March tutorial-REV 2

Charles Dingee

Informations

• Publié par: Phawyug
• Nombre de lectures: 13
• Langue: English

Extrait

tutorial
Accurately measuring surface
roughness requires under-
standing the capabilities
and drawbacks of your
instrument.
Rough
By Theodore Vorburger and Joseph Fu,
National Institute of Standards and
Technology, and Ndubuisi Orji, University of
North Carolina Charlotte
S urface roughness affects the function of a wide variety of
engineering components, including airport runways, highways,
ship hulls, and mechanical parts. Perhaps the most demanding
applications are in the optics and semiconductor industries.
Surface roughness causes scattering and stray light in optical documentary standards and has often been represented by σ in
1-3systems and degrades the contrast and sharpness of optical the optics literature.
images, so in general, the smoother the surface, the better the Because surface profiles z(x) are closely approximated in
component will function. nearly all modern instruments by a digitized set of points z , thei
In the optics industry, the terms “surface roughness” and above formula is replaced in practice by its digital equivalent:
“surface finish” are synonymous. The rms roughness is perhaps
the most widely used parameter for specification of the rough-
ness of optical surfaces. For high-performance optics, such as
those in lithographic steppers, space optics, and laser gyro sys-
tems, the rms roughness is specified in the subnanometer range.
If the measured surface topography is represented as a surface where N is the number of data points in a measured surface
profile z(x), the rms roughness (Rq) is defined as the root mean profile.
square of the deviations of the surface profile z(x) from the If the measured surface topography is represented as a 3-D
mean line (see figure 1). That is, topographic image z , the analogous formula isij
where L is the length of the surface profile along the x-direc- where the S indicates that the quantity is averaged over a sur-
tion. The rms roughness is currently designated by Rq or R in face, and N × N is the number of pixels in the image. Forq x y
march 2002 spie’s oemagazine 31|topographic images, Rq and ARq can represent rms roughness. the quantity measured by the instrument is related to a statistical
parameter of the surface roughness by modeling the probe-sur-
measuring roughness face interaction. An example of an area averaging technique is
According to the American Society of Mechanical Engineers angle-resolved light scattering (ARLS), which is closely related to
(ASME) standard, techniques for the measurement of surface the amount of stray light produced by the surface, an important
roughness may be classified as profiling methods, area profiling functional property. We will emphasize the profiling and area
methods, and area averaging methods. Profiling methods probe profiling techniques here.
the peaks and valleys of the surface under test with a high-resolu- A number of profiling techniques are capable of measuring
tion probe that senses the height of the surface and produces a surfaces with subnanometer roughness, which is characteristic of
4quantitative surface profile z . Area profiling methods extend the the finest optical surfaces. These include stylus-based profiling,i
5 6technique into three dimensions, either by rastering a series of phase-shifting interferometric microscopy, Nomarski profiling,
7profiles or by some type of quantitative imaging process. and atomic force microscopy.
In contrast to these approaches, area averaging methods do not A stylus-based profiler incorporates a stylus that traverses the
involve measuring the resolved surface topography z or z at all. surface in direct contact at low force, moving up and down as itij i
Rather, an area of the surface under test is probed all at once, and rides over the surface peaks and valleys. The instrument converts
the vertical motion of the stylus to an electrical signal, often by
magnetic or optical displacement-sensing techniques, thus pro-
ducing the surface profile z(x). The lateral resolution is limited by
the lateral dimensions of the stylus tip, which can be as small as
80.1 µm or less. The surface profile of silicon nitride (Si N )3 4
shown in figure 2, for example, has a measured Rq value of 0.06
nm—approximately one-fifth the size of a typical atom in a solid.
Such small values are possible because the stylus tip, roughly 1
µm in diameter, is bearing on and averaging over a number of
surface atoms at once, thus producing a smoothing effect in the
surface profile. Although this measured profile is dominated by
instrument noise, such a small Rq value shows both the quality of
Figure 1 A surface roughness profile z(x) can be
the surface and the quality of the instrument. We can tell both
approximated by digital means (z …z ).1 N that the surface is mighty smooth and that the instrument can
measure mighty smooth surfaces.
One disadvantage of the contacting stylus instrument is the
potential for surface damage. Optical techniques such as phase-
shifting interferometric microscopy avoid this because they are
non-contacting. The phase-shifting interferometric microscope
(PSIM) has the additional advantage that it is generally based on
electronic imaging technology and, hence, is an area profiling
technique producing a topography image z . The PSIM is capa-ij
ble of z-resolution in the 0.1-nm range, particularly if a
reasonable degree of signal averaging is used and if the imperfec-
Figure 2 This stylus instrument profile of a Si N film on tions of the reference surface of the instrument are separated3 4
8
fused silica yields an Rq value of 0.06 nm. from the measured surface topography (see figure 3).
The Nomarski profiler uses an interferometric height differ-
encing technique to measure surface profiles z(x) over surface
lengths up to about 100 mm. The noise resolution for this differ-
encing technique over a roughness sampling length of about 80
µm is in the 0.01-nm range.
The atomic force microscope (AFM) produces the highest lat-
eral resolution of the four techniques. The achievable lateral
resolution can be 1 nm or less. Under optimal conditions, indi-
vidual atoms can be resolved on certain types of surfaces. An
AFM operates similar to a stylus instrument. A probe tip
mounted on a cantilever contacts the surface. Two modes of con-
tact are typically used: a contact mode with an extremely low
contact force, or an intermittent contact mode in which the can-
tilever is vibrationally excited. Any deflection of the cantilever orFigure 3 Phase-shifting interferometric microscope produced
change in the mechanical vibration characteristics due to interac-this surface topographic image of a silicon carbide surface,
tion with the surface peaks and valleys produces a signal in ayielding a calculated Rq value of 0.12 nm. This method uses
piezoelectric or optical sensor. This signal is held at a null value,averaging and reference surface subtraction techniques
usually by displacing the surface in the z-direction to compensatedescribed in reference 5.
for any sensed z-change. The driving signal for the surface z-dis-
32 spie’s oemagazine march 2002| placement yields a topographic image of the surface for a wide
9range of measurement conditions (see figure 4).
The AFM is especially useful for measuring optical surfaces
with high lateral resolution. This may be important when mon-
itoring surface defects for manufacturing process control. It is
also important when studying surfaces designed for short opti-
cal wavelengths, such as mirrors working in the extreme
ultraviolet (EUV) with a wavelength of 13.6 nm.
understanding measurement
Figure 4 2.5 nm × 2.5 nm AFM image of an individualThus, there are several useful profiling or area profiling tech-
molecule of sorbic acid on a well-ordered graphiteniques for studying optical surfaces. AFM is advantageous if high
surface clearly shows the atomic corrugations of thelateral resolution is required. The Nomarski profiler is a conve-
9
graphite. (Measurements taken by T. Albrecht, D. Smith,nient way to measure long profiles. Interferometric microscopy is
and C. Quate.)best for measuring topography of a significant area of a surface.
The stylus method offers good sensitivity and dynamic range in
both the lateral and vertical directions.
One important fact to note is that the rms roughness is not an
intrinsic property of the surface. Rather, roughness on a surface is
analogous to noise arising in time-series data. The value of rms
roughness depends on the bandwidth of surface spatial wave-
10lengths that the instrument can sense. That means that two
important parameters should be specified for any measurement
of a surface parameter such as rms roughness: the lateral resolu-
tion, which represents the finest spatial wavelengths that can be
measured; and the sampling length, which is approximately equal
Figure 5 Topographic image of a rectangular profileto the longest spatial wavelengths that are measured. It is impor-
roughness specimen measured with an AFM has atant to know the values for these two limiting factors for any
calculated roughness of 0.5 nm.measurement condition.
Usually only one of several factors limits the lateral resolution
for a particular measurement. These factors include probe-tip size
in the case of a stylus or the point-spread function in the case of
an optical microscope.