Calibration standard for microroughness measuring instruments

A metrology standard that is useful for calibrating instruments for the levels of microroughness encountered in semiconductor, disk drive, and related industries today. In advanced applications, this level is about 5 .ANG. rms in a 0.01-1.0 .mu.m.sup.-1 spatial bandwidth range. This standard uses a one-dimensional square wave pattern etched in a silicon wafer to reduce the effects of instrument spatial bandwidth. The standard has approximately a 20 .mu.m pitch with feature depths as small as 8 .ANG..

TECHNICAL FIELD 
The invention relates to a microroughness standard for calibrating 
instruments such as optical surface profilometers, mechanical profilers, 
and scanning probe microscopes. 
BACKGROUND ART 
Microroughness is defined as "surface roughness components with spacings 
between irregularities (spatial wavelength) less than about 100 
micrometers." This definition differentiates microroughness from the 
larger scale surface variations of bow and warp, which have spatial 
wavelengths typically on the order of several millimeters. 
The very small levels of surface texture associated with microroughness are 
becoming more problematical in a number of industries as the complexity of 
integrated circuits and the amount of information stored on disk drives 
increases. As an example, geometries in the integrated circuit industry 
are fast approaching molecular dimensions. The June 1994 report, the 
National Technology Roadmap for Semiconductors (NTRS), has published a 
requirement for gate oxide thicknesses approaching 4.5 nm.+-.4%. As a 
point of reference, the lattice constant for lightly doped (i.e., nearly 
pure) silicon is 0.543 nm. The gate dielectric molecule, silicon dioxide, 
is nominally 0.355 nm "diameter" (based on the cube root of the volume 
ratio). The ability of silicon dioxide or any film layer to function 
efficiently as an insulator depends partially on the underlying 
microroughness of the silicon surface. For oxides less than 10 nm, 
breakdown voltages are reduced commensurately with increased levels of 
microroughness. This can be readily understood by envisioning the "peaks" 
of the microroughness terrain as being much closer to the film surface 
than the overall average level of the peaks and valleys combined. 
Additionally, there are similar effects on film layers deposited in later 
processing steps, and an effect on bonding for silicon-on-insulator (SOI) 
applications. 
Currently, there are several techniques available for measuring 
microroughness. However, the results tend to be qualitative. Until 
recently, there was no metrology standard available to correlate the 
accuracy of various instruments. This becomes especially important when 
comparing instruments with differing spatial bandwidths, each possessing a 
unique transfer function. Due to the varying spatial bandwidths, different 
types of instruments can give rms microroughness values that differ by 
over an order of magnitude, even when measuring the same surface. 
An object of the invention is to provide a calibration standard used to 
verify the accuracy and precision of analytical test equipment for 
measuring microroughness, and thereby allow such equipment to provide 
absolute quantitative values based on such a standard instead of the 
relative qualitative results that are presently all that is available. 
DISCLOSURE OF THE INVENTION 
The object is met by a metrology standard for calibrating microroughness 
measuring instruments, which comprises a physical artifact having a 
generally smooth reflective surface, such as a clean, polished single 
crystal silicon wafer, providing a low level of isotropic background 
roughness, but with regular features formed on that surface. These 
features are characterized by a one-dimensional, 50% duty cycle, square 
wave pattern, such as a series of parallel, spaced apart, raised flat 
linear plateaus or mesas with essentially vertical sides alternating with 
parallel, spaced apart flat linear valleys between the mesas formed on the 
wafer surface, with the features having a periodicity or pitch of less 
than 100 .mu.m, and preferably about 20 .mu.m, and a single known feature 
depth of at least about 8 .ANG.. This square wave pattern of features with 
a 50% duty cycle produces a one-dimensional power spectral distribution 
(PSD) which is not a continually smooth distribution, but rather has 
discrete peaks with 90% of the spectral power in the immediate spatial 
frequency range of the inverse of the pattern's pitch and with other peaks 
located at odd order harmonics of that primary or fundamental peak, as 
predicted by the Fourier transform of a square wave with 50% duty cycle. 
With a preferred 20 .mu.m pitch, the primary spatial frequency peak is at 
0.05 .mu.m.sup.-1, which is in the range available to most measurement 
instruments. Because 90% of the power is at this spatial frequency peak, a 
fairly accurate measure of rms-microroughness can be obtained using this 
standard even when the exact spatial bandwidth of the instrument is 
unknown, assuming that at least this first peak is captured. 
Calibrating a microroughness measuring instrument involves placing the 
metrology standard in microroughness measuring relation to the instrument 
and measuring the microroughness of the standard. This measurement 
includes calculation of the observed PSD over a range of spatial 
frequencies characteristic of the instrument, including the primary 90% 
power peak, then integrating the PSD over the measured spatial frequency 
range and taking the square root of the integrated PSD. The root is a 
measure of rms-roughness of the standard. Comparing the roughness value 
obtained in this way with a calculated roughness value associated with the 
known feature depth of the standard allows a user to calibrate the 
instrument to obtain a quantitative measure of microroughness of any 
surface that is subsequently placed in the instrument. (This can be 
obtained by measurement with a proven instrument.) Multiple standards with 
different single known feature depths, or a single standard with different 
single known feature depths in different quadrants or regions of the 
wafer, could be used. Instruments that can be calibrated with this 
standard include mechanical profilers, atomic force microscopes, optical 
profilometers, interferometers, total integrated scatterometers and 
angle-resolved scatterometers.

BEST MODE FOR CARRYING OUT THE INVENTION 
I. Introduction 
The RQS (from the abbreviation for rms-roughness, Rq standard) uses a 
one-dimensional square wave to reduce the effects of bandwidth. Although 
the spatial bandwidth of the instrument is still important to know for the 
most accurate readings, the RQS makes use of the nature of the square wave 
to allow for fast, albeit somewhat less accurate, measurements with 
similar results obtained for many different types of microroughness 
measuring instruments. These concepts are discussed in detail below in 
sections II (Instrument Considerations) and IV (Determination of Specific 
Microroughness Values). The methodology used to produce this standard 
provides a known surface texture on a substrate with feature depths on 
different standards ranging from 1 nm to 10 nm. Generally, there is a 
single feature depth on any given standard, although different quadrants 
or regions of a wafer might contain different standards. In either case, 
different feature depths are not mixed. This is accomplished by precisely 
etching a square wave feature into silicon at known locations on a wafer, 
as seen in FIGS. 1-4. The imparted texture is fully quantifiable by angle 
resolved light scattering, measurements performed by atomic force 
microscopy, and other measurement techniques. By having these data 
available and knowing the spatial bandwidth of a given instrument, it is 
possible to provide a direct method of quantifying a prescribed surface 
texture or microroughness value. 
With reference to FIG. 1, a silicon wafer 10 is shown divided into a 
plurality of imaginary sections 12. The wafer is a highly polished 
semiconductor substrate, i.e., a bare polished wafer. The sections 12 are 
not physically marked on the wafer and do not extend all the way to the 
edge of the wafer. The sections 12 are for the purpose of indicating that 
selected sections, such as a checkerboard pattern, could be used to 
contain features of the present invention. Alternatively, the entire 
surface may be covered with the features, which are designed to mimic the 
effect of haze on a highly polished wafer surface. 
In FIG. 2, an enlargement of zone 11 of wafer 10 in FIG. 1 shows a pattern 
of parallel linear features 15 and 17 with regular pitch. In the sectional 
view in FIG. 3 and enlarged perspective view of FIG. 4, it is seen that 
the pattern consists of alternating raised and depressed features which 
form plateaus or mesas 15 and valleys or troughs 17 separated by 
essentially vertical side walls. Both the mesas 15 and valleys 17 have an 
essentially flat surface. The period or pitch is preferably about 20 .mu.m 
and both the mesas 15 and valleys 17 have the same width of about 10 
.mu.m, providing a 50% duty cycle for both types of features 15 and 17 in 
the overall pattern. 
FIG. 4 also shows parameters for an atomic force microscopy scan of the 
square-wave structure. In order to characterize surfaces, it is useful to 
calculate statistical properties from the measurement data obtained from 
various instruments. The two most widely used of these parameters are the 
centerline average roughness, R.sub.a, and rms roughness, R.sub.q 
(equation 1). Roughness values are calculated from the measured values of 
height variation, Z.sub.i, over a portion of a surface with a given number 
of sample points, N. 
##EQU1## 
However, these parameters do not uniquely define a given surface as 
surfaces with completely different profiles may have identical height 
averages. FIGS. 5a and 5b contrast two significantly different surfaces 
exhibiting the same measured rms roughness value. 
Moreover, measured roughness averages will depend on the spatial bandwidths 
over which they are taken. Surface texture is fractal in nature. A 
measurement system that samples, say, every 10 micrometers of a surface 
would totally miss the high spatial frequency variations on Surface I in 
FIG. 5a and reduce its average roughness. This produces a microroughness 
value that is much lower than would be obtained had it sampled every 1 
micrometer. 
A more complete surface quantification that takes instrument spatial 
bandwidth into account is the power spectral density (PSD) curve. The PSD 
function is the frequency spectrum of the surface roughness measured in 
units of spatial frequency, typically inverse micrometers. The PSD 
function provides information about both the amplitude and spatial 
wavelength (1/.function.) of the surface. From the PSD data, readings from 
various instruments may be correlated by incorporating their spatial 
bandwidths. This concept will be discussed in more detail later. 
II. Instrument Considerations In Determination Of Microroughness 
Consider the surface from FIG. 5a, magnified to show a similar section 5 
.mu.m in length. As seen in FIGS. 6a and 6b if this surface is measured by 
an instrument which samples, say, every 0.5 .mu.m (FIG. 6b) as opposed to 
every 0.1 .mu.m (FIG. 6a), then the reported surface tends to look 
smoother since the high spatial frequencies are missed. This is analogous 
to the electrical phenomenon of aliasing. In this case however, rather 
than sampling a time-varying function at too low of rate, a 
spatially-varying function is sampled too infrequently for a proper 
representation of the actual surface. In other words, the high end spatial 
frequency capability (measured in units of inverse micrometers) of the 
sampling instrument is too low. On the other extreme, if the warp in a 200 
mm silicon wafer is measured by a stylus profilometer with a traversing 
length of 50 .mu.m, it never senses the warped condition of the surface. 
Since the warp in the wafer tends to be near the wafer diameter, this 
implies that the spatial wavelength is 200 mm (or, conversely, a spatial 
frequency of 5.times.10.sup.-6 .mu.m.sup.-1). 
The high frequency limit, f.sub.max, of an instrument may be calculated 
directly by knowing the sampling distance, .tau..sub.0, where .tau..sub.0 
is greater than or equal to the lateral resolution of the instrument. 
##EQU2## 
The factor of 2 in the denominator assures that the minimum Nyquist length 
criterion is met. This helps to minimize aliasing effects. 
The low frequency limit, f.sub.min, is simply determined from the 
evaluation length, L, such that 
##EQU3## 
where L is less than or equal to the traversing length, L.sub.t. The 
spatial bandwidth (or bandpass) is then defined by these spatial frequency 
limits, or may be electronically narrowed (e.g., an electrical cut-off 
filter on a stylus profilometer). 
In the case of a laser based instrument, such as an integrating 
scatterometer, the bandpass is defined somewhat differently. If the 
incident monochromatic laser beam, at incidence angle .theta..sub.i, 
specular beam and scatter beams (at angles .theta..sub.s) are all in the 
same plane, the spatial frequency is related to the scatter angle by the 
one-dimensional grating equation 
##EQU4## 
where f is the spatial frequency and .lambda. is the laser illumination 
wavelength. The .phi..sub.s term takes on values of 1.0 and -1.0 for 
.phi..sub.s =0.degree. and 180.degree. respectively. 
Ideally, the instrument transfer function is flat in the bandpass region 
and zero elsewhere. This is never achieved in practice and the spatial 
bandpass must always be convolved with the transfer function (if 
available) in order to achieve true inter-instrument comparisons. 
Referring back to FIG. 6a, the first surface is reported by an instrument 
with a high frequency limit of at least 5 .mu.m.sup.-1 (f.sub.max 
=1/2.multidot.(0.1 .mu.m)). This instrument reports an rms roughness level 
of 2.73 .ANG.. In FIG. 6b, the second instrument is reporting 2.54 .ANG. 
rms but has a high-end limit of 1 .mu.m.sup.-1 (f.sub.max =1/2(0.5 
.mu.m)). However, this could be the same instrument with a low-pass filter 
employed. It is shown later that this difference in reported roughness can 
be much more drastic with even more diverse instruments. 
FIG. 7 shows scans of an RQS nominal 5 .ANG. standard of the present 
invention made with an angle-resolved scatterometer. The format of this 
graph is a one-dimensional power spectral density plot which relates 
surface roughness power per unit of spatial frequency. The PSD plot (the 
curve starting at the upper left corner of the graph and heading downward 
to the lower right corner) is the square of the modulus of the Fourier 
transform. Recall that the Fourier transform of a square wave with a 50% 
duty-cycle is an infinite series of odd-order harmonics. In the case of an 
exact 50% duty-cycle, there is an added benefit in that R.sub.q, or the 
rms-roughness value is identically equal to the arithmetic, or R.sub.a, 
roughness. This value then equals half the overall height (peak-to-valley) 
of the square wave. Referring again to FIG. 7, there are even order 
harmonics apparent here, but their amplitude is over two orders of 
magnitude lower than the primary peak at low spatial frequencies. Keep in 
mind that this is a log-log scale. 
The most useful feature of the PSD function is that it relates information 
about the Fourier transform of the surface into a form that makes it 
possible to readily compare information generated from various 
instruments. The rms roughness may be calculated directly as the square 
root of the integral of the one-dimensional PSD curve. In the case of the 
RQS standard, an isotropic roughness value needs to be added in as well to 
account for the inherent roughness of the silicon; this is described in 
section IV. Another compelling reason for making use of a square wave to 
produce a PSD plot is that over 90% of the power is contained in the first 
peak. This means that the standard is somewhat less sensitive to the exact 
instrument spatial bandwidth as long as at least the first peak is 
captured. Of course, it is important to completely integrate under the 
curve with the integration limits set equal to the instrument bandwidth 
for best results. FIG. 8 shows some typical bandwidth limits for various 
pieces of surface texture measuring equipment. 
The scale on the right side of FIG. 7 indicates rms-roughness. Notice the 
curve starting at the lower left hand corner by 0.01 .mu.m.sup.-1. This is 
the square root of the integrated value under the PSD plot--yielding 
rms-roughness. At the cursor location on the curve corresponding to 0.06 
.mu.m.sup.-1, the rms roughness value is 4.62 .ANG. (indicate in the upper 
right corner), or about 93% of the total 4.98 .ANG. level at 0.6 
.mu.m.sup.-1. 
FIG. 7 was generated by a TMA CASI(r) angle-resolved light scattering (ARS) 
instrument. This is a specialized tool that allows for first-principles 
traceability based on the wavelength of light and optical geometries of 
the instrument. Details of the ARS procedure are presented in depth in 
section IV (Determination of Specific Microroughness Levels). For now, it 
is important to realize how the same surface can be measured by completely 
dissimilar instruments and give the same results within the same bandpass. 
The realization of the graph being on a log-log scale emphasizes the 
assertions made earlier about the essential importance of knowing the 
spatial bandwidth limits of a given instrument. In the case of a typical 
measured surface (one that does not possess the unique features of a 
square wave), there will be a continuous power spectrum. In this case, 
integration between the limits of 0.01 .mu.m.sup.-1 to 0.1 .mu.m.sup.-1 
(which may be typical for an optical profilometer) may result in a rms 
roughness value over an order of magnitude higher as compared with a 1 
.mu.m.times.1 .mu.m AFM scan (bandwidth of 1 .mu.m.sup.-1 to 256 
.mu.m.sup.-1 ; recall that the high spatial frequency, based on 512 sample 
points, is calculated from equation 2 as 
##EQU5## 
Knowing the PSD of a given surface allows determination of rms-roughness in 
a straightforward manner. The rms roughness, Rq, between spatial 
frequencies f.sub.min and f.sub.max, from a one-dimensional power spectral 
density function, PSD.sub.1D, is 
##EQU6## 
III. Design Considerations 
The relationship between the surface PSD and the resulting scatter was 
introduced by Church into the optics literature in 1975 and has been 
extensively used to monitor micro-roughness via scatter measurement. The 
general technique is explained in the next section, with the key 
relationship, sometimes called the "Golden Rule" appearing as Equation 9. 
In order for this relationship to be used to find the PSD from the 
measured scatter, virtually all of the scatter must come from surface 
topography. Non-topographic sources of scatter include surface bound 
particles, films, oxide layers, and smooth surface index variations, such 
as those found across grain boundaries. Non-topographic sources of scatter 
follow other scatter laws besides that found in Equation 9. Sources of 
topographic scatter have the property that regardless of changes in 
wavelength, or incident angle, the same PSD will be calculated. This 
property is called wavelength scaling in the literature. Significant 
scatter from particles and grain boundaries as well as the interference 
effects associated with surface films have all been shown to produce 
significant variations in the calculated PSD. In other words, they do not 
wavelength scale. 
Clean, polished silicon wafers have been shown to scatter topographically 
from the near IR to the UV. They can be produced virtually free of 
contamination and films, and as single crystal surfaces, they are free of 
effects from grain boundaries. In general, these surfaces are very low 
scatter, and for the spatial bandwidths in question can be characterized 
by a low level isotropic background roughness. Because techniques are 
available for producing designed surface structures on silicon, this is an 
ideal material for a micro-roughness standard. 
The basic design employs a nominally 50% duty-cycle square wave with a 
period of 20 .mu.m. This produces a fundamental spatial frequency 
component of 0.05 mm.sup.-1 followed by odd harmonics at 0.15 mm.sup.-1, 
0.25 mm.sup.-1, etc. 
IV. Determination Of Specific Microroughness Levels 
Since all of the data from angle-resolved scatterometry are binned into 
discrete points, the "integration" required to turn these data into a 
rms-roughness value merely becomes the square root of the summation of the 
one-dimensional PSD function, PSD.sub.1D (f), multiplied times the 
differential frequency step size within the appropriate limits of 
integration. 
##EQU7## 
Note also that the equation signifies the limits of integration denoted fl 
and f.sub.h which are set according to the spatial bandwidth limits of the 
instrument under test. To account for the inherent isotropic roughness of 
the silicon, we also need to add in an additional term PSD.sub.iso to 
equation 6. The final formula for the RQS standard takes the form of 
equation 7. 
##EQU8## 
This is the equation that is used to certify a rms-roughness value for the 
standard for a given range of integration limits. 
IV.1 Development of the PSD Calibration Curve 
The actual quantity measured through angle-resolved scatterometry is the 
bi-directional reflectance distribution function (BRDF), 
##EQU9## 
where P.sub.s is the power of the scattered light collected over the solid 
angle .OMEGA..sub.s as a function of the angle .theta..sub.s. The factor 
P.sub.i indicates the incident laser power at angle .theta..sub.i from the 
wafer normal. Therefore, BRDF is physically nothing more than the 
redistributed energy scattered into a given solid angle. Recall from 
equation 4 that the spatial frequency, f, is related to the scatter angle 
by the one-dimensional grating equation 
##EQU10## 
The PSD function then is calculated from the BRDF and is a measure of the 
scattered power per unit of spatial frequency in units of .ANG..sup.2 
.mu.m.sup.2. 
##EQU11## 
where, for s-polarization, the factor Q is approximated by the specular 
reflectance of the wafer surface. The reflectance is a function of 
wavelength, incidence angle, and polarization. If the surface is 
isotropic, PSD(f.sub.x, f.sub.y) may be integrated around the azimuthal 
angle .phi..sub.s to obtain an isotropic PSD function 
##EQU12## 
with units of .ANG..sup.2 .mu.m and f equals the root-sum-of-squares of 
f.sub.x and f.sub.y. It is this function, PSD.sub.iso (f) in equation 10, 
that is added to the one-dimensional PSD function and becomes the function 
from which rms roughness is calculated. The square wave is a 
one-dimensional scatterer, however, the roughness of the silicon "peaks 
and troughs" are isotropic scatterers. Therefore, two measurements are 
made--one with the direction of the square wave surface perpendicular to 
the plane-of-incidence of the laser (for the overall one-dimensional PSD 
curve generation), and one where the surface is parallel. The second scan 
measures the silicon roughness, independent of the etched features. This 
value is then converted to an isotropic value, equation 10, and then added 
as the root-sum-of squares to the one-dimensional scan (equation 7). The 
silicon roughness is really only significant at low nominal roughness 
values but is consistently measured as a matter of practice. 
FIG. 9 provides some reference as to what type of one-dimensional PSD 
function may be expected for various surfaces typically encountered. 
(These examples are adapted from W. Murray Bullis, ECS presentation at 
Particles, Haze and Microroughness Symposium, San Jose, Calif., September 
1994). The reader versed in signal theory will also note the analogy to 
Fourier analysis of communications signals. 
FIGS. 10 and 11 summarize the determination of the power spectral density 
function and spatial frequency bandwidth for scattering instruments (e.g., 
total integrated scatterometers) and profilers (e.g., atomic force 
microscopes), respectively. Notice that the instruments may be correlated 
directly in the region of bandpass overlap. In particular, FIG. 10 
illustrates the determination of the PSD and related spatial frequencies 
for a generic total integrated scattering inspection system. PSD is a 
measure of the scattered power per unit of spatial frequency. The PSD is 
calculated as per equation (9). FIG. 11 illustrates the determination of 
the PSD and related spatial frequencies for a surface profiling system 
(e.g., an atomic force microscope). The PSD is calculated as the square of 
the Fourier transform from a 2-D surface profile: 
##EQU13## 
where f.sub.x, f.sub.y are the spatial frequencies such that f.sub.x =K/L 
with K being an integer 1,2, . . . , N/2, and d is the same in both the x- 
and y-directions. Again, the units are .ANG..sup.2 .mu.m.sup.2. 
V. Manufacture of Standard 
The standard may be manufactured according to the techniques described in 
U.S. Pat. No. 5,599,464. In FIGS. 12-17, manufacture of a single feature 
is shown, but in practice, all of the features on the wafer, perhaps 
millions, would be made simultaneously. FIG. 12 shows a silicon wafer 20 
having a uniform layer 21 of silicon dioxide thermally grown onto the 
silicon substrate. The silicon dioxide layer has a thickness of between 
500 .ANG. and 1000 .ANG.. In the book Silicon Processing for the VLSI Era, 
vol. 1, p. 200-212, the thermal oxidation of silicon is explained. The 
book mentions that Deal and Grove described silicon oxidation as 
proceeding by the diffusion of an oxidant, such as molecular oxygen, 
through an existing oxide to the silicon-silicon dioxide interface, where 
molecules react with silicon to form silicon dioxide. In other words, 
oxygen migrates to the bare silicon substrate, where it interacts with 
silicon, thereby lowering the level of the silicon/silicon dioxide 
interface in places where oxidation has occurred. This is a key aspect of 
the present invention. 
In FIG. 13, a thin layer 23 of positive photoresist is applied. The 
photoresist may be patterned 10 with the desired location, areawise 
extent, and overall density of features by means of a mask. When light is 
used to expose the photoresist layer 23 through the mask, a latent image 
of the features is formed in the photoresist by light. In other words, the 
chemical bonds in the exposed photoresist are broken, altering the 
molecular weight and solubility of the resist, which allows the latent 
image to be developed, removing the exposed photoresist in the etched 
area, uncovering the underlying silicon dioxide layer. In the case of 
positive photoresist, the bonds of the exposed photoresist are broken. 
In FIG. 14, portions of the resist layer 23, now removed, create an 
aperture 25 where the resist has been exposed by light. An oxide etchant 
is used to remove silicon dioxide down to the upper surface 27 of the 
silicon substrate 20, which is uniformly lower than the original level. 
In FIG. 15, the photoresist is stripped from the oxide layer 21. The 
aperture region 25, now a single pit 31 in an array of similar pits which 
will form topographic features, including the light scattering features of 
the present invention, undergo self-limiting reoxidation due to exposure 
to air. Any oxidizing ambient environment could be used, but air is 
effective and inexpensive. Air oxidation at room temperature produces 
native oxide which has a thickness of approximately 17 .ANG.. 
Approximately half of the native oxide layer consumes silicon at the 
substrate interface. This is shown in FIG. 16, where the native oxide at 
the bottom of a pit extends into the silicon substrate, below the former 
level 27 supporting the silicon dioxide. The formation of the native oxide 
layer is rapid, but generally stops by itself after a short time. 
Next, all of the oxide is stripped, as shown in FIG. 17. It is now apparent 
that a differential step height exists between the bottom of the pit 33 
and the former base 27 which supported the silicon dioxide. 
In FIGS. 12-17, the construction of a topographic feature has been shown 
using a dark field mask, resulting in a pit 33 within a light reflecting 
field 27. A reverse process could be used, producing a feature having a 
step height, rather than a pit. The reverse process could be achieved with 
reverse masks or with photoresist of the opposite type. This reverse 
process is illustrated in FIGS. 18-23. 
In FIG. 18, a uniform thermal oxide layer 41 is grown on a polished, 
light-reflective silicon wafer 40 to a thickness which is between 700 
.ANG. and 1000 .ANG.. Such layers are readily produced in the 
semiconductor industry with good consistency and uniform thickness over 
the surface of a wafer. Lesser thicknesses could be produced, but the 
range of 700 .ANG. to 1000 .ANG. is preferred because of the ease of 
manufacturing and of verifying the thickness with measuring instruments. 
In FIG. 19, a layer of photoresist 43 is disposed over the thermal oxide 
layer 41. The photoresist is exposed to light through a mask which is the 
optical complement of the mask used for the exposure previously described 
with respect to FIGS. 13 and 14. 
After removing the exposed portions of the photoresist and etching the 
oxide, a mesa is left, as shown in FIG. 20. The mesa 45 consists of a 
small layer of photoresist 43 atop a similarly sized layer of thermal 
oxide 41. In FIG. 21, the photoresist portion is shown to be stripped 
away. 
In FIG. 22, a very thin layer of native oxide 51 grows on the exposed 
silicon as air is allowed to be in contact with the wafer, consuming 
silicon below the initial wafer level. The silicon dioxide island 41 is 
removed, leaving a small mesa or feature 53, which also is exposed to air 
and has a uniformly thin native oxide layer. The feature 53 extends 
approximately 8 .ANG. to 9 .ANG. above the surface of the surrounding 
silicon field. 
VI. SUMMARY 
When making comparisons between different types of texture measurement 
tools, it is extremely important to report the spatial bandwidth along 
with the reported rms-roughness value. Even when comparing results between 
the same instrument type, the operating parameters can significantly 
affect the reported results. This variation can be well over an order of 
magnitude different. Ideally, the transfer function for a given instrument 
must also be known for the best quantitative comparison between toolsets. 
Finally, a practical microroughness standard has been developed that is 
based upon the principles of optical scatterometry for certification. This 
standard allows for comparison between seemingly uncorrelatable tools, 
within the proper spatial bandwidth for each toolset. Using this 
methodology, it is possible to compare microroughness readings on a TIS 
system to the microroughness readings on an atomic force microscope.