NANOSCALE SURFACE ROUGHNESS MEASUREMENT OF A
SEMICONDUCTOR WAFER USING LASER SCATTERING
TECHNIQUE
C.J. Tay, S.H. Wang, and C. Quan
Department of Mechanical Engineering,
National University of Singapore, 9 Engineering Drive 1, Singapore 117576
ABSTRACT
A technique which incorporates an integrated laser scattering model for surface roughness
measurement of a semiconductor wafer has been developed. The proposed system employs a He-Ne
laser and conventional optical components to record surface roughness in the nanometre range with a
high degree of accuracy. The total integrated scattering (TIS) model is modified to retrieve parameters
on a surface nano-topography. The experimental results obtained show excellent agreement with the
Atomic Force Microscope (AFM) method with only minor discrepancy. In addition, unlike previous laser
scattering method which uses a spherical arrangement to record diffused light, the proposed technique
detects reflected light normal to the test surface and hence results in a simpler and more stable optical
arrangement.
Introduction
In recent year demands on material quality have become more stringent due to miniaturization of
product components, particularly in the precision engineering and semiconductor manufacturing industry
[1, 2]. To ensure the integrity of material quality accurate surface roughness measurement of machined
workpieces is of fundamental importance. For instance, in the disk drive industry to control the quality of
electrical components mounted on an optical disk, accurate surface roughness of the disk must be
maintained. Hence, the surface finish, normally expressed in terms of surface roughness, is a critical
parameter used for the acceptance or rejection of a product. Surface roughness is also one of the
parameters that affect the lifespan of an integrated circuits (IC) chip in precision engineering and
semiconductor industry [3, 4]. Hence, it is also critical to monitor and control the surface roughness of a
semiconductor wafer as it is a basic component used in IC fabrication.
Currently, there are several methods for determining surface roughness of a semi-conductor wafer. The
most common method is the use of a mechanical stylus instrument [5], particularly Taylor Hobson serial
instruments installed with stylus tips have been accepted as international standards for measuring
surface roughness. However, there are certain limitations associated with the use of a stylus instrument,
such as inadvertent damage of wafer surface while the stylus moves across a specimen and stringent
vibration isolation requirement. Furthermore, the accuracy of the measurement is also highly dependent
on the size of the stylus tip and the process often requires costly equipment and is time consuming.
In this paper, we have modified a conventional total integrated scattering model by capturing the
reflected beam normal to the test surface. An experimental setup to measure the surface roughness of a
semiconductor wafer is demonstrated.
Method
Based on Beckmann and Spizzichino’s model [6], there are two approaches to implement surface
roughness measurement: a) parametric and b) total integrated scattering (TIS) methods. The
parametric method measure surface roughness indirectly using a certain pre-calibrated procedure [710]. However, the total integrated scattering (TIS) model [10, 11] provides a direct mathematical relation
between the surface roughness and the scattered light. The TIS model is applicable to measuring
surface roughness as the instrumentation is simple, and the calibration of the root-mean-square (RMS)
roughness (Rq) values is straightforward. Since Rq is weighted by the square of the heights, it tends to
be more sensitive to the peak and valley amplitudes. Fig. 1 shows a well polished silicon wafer with an
isotropic surface and surface roughness (Rq) of 20.7 nm obtained using AFM. Using He-Ne laser (λ =
632.8 nm) as a light source, its dynamic range of 316.9 nm (λ/2) is sufficient for semiconductor wafer
surface roughness measurement as its surface roughness is normally less than 50 nm.
As shown in Fig. 2, a laser beam directed normally at an isotropic rough surface results in specularly
reflected and diffused beams. In the TIS model, scattered light is normally captured by a hemispherical
mirror and focused onto a detector within the Coblentz sphere [11, 12]. The scattered light pattern
consists of diffuse and specular components, and the governing equation for the TIS model is as
follows:
I o − I s I d  4πσ 
= =

Io
Io  λ 
2
(1)
where σ (or Rq) is the root mean square (RMS) roughness, λ the wavelength of the light source, Io the
total reflected light intensity, Is the reflected light intensity at normal incidence, and Id the diffused light
intensity. Hence, the RMS roughness Rq of the specimen can be determined by measuring the diffused
light intensity. Note that two beams (Io and Is) would be converted into electrical current using
photodiodes connected to an amplifier.
In practice, since the light reflectance is dependent on the absorption characteristic of the material of the
specimen, the TIS model should be modified to compensate for the loss of light due to absorption. The
incident light beam intensity (Io) on a test surface consists of three components, namely diffuse (Id),
specular (Is), and absorbed (Ia) components, where:
Io = Id + Is + Ia
(2)
Assuming that Ia, the absorbed component, is approximately equal to ksIs, where ks is a constant which
can be determined experimentally, then
I d = I o − (1 + k s ) I s
(3)
Hence, the governing equation for the modified TIS model is
I d I o − (1 + k s ) I s  4πσ 
=
=

Io
Io
 λ 
Simplifying Eq. (4), the RMS surface roughness (
Rq =
λ
4π
2
(4)
or Rq) is given by:
 I o − (1 + k s ) I s

Io




(5)
Incidental laser
beam
Diffused reflected
beam
Specularly reflected
beam
Z
X
Test wafer
surface
Figure 1. Nanoscale surface irregularity of silicon wafer
Y
Figure 2. Schematic of laser beam scattered from
an isotropic rough surface.
Experimental Work
As shown in Fig. 3. a laser beam from a 30 mW He-Ne laser source (λ = 632.8 nm) is directed through
lens 1 (focal length, ƒ = 10 mm), a pinhole (a 25 µm spatial filter), and lens 2 (focal length, f = 50 mm). A
steering mirror unit consisting of mirrors 1, 2 and 3 are used to direct the collimated laser from lens 2
along the Z-axis onto a test specimen. A beam splitter (reflection ratio 50%) is placed between mirror 3
and an objective lens. After passing through the beam splitter, one beam I1 of intensity Io/2 emerges in
the X-direction and after passing through aperture 1 and lens 4, falls on photodiode 1. Another beam
emerges in the Z-direction and is directed through an objective lens onto the test surface placed on a 3axis translation stage. The beam reflected from the test surface passes through the objective lens and
travels along the Z-axis towards the beam splitter. A beam I2 of intensity Is/2 subsequently emerges and
is directed at photodiode 2 after passing through aperture 2 and lens 3.
It is noteworthy that the experimental setup is incorporated with a light intensity stabilized laser and
apertures which block away any external background light, the system is immune to fluctuation of light
intensity and surface roughness measurement can be consistently implemented.
Steering Mirror 3
Steering Mirror 2
Beam Splitter
Aperture 2
Photodiode 2
I1
Z
X
Aperture 1
I2 Photodiode 1
Y
He-Ne Laser
Lens 3
Pinhole
Lens 4
Objective Lens
Lens 1
Lens 2
Wafer
Steering Mirror 1
3-axis translation stage
Current
Amplifier
Figure 3. Experimental arrangement
Results and Discussion
Fig. 4 shows the results obtained on various wafers using conventional stylus profilometer, AFM, TIS
and the proposed model. In order to allow effective comparison and considering the limitation in the
sampling area of AFM, a sampling area of 50 µm × 50 µm is evaluated as shown in Fig. 1. This is
achieved by directing a laser beam of 52 m (which is close to that of the AFM sampling area) onto the
test surface. Though the sampling length of 250 µm used in the stylus profilometer is much bigger than
that of the AFM and the proposed method, the discrepancy of the sampling length has no significant
influence on the statistical surface roughness measurement. This is due to the isotropic and very fine
surface structure of the polished wafer as shown in Fig. 4. The surface irregularity is uniformly
distributed within a segment of stylus measuring length.
Figure 4. Surface roughness structure obtained through stylus profilometer shows
a uniform surface irregularity of the wafer surface.
On Table 1, it is obvious that the proposed modified TIS model shows excellent agreement with the
AFM results and the maximum discrepancy is less than 2%. The unmodified TIS model shows that on
the whole the results agree reasonably well. However, there are some noticeable discrepancies and the
maximum discrepancy is about 3.4%.
Table 1. Experimental data for semiconductor wafers
Method
AFM
(A)
TIS
(B)
Proposed
method
(C)
% difference
between A & B
% difference
between A & C
Sample
Rq (nm)
Rq (nm)
Rq (nm)
―
―
1
20.9
21.1
20.7
-0.96
0.96
2
20.5
20.8
20.6
-1.46
-0.29
3
20.8
21.5
21.2
-3.37
-1.92
4
21.8
21.9
21.6
-0.46
0.92
5
20.3
20.5
20.2
-0.99
0.49
6
19.9
20.2
19.8
-1.51
0.50
A−B
× 100 % ,
A
A−C
d
% difference between A & C =
× 100 %
A
c
% difference between A & B =
c
d
To validate feasibility of the proposed method and investigate the relation of the reflected light intensity
(Is) and the roughness magnitudes obtained using different methods, the relations of the Is versus Rq
have been plotted. As shown in Fig. 5, there is a correlation between Is versus Rq. The results obtained
using the Taylor Hobson method indicate that the roughness on the same set of wafer ranges from
approximately 14 nm to 18 nm, while the results from the AFM, TIS and proposed methods indicate a
roughness range of between 20 nm to 22 nm. The consistently lower values of the Taylor Hobson
method are mainly due to the relatively large stylus tip used which may not accurately pick up the
troughs of the micro-profile of the fine lateral structure on the polished wafer surface.
1.39
1.38
Is (mA)
1.37
AFM
TIS
1.36
Proposed method
Taylor Hobson
1.35
1.34
1.33
12
14
16
18
20
22
24
Rq (nm)
Figure 5. Relation of Is against Rq for a semiconductor wafer.
The results in Fig. 5 were linearized (least square method) and the relationships between Is and Rq are
summarized as follows:
a)
Proposed method
: Rq = -38.035 Is + 72.698
(correlation coefficient = 0.996)
(8)
b)
TIS
: Rq = -37.284 Is + 71.968
(correlation coefficient = 0.996)
(9)
c)
AFM
: Rq = -36.098 Is + 70.059
(correlation coefficient = 0.877)
(10)
d)
Taylor Hobson
: Rq = -65.988 Is + 105.8
(correlation coefficient = 0.642)
(11)
To study the repeatability of the proposed technique, measurements were taken on various test
specimens under normal laboratory conditions. It is found that the maximum variation of Rq values of the
same test area on a given wafer is less than 0.3%. Hence, the results indicate that high repeatability can
be obtained with the proposed method.
Concluding Remarks
In this paper, it has been shown that the roughness of semiconductor wafers in the nanometer range
can be accurately determined using the proposed technique. The results obtained show excellent
agreement with AFM with a maximum discrepancy of 2%. This is a significant improvement over the TIS
and conventional stylus methods. Using the proposed optical arrangement, accurate and repeatable
measurement of a semiconductor wafer surface roughness in the nanometer range can be readily
obtained. In addition, the proposed non-contact arrangement has the advantage of simplicity in its setup as well as being able to provide speedy and accurate information on surface roughness.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
P. Wilkinson, R. L. Reuben, J. D. C. Jones, J. S. Barton, D. P. Hand, T. A. Carolan, and S. R.
Kidd: Surface finish parameters as diagnostics of tool wear in face milling. Wear 25 (1997) 47 –
54.
I. Sherrington and E.H. Smith: The significance of surface topography in engineering. Precis.
Eng. 8 (1986), 79 – 87.
R. E. Reason: Progress in the appraisal of surface topography during the first half-century of
instrument development. Wear 57 (1979) 1 – 16.
T. V. Vorburger: Measurement of roughness of very smooth surfaces. CIRP Annuals 36 (1987)
503 – 509.
D. J. Whitehouse: Stylus techniques in characterization of solid surfaces, P.E. Kane and G.R.
Larrabee, Eds. Plenum, New York 1975.
P. Beckmann and A. Spizzichino: The scattering of electromagnetic waves from rough
surfaces. Nirwood, MA: Artech House, Inc., 1987.
E. L. Church, H. A. Jenkinson, and J. M. Zavada: Relationship between surface scattering and
microtopographic features. Opt. Eng., 18(1979) 125-136.
S. H. Wang, Chenggen Quan, C. J. Tay, and H. M. Shang: Surface roughness measurement in
the submicrometer range using laser scattering. Opt. Eng. 39 (2000) 1597 – 1601.
C. J. Tay, S. L. Toh, H. M. Shang, and J. B. Zhang: Whole-field determination of surface
roughness by speckle correlation. Applied Optics 34 (1995) 2324 – 2335.
M. Bjuggren, L. Krummenacher, and L. Mattsson: Noncontact surface roughness measurement
of engineering surfaces by total integrated scattering. Precs. Eng. 20 (1997) 33 – 45.
J. C. Stover: Optical Scattering: Measurement and Analysis. McGraw-Hill, New York 1990.
H. Davies: The reflection of electromagnetic waves from a rough surface. Proc. IEE 101 (1954)
209 – 214.