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A high speed precision automatic ellipsometer
SURFACE
SClENCE
A HIGH
16 (1969)
SPEED
166-176
PRECISION
‘0 North-Holland
AUTOMATIC
Publishing
Co., Amsterdam
ELLIPSOMETER
B. D. CAHAN John Harrison
Laboratory Philadelphia,
of Chemistry, Pennsylvania
University of Pmnsylvania, 19104, U.S.A.
and R. F. SPANIER
An ellipsometer is described Fifty data points per second of 0.01”.
which can measure the characteristics of a film in 0.02 sec. are generated. Azimuth can be measured with an accuracy
I. Introduction Although ellipsometry has proven to be an eminently sensitive and useful tool for the study of surfaces, the standard experimental techniques are relatively slow. Manual balancing of the polarizer and analyzer by the method of swings takes a skilled operator two to five minutes under steady state conditions, and is almost impossible in a dynamically changing system (for example, during film growth). We propose below a fast, automatic ellipsometer that will measure the azimuth c(, and ellipticity E of elliptically polarized light in 0.02 sec.
2. Automatic ellipsometry The essentials of an ellipsometer (shown diagrammatically in fig. 1) consist of a collimated and monochromatic light source, a polarizer, with or without a quarter-wave plate, a surface, an analyzer, and some form of photodetector. In simple nulling systems the detector (e.g. the human eye or a photomultiplier) is used to determine the positions of the polarizing optics for which the light is a minimum. When the quarter-wave plate is located before reflection with its fast (slow) axis oriented at 45” to the plane of incidence, the intensity of transmitted light is related to the ellipsometer angles as in eq. (1): i = I,,,,, [sin’(A
- A,) + sin2A, 166
sin2A sin2(P
- P,)] ,
(1)
HIGH SPEED
PRECISION
AUTOMATIC
167
ELLIPSOMETER
Photo-detector
/
Surface
Fig. 1.
The essential components
of an ellipsometer.
where A and P refer to the orientations of the analyzer and polarizer tively, and the subscript zero refers to the extinction orientation. polarizer is set at extinction (P= PO),
respecIf the
I = I,,,,, sin’ (A - A,) = I,,, sin’ 0, as shown in fig. 2. In addition,
if A is near extinction I E Imax&
(3)
I-
(Asin8j2
28
= A2
sin
=$
(I-cos
y
L-
2814
(,_,+(z$‘- l&t+__) 4!
=
;
(282-$
+___
)
8=0 O 61 _zI
Fig. 2.
The transmitted
288 8
intensity as a function of analyzer orientation
A = I,,,.
168
That
CAHAN
is, near extinction,
approximated
AND SPANIER
the dependence
by a parabola,
of transmitted
intensity
may
be
and dl
2 U’O
1
I)’
A null can be found by measuring a particular (but arbitrary) 0 on each side of the null for which the transmitted light intensities are equal. The technique is called the method of swings and can be done manually or, as recently developed, automaticallyl). With such an automatic ellipsometer the operator is replaced by an on-line computer, and his hands with a set of stepping motors to turn the polarizing crystals more rapidly. Another ellipsometer developed in the past employs continuous modulation of the polarization state of the light. Different means of achieving the modulation are; electrooptica12), where the polarization state is altered by the Kerr, Faraday or Pockels effects; or electromechanical”), where the polarizer is mechanically moved by a motor or rocker arm. Fig. 3 shows a sinusoidal modulation applied to the parabolic approxiL‘l
Fig. 3.
Effect
of parabolic
transfer
curve
on shifted
sine wave
modulation.
HIGH
mation
SPEED
to the transmitted
PRECISION
AUTOMATIC
intensity,
169
ELLIPSOMETER
and the resultant
output
waveforms.
Let the exciting wave be sinwt (o=modulation frequency), and 6’ be the displacement of the analyzer from extinction (O=A - A, ; see eq. (1)). Then the transmitted intensity is a function of both 0 and cc)t: I = I,,,(0
+ sin cot)‘,
I = Imax[02 + 20 sinot
+ +(l - cos20t).
When 0 =0 (analyzer at extinction) the transmitted intensity is a pure sinusoid with frequency equal to twice the modulation frequency (case 2, fig. 3). But if O# 0, a signal is produced with amplitude proportional to 8 and which undergoes phase reversal as 0 changes sign. If this sign wave is detected synchronously with the input, a signal can be developed whose sign indicates direction of the error and whose magnitude increases with the displacement. The foregoing analysis applies to any of the modulating systems mentioned above, and for any modulating waveform, be it sine, square, or triangular. The error signal is not used directly to measure the ellipsometric angle because the transfer curve is quadratic only for small 0. A, and PO are determined by using the error signal to control a servo, or control a stepping motor, or change the bias voltage across a Kerr or Pockels cell, or change the bias current through a Faraday cell. Both analyzer and polarizer can be modulated. If two widely different frequencies are used, A and P can be monitored simultaneously4’5). Alternatively, the signal can be chopped so that one element is measured and adjusted and then the other. The systems described have inherent disadvantages. 1) The light source intensity must be constant. Obviously, any noise in the light source will also be modulated and affect the null. For example 50 or 60 Hz (or 100 or 120 Hz) hum from the line voltage can produce objectionable beats with the modulating source. 2) The modulating source must respond linearly to the exciting signal. Any harmonic distortion (especially even harmonics), will give an apparent offset which may not be constant with different P and A. Even a small harmonic content in either the driving signal or the modulating cell can cause appreciable errors. 3) The detection system must be phase linear. Any differences in phase between the harmonics and the fundamental will appear as errors in the angles. 4) Tn order for a chopped or modulated system to be stable and to avoid oscillations, the response time should be about eight times longer than the
170
CAHAN
AND SPANIER
chopping period. This problem can be especially severe in ellipsometry where several stable sets of angles are possible for a given surface. 5) A highly accurate readout is required for an instrument that covers even the limited range of IO”. A 0.1% linearity is required in the polarization transducer. 6) In order to stay in the region where the parabolic approximation is valid, and to avoid driving a capacitive Kerr cell or inductive Faraday cell with a large signal, the modulating signal must be kept low. Unfortunately, this means working at low signal levels with the attendant noise and response time problems. 7) Unless a rather complex gating system or a dual frequency modulation is used, or a digital computer, it is only possible to follow one of the ellipsometric parameters at a time, and generally both are varying. 3. Modulation
over 360“
In our automatic ellipsometer the desired information is obtained by a 360” rotation of one of the polarizers. For example, if elliptically polarized light is incident on the analyzer and if the analyzer is rotated at constant frequency o, the transmitted intensity I varies in time as indicated in fig. 4, where Q=A -A, = ol. Curve A represents the transmitted intensity for incident light with ellipticity, E=E~, and azimuth CI=C(~. Curves B and C show the effect of changing E to s1 and !I to cur respectively. Though changes in E and Mgenerally occur simultaneously in ellipsometry, they are indepen3=
Fig.
4.
Phase
Shift
The effect of changing the orientation and ellipticity incident on a rotating polarizer.
of elliptically
polarized
HIGH
SPEED
PRECISION
AUTOMATIC
ELLIPSOMETER
171
dent and separately measurable. Azimuth is merely a phase shift and ellipticity is the arctangent of the square root of the ratio of minimum to maximum intensities. 4. Measurement
of azimuth
To measure the azimuth of the ellipse with an accuracy of 0.01” requires the phase of the transmitted light to be measured with an accuracy of 0.003%. We accomplish this using a digital counting method. The analyzer is mounted in the hollow shaft of a special rotating cogless direct drive servo-system. The unit is aligned so that the rotational axis coincides with the optical axis. This adjustment, together with a minimal optical wedge effect, insures that the ray of light always passes through the same area of the polarizer regardless of orientation, and reduces unwanted phase shifts inherent in the analyzer.
Fig. 5.
Measurement
of phase shift.
The electronic system used to measure the phase operates on the principle shown in figs. 5 and 6. In general, the output from the photodetector will be a pure sine wave with frequency twice that of the angular rotation displaced above the zero line. It can be seen that dZ/dtI is greatest at the 45” point (level A). An electronic level detector set at A will produce a constant output which is plus when the intensity is greater than A, and off otherwise.
172
CAHAN
AND
SPANIER
L
_
Fig. 6.
Digital
phase
comparator
for Y.
A modified quadrature detector is used to compare the square wave output from the level detector with a reference square wave. The modified quadrature detector produces a signal that is plus when the square wave from the level detector changes (from 0 to + V or + V to 0) after the reference wave charlges, and a negative signal for the opposite situation. The quadrature detector signal is zero when the level detector signal and reference signal are both high or both low (see “Advance” and “Retard” in fig. 6). The phase of the sine wave is thus obtained by analog integration or digital counting of the quadrature detector signal. This system is unaffected by light source intensity variations and level detector fluctuations that are slower than 0.01 set as indicated by cases B and C in fig. 5. Analog integration of the quadrature signal is not accurate to 0.01” for large phase shifts. Therefore, the digital system shown in fig. 6 was developed. The servo-rotator has its speed controlled by an optical encoder disc with two tracks, one with 720 lines (or 2 per degree) and one half black and half clear to provide an absolute mechanical zero reference point. The master oscillator (A) produces a 3.6 MHz square wave which is counted down to 36 kHz by (B) to lock the servo to a precise 50 rps drive. The 36 kHz signal is divided again at (C) by 2 producing one pulse (or one cycle of a square
HIGH
SPEED
PRECISION
AUTOMATIC
ELLIPSOMETER
173
wave) per degree of analyzer rotation while each degree is split into 200 parts by the master oscillator. The “zero” pulse from the optical encoder sets flipflop (E) which allows the first degree pulse from (C) after the “zero” to pass through the gate (F), resetting a counter (G) to zero. The gate then turns off (E) preventing further pulses from coming through. In the storage register (H) is a number which we shall return to later and which we shall call zero initially. When the comparator (I) sees the same number in (G) and (H) it emits a signal which resets counters (Ji), (J2) and (J3), sets flipflop (K), which turns on gate (L), which lets counter (J) start counting degree pulses. The output from (J,) is thus a square wave with frequency twice the analyzer rotation frequency and phase tied to the mechanical zero. After 270” of analyzer rotation, or two “up” portions of the square wave, flipflop (K) is turned off to wait for the next zero signal. Meanwhile, the photodetector (M) and the level detector (N) produce a signal square wave which is fed with the reference signal into the quadrature detector (0). This produces a + or - signal, that controls an up-down counter (P), which counts the 3.6 MHz from (A) after division by 8 at (Q) since there are 4 counting periods per revolution and 200 pulses per degree of analyzer rotation. The 360 counter counts integral degrees of phase, while the 100 counter counts fractional parts, and can be displayed, or read out at (R). At the end of one revolution, the integral degree part in (P) is transferred into the storage register (H), and the fractional part is cleared. On the next revolution, (I) will not produce a pulse until the drive has advanced through the number of degrees in (H). Thus the reference wave is shifted to follow closely the optical signal, while the counter (P) follows and remembers this shift. In this manner the unit can track through 360” or more, without ambiguity, presenting a digital readout of a every revolution (or 50 times/set) with an accuracy of 0.01”. The level detector (N), will work with almost any reference level between the minimum and maximum, but has its best sensitivity and accuracy near the average of the two or at the 45” point. Fig. 7 shows the photodetector at (A), and an average value circuit (B). A differentiator (C) determines the peak and valley points of the transmitted light and a pulser (D) activates a track and hold circuit (E). This unit maintains the average value over each 180” of analyzer rotation for the level detector (F). Unit (C) also supplies a set of enabling signals to two sets of cascaded track and hold circuits (G) and (H), which store voltages proportional to I,,, and Zminrespectively. These voltages can then be processed with a digital ratio meter to produce tan* E or with an analog circuit to produce tan& or a.
174
LIGHT
CAHAN
3
AND
SPANIER
PHOTODETECTOR
TO DETECTOR
-
O”ALl
DETECTOR
AMPLIFIER
I DIFFERENTIATOR 8 LEVEL DETECTOR
I_
-
TBH
Fig. 7.
Measurement
of Ima, and kin.
While tan’& could be used for any ellipsometric computations E can be computed directly using the novel analog circuit shown in fig. 8. Four matched logarithmic amplifiers are connected in a division network. With this circuit, if b = 1, the ratio I,,,i,,/Z,,,ax= tan2 E is produced. If b = 2, the square root is taken and V,, = tan E. If another resistor is connected at A or at B, it can be shown that an output of the form
b=2:
If bR
for proper b
choice
of
, C 9 Vet.
for O” (E ( IO0 (.3% for 00 ( t( 450 1
(.l%
Fig. 8.
Computation
of E from tan2E.
HIGHSPEEDPRECISIONAUTOMATIC ELLIPSOMETER
results,
where
I/ref, b and c are arbitrary
constants.
These constants
175
can be
optimized to a give a five point fit to the arctangent curve within the tolerances shown. Slightly different values of these constants may be used to fit a wider range at slightly reduced accuracy. It should be noted here that since a ratio is taken, the effects of drift in lamp brightness or change in surface reflectivity are greatly reduced.
5. Conclusions The fully automatic ellipsometer described is rapid and precise, producing a set of data points 50 times per second with CCaccurate to 0.01” and E to 0.1%. The primary sources of error in phase measurement have been eliminated or minimized by symmetric measurements. Even higher resolution can be obtained (at the expense of time resolution) by lowering the drive frequency to the servo-system or by counting over n cycles and dividing the count by n. The system is thus equally suited for the study of transients during film growth studies (where a high degree of sensitivity is required in very short times), for steady state work on a large number of samples (here balance time must be minimized) or as a production monitor, where “instantaneous” readings for feedback to a process controller are required.
References 1) J. L. Ord and B. L. Wills, Appl. Opt. 6 (1967) 1673. 2) Ellipsometry in the Measurement of Surfaces and Thin Films, Eds. E. Passaglia, R. R Stromberg and J. Kruger (Natl. Bur. Std. Misc. Publ. 256, U.S. Govt. Printing Office, Washington, 1964) pp. 97, 115. 3) For example: B. Rao, Dissertation, University of Pennsylvania, 1966. 4) I. Wilmanns, Surface Sci. 16 (1969) 147. 5) H. Takasaki, J. Opt. Sot. Am. 51 (1961) 463.
Discussion D. E. ASPNES(Bell Telephone Laboratories) The determination of either d or # by your method requires the amplitude ratio of the ac and dc components of the intensity as well as the phase of the ac component. In order to make full use of the 0.005 % resolution which you obtain in the phase, the amplitude ratio should also be determined to the same order of accuracy, or N 0.01”/57.3” N 10e4 as compared to unity. This places a limitation of one part in lo4 on the linearity of the detector, which has been implicitly assumed throughout the discussion. Have you a method of compensating detector nonlinearities to this order of accuracy? B.D.CAHAN Using a matched pair of phototransistors
mounted in a common heat sink, and connect-
176
CAEIAN
ANDSPANIER
ed as a differential preamplifier (and consequently biased out of the dark current region), the conversion sensitivity (dlx/dH) of base current to equivalent photocurrent in the emitter base diode is quite linear. Connecting this different~a1 preamp to a stabilized operational amplifier, and feeding back a current into the base of the input transistor proportional to the output voltage, an extremely linear photodetector results. Even if this linearity were not obtainable, however, the accuracy of d /I for small changes of $I would still be quite good and $initiar can be found from a “steady-state” reading on the original surface using the automatic ellipsometer in slightly more conventional manner (i.e., determining $ by manual rotation of the polarizer using the “$-readout” as a null device, and then calibrating the “#-readout” with this value with the polarizer set at 45” again. Since Ji changes are usually much smaller than d changes during the initial period of film growth, much less stringent requirements are found for the measurement of J, than for d in determining film thickness. Far more severe problems occur during a transient when #J -45”, the light becomes circularly polarized, all phase information is lost, and the digital detector stops tracking. This problem area can be avoided by offsetting the quarter wave plate or the polarizer from 45”, but at the expense of a lack of complete separation of d and #. H. G. JERRARD(University of Southampton) 1 would have thought that with a quarter-wave plate you get a linear system, which would be preferable to the quadratic system you have without it. M. GENSHAW(University of Pennsylvania) If an exact quarter-wave plate is positioned between the reflection and rotating analyzer and oriented at 45”, a complete separation of d and #results. The phase of the light output signal is linearly dependent on d. The intensity ratio Imin/l~nsx is a function of 4. For a 45” setting of the polarizer the function simplifies to the form: * -- 45 - arc tan(Imin/ZmaX)*. 6. D. CAHAN The system does, in fact, usually use a quarter wave plate, to separate d and 9, as Dr. Genshaw points out. Although the phase, d, is made linear, $J is not. Occasionally, the system would be operated without a quarter wave plate, giving azimuth and ellipticity, in those cases where If,equals 45” and the phase detector cannot track at that point. Even in this case, if the quarter wave plate is used, as soon as $ passes through 45” the phase detector would lock back in, although with a possible 180” uncertainty induced at the transition.
SClENCE
A HIGH
16 (1969)
SPEED
166-176
PRECISION
‘0 North-Holland
AUTOMATIC
Publishing
Co., Amsterdam
ELLIPSOMETER
B. D. CAHAN John Harrison
Laboratory Philadelphia,
of Chemistry, Pennsylvania
University of Pmnsylvania, 19104, U.S.A.
and R. F. SPANIER
An ellipsometer is described Fifty data points per second of 0.01”.
which can measure the characteristics of a film in 0.02 sec. are generated. Azimuth can be measured with an accuracy
I. Introduction Although ellipsometry has proven to be an eminently sensitive and useful tool for the study of surfaces, the standard experimental techniques are relatively slow. Manual balancing of the polarizer and analyzer by the method of swings takes a skilled operator two to five minutes under steady state conditions, and is almost impossible in a dynamically changing system (for example, during film growth). We propose below a fast, automatic ellipsometer that will measure the azimuth c(, and ellipticity E of elliptically polarized light in 0.02 sec.
2. Automatic ellipsometry The essentials of an ellipsometer (shown diagrammatically in fig. 1) consist of a collimated and monochromatic light source, a polarizer, with or without a quarter-wave plate, a surface, an analyzer, and some form of photodetector. In simple nulling systems the detector (e.g. the human eye or a photomultiplier) is used to determine the positions of the polarizing optics for which the light is a minimum. When the quarter-wave plate is located before reflection with its fast (slow) axis oriented at 45” to the plane of incidence, the intensity of transmitted light is related to the ellipsometer angles as in eq. (1): i = I,,,,, [sin’(A
- A,) + sin2A, 166
sin2A sin2(P
- P,)] ,
(1)
HIGH SPEED
PRECISION
AUTOMATIC
167
ELLIPSOMETER
Photo-detector
/
Surface
Fig. 1.
The essential components
of an ellipsometer.
where A and P refer to the orientations of the analyzer and polarizer tively, and the subscript zero refers to the extinction orientation. polarizer is set at extinction (P= PO),
respecIf the
I = I,,,,, sin’ (A - A,) = I,,, sin’ 0, as shown in fig. 2. In addition,
if A is near extinction I E Imax&
(3)
I-
(Asin8j2
28
= A2
sin
=$
(I-cos
y
L-
2814
(,_,+(z$‘- l&t+__) 4!
=
;
(282-$
+___
)
8=0 O 61 _zI
Fig. 2.
The transmitted
288 8
intensity as a function of analyzer orientation
A = I,,,.
168
That
CAHAN
is, near extinction,
approximated
AND SPANIER
the dependence
by a parabola,
of transmitted
intensity
may
be
and dl
2 U’O
1
I)’
A null can be found by measuring a particular (but arbitrary) 0 on each side of the null for which the transmitted light intensities are equal. The technique is called the method of swings and can be done manually or, as recently developed, automaticallyl). With such an automatic ellipsometer the operator is replaced by an on-line computer, and his hands with a set of stepping motors to turn the polarizing crystals more rapidly. Another ellipsometer developed in the past employs continuous modulation of the polarization state of the light. Different means of achieving the modulation are; electrooptica12), where the polarization state is altered by the Kerr, Faraday or Pockels effects; or electromechanical”), where the polarizer is mechanically moved by a motor or rocker arm. Fig. 3 shows a sinusoidal modulation applied to the parabolic approxiL‘l
Fig. 3.
Effect
of parabolic
transfer
curve
on shifted
sine wave
modulation.
HIGH
mation
SPEED
to the transmitted
PRECISION
AUTOMATIC
intensity,
169
ELLIPSOMETER
and the resultant
output
waveforms.
Let the exciting wave be sinwt (o=modulation frequency), and 6’ be the displacement of the analyzer from extinction (O=A - A, ; see eq. (1)). Then the transmitted intensity is a function of both 0 and cc)t: I = I,,,(0
+ sin cot)‘,
I = Imax[02 + 20 sinot
+ +(l - cos20t).
When 0 =0 (analyzer at extinction) the transmitted intensity is a pure sinusoid with frequency equal to twice the modulation frequency (case 2, fig. 3). But if O# 0, a signal is produced with amplitude proportional to 8 and which undergoes phase reversal as 0 changes sign. If this sign wave is detected synchronously with the input, a signal can be developed whose sign indicates direction of the error and whose magnitude increases with the displacement. The foregoing analysis applies to any of the modulating systems mentioned above, and for any modulating waveform, be it sine, square, or triangular. The error signal is not used directly to measure the ellipsometric angle because the transfer curve is quadratic only for small 0. A, and PO are determined by using the error signal to control a servo, or control a stepping motor, or change the bias voltage across a Kerr or Pockels cell, or change the bias current through a Faraday cell. Both analyzer and polarizer can be modulated. If two widely different frequencies are used, A and P can be monitored simultaneously4’5). Alternatively, the signal can be chopped so that one element is measured and adjusted and then the other. The systems described have inherent disadvantages. 1) The light source intensity must be constant. Obviously, any noise in the light source will also be modulated and affect the null. For example 50 or 60 Hz (or 100 or 120 Hz) hum from the line voltage can produce objectionable beats with the modulating source. 2) The modulating source must respond linearly to the exciting signal. Any harmonic distortion (especially even harmonics), will give an apparent offset which may not be constant with different P and A. Even a small harmonic content in either the driving signal or the modulating cell can cause appreciable errors. 3) The detection system must be phase linear. Any differences in phase between the harmonics and the fundamental will appear as errors in the angles. 4) Tn order for a chopped or modulated system to be stable and to avoid oscillations, the response time should be about eight times longer than the
170
CAHAN
AND SPANIER
chopping period. This problem can be especially severe in ellipsometry where several stable sets of angles are possible for a given surface. 5) A highly accurate readout is required for an instrument that covers even the limited range of IO”. A 0.1% linearity is required in the polarization transducer. 6) In order to stay in the region where the parabolic approximation is valid, and to avoid driving a capacitive Kerr cell or inductive Faraday cell with a large signal, the modulating signal must be kept low. Unfortunately, this means working at low signal levels with the attendant noise and response time problems. 7) Unless a rather complex gating system or a dual frequency modulation is used, or a digital computer, it is only possible to follow one of the ellipsometric parameters at a time, and generally both are varying. 3. Modulation
over 360“
In our automatic ellipsometer the desired information is obtained by a 360” rotation of one of the polarizers. For example, if elliptically polarized light is incident on the analyzer and if the analyzer is rotated at constant frequency o, the transmitted intensity I varies in time as indicated in fig. 4, where Q=A -A, = ol. Curve A represents the transmitted intensity for incident light with ellipticity, E=E~, and azimuth CI=C(~. Curves B and C show the effect of changing E to s1 and !I to cur respectively. Though changes in E and Mgenerally occur simultaneously in ellipsometry, they are indepen3=
Fig.
4.
Phase
Shift
The effect of changing the orientation and ellipticity incident on a rotating polarizer.
of elliptically
polarized
HIGH
SPEED
PRECISION
AUTOMATIC
ELLIPSOMETER
171
dent and separately measurable. Azimuth is merely a phase shift and ellipticity is the arctangent of the square root of the ratio of minimum to maximum intensities. 4. Measurement
of azimuth
To measure the azimuth of the ellipse with an accuracy of 0.01” requires the phase of the transmitted light to be measured with an accuracy of 0.003%. We accomplish this using a digital counting method. The analyzer is mounted in the hollow shaft of a special rotating cogless direct drive servo-system. The unit is aligned so that the rotational axis coincides with the optical axis. This adjustment, together with a minimal optical wedge effect, insures that the ray of light always passes through the same area of the polarizer regardless of orientation, and reduces unwanted phase shifts inherent in the analyzer.
Fig. 5.
Measurement
of phase shift.
The electronic system used to measure the phase operates on the principle shown in figs. 5 and 6. In general, the output from the photodetector will be a pure sine wave with frequency twice that of the angular rotation displaced above the zero line. It can be seen that dZ/dtI is greatest at the 45” point (level A). An electronic level detector set at A will produce a constant output which is plus when the intensity is greater than A, and off otherwise.
172
CAHAN
AND
SPANIER
L
_
Fig. 6.
Digital
phase
comparator
for Y.
A modified quadrature detector is used to compare the square wave output from the level detector with a reference square wave. The modified quadrature detector produces a signal that is plus when the square wave from the level detector changes (from 0 to + V or + V to 0) after the reference wave charlges, and a negative signal for the opposite situation. The quadrature detector signal is zero when the level detector signal and reference signal are both high or both low (see “Advance” and “Retard” in fig. 6). The phase of the sine wave is thus obtained by analog integration or digital counting of the quadrature detector signal. This system is unaffected by light source intensity variations and level detector fluctuations that are slower than 0.01 set as indicated by cases B and C in fig. 5. Analog integration of the quadrature signal is not accurate to 0.01” for large phase shifts. Therefore, the digital system shown in fig. 6 was developed. The servo-rotator has its speed controlled by an optical encoder disc with two tracks, one with 720 lines (or 2 per degree) and one half black and half clear to provide an absolute mechanical zero reference point. The master oscillator (A) produces a 3.6 MHz square wave which is counted down to 36 kHz by (B) to lock the servo to a precise 50 rps drive. The 36 kHz signal is divided again at (C) by 2 producing one pulse (or one cycle of a square
HIGH
SPEED
PRECISION
AUTOMATIC
ELLIPSOMETER
173
wave) per degree of analyzer rotation while each degree is split into 200 parts by the master oscillator. The “zero” pulse from the optical encoder sets flipflop (E) which allows the first degree pulse from (C) after the “zero” to pass through the gate (F), resetting a counter (G) to zero. The gate then turns off (E) preventing further pulses from coming through. In the storage register (H) is a number which we shall return to later and which we shall call zero initially. When the comparator (I) sees the same number in (G) and (H) it emits a signal which resets counters (Ji), (J2) and (J3), sets flipflop (K), which turns on gate (L), which lets counter (J) start counting degree pulses. The output from (J,) is thus a square wave with frequency twice the analyzer rotation frequency and phase tied to the mechanical zero. After 270” of analyzer rotation, or two “up” portions of the square wave, flipflop (K) is turned off to wait for the next zero signal. Meanwhile, the photodetector (M) and the level detector (N) produce a signal square wave which is fed with the reference signal into the quadrature detector (0). This produces a + or - signal, that controls an up-down counter (P), which counts the 3.6 MHz from (A) after division by 8 at (Q) since there are 4 counting periods per revolution and 200 pulses per degree of analyzer rotation. The 360 counter counts integral degrees of phase, while the 100 counter counts fractional parts, and can be displayed, or read out at (R). At the end of one revolution, the integral degree part in (P) is transferred into the storage register (H), and the fractional part is cleared. On the next revolution, (I) will not produce a pulse until the drive has advanced through the number of degrees in (H). Thus the reference wave is shifted to follow closely the optical signal, while the counter (P) follows and remembers this shift. In this manner the unit can track through 360” or more, without ambiguity, presenting a digital readout of a every revolution (or 50 times/set) with an accuracy of 0.01”. The level detector (N), will work with almost any reference level between the minimum and maximum, but has its best sensitivity and accuracy near the average of the two or at the 45” point. Fig. 7 shows the photodetector at (A), and an average value circuit (B). A differentiator (C) determines the peak and valley points of the transmitted light and a pulser (D) activates a track and hold circuit (E). This unit maintains the average value over each 180” of analyzer rotation for the level detector (F). Unit (C) also supplies a set of enabling signals to two sets of cascaded track and hold circuits (G) and (H), which store voltages proportional to I,,, and Zminrespectively. These voltages can then be processed with a digital ratio meter to produce tan* E or with an analog circuit to produce tan& or a.
174
LIGHT
CAHAN
3
AND
SPANIER
PHOTODETECTOR
TO DETECTOR
-
O”ALl
DETECTOR
AMPLIFIER
I DIFFERENTIATOR 8 LEVEL DETECTOR
I_
-
TBH
Fig. 7.
Measurement
of Ima, and kin.
While tan’& could be used for any ellipsometric computations E can be computed directly using the novel analog circuit shown in fig. 8. Four matched logarithmic amplifiers are connected in a division network. With this circuit, if b = 1, the ratio I,,,i,,/Z,,,ax= tan2 E is produced. If b = 2, the square root is taken and V,, = tan E. If another resistor is connected at A or at B, it can be shown that an output of the form
b=2:
If bR
for proper b
choice
of
, C 9 Vet.
for O” (E ( IO0 (.3% for 00 ( t( 450 1
(.l%
Fig. 8.
Computation
of E from tan2E.
HIGHSPEEDPRECISIONAUTOMATIC ELLIPSOMETER
results,
where
I/ref, b and c are arbitrary
constants.
These constants
175
can be
optimized to a give a five point fit to the arctangent curve within the tolerances shown. Slightly different values of these constants may be used to fit a wider range at slightly reduced accuracy. It should be noted here that since a ratio is taken, the effects of drift in lamp brightness or change in surface reflectivity are greatly reduced.
5. Conclusions The fully automatic ellipsometer described is rapid and precise, producing a set of data points 50 times per second with CCaccurate to 0.01” and E to 0.1%. The primary sources of error in phase measurement have been eliminated or minimized by symmetric measurements. Even higher resolution can be obtained (at the expense of time resolution) by lowering the drive frequency to the servo-system or by counting over n cycles and dividing the count by n. The system is thus equally suited for the study of transients during film growth studies (where a high degree of sensitivity is required in very short times), for steady state work on a large number of samples (here balance time must be minimized) or as a production monitor, where “instantaneous” readings for feedback to a process controller are required.
References 1) J. L. Ord and B. L. Wills, Appl. Opt. 6 (1967) 1673. 2) Ellipsometry in the Measurement of Surfaces and Thin Films, Eds. E. Passaglia, R. R Stromberg and J. Kruger (Natl. Bur. Std. Misc. Publ. 256, U.S. Govt. Printing Office, Washington, 1964) pp. 97, 115. 3) For example: B. Rao, Dissertation, University of Pennsylvania, 1966. 4) I. Wilmanns, Surface Sci. 16 (1969) 147. 5) H. Takasaki, J. Opt. Sot. Am. 51 (1961) 463.
Discussion D. E. ASPNES(Bell Telephone Laboratories) The determination of either d or # by your method requires the amplitude ratio of the ac and dc components of the intensity as well as the phase of the ac component. In order to make full use of the 0.005 % resolution which you obtain in the phase, the amplitude ratio should also be determined to the same order of accuracy, or N 0.01”/57.3” N 10e4 as compared to unity. This places a limitation of one part in lo4 on the linearity of the detector, which has been implicitly assumed throughout the discussion. Have you a method of compensating detector nonlinearities to this order of accuracy? B.D.CAHAN Using a matched pair of phototransistors
mounted in a common heat sink, and connect-
176
CAEIAN
ANDSPANIER
ed as a differential preamplifier (and consequently biased out of the dark current region), the conversion sensitivity (dlx/dH) of base current to equivalent photocurrent in the emitter base diode is quite linear. Connecting this different~a1 preamp to a stabilized operational amplifier, and feeding back a current into the base of the input transistor proportional to the output voltage, an extremely linear photodetector results. Even if this linearity were not obtainable, however, the accuracy of d /I for small changes of $I would still be quite good and $initiar can be found from a “steady-state” reading on the original surface using the automatic ellipsometer in slightly more conventional manner (i.e., determining $ by manual rotation of the polarizer using the “$-readout” as a null device, and then calibrating the “#-readout” with this value with the polarizer set at 45” again. Since Ji changes are usually much smaller than d changes during the initial period of film growth, much less stringent requirements are found for the measurement of J, than for d in determining film thickness. Far more severe problems occur during a transient when #J -45”, the light becomes circularly polarized, all phase information is lost, and the digital detector stops tracking. This problem area can be avoided by offsetting the quarter wave plate or the polarizer from 45”, but at the expense of a lack of complete separation of d and #. H. G. JERRARD(University of Southampton) 1 would have thought that with a quarter-wave plate you get a linear system, which would be preferable to the quadratic system you have without it. M. GENSHAW(University of Pennsylvania) If an exact quarter-wave plate is positioned between the reflection and rotating analyzer and oriented at 45”, a complete separation of d and #results. The phase of the light output signal is linearly dependent on d. The intensity ratio Imin/l~nsx is a function of 4. For a 45” setting of the polarizer the function simplifies to the form: * -- 45 - arc tan(Imin/ZmaX)*. 6. D. CAHAN The system does, in fact, usually use a quarter wave plate, to separate d and 9, as Dr. Genshaw points out. Although the phase, d, is made linear, $J is not. Occasionally, the system would be operated without a quarter wave plate, giving azimuth and ellipticity, in those cases where If,equals 45” and the phase detector cannot track at that point. Even in this case, if the quarter wave plate is used, as soon as $ passes through 45” the phase detector would lock back in, although with a possible 180” uncertainty induced at the transition.