Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
1999-12-17
2002-11-19
Siek, Vuthe (Department: 2825)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
C716S030000, C430S005000, C378S035000, C382S144000, C382S149000, C700S105000, C700S110000, C700S120000, C700S121000
Reexamination Certificate
active
06484306
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
Not Applicable
REFERENCE TO A MICROFICHE APPENDIX
Not Applicable
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention pertains generally to integrated circuit fabrication, and more particularly to a scanning method for use in a defect inspection system.
2. Description of the Background Art
During the process of integrated circuit fabrication, masks and wafers at various stages are inspected for defects. The inspection process consists typically of sequentially scanning areas of the mask, or wafer, with a beam of light while taking accurate measurements to detect if a defect exists at each location scanned. The beam is retained at any particular spot on the item under inspection for a period of time related to the accuracy of the measurement required, and the measurement results are compared against a threshold value to determine if the location contains a defect. The measurement accuracy, and thereby the time required to perform the measurement, depends largely on the number of false alarms which are permissible per unit of area when performing the test.
Properties of a defect inspection system include such important metrics as throughput, capture-rate, and false-alarm rate for a defect of a given size. The throughput is the number of units (i.e. mask blanks, or wafer blanks) that can be inspected per unit of time at a specified capture-rate and false-alarm-rate. Throughput is dependent on scanning speed, which is defined as the time to scan a unit area of the mask blank. False-alarm-rate is the probability of a non-defective area being considered defective during the test scan. The capture-rate is the probability that a defect of a given size will be detected by the test scan. Both false-alarm-rate and capture-rate depend on quality of the measurement. Within an inspection system that employs single level scanning, the quality of the measurement can also be considered as the signal-to-noise ratio that should be achieved so that a measurement threshold value can properly distinguish a defect.
To more fully exemplify defect scanning, the scanning of (Extreme UltraViolet Lithography) EUVL mask blanks is described. One form of defect inspection is to inspect reflective EUVL mask blanks using an at-wavelength inspection tool. Reflective masks contain multiple reflective layers whose spacing relates to the intended wavelength to be reflected. Reflective masks therefore can only be accurately tested for subsurface defects if the test is performed with an at-wavelength beam. One form of testing EUVL mask blanks involves scanning the area of the mask with a small diameter EUV beam (approximately 1.7×5 &mgr;m) and measuring changes in reflected intensity (bright field detection), scatter intensity (dark field detection), and/or the photoemissive current. In order for small defects to be detected, the size of the incident beam is very small, while the measurement itself must be taken over a large enough interval to assure accuracy. An inspection station used for this testing process typically comprises a mask blank held on a moveable stage within a vacuum chamber operating at about 10
−6
Torr. A small spot of EUV light is created by demagnifying a beam from an illuminating pinhole through a pair of Kirkpatrict-Baez (KB) mirrors. The beam is focused on the sample at approximately 9° off-normal. A channeltron electron multiplier may be used for a bright field detector, while a microchannel plate with a reflective beam aperture for the bright field may be used as a dark field detector. To attain accurate defect inspection by this method the mask is generally inspected as a set of pixels, each about 3×5 &mgr;m, wherein each pixel is tested for approximately 50 mS.
A mathematical description of a defect inspection device as a shot-noise limited system can provide further explanations of capture-rate and false-alarm-rate for a defect of a certain size. A shot-noise system is one in which the dominant noise source is a shot-noise due to the finite number of photons detected by the detector. In a shot-noise limited system the distribution of signal can be represented by a Gaussian distribution with a mean m and standard deviation &sgr;.
f
(
x
)
=
(
1
2
π
×
σ
)
e
-
(
x
-
m
)
2
/
(
2
σ
2
)
(
1
)
The signal from the clear region, or the region where there is no defect, can therefore be represented by a Gaussian distribution centered at m
2
, furthermore a signal from a 100 nm defect provides another Gaussian distribution centered at m
1
. Assuming simple area scaling of signal strength from a defect, and the spot size of 1 um, m
1
=0.99 m
2
. Simplified for m
2
=1, then m
1
=0.99. The standard deviation &sgr;, is determined by the number of photons detected per pixel, wherein the area of each pixel is assumed to be the same as the spot size. The following relationship then holds for &sgr;.
&sgr;=1/
Nd
(2)
The value Nd is the number of photons detected per pixel. Based on these assumptions, the capture-rate is determined by the probability of a 100 nm defect generating a signal smaller than threshold value s. A defect herein is assumed to cause a reduction of bright field signal such that the measured signal is smaller than the threshold.
capture_rate=
P
(
x<s;m
1
,&sgr;) (3)
False-alarm rate is the probability of the clear region giving a signal smaller than the threshold value.
false_alarm_rate=
P
(
x<s;m
2
,&sgr;) (4)
As described above, the false-alarm-rate is the probability P of the signal (or pixel value) being lower than a threshold value s, when the distribution is characterized by mean m
2
and standard deviation &sgr;.
FIG. 1
shows a distribution corresponding to m
1
, and a second distribution corresponding to m
2
, both of which are shown in relation to the threshold value s.
Using the error function erf(x), the capture and false-alarm rates can be cast into a form which is an integration of the Gaussian distribution. The error function erf(x) is given by:
erf
(
x
)
=
2
×
∫
0
x
e
-
t
2
π
(
5
)
P
(
x
<
s
;
m
1
,
σ
)
=
∫
s
∞
f
(
t
)
(
6
)
where f(t) is the normalized Gaussian distribution. The integration variable is changed and the following is therefore derived:
P
(
x
<
s
;
m
1
,
σ
)
=
1
+
erf
(
s
-
m
1
2
σ
)
2
(
7
)
The capture-rate and false-alarm-rate can therefore be expressed as:
capture_rate
(
s
,
σ
)
=
1
+
erf
(
s
-
0.99
2
×
σ
)
2
(
8
)
false_alarm
_rate
(
s
,
σ
)
=
1
+
erf
(
s
-
1
2
×
σ
)
2
(
9
)
The scanning time required per unit area is given by:
T
/
A
=
(
dwell time per pixel
)
×
(
no. of pixels per unit area
)
=
Nd
/
F
0
×
Np
=
Np
/
(
F
0
×
σ
2
)
(
10
)
where F
0
is the total number of photons focused onto the 1 &mgr;m spot per unit time, while Np is the total number if pixels per unit area (Np=10
8
per cm
2
for 1 &mgr;m spot size). Therefore, for any given spot size, minimum capture-rate, and maximum false-alarm-rate, the scanning time is mainly determined by the standard deviation of the Gaussian distribution of the signal.
As an example, when the signal to noise ratio is at 2 (i.e. &sgr;=0.5%) and the threshold is set at 0.99, the capture-rate is 50% and the false-alarm-rate is 2.28% with the false-alarm count being 2.28e6 per cm
2
. The scanning time for F
0
=1.4e8 is therefore approximately 8 hours per cm
2
. The value F
0
=1.4e8 is one that has been achieved using a 10× Schwarzchild with a 100 &mgr;m
2
aperture with 100 &mgr;m exit slit with a grating. Using white light with a 20× Schwarzchild, the number increases about 4*50=200. The factor of 50 results from the expected flux increase anticipated from using the white light approach. Therefore it appears that at least F
0
&equ
Bokor Jeffrey
Jeong Seongtae
Kik Phallaka
O'Banion John P.
Siek Vuthe
The Regents of the University of California
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