is the PSD of the uncoatedsubstrate (black curve). It is obviousthat at low spatial frequencies (i.e.
roughness components of larger lateralextension) the PSD of the coatingcoincides with the PSD of thesubstrate, which means that thesubstrate microstructures replicated by
the film determine the PSD in thisregion. The thin film structure isrepresented by the “bump” in the PSD
at frequencies above 10µm-1. Now
look at the bars indicating the spatial
frequency region to which a typical
total integrated backscattering
measurement (with the scattering angle
typically extending from 2° to 85°)3
would be sensitive when performed in
the visible and ultraviolet region (forinstance at 633nm, 248nm and193nm). It is obvious that neither in thevisible, nor in the UV, does the film
structure cause any measurable scatter;i.e., the scattering is dominated by thesubstrate. Hence, the PSD reveals thatin this case, reduction of scatter loss
can only be achieved by improving
the substrate polish, not by changing
the deposition parameters.

Figure 2a. PSD curves calculated from AFM measurements
for an uncoated quartz substrate (black curve), the LaF3 film(red curve), a three-layer fluoride system (blue curve), and a
HR multilayer fluoride system (green curve). The bars indicate
the spatial frequency ranges to which scattering measurements
at various wavelengths are sensitive. See text for usefulconclusions drawn from data.

The blue curve in Figure 2a is the PSD
for a 3-layer system of alternating
LaF3/MgF2 layers on a quartz
substrate. First, we see the overall
increase in roughness – to 2.7nm –relative to the single layer (1.3nm, seeabove). The most important change,
however, is the shift of the “bump”
towards lower spatial frequencies. In
the visible range, this does not cause
any significant scattering effect, but inthe UV the effect is significant.
Now consider a multilayer system
consisting of 42 alternating
MgF2/LaF3 layers, designed as aHR-mirror for 248nm, again on aquartz substrate. The corresponding
AFM image of the film morphology isshown in Figure 2b. The structures
have extended both in height andwidth, with an rms roughness of 6nm(for the 500nm scan size of Figure 2b).
In addition, the PSD (green curve) inFigure 2a reveals that the “bump” hassignificantly broadened and extended
to low frequencies, indicating that thefilm structure is now the dominating
factor affecting scatter, even in thevisible range.

Figure 2b. AFM image of the surface
structures of a HR multilayer of 42 alternating
MgF2 LaF3 films. 500nm scan.

Scattering Measurements
Using a total integrated scattering
apparatus (described in detailelsewhere4), the total backscattering at
248nm on the multilayer system justdescribed was 1%. The scattering of
the uncoated quartz substrate was0.004%. The increase in scattering,
attributed to the enhancement ofreflection caused by the mirror system,
would result in a scatter value about
one order of magnitude lower. Thus,
the measured scattering of the fluoride
coating is in fact governed by themicrostructure of the films.
But does this mean that in the case ofa multilayer system the film structures
will be the dominant factor determining
scatter, whatever the substrate and thefilm material? Not at all. The same
fluoride multilayer system discussedwas also deposited onto a MgF2
substrate, which is useful in certain
Excimer laser applications. Figures 3
and 4 show 10µm x 10µm imagesof the multilayer on quartz and MgF2,respectively. Differences can beperceived (scratches on the MgF2
substrate which are replicated by thefilm), but they do not appear to cause
tremendous differences in scattering.
Again, the corresponding PSDs
provide the answer. Figure 5a and 5bcompare the PSDs of the multilayer
coating on quartz and MgF2,respectively. For the coating on MgF2,
the PSD indicates that at 633nm thesubstrate-related scatter will clearly
dominate (note that the smallenhancement after coating around 0.1
to 0.2µm-1 is caused by formations oflarger defects that occasionally occur
when the films are deposited on MgF2substrates). Even at 248nm, theinfluence of the substrate is still verysignificant, and only at shorter
wavelengths does the film structure
become dominant for the scatter. Thishas been proven experimentally. The
measured total scattering at 248nm
was 1% for the system on quartz, and
3% for the same system on MgF2. So
the scatter losses of the two samples
differ by a factor of three as a resultof the different substrate qualities.

a.

Figure 3. AFM image of the surface of theHR multilayer when deposited on a quartz
substrate. 10µm scan.

Figure 4. AFM image of the surface of theHR multilayer when deposited on an MgF2substrate. 10µm scan.

What the PSDs reveal here is that forthe system on the MgF2 substrate, any
improvement of the deposition process
would hardly be worthwhile. This
substrate topography effect illustrates
the influence substrate polish can haveon the overall coating microtopography
and related scatter in general. For
instance, with CaF2 becoming amaterial of choice in UV-lithography, thequestion of how much polishing quality
matters relative to thin film microstructure
is becoming increasingly important –especially since high-quality polishingof this material is difficult to achieve.

Returning to the case of the multilayer
system on the smooth quartz substrate,
the height and location of the “bump”
in the PSD curve quantify the effect thefilm structure has on the scattering loss
at a particular wavelength.
Improvement of the optical coating
here requires improvement of thedeposition process such that the bumpheight is reduced (smoother structure),or shifted further out of the spatial
frequency region of scattering (growingof structures with lower diameters).
Ideally, both improvements shouldbe achieved.

b.

Figure 5ab. PSD curves of the HR multilayers on quartz (a) and MgF2 (b) together with the PSDs for the uncoated substrates (black curves).