Mathematical Modeling of the Nikon Lampas Reflection Measuring Microscope

1985

Mathematical Modeling of the Nikon Lampas

Reflection Measuring Microscope

William O. Bennett

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Recommended Citation

OF THE NIKON LAMPAS REFLECTION MEASURING MICROSCOPE

by

William

o.

A thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in the School of Photographic Arts and Science in the College of Graphic Arts and Photography of the Rochester Institute of Technology

May 1985

Signature of the Author . . . • . . . • . . . . • . . . • . . •

Certified

Accepted

Photographic Science and Instrumentation Diana Nyyssonen

by •...••.•...•..•• • •....•.••••. -••••.•.••.... -..• Thesis Advisor

by

William 0. Bennett

Submitted to the

Photographic Science and Instrumentation Division

in partial fulfillment of the requirements for the Bachelor of Science degree

at the Rochester Institute of _Technology

ABSTRACT

A mathematical model of the Nikon Lampas Reflection

Measuring Microscope for the fine-line _lithography in

integrated circuit manufacture has been developed. Optical intensity profiles of a perfect line were computed _using computer software supplied _by the National Bureau of Standards. The programs were modified for the Lampas

microscope. From line _profiles, the _accuracy of the

microscope was calculated. The microscope is accurate

down to 6/10 of a micron. _All lines below 6/10 of a micron

COLLEGE OF GRAPHIC ARTS AND PHOTOGRAPHY

PERMISSION FORM

Title of Thesis MATHEMATICAL MODELING OF THE NIKON LAMPAS

REFLECTION MEASURING MICROSCOPE

I William Q. Bennett _hereby grant permission to

Wallace Memorial _Library, of _R.I.T., to reproduce _my thesis

in whole or in part. _Any reproduction will not be for

commercial use or profit.

ACKNOWLEDGEMENTS

The author would like to express a special thanks

to Dr. Diana Nyyssonen of the National Bureau of Standards

for her patience and absolute support of this work.

In _addition, thank you _{is in} order for Dr. Hans R.

Rottmann and John J. Nahlik of IBM East Fishkill who

supplied data from the Nikon microscope.

A word of appreciation and good-bye is in order

for Dr. Ronald Francis of R.I.T. who read _my last minute

Page No .

1 Abstract

2 Copyright Statement

3 Acknowledgement

5 List of figures

7 Introduction

11 Experimental

15 Results

30 Discussion

*3 Conclusions

kk Appendix

48 References

Figure #1. Figure #2. Figure #3. Figure #4. Figure #5-Figure #6. Figure #7. Figure #8. Figure #9. Figure #10. Figure #11. Figure #12. Figure #13. Figure #14. Figure #15-Figure #16. Figure #17.

National Bureau of Standards basic

ment pattern SRK 4-74

Intensity profile for a .60 micron line

Intensity profile for a .80 micron line

Intensity profile for a l.'OO micron line

Intensity profile for a 1.20 micron line

Intensity profile for a 1.40 micron line

Intensity profile for a 2.00 micron line

Intensity profile for a 5.00 micron line

coherent illumination

Intensity -profile for a 5.00 micron line

incoherent illumination

Graph of theoretical _accuracy

Intensity profile for a 5.00 micron line

no phase

Intensity profile for a 500 micron line

pi phase

Graph of experimental _accuracy

Fourier transform of a line

Fourier transform of a line with _detectors

Nikon Lampas optical system

Nikon Lampas optical system _using a point

object plane

Figure #19. Dark-field optical system

Figure #20. _{Reversability} principle

Figure #21. Transmission cross-coefficient rectangle

function

Fine-line geometries for the fabrication of

circuits have been pushed to smaller feature sizes ( r- 5um)

for the purposes of _Very Hish Speed Integrated Circuits (VHSIC) and _Very Large Scale Integration ("LSI) technolo

gies. _In order to _accurately reproduce features on photo

masks and _wafers, critical dimensions (CD's) must be known

to a tolerance of + lOfS or better for 1 to 2 micron feature

sizes. Measurement systems can be categorized as acous

tical microscopes, electrical _probing, and _scanning electron

microscopes (SEM's).

Ac'oustical microscopes are used _primarily for

diagnostics, but the minimum measurable dimensions are

not _presently comparable to optical microscopes because cf

2

their _relatively crude lenses. Electrical _probing can

only be applied to geometries which pass current such as

Totalization layers. _Scanning electron microscopes can measure below the one micron barrier. _{However, they} contaminate the object IC's with debris. In _addition, SEM's erode the imaged area, similar to sandblasting.

SEM's, like optical microscopes, need to be modeled to

circuit industry.

Most optical _measuring systems are _based, in princi

ple, on the microscope from which a multitude of variations

can be made and attachments added. Attachments fall into

three categories! (1) _filar, (2) _{image-shearing,} (3) image

scanning. Television devices _may also be used to improve

visibility, speed _accuracy and precision.

Historically, the filar eyepiece is the oldest and most

used apparatus. It consists of two crosshairs and an object

imaged onto the plane of the eyepiece. The object is placed

so that the _leading edge touches the superimposed crosshairs.

One crosshair is _stationary, the other moveable via a cali

brated micrometer. The moveable crosshair is _manually or

electronically positioned at the _trailing edge of the object,

The difference between the point where both crosshairs over

lap and the final position of the moveable crosshair will be

the critical dimension of the object.

Image-shearing systems incorporate a beam-splitter

which separates the incident illumination into two identical

images. The images are _initially superimposed with respect

to each other and are shifted until the edge of one _barely

to a

Image _scanning microscopes come under two categories,

those _{incorporating} photomultiplier tubes and those

incorporating television monitors. In the photomultiplier

tube _type, a lead screw moves the slit across the image of

the object. The photomultiplier tube samples the intensity

of the image, and a microsprocessor computes the feature

size, similar to an automated microdensitometer. Television

measuring systems come under _many variations and types.

Thus, only one example shall be given. The ITP measuring

microscope system incorporates a transmission and/or

reflection illumination system which is enlarged _optically

and imaged onto a vidicon tube. The measurement is made

electronically via two rectangles which are placed on

either edge of the object profile. Within each _rectangle,

the average of each edge profile is computed _{by sampling}

the edge one thousand times. _Knowing the average of each

edge, the critical dimensions can be calculated _by

subtract-4

ing one edge average from the other.

In the past four years, Nikon of Japan has introduced

a new and innovative _measuring system for semiconductor

manufacture in which the measurement is made from scattered

light rather than reflectance or transmittance. A laser

edge irregularities and system noise) is imaged on the

object _using a .75 N.A. objective. The object is moved

under the microspot and when the _leading edge encounters

the laser microspot the illumination is scattered to one

of two off-axis detectors. As the object is moved further,

the _trailing edge scatters light to the second off-axis

detector producing a reflectance profile from which

line-widths and edge profiles can be determined.

With several different _measuring systems available to

the semiconductor _industry, each with its own edge detection

criteria, accuracy differences in linewidth measurements

have been found to be as great as one micron. VLSI tech

nologies require linewidth geometries _approaching submicron

feature 'sizes. For this reason, the investigation and

research into optical measurement techniques and criteria

is of. _primary importance to the integrated circuit industry.

The purpose of this thesis is to derive a theoretical

model of the Nikon Lampas off-axis reflection _measuring

EXPERIMENTAL

In order to _verify theoretical predictions of accuracy,

experimental data was collected _using IBM's East Fishkill,

New _{York Nikon microscope. The sample} artifact was a two

inch silicon dioxide on silicon wafer. The _SiOp was 150nm

thick, thermally grown and contact printed. The oxide was

etched _{away using} a BERREL plasma etcher. It turns out that

the edge profiles are not _perfectly rectangular but rather

have a

45

slope. _{This is} different from the model which

assumes rectangular image profiles, i.e. straight edges. Due

to _{availability,} this sample must _do, which reduces the

accuracy of the data.

The wafer sample supplied _by N.E.S. had imaged into it

the N.B.S. SRM 474 line pattern (figure #1). The individual

lines are located _{by referencing} an alphanumeric grid. The

rows are designated _by the letters A through G. Individual

lines are located _by the numbers 0 through 9. Linewidths

in row _{A vary from 0.58} microns _up to 10 microns.

The microscope at IBM is a production _facility and con

sequently was _only available for a short period of time per

day. Therefore _only row A was scanned. The microscope _is

programmed to scan the N.B.S. SRM 474 basic measurement

pattern ten times on rows A and B. _{Unfortunately,} each

F

D1S3H

5 5 16 9

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B

I

D 1

5

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H

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D 1 a 3

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E

HH"hBH-E-l"HHHH"h

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9

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0

1

G

I

in

G

A view of the basic measurement pattern on SRM 474. The _{individual lines and}

patterns are located _by reference to an _{alphanumeric grid with}

the _letters

A through G _identifying the row'and the numbers 0 through 9 _{identifying the} column.

artifact was not removed from the microscope chuck reposi

tioned and refocused. _Instead, the artifact was left in the

chuck for all ten repetitions. In this way, the pattern of

variability was less. To get a better representation of

the _variability of the _system, ten scans were made on three

TAELE #1

tvt _-q n

LINE SAMPLE

MEAN VALUE

(microns) (microns)

A-0 2.30 _2.35

A-l I.74 1.78

A-2 O.58

A-3 4.05 4.14

A-4 IO.36 10.42

A-5 5.06 _5.13

A-6 3.44 3.52

A-7 7.23 7.29

A-3 1.10 1.14

A-9 5-92 6.00

Experimental linewidth versus National Bureau of Standards

RESULTS

Computer software was used to compute optical intensity

(proportional to flux) as a function of object linewidth.

Intensity values were normalized such that _they range in value

from 0.00 to 1.00. Linewidth values range from 0.50 microns

to a maximum of 2.00 microns. The Nikon optics operate at a

mean wave length of 632. 8nm. _{Unfortunately,} the numerical apertures of the microscope are unavailable. _However, the

results of this work indicate that the _accuracy of the

microscope does no"

change with different numerical apertures.

For this _thesis, the microscope is assumed to have an object

ive numerical aperture of _0.75 while the collectors have an

in?ide diameter of 0.80 and an outside diameter of O.95.

Figure #2-#9 show change in image profiles for _varying linewidths while all other parameters are kept constant.

Table #2 shows the definition of the parameters that can

be altered within the software. Linewidths varied from a

minimum of 6/10 of a micron to 2.00 microns. _Anything below

6/10 of a micron caused the program to produce erroneous data.

This leads to the conclusion that the cut-off _frequency from a theoretical view is 6/10 of a micron. Above 6/10 of a

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ACTUAL LINEWIDTH (urn)

TABLE #2

WIDTH - Object

Linewidth

WAVE - Source Wavelength

OBJ - Objective Numerical Aperture

SS - Inside Numerical Aperture

of

Detector

SA - Outside Numerical Aperture

of

Detector

3-phase - Background Phase

I-phase - Object Phase

3y changing the numerical aperture of both the detector

and objective _lens, it was found the theoretical _accuracy

does not change. This _only applies to the Nikon illumination

system. When the detector inside numerical aperture is

reduced to approximate the light-field illumination _system,

the accuracy v/ill change for different numerical apertures.

By changing the numerical aperture of either the objective

or _detector, the slope of the intensity profiles change but

not the _accuracy (figure #8

-#9 ) It has also been deter

mined that Nikon optics are phase insensitive. This means

that when the background phase is different from that of the

object the intensity profile does not change (figure #11

-;r'i2). In conventional optics (light-field), the intensity

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Experimental data has shown that the cut-off _frequency

of the Lampas is 1/10 microns (figure #13). This is about

two times the _theoretical prediction. _However, theoretical

predictions are always better than experimental results,

because _theory assumes a perfect system. Therefore, the

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DISCUSSION

The basic _underlying equation for all theoretical

modeling of optical systems comes from Born and Wolf

as is shown here.

OO OO

Kf) = S S _{T (f+}

f\ f) F _(ft f*)-F* _{(f) df}

(1)

-CO_DO

where

OO

T(f , f ) =

j-S j _(r, g") k (f, ? _{f, g")}

K*

(f2

Nov;, "the image spatial _frequency spectrum I (f) at the image

plane is defined to be the Fourier transform of the image

intensity distribution through the equations":'

oo

Kf) = S I(x)exp _{(2rrifx) dx}

(3)

-pa

oo

I(x) = S Kf)

exp (-2irifx) df (4)

-JO

Similarly, : if the complex amplitude transmittance (or

reflectance) of the objective is given _by the function F _(x,y)

its spatial _frequency spectrum is given _by the fourier

transform.

oo oo

F(f,g) = S S _J(x,Y)

exp (2iri (xf + yg)) dx _dy (5) _O_0O

"V/hen the _partially coherent illumination is _stationary

(which in effect implies wide field illumination), the

mutual _intensity of the illumination of the object plane

may be described by the function J(x,y). Its Fourier

-7

transform is called the effective

source,"

_oo_oo

this is the _{intensity distribution in} the aperture of

the _{condensing lens. The function K(x,y) describes the}

amplitude point spread function whose fourier transform

K(f,g) may be identified with the pupil function of the

objective lens.6 _{The function TCf-.f-) is} called the

transmission cross-coefficient and is equivalent to the

optical transfer function for an _incoherently illuminated

system. For a _{coherently illuminated} system the transmis

sion cross-coefficient represents an autocorrelation of

the two pupil functions K and K* (where the asterisk denotes

complex _conjugate) when the mutual _intensity (I) goes to

1.0. 8

P

(x1

-x2, _y1

-y2) = 1.0

Equation (1) is further simplified if the object is

periodic (e.g. a bar grating). _The object _may be represented

by a fourier series _expansion, whose transform is a distri

bution of delta functions (comb function). If the periodic

function is even the sine term goes to zero and the fourier

series consists of consine terms only. _Thus an even periodic

function with period P = l/f _{may be} represented _by the

IT

Fourier series

F (x) =

E _an cos (2trnf x) (7)

_oo

"

v/hose fourier transform is simply an _array of delta functions

in one _dimension,

?(f) e

Z *J (nf_ * f) (8)

_oo

by inserting equation (8) into equation (1), equation (1)

becomes after simplification.

oo oo

Kf) - I

(a a*

T(nf t0)+ _{2 (a}

_ .

a* _T

(( n n'f no _p' '

_ v n+n n " " p oo

n'f )) + Z

(an

_,

a*

K(n-n') f : -nf) ) )d(nf -f)

P n*

1 -n p p

- E _c

d(nf -f) where c = _c (9)

n

=-n P n _-n

Therefore the _intensity in the image plane is given _by

oo

Kx) - E _c

cos (2:mf x)" (10)

n

-*n P

Equations (9) and (10) represent Kintners method for

the calculation of image profiles for _partially coherent

illumination. In order to increase the speed and _accuracy

in the calculation of image profiles from these equations,

computer software has been utilized. Ms. Nyyssonen of the

National Bureau of Standards has provided computer software

that can be 'adapted to the Nikon Lampas optical system.

In order to mathemeatically model the Nikon Lampas

optics, certain assumptions must be made. The source inten

sity is made sinusoidal _by a _vibrating mirror to eliminate noise in the system (electrical as well as optical noise).

This will not effect the mathematical model because the stage moves considerable slower than the 3KHx fluctuations

in intensity/ It was assumed the stage _positioning mechanism

to be _highly repeatable and therefore negligible with respect

A mean wavelength of the source will be assumed rather than

the spectral distribution. _{This is} a good assumption since

the system uses a laser source which is monochromatic.

When measuring on a semiconductor silicon wafer or

photomask, the object is _typically a line that is longer

in one _{dimension than the other. The lesser of the two}

dimensions, the width of the _line, is measured rather than

its length. _{By taking} the fourier transform of a _line, a

two dimensional sine function is produced (figure #14).

Since the microscope _only samples in one _dimension, the

second dimension is useless information and is _consequently

not a factor. In figure _#15, the Y direction (second dimen

sion) does not change _signficantly as the fourier transform

of the object (line) is scanned in the X direction. _Thus,

2

the problem simplifies to one dimension rather than two.

The Nikon Lampas optical system in figure #16 must

undergo a few changes before the model can be derived.

First an unresolved point source will replace a coherent

source _producing the same degree of coherence in the

influx optics. The optical system will then look like

figure #17. The next _step is to unfold the optical system

at the object plane so that we can talk in terms of trans

-mittance rather than reflectance (figure #18). This is a

good assumption for thin films but will fail for thick

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COHERENT

SOURCE

LENS

DETECTOR

#1

DETECTOR

#2

OBJECT

by a dark-field _{illumination system as} shown in Figure #19.

In a dark-field _{illumination system the} central radius of

the objective lens is opaqued out and light is diffracted

around the radius to the object plane. Dark-field illumina

tion systems are not used _very much because of poor

signal-to-noise ratio but will work as a model.

The problem is to _apply Kintner's method of _partially

imaging to a coherent illumination system such as the Lampas.

This is _easily solved _by the optical principle of rever

sibility or equivalence. In its original _form, the equival

ence principle states that, when the source is a point

source, "the output of the detector is proportional to the

irradiance that would be obtained at the source _if the surface

of the detector became an incoherent uniform source of light

and the source did not

radiate."

i

In layman's terms, the

equivalence principle _{may be} stated simply; when _{interchanging}

the source with the _detector, the _intensity (power) at the

detector is the same. The principle of equivalence also

implies that an incoherent or _partially coherent optical

system can _{theoretically} produce the same response as a

coherent source (Figure #20). By using the principle of

reversibility, the Nikon Lampas optical system may be repre

sented _by a dark-field illumination system. By reversing

the source with the detector on the Nikon system, instead

POINT

SOURCE

DETECTOR

#1

DETECTOR #2

OBJECT

POINT SOURCE

OBJECT

PLANE

DETECTOR

#1

DETECTOR

#2

POINT

SOURCE

CONDENSER

LENS

OBJECT

PLANE

OBJECTIVE

LENS

IMAGE

PLANE

partially coherent _illumination system. In this way,

Kintner's (N.E.S.) computer programs for the calculation of

partially coherent image profiles _may be used.

National Bureau of Standards programs have been trans

cribed onto the _{Sigma-9 (R.I.T.)} computer facility. To

check the operation of the program for the light-field

case (standard _microscope), Ms. Nyyssonen (N.B.S.) ran

the program on N.B.S. computer facility. The _intensity pro

files for both programs agreed except for a normalized factor

at the origin. The N.B.S. program normalized at the Y-axis

while _my program normalized at the peak intensity. This

will not effect the outcome of the thesis.

To utilize the programs for the dark-field case, the

transmission cross-coefficient (equation #2) must be

altered. Since the problem simplifies to a one dimensional

problem, equation #2 simplifies to the autocorrelation of

3 rectangle functions. The derivation of the transmission

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CONCLUSIONS

The model predicts that the microscope _is theoretically

accurate down to 6/10 of a micron. Experimental data appro

aches _theory with a cut off _frequency of 1.1 microns.

The model also predicts that the microscope is phase

insensitive. A change in the object phase with respect

to the background phase does not change the _intensity pro

file or accuracy.

Ey changing the numerical aperture of either the

detector and/or the objective, the accuracy does not change.

The slope of the intensity profile will vary, i.e. constant

APPENDIX I

This appendix shows _how the transmission cross-coef

ficient was computed _{using R.I.T. 's Sigma-9} computer for

the Nikon Lampas case. If the system were a two dimen

sional _problem, the pupil function K _(f,g) and effective

source _J(f,g) of the microscope would be represented _by

circles. The problem as pointed out in the discussion is

a one dimensional problem. Thus the pupil function _K(f),

K*(f) and the effective source _{J(f) may} be represented _by

rectangles (Figure #21). If the height of these rectangles

were _unity, the area of _overlap of the rectangles would be

the width from the _leading edge to the _trailing (Figure #22).

Using this simple _way to calculate the transmission

cross-coefficient for the dark-field case, a computer

algorithm was made for four different cases. There is

no _overlap when the pupil function K(f) and its complex

conjugate K*(f) are moved in opposite directions.

CASS I

(R0

-Pt)

_R2 _{_C-Rp}

+ _*!>

&

(R

f2) _

R2

(-Rx

+ _f2)

OVERLAP ? _{(Amin (}

(RQ

(Rt

K(f0 +'f")

*R3 "R2

1.0

J(f)

R2

R3

r

i

i

1.0

-R.

"R2 "Ro

f"

R2 RQ

CASE II

(Rt

_R2 _

(-R1

+ ft)

R3

("R0

* fl>

-R2

OVERLAP =

Amin ( _{( R^,}

(^

(.Rq

CASE III

(R0

-R2 -

(-R0

+

V

R3

("R1

+

f2) -

R2

OVERLAP =

Amin _((1^),

(RQ

-(-^

CASE IV

H3

(-R0

+ _fx)

_

R2

&

R3

(-Rx

* _f2)

_

R2

OVERLAP =

R3

-RQ ? j^), ( -R1 + f))

In all _{cases, above,} it is assumed that J _(f), the effective

source, is stationary while the pupil function K(f) and

its complex conjugate K*(f) move, similar to the convol

REFERENCES

1) Nyyssonen, D., "Linewidth Measurement Spotlight,"

Semiconductor _{International. , 39 (1980)}

2) As per _{personal communication with D. Nyyssonen,}

January 10, 1982

3) Nyyssonen, D. , "Theory and Use of the Optical

Microscope for Linewidth Measurement on IC Photo

masks and _Wafers, " N.B.S. Linewidth

Measurement-Seminar _{IV, 5} - 11 (1981)

4) Ponerene, A. T. _S., Coherent Optical Linewidth

Measurement of Thick Films on integrated Circuit

Wafers. R.I.T. Bachelors _{Thesis, May 1981,} p. ₇

5) Nakazawa, K, Measuring System for Fine-line

Lithography. Kodak Microelectronics Seminar Pro

ceedings, October 1980. p. 69

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January 23, 1982

12) As per pergonal communication with D. _Nyyssonen,

VITA

The author was born and raised in Honolulu, Hawaii.

He attended Punahou High School from ₁₉₇₃ to 1977. Upon

completetionof the high school _degree, he moved to Rochester,

New York to attend the Rochester Institute of Technology.

He enrolled in the School of Graphic Arts and Photography