IOTA, a new computer controlled thin film thickness measurement tool

Solid-Store

Electrwzics,

1972, Vol.

15, pp. 37 I-380.

Pergamon

Press.

Printed

in Great

Britain

IOTA, A NEW COMPUTER CONTROLLED THIN FILM THICKNESS MEASUREMENT TOOL K. L. KONNERTH

and F. H. DILL

IBM Thomas J. Watson Research Center, Yorktown Heights, New York, U.S.A. (Received

7 June 1971; in revisedform

9August

1971)

Abstract- IOTA is a very simple high-speed scanning spectrophotometer. A computer, an essential part of the tool, controls data acquisition, corrects systematic errors, normalizes data, and provides data reduction for the specific problem of measuring the thickness of thin oxide films on silicon semiconductor wafers. Data reduction techniques used with this computer-controlled measurement are different from those conventionally used with manually acquired data. Independence from operator induced bias and error is obtained with fully automatic measurement. INTRODUCTION

ONE OF the problems of modern semiconductor technology is the rapid determination of the thickness of transparent thin films on semiconductor substrates. This measurement can be performed indirectly in several ways using optical interference techniques. During the last decade or so there have been many papers written on the CARIS [I, 21 (Constant Angle Reflection Interference Spectroscopy) and VAMF0[2.3] (Variable Angle Monochromatic Fringe Observation) techniques. These have the advantage of being adequately accurate and non-destructive, but the equipment generally used for them is slow and the data reduction tedious. The present paper describes a system which operates under computer control to provide very rapid data acquisition and subsequent on-line reduction of the data. Nicknamed the lnstant Oxide Thickness Analyzer (IOTA), this new tool provides accurate measurement of silicon dioxide films on silicon in a few seconds. Whereas it is similar to CARIS in requiring measurement of reflectivity versus wavelength, the instrumentation used and the analysis of the data are handled very differently. The reported result of the measurement is thickness rather than a curve of optical intensity vs. wavelength or angle of incidence. There is no use of human operators in the measurement loop; thus there is freedom from operator bias and error. Although the present study describes only filmthickness measurement, many other tasks can be

performed rapidly by writing new data acquisition and/or reduction programs, for the instrument is really a computer controlled spectrophotometer.

PHILOSOPHY

OF COMPUTER

CONTROL

The purpose of computer control of a measurement is to provide rapid measurement capability with data reduction, recording, and reporting capability. Although the computer can provide many of the functions normally built into instrumentation designed for human operation, the computer is a very different observer. Humans are good at finding maxima, minima, and nulls, but are only moderate quantitative observers. Computers perform quantitative observations very rapidly, but find maxima and minima only with considerable analysis. Thus the practice of designing computercontrolled measurements using the tools built for humans, with stepping motors turning the knobs and digital outputs provided instead of meters, is highly questionable. Making the computer take an integral part in the measurement instead of an add-on to instrumentation designed for humans considerably simplifies and speeds up the instrumentation required. In the present application the computational capability of the computer, combined with additional use of the physics of thin film optics, allows one to make use of all the data collected, rather than just the maxima and minima as in manual techniques. 371

372

K. L. KONNERTH THE

IOTA

SYSTEM

The IOTA system had a design aim of measuring oxide thickness in 5-15 set; it has easily exceeded this. It was designed from the start around a small available computer system. It currently covers the thickness range from 700 to 20,000 A. The precision of the measurement[41 as determined by repeated measurements gives a standard deviation of 10 A or less over the entire range. to independent The accuracy, as compared measurements made by a variety of techniques including ellipsometry. VAMFO and CARIS, seems as good as any of these measurements (i.e., within k-30 A or so). Other features such as independence of sample placement and convenience of fiber-optic optical paths have made the measurement easy to utilize. Three components make up the oxide thickness measuring tool: the instrumentation. the general purpose computer, and the programming or software. The instrumentation consists of a very simple reflectance spectrophotometer in which the monochromator element is a variable wavelength interference filter. This spectrophotometer operates in a two-path mode over the wavelength range from 4000 to 7000 A, providing data to the computer at 54 sampled wavelengths for each path. One path provides direct data for the computer to use in removing the overall spectral response of the system. The other path includes the reflectance of the oxide coated semiconductor, which carries with it the information needed for the thickness determination. The computer used to control the measurement is an IBM 1130 computing system with suitable interface attachments to allow control of the experiment and collection of the data. Because of the general purpose nature of digital computers. the system personality does not play an important role in the design of the experiment, but will affect such attributes as speed of data reduction. The and programming are same instrumentation planned for connection to an IBM 1800 system, and implementation on an IBM System 7 looks practical. The choice of a small dedicated system allows a good match between instrumentation capability and computational speed. It also allows simple data acquisition programming. The instrumentation could, however, be matched to a larger and faster system in a time-share mode. The programs include those necessary for data

and F. H. DILL

acquisition, those that provide functions normally built into the instrumentation, and those which reduce the data and provide the result desired for the measurement. In addition, a family of debugging, calibration, and statistical analysis programs have been written which facilitate the set-up and performance evaluation of the system. Most of these programs, except for subroutines that handle specific aspects of the data acquisition and control, have been written in the FORTRAN language. Since all the system dependent programming is confined to FORTRAN callable subroutines which control the data acquisition, adaptation of IOTA to other computers involves changing only these subroutines. INSTRUMENTATION

IOTA spectrophotometer was Since the designed for use in a computer-controlled environment, it was possible to keep it very simple and inexpensive while providing large gains in operatspectroing speeds over other inexpensive photometers. Figure I shows a sketch of the spectrophotometer. The heart of the system is an Optical Coating Laboratories. Visible Circular Variable Filter (CVF). It allows construction of a scanning monochromator based upon a rotating variable wavelength interference filter. Although this does not give exceedingly high spectral purity, it is adequate for the thin-film thickness measurement and many other applications. The filter provides a stable wavelength reference determined only by the angular position of the filter. The spectrophotometer consists of a light source and input fiber bundle, the filter monochromator. a sample reflectance measuring system and a reference path, a photomultiplier with its analogto-digital converter, and a timing system to control the wavelengths at which measurements are made. The light source is a special lamp assembly normally used to illuminate fiber optic bundles for IBM card readers. It illuminates a randomized split fiber-optic bundle which has legs to provide illumination for both the direct and reference paths. Other legs provide illumination for the timing system. This and the other fiber optics used in the system were provided by Welch-Allyn. Randomization of the bundle insures that the illumination of each leg of the bundle will have the same optical characteristics. This avoids the possibility of the illumination for the sample and reference paths

COMPUTER

CONTROLLED

FILM

373

MEASUREMENT

SLITS FOR FILTER (INNER) AND TIMING SIGNALS (OUTER)

CIRCULAR

VISIBLE

FILTER

.V. AND OTHER

FROM PHOTO TRANSISTORS HOLE FOR START SIGNAL INCANDESCENT LIGHT

1

Fl8ER

JUNCTION

OPTICS

Fig. 1. Schematic representation coming from portions of the lamp filament having different temperatures. The lamp is powered by a constant current source to eliminate short-term variations in lamp temperature and its spectral output. The optical filter is in the form of a 4 in. dia. half-circular segment which is mounted in a continuously rotating 8 in.. circular disc. The transmission wavelength of the filter varies linearly with angular position from 4010 to 7 190 A over a little less than 159” of rotation. Sampling every three degrees over this span gives 54 points 60 A apart. Two stationary slits are placed behind the rotating disc in diametrically opposite positions. With the filter and the two source illumination bundles in front, the slits are alternately scanned through the spectral range of the filter. Two fiber-optic bundles with one end fanned out into a line to get good optical pick-up are placed behind the slits. One bundle provides a direct optical path to the photomultiplier detector. The other bundle is one end of the split bundle used both to illuminate the sample and to collect the light reflected from the sample and carry it to the detector. This split bundle is also randomized and its diameter determines the area over which

of the IOTA system.

readings are taken on the sample. In the current model this is about 0.1 in. in diameter. The light coming out of the split bundle in the sample holder covers a broad cone because of the very small diameter of the fibers. As shown in Fig. 2,

REF S

:CTED NAL IT

:LEICTED IGINAL OLIT

LIGHT IN

RANDOMIZED

SP

‘LE

d

Fig. 2. Only the light striking the sample at or near normal incidence is collected regardless of sample orientation.

374

K. L. KONNERTH

angular

misalignment

the position ment

is made.

is reflected angular

of the sample

on the sample since only

back

into

only

the measure-

normally

incident

the split

misalignment

changes

at which

bundle.

and change

light

Although

in spacing from

the bundle to the sample affect the level of the output to the photomultiplier. by

requiring

only

and F. H. DILL equal to the filter linewidth, Another with

of relative

re-

an associated

to indicate A

a signal

that the wheel is in the proper

position

number

of refinements

filter

istics

order transmission

by calibration

utilizing

a bare silicon sample.

Thz

use of the split bundle

light collection There and

from

is essentially output

fibers

the sample

surface.

The

operated

in a transmission

mode

spectrophotometer

by substituting bundle.

for

(Schott

well.

middle

the input

by the rotating

end. In addition

FG-3)

be

it has been found

incidence,

spectral

data

for the split

quicker

than any simple

allows

noise suppression.

interference

of the variable

five

times

data points together than I .? sec.

detector

chosen

is not critical.

as few

in general

system

for photons of any wave-

they are not driven too hard. Since

they have very good high frequency do not limit

photo-

the

Photomultipliers

are good linear detectors length, provided

for

response

the speed of the system.

The

they

photo-

1. Its output is converter which is read by the computer when the computer receives a conversion complete signal. multiplier

currently

connected

The

in use is a I P2

to an analog-to-digital

trigger

signal to the A/D

vided by the timing of 54 timing

system.

slits. These

the

disc

There

in line

by two legs of the

bundle.

an optical signal whenver slit.

Phototransistors The

behind

these

a hole passes

phototransistor

output

triggers the A/D converter to start conversion. The system alternately takes 54 spectral points in reflectance

and 54 spectral

as possible.

points for the reference

Since conversion is rotating

filter

moves

time

is about

at approximately

less than 0.02”

This makes the resolution

in the

and

average

integrating Five

noisy

to take

the

it. This

scheme

is

which

readings of the IO8 takes less

is designed

to place

requirements

on the

the optical

filter

needs to have long term

The

matched

or be calibrated

fiber optical

characteristic

paths need only to stay one relative

reflectance

to another.

data is needed as an

input to the data reduction

and this can be derived

by dividing

the reflectance

path data by the refer-

ence

only

data,

short-term

few seconds) is required

stability

(i.e.,

under

of the illumination

a

system

and the detector. OPERATION

OF THE 1OTA SPECTROPHOTOMETER

The operation tus with

during

10 psec and the 4 rev/min,

the

measurement.

of the system essentially

of the spectrophotometer

a computer

quite simple. data.

When

(IBM

1130

the program

it sets a latch which

latch, the computer rupt

occurs.

to

permit

is ready to acquire the ‘start’

light

when it hits the After setting this

goes into a wait until the interreception

of this

signal,

the

then resets the first latch and sets another conversion-complete

analog-to-digital photomultiplier ADC

Upon

appara-

in this case) is

enables

signal to produce an interrupt corresponding phototransistor.

computer

path. filter

in the red

Only

stability.

the measuring

slits receive

of the

expedient

system

are two stationary with

slits are illuminated

helps com-

is a relatively

stability

of the interference

of the rotating

illumination in front

is pro-

term

Since only relative

filter

consists of a set

holes in the periphery

disc that holds the filter. slits behind

converter

This

long

This

response

with their averaging

The instrumentation photomultiplier

high

in the

and low lamp emission

detector

is operated

optical

cutoff

filter at the long-

range.

blue. Since the photomultiplier

also

absorb.

a broad absorbing

of the wavelength

to

Corning

is used to cut transmission

pensate for low photomultiplier

filter. The

U.V.

could

optics

calibration

transmit

end of the spectrum

use of normal

using

wavelength

(visible

of a reflecting

In fact the spectrophotometer mode

very

and

mode, or in a reflection

a pair of fiber

in transmission filters

works between

absence

that did not make

3.75

are used in order

of the apparatus.

at 3800 A) is used in the optical path to prevent wavelength

for illumination

no coupling in the

procedures

to start.

the performance

flectance by the spectrophotometer. The effect of small differences in the two optical path characcan be removed

bundle,

is used to provide

for the data acquisition improve

hole in the disc together

leg of the illumination

slit. and phototransistor

this is made unimportant

a measurement

which is I70 A or less.

single sampling

converter output

is continually

signals (ADC),

to produce

being triggered

from

the

reading interrupts.

the (The

to convert

by

COMPUTER

CONTROLLED

the output of the two trigger phototransistors). The computer ‘waits’ for each interrupt and upon its reception stores the reading of the ADC. A counter in the program is used to determine when both the data and calibration scans have been completed. Reception of another start pulse could also be used for this purpose. In practice data from several revolutions of the wheel are generally used to minimize noise effects. The reproducibility of the measured data is quite good, as can be seen in Fig. 3 in which 25 sets of measurement points are superimposed on the same graph.

0.1 __

FILM

MEASUREMENT

315

incidence of the light, and only the angles of minima and/or maxima are used. In neither case is quantitative data utilized except to indicate the location of maxima and minima. In the computer-controlled environment it was felt that it would be worthwhile to take advantage of the computational power of the digital computer to use all, or most of, the data collected. Since the data was put directly into the computer by the instrumentation, there is no problem trying to read many points from a plotted curve manually into the computer. The approach that we have used can be summarized very simply. The data is first acquired with a degree of accuracy consistent with the results desired. In order that absurdly tight restrictions not be placed on the spectrophotometer and the mounting of samples. only relative reflectivity versus wavelength is obtained at points uniformly spaced through the visible spectrum. By understanding the physics of thin film reflectance this data can then be converted into absolute reflectivity data. Knowing the wavelength at which each measurement was made and having derived the corresponding absolute reflectivity, we can solve directly for the film thickness at each measurement point. For the ideal case, the thickness calculated at all data points should be the same. In practice, noise of various types causes scatter in these results but their average gives an estimate of the thickness and the scatter provides some measure of the accuracy of the measurement.

40000 l-

THEORETICAL BACKGROUND WAVELENGTH (ii,

Fig. 3. Twenty-five superimposed experimental reflectivity curves demonstrating reproducibility of the apparatus. DATA REDUCTION FOR IOTA

Both CARIS and VAMFO are designed for human reduction of the data taken. In CARIS, where the spectral reflectance curve of the oxidecoated sample is measured with a conventional spectrophotometer, only the wavelength information associated with the minima and/or maxima of the reflectance curve is used to determine the film thickness. AI1 data taken at points between is thrown away. Similarly in VAMFO the reflected intensity is measured as a function of angle of

At normal incidence the reflectivity from a lossless film with index of refraction N, on a substrate with index of refraction N, and extinction coefficient K, in an ambient with index of refraction N,, is related to the thickness of the film as follows: film thickness = &

{$I + 2~7(order) 1 + cos-’

Refl (1 + R12R22) - RI2 - Rz 2R,R2 (Refl- 1) I)

where d, = tan-’

~NIKz N,’ -No’ - K,

K. L. KONNERTH

376

R 2 = (N,-N,)‘+Ke’ ’ (NZ+N,)2+KLZ’

and F. H. DILL

This is shown in Fig. 4. Thus given a general relative reflectivity curve as shown in Fig. 5 it can be converted into the absolute curve (also shown in Fig. 5) by multiplying the entire curve by whatever constant is necessary to bring it tangent to the envelope curves.

Thus, given a wavelength and the corresponding reflectivity one can directly calculate the film thickness if the optical constants and two other factors are known. The other factors are the fringe order in which the given point lies and whether the point lies with a maximum of the adjusted reflectivity curve on its right and a minimum on its left or vice versa. The latter is required to determine the correct sign for the arc cosine. If great care were taken in making the reflectivity measurements the absolute reflectivity could be measured directly, the values put into the equation, and the thickness determined. However this requires, among other factors. that the surface of the film always be located in exactly the same place at the same angle. It was chosen to avoid this restriction since one can make relative reflectivity measurements and later convert them to absolute values. The mathematical characteristics which permit this conversion can be seen by looking at the equation for reflectivity:

absolute

I

Reflectivity

RIZ + RPP+ 2R, Rr cos (2p - $J) = 1-t R,2R,2 + 2R, R, cos (2p -4)

where P=_

2vi-dN,

'0

I 5000

I

I

I

6000

WAVELENGTH

I

7000 (it,

Fig. 4. Theoretical reflectivity curves for various film thicknesses of SiO, with envelope curves. The + curve is for bare silicon.

d = film thickness. Analysis of this equation shows that all curves of reflectivity vs. wavelength (wavelength appears both explicitly and implicitly in the optical constant variation) must be bounded by envelope curves produced by setting the cosine term equal to either + 1 or - 1. The higher curve obtained by setting the cosine equal to + 1 is in this case very near the reflectivity of a bare silicon substrate. The analysis shows further that at order changes and a point between them the reflectivity curve must be tangent to one of these two bounding curves.* ‘In both CARIS and VAMFO correction terms are needed since maxima and minima are used instead of points of tangency to their limiting curves.

LIMITATIONS It is

OF THE ANALYSIS

TECHNIQUE

evident from the preceding discussion that this technique requires that at least one maximum or minimum (or. more specifically a point of tangency to the limit functions) be included in the wavelength region scanned. This places a lower limit on the thicknesses that can be measured since such a condition does not exist for SiO, film thicknesses of less than about 700 A. If the data indicates that the film is thinner than this, the program can branch to a curve-fitting routine which has been used experimentally. Otherwise it can give a noresult indication. Another region with no extrema exists between 1225 and 1375 A; however in this region either the left end of the curve is near enough

COMPUTER

CONTROLLED

FILM

MEASUREMENT

377

O’-dcir

4000 WAVELENGTH

(A,

Fig. 5. + shows a measured relative reflectance for a sample intentionally tilted to return a low signal level. x shows the data after adjustment by the program.

to a minimum or the right to a maximum that, with suitable analysis, very little error is introduced. Another limitation on the use of the system occurs for very thick films. With the present 54 data points per scan, the significant characteristics of the data cannot be resolved for thicknesses greater than about 20,000 A. There are simply too many fringes contained in the scanned wavelength region. The system can easily be modified to take more data points and alleviate this problem. For thick samples the finite line width of the monochromator washes out the detail in the curves because they contain many fringes. This effect causes less of a problem than might be expected, however, because some of the data points give results which are too large and others too small. Theoretical studies show that the average comes quite close to the real value. Figure 6 shows a theoretical reflectivity curve for a 20,000 A film for perfectly monochromatic light as well as for light which has a line width of 200 A. The film thickness determined by feeding these sets of data into the analysis program is 19,999 8, for the former and 19,994 A for the latter.

SSEVol.

15,No.LI3

5000

i

6000

WAVELENGTH

(A,

Fig. 6. Comparison of theoretical reflectivity curves for a 20,000 A thick film assuming (a) zero source linewidth (curve with touches the envelope) and (b) 200 A source linewidth (which approximates the real case). Insensitivity of the programming to this distortion is apparent if both sets of data are processed by the program. The first produces a thickness determination of 19,999 A and the latter, 19,994 A.

RESULTS

As long as one does not get too close to the limits of thickness discussed above, the precision of the measurement is very good[4]. Multiple measurements (generally 480) have been made on samples with oxide film thicknesses of from about 750 8, to 17,000 A. In all cases the standard deviation of the measurements was 10 A or less. Histograms of some typical results are shown in Figs. 7, 8 and 9. The double or multiple group effect noted in Fig. 7 is frequently seen in measurements of thick (> 10,000 A) films. It occurs in a particular class of reflectivity curves where a slight amount of noise on a data point causes a quantized error in the calculation of the curvemultiplying factor. The effect is not very serious, though, since the peaks are not far apart, percentagewise. Determining the accuracy of a system such as this is much more difficult than evaluating the

378

K. L. KONNERTH

7

and F. H. DILL

3oor7777

i i DEVIATION

FROM

AVERAGE

T IO

6%

Fig. 7. Typical histogram for the conditions where the system picks one of two values depending upon slight noise fluctuations. This effect only occurs for thick films where separation between the peaks is a very small percentage of the thickness. For 480 readings the average thickness is I 1,645 p\ and a standard deviation of 6 A. precision. Comparison has been made with CARIS. VAMFO, and ellipsometer measurements on the same samples. In an environment where

measurements are performed routinely by operators, the agreement between techniques and between laboratories using the same technique is not good enough to allow us to specify accuracy very closely. Ellipsometer measurements by a careful Ph.D. in a research environment show a systematic error on the part of IOTA. This probably is due to our choice of optical constants for the SiO, films and could be corrected. A comparison of results measured by IOTA and two different ellipsometers is shown below. Ellipsometer A. which shows readings consistently lower than IOTA, was operated by a scientist and probably should be considered to be correct values. The ellipsometer B measurements were made in a routine measurement environment and are scattered above and below the other two sets. This seems to represent typical accuracy of ellipsometer

DEVIATION

FROM

AVERAGE

(8,

Fig. 8. Typical histogram for a thinner sample in which the multiple peak effect of Fig. 7 does not occur. This is the usual case. For 480 readings the average measured thickness is 4447 A and a standard deviation of I .8 A.

measurements made by non-scientifically trained operators. This is more or less typical of results obtained with VAMFO and CARIS as well. In the present apparatus data acquisition requires approximately 1.3 sec. The analysis time is dependent upon the number of data points actually used in the calculations which is determined automatically by the program. (Only a portion of the measured points are actually used for calculation on relatively thin films). If only 18 are used the calculations require about 1.5 set whereas if all 54 are used they take about 4 sec. SYSTEM MODIFICATION The program described here was designed for very general purpose SiO, thickness measurement. That is, any sample can be placed in the apparatus with a film thickness of from 750 to 20,000 A and the program will automatically determine the thickness in 5 set or less. If such a general purpose routine is not required, since there may be some a priori knowledge about the range of sample thickness, the system can be easily altered to provide higher speed, better precision, better accuracy

COMPUTER

CONTROLLED

FILM

MEASUREMENT

379

Table 1. Ellipsometer A 1OTA (Average 50 readings)

(2 readings) thickness

142 1215 2441 4378 4800 7867 10067 12224 14139 15667 17975 22676

Ellipsometer B

% difference from IOTA

(1 reading) thickness

-2.0 -1.5 -0.1 -0.6 -0.2 -0.2 -0.2 -0.2 -0.1 -0.2 -0.1 -0.2

727 1202 2551 4470 5037 7870 10012 12114 14855 15592 17797 22440

121 1197 2424 4350 4790 7850 10050 12200 14120 15640 17960 22640

% difference from IOTA -2.0 -1.1 4.5 2.1 4.9 0.04 -0.5 -0.9 5.1 -0.5 - 1.0 -1.0

noise suppression and thus greater precision. Many other modifications can be made to tailor the system to the need. CONCLUSION

0.

r-

-6

-4 DEVIATION

-2 FROM

0 AVERAGE

2 (%,

Fig. 9. Another typical histogram. For* this sample the average of 480 measurements was 1024 A with a standard deviation of 1.6 A.

of these. Better data smoothing algorithms can be used if the data is known to fall within a limited range. More accurate values of the optical constants could be used if all samples came from the same process. Where speed is not essential, an integrating digital voltmeter has been used for the data acquisition to provide vastly greater or a combination

The IOTA system as described is in current use measuring thickness of SiOz films, photoresist, and other dielectric films. It measures and reduces the data at a rate far greater than any other known tool. The current speed is chiefly program limited, and could be improved an order of magnitude by using fixed-point arithmetic. Further programming planned will allow measurement of the index of refraction and optical absorption of films as well, provided that the optical constants of the substrate are known. With other programs IOTA can perform the functions of a general purpose spectrophotometer either in transmission or reflectance. The concepts used in its construction can be extended from the near i.r. to the near U.V. With design modifications the system could be set-up to be N-path rather than dual path. This would allow measurements on N - 1 samples or at N - 1 points on a single sample simultaneously. Acknowledgements-The authors would especially like to acknowledge the contributions of Mitchell Phillips who provided the interface hardware for connection of the IOTA spectrophotometer to the 1130 system.

REFERENCES 1. F. Reizman and W. VanGelder, 10,625 (1967).

Solid-St. Electron.

380

K. L. KONNERTH

2. W. A. Pliskin, Progress in Analytic Chctni.ytry. Vol. II. pp. I-34, Plenum Press, New York (1969). 3. W. A. Pliskin and E. E. Conrad. IBM J. Nes. Dev. 8, 43 (1964).

and F. H. DILL 4. E. M. Pugh and 0. H. Winslow. The Anu1ysi.s oj Plzysicul Meusurements. pp. 6- 14. Addison Wesley.

Massachusetts.

(1966).