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A new Self-Calibrating Modulation Ellipsometer has demonstrated unprecedented accuracy, utility, reliability, and speed. The Ellipsometer is well suited to in-situ monitoring of surface degradation, film growth or etching, and quality control. The design incorporates several novel features including: 1) Full self calibration, 2) High speed, 3) High accuracy, 4) High signal-to-noise ratio 5) Compactness, 6) Reliability, and 7) No moving parts. The design is portable, can be fully automated, and is suitable for use in remote and harsh environments. A complete prototype instrument includes all optical components, mechanical mounts with flexible configuration options, custom electronic components, signal acquisition, computer control, data analysis, and a user interface, all integrated into a self-contained, user-friendly, system. It operates at fixed wavelength and incidence angle, though both can be changed by the operator in a few minutes as desired. Quantitative testing verified the absolute accuracy and suitability for monitoring real-time in-situ film growth and etching.
1. INTRODUCTION
2. ELLIPSOMETRY
3. THE SELF-CALIBRATING MODULATION ELLIPSOMETER
6. FUTURE WORK
8. REFERENCES
7. PHOTOS
1.1. In-Situ Surface and Film Characterization
The function of many technological materials is highly dependent on the structure and composition of surfaces and coatings. These functions include: integrated electronic devices, electrical contacts, electrical insulation, thermal contact, thermal insulation, mechanical contact (bearings and fasteners), appearance, and protection. Detailed knowledge of surface and film composition, thickness and microstructure can be obtained by non-destructive techniques based on optical reflection. Reflectance measurements, including ellipsometry, can be used to monitor and control surface growth, coating, cleaning, annealing, etching and other processes associated with fabrication and refurbishment of material surfaces. The same methods can also be used to monitor degradation due to, e.g., contamination, wear, corrosion, or fatigue.
Ellipsometery can provide real-time feedback on surface and film quality and thickness for monitoring and process control. Ellipsometery offers an accurate and reliable nondestructive measurement of the optical constants of interfaces and the optical constants and thickness of thin films. Film growth and etching are two key processes used in materials growth in general an electronic components in particular.
The degradation of surfaces in a space ambient, particularly in low earth orbit, deserves considerable attention because of the extreme hazards posed by structural or functional failure to personnel and equipment. Considerable time effort has been invested in the study of space materials degradation, primarily through laboratory simulation of space conditions or post-flight analysis of samples. In-flight monitoring of materials degradation is a desirable adjunct to laboratory simulation and is in many ways more useful than post-flight analysis because degradation can be correlated to specific in-flight events such as solar flares, thruster firing, hatch operation, etc. The primary difficulties with in-flight monitoring are the weight, size, and calibration of space-qualified instruments and the need to provide instrument access to samples at ambient conditions.
1.2. General Design Criteria
The SCME is free of moving parts, self-calibrating, tolerant of alignment errors, insensitive to low frequency noise, compact, and suitable for remote and harsh environments. The instrument is designed to be accurate, fast, rugged, reliable, lightweight and compact. These features make the instrument suitable for a wide range of in-situ applications in the laboratory, in the manufacturing plant, and in the field.
The present device was designed specifically for materials degradation studies in the harsh and remote environment of low-earth-orbit. The severe environment includes extremes of temperature, pressure, vibration and shock. The remote location limits or prohibits regular operator intervention, routine service, and repair and refurbishment. Fuel and space considerations severely limit the mass and size.
Accuracy: Ellipsometric measurements are sensitive to minute changes in the structure and composition of surfaces, even layers with single atom thickness without need for external calibration or special calibration procedures before measurement.
Reliability: The instrument's mechanical, electronic and optical components are resistant to degradation or failure due to ambient conditions, shocks, vibration, etc. Accuracy is maintained even in a range of environmental conditions presented to the instrument components.
Remote Operation: The instrument can operate without operator intervention, adjustment, or repair under nominal operating conditions. It accomodates temperature and pressure changes without losing calibration, compensates for small misalignments of the critical optical elements.
In-Situ Operation for Process Control: The instrument is self-calibrating during each measurement and returns complete measurements quickly in real time. For in-situ use, there is often not time to recalibrate temperature-sensitive elements, like the polarization modulator.
Compactness and Efficiency: The instrument is compact and light without compromising its operational utility. Each subsystem (optical, electronic, mechanical and computer) and the integrated whole is designed with size, weight, power consumption considerations in mind.
Novelty: The SCME differs from other modulation ellipsometers in the algorithms used to determine retardance
and reflectance ratio
values free of all the calibration constants and corrected for small alignment errors.
Characterization of surfaces, interfaces and films is a rapidly expanding field of materials research. One of the most versatile methods of surface and film characterization is ellipsometry, in which the change in the polarization state of light transmitted or reflected from a sample is measured. The optical constants, thickness of layers, anisotropy and surface roughness can all be measured in this way. A thorough treatment of ellipsometry and its applications is contained in Ellipsometry and Polarized Light, by R. M. A. Azzam and N. M. Bashara (North-Holland, Amsterdam, 1977),[1] hereafter referred to as 'AB'. A brief summary of modern ellipsometric techniques and their salient features follows.
Ellipsometry uses polarized light to characterize samples. The most common representation for the effect of a sample on an incident beam of polarized light is given by:
, (1)
where rp and rs
are the complex reflection coefficients of the 'p' polarization
component (in the plane of incidence formed by the incident beam
and the normal to the surface) and 's' polarization component
(perpendicular to the plane of incidence), respectively. An ellipsometer
measures the reflectance ratio and the phase difference of the 'p' and 's' polarized
components of light reflected from the sample. Ellipsometry can
also be performed in a transmission mode; the Fresnel coefficients
in the above formula are simply replaced by the complex transmission
coefficients tp and ts.
Ellipsometry obtains the two important sample parameters and by measuring
ratios of reflected intensities in different polarization states.
The absolute reflectivity is not measured or needed, eliminating
the need to calibrate or monitor the intensity of the optical
source.
There are three ellipsometric methods that have been widely used:[1]
1) In Null Ellipsometry ('NE'), light of known polarization is directed to the sample and through appropriate reference optical elements (polarizers, wave plates, lenses, filters, etc. ) arranged in such a way that the net system transmission is zero, or 'null'. The null can be obtained for several distinct arrangements of the reference optical elements and, from an analysis of these arrangements, the values of
2) In Rotating Element Ellipsometry ('REE'), light of a specific polarization state is directed to the sample and then through an exit polarizer. The intensity of the light transmitted through the system is measured as one of the polarizing elements rotates. Possible rotating elements include the input or output polarizers or a wave plate inserted in the optical path. The values of
3) A third, more recent, technique is Modulation Ellipsometry ('ME')[2],[3], where an oscillating waveplate (the polarization modulator) is placed in the optical path (either before or after the sample) along with other static optical elements. The intensity of the beam transmitted through the entire system is measured as the modulator retardation is varied over a carefully specified range, requiring precise and frequent calibration because the modulator retardation is sensitive to changes in temperature, pressure and wavelength. Typically, the modulator consists of a vibrating plate of quartz.
The Self-Calibrating Modulation Ellipsometer (SCME) is a variation
on the polarization Modulation Ellipsometer (ME). The SCME improves
upon previous modulation ellipsometers by the use of variable
modulation amplitude Mo which is allowed to vary over a
wide range and a patented analysis algorithm which permits the
simultaneous and continuous measurement of the sample and without reference to external
calibration or to elaborate alignment procedures. Calibration-free
operation is the most significant and useful feature that distinguishes
the SCME from all other ellipsometers. In addition, the SCME compensates
for errors in system alignment that may occur at initial construction,
or through later disturbance of the optical elements.
The present instrument is designed specifically for in-situ monitoring of, e.g., surface degradation, film growth, or etching. The SCME is particularly suited to accurate and reliable unattended operation in remote or inaccessible locations. It operates at fixed wavelength and incidence angle, though both can be changed by the operator in a few minutes as desired. The SCME also has no moving parts and uses all solid-state electronic and optical components, contributing to its overall ruggedness and reliability. A complete acquisition, control, and analysis computer program has a user-friendly interface for set-up and alignment, diagnosis and testing, and data acquisition and display.
3.1. SCME Construction and Operation
The Self-Calibrating Modulation Ellipsometer (SCME) System consists of the general optical, electronic and computer components shown schematically below. There are variations of this configuration which may be suited to certain uses, but this configuration has proven the most versatile. The block diagram in Fig. 1 shows the functions of the major components working as a system.
The optical, electronic and computer systems operate as follows (refer to Fig. 1.):
Source The light Source may be any collimated monochromatic source with fixed or variable wavelength. Laser diode sources are compact, rugged, reliable, can be directly modulated, and are sufficiently powerful. Laser diodes are available in a number of output wavelengths in the red and near-infrared spectral region and, with integral harmonic generation, with green and blue wavelengths. The instrument as tested operates at a single wavelength but the lasers can be exchanged by the operator in a few minutes.
The Source amplitude is modulated to place all signals at a high carrier frequency fc generated from the polarization modulation frequency fc by the PLL. The purpose of this amplitude modulation (AM) is to carry all signals at high frequency, thus reducing low frequency interference and '1/f' noise and, particularly, eliminating ubiquitous dc offsets present in the amplifiers and the ADC. Amplitude modulation can be achieved by direct modulation of a laser source or by use of an external modulator such as an acousto-optic or electro-optic modulator. The signals from the two detectors are composed of the amplitude modulated carrier signal at frequency fc with sidebands at the polarization modulation frequency fm and harmonics nfm as well as undesired dc and ac noise and interference. The electrical signals are demodulated by means of standard demodulation techniques (a Digital Fourier Transform in the present instrument). Demodulation extracts the desired those signals at frequencies fc - nfm, where n = 0, 1, 2, 3, 4.
Polarizer Light from the Source passes through the Polarizer which produces a well-defined linear polarization state. High quality Glan-Thompson polarizers offer extinction ratios (polarization purity) exceeding 1:105, and do not limit the system performance. The Polarizer is oriented with its polarization axis at +45° with respect to the sample s-plane.
Modulator The linearly-polarized light emerging from the Polarizer passes through the Modulator which alters the polarization state of the light at a frequency fm. The Modulator is normally oriented with its optical axis at 0° with respect to the sample plane. The modulator generally has its own controller which also generates a reference signal at fm.
Sample The light reflects from or passes through the Sample, as appropriate. The retardance
and anisotropy
Analyzer The light passes through a dual output Analyzer, such as a Wollaston prism, which separates the beam into two orthogonally polarized components. The two orthogonal polarization axes of the Analyzer output are oriented at ±45° with respect to the sample plane. Therefore one output, denoted 'channel a', has the same polarization as the Polarizer, and the other output, denoted 'channel b' is crossed (orthogonal) to the Polarizer.
Detectors The two orthogonally polarized components of the light beam are incident on two light Detectors. The Detectors should have linear response in optical power independent of frequency up to the carrier frequency fc. Silicon PIN photodiodes are preferred for visible and near IR wavelengths.
AGC Automatic Gain Control (AGC). The signals from the two Detectors are amplified as needed by broad-band amplifiers. The amplifier gains are automatically set by the computer Controller to adjust the signal amplitude from each detector to match the range of the ADC.
ADC The Analog-to-Digital Converters (ADCs) convert the modulated signals from the two Detectors into digital form for further analysis by the computer Computer .
PLL Phase-Locked Loop (PLL) circuitry multiplies the modulator reference frequency fm to generate the carrier frequency fc used to modulate the Source and the acquisition frequency 2fc used to trigger the ADCs.
Computer The PC-based Computer controller incorporates programs for instrument control, data acquisition and analysis. The Computer processes the digital data from the ADC to extract the values of
as well as other instrument operating parameters by applying two basic algorithms: 1) A Digital Fourier Transform (DFT) algorithm isolates the desired Fourier components at frequencies fc, fc -1fm, fc -2fm, fc -3fm and fc -4fm; 2) An algorithm derived from a Jones matrix analysis of the optical components calculates the values of
from these Fourier coefficients.
User Interface The User Interface is a custom program running on the Computer that provides user control and monitoring of the instrument, data acquisition and analysis as well as on-line help.
3.2. Jones Matrix Analysis
The polarization state of the light beam is traced from the
source to the detectors. The sample has unknown retardance and reflectance
anisotropy
while the other optical elements (see Fig. 1) are assumed to have
precisely known polarization characteristics.
The optical electric field at each detector is given by the following Jones Matrix expression:
, (2)
where qp, qm and qa are the orientations of the polarizer, modulator and analyzer about the optical axis measured with respect to the sample plane. Eqn. 2 is repeated for both analyzer a and b outputs with the two different values of qa = ±45°. The individual Jones matrices are:
,
,
, (3)
for, respectively, the laser polarization (usually oriented so that b Å 0), an ideal polarizer, and a generic rotation matrix applied between optical elements with the angles defined as in Eqn. 2. The sample and polarization modulator have the Jones matrices:
,
,
, (4)
where
is defined over the range 0 < < 360° and 'tau' = is defined over the range
0 < 'tau' < (or 0 < < 90°). The modulation amplitude
is Mo and W = 2(pi)fm is
the modulation angular frequency. Ai, Ap, As and Am are the scalar
amplitude transmission coefficients of the optical elements. In
the present instrument, the nominal orientation angles have the
values,
where em and ea are small angles (< 4°) that measure misalignments of the modulator and analyzer, respectively. The Jones Matrix for the system is (dropping the scalar amplitude coefficients like As):
. (6)
The intensity at each detector is obtained by taking the absolute square of Eqn. 6 with the appropriate sign, "+" for channel a and "-" for channel b. The detector signals are anharmonic functions of time because the modulation M, which is itself harmonic (Eqn. 4), is contained within the function exp(iM).
The signals Va and Vb in the two detector channels contain harmonic components of the modulator angular frequency W = 2_fm that can be separated by filtering or by Fourier analysis:
, (7a)
. (7b)
The modulation signals in the two orthogonal polarizations at the output of the analyzer are readily written as a harmonic expansion in the modulation amplitude M = Mo cos (Wt) as follows:
, and (8a)
. (8b)
The 5W and higher harmonics are discarded as they repeat the
3W and 4W terms and are not needed. The Fourier coefficients are
functions of the modulation amplitude Mo, the retardance
,
the anisotropy 'tau' = , and the alignment errors ea and em.
One of the most valuable and unique features of the SCME is its ability to determine and without calibration by solving Eqns. 7 to eliminate the unknown and unneeded detector calibration factors as well as the small modulator and analyzer angles em and ea which might arise due to misalignment. The modulation amplitude Mo is also uniquely determined by solving one of the following transcendental equations:
. (9)
where 
is an ordinary Bessel function of interger order n. The
desired values of the retardance, the anisotropy 'tau' = are calculated from the
value of Mo and the Fourier coefficients from Eqns. 8 as
follows:
, (10a)
, (10b)
(10c)
Note that the present instrument can uniquely determine the
value of
through its entire range (0 < < 360°) by examination of the
signs of Va1 and Va2 in (first quadrant = ++; second
quadrant = +-, third quadrant = --, and fourth quadrant = ++).
However, the instrument cannot distinguish between two ranges
of 'tau'; the upper sign corresponds to the range 1 < t <
infinity (45° < < 90°) and the lower sign corresponds to
the range 0 < tau < 1 (0 < < 45°). This ambiguity, analogous
to the ambiguity in determining with the rotating analyzer and rotating
polarizer ellipsometers, comes about because the birefringent
modulator probes the entire range of retardance , but not the entire range
of
. The ambiguity in can be removed if two or more measurements are
made with different analyzer orientation angle (theta-a) settings.
The user interface of the present instrument incorporates an optional
procedure to guide the user through this measurement in the event
that the user does not know enough about the sample to determine
the range of .
Therefore, with the extra measurement, the present instrument
can determineunambiguously
throughout its entire range of 0-90°.
3.3. Correction for Alignment Errors
The instrumental calculation of modulator and analyzer angle errors em and ea are useful for checking and correcting alignment (as well as the determination of the proper range of PSI as noted in the previous paragraph). The values of em and ea are also readily obtained from the following equations:
, (11a)
. (11b)
The optimum range for the modulation amplitude Mo is
bracketed by the digitizer resolution on the lower end and the
by the reliability of the algorithms for determining , and on the higher end. The
12-bit resolution of the current digitizer requires operation
at Mo _ 0.75 radians. With 100 cycles of signal averaging
the rms error in was at most ± 0.03 ° (at = 90°) down to ±
0.006° (at
= 0°). A 14-bit D/A converter will reduce the signal averaging
time 16-fold to 0.25 ms, assuming we remain resolution, and not
noise, limited. The algorithms for determining and are most reliable when
the modulation amplitude Mo is less than 2.4 radians, the
first zero of the zeroeth-order Bessel function. However if is not
within the critical rang of 40-50° the modulation amplitude
Mo can be set as high as 3.5 radians, just below the first
zero of the first-order Bessel function. Note, however, that both
em and ea must be less than 4° to maintain sufficient accuracy
in the values of DELTA and PSI obtained from Eqns. 9.
3.5. Computer Algorithms
The calculation of and from the raw data proceeds follows:
1. Acquire data for the Requested # of Waves.
2. Calculate the Fourier Coefficients for both Channels.
3. Calculate Mo from one of Eqns. (9).
4. Calculate and , as from equations 10a-c.
3.6. Operator Interface and Control Software
The operator interface is a user-friendly environment for conducting in-situ (time-series) measurements. The interface has four basic modes:
1) Alignment-Guides the operator in sample and laser beam alignment.
2) Diagnosis-Displays detailed system information for troubleshooting and for adjustments.
3) Data Acquisition-Controls routine data collection and storage functions.
4) Context-Sensitive Help-Guides the user in ellipsometer operation
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The control software performs many critical control and monitoring functions: 1) System Initialization-An initialization subroutine called at program execution prepares the instrument for data acquisition. This subroutine resets the amplifier gains, and initializes the ADC. The ADC is set for external triggering (positive edge) and unipolar 0-5 V input. 2) Data Acquisition-After initialization the ME is ready to acquire data. The user selects the number of waves to be acquired. Every wave is 18 data points per channel for a total of 36 points per wave for both channels. The total number of points to be acquired (36 times the number of waves) is sent to the ADC. When an acquisition is issued the ADC begins acquiring data at the next external trigger, continuing at the 900 kHz acquisition rate until all points are collected. (As described previously, the 900 kHz external trigger is derived from the 50 kHz PEM-90 and PLL circuit.) The ADC is equipped with a fast multiplexer that switches channels at every data point, alternating between signal channels Va and Vb. Once all data points are recorded, the ADC data are converted to voltages and the multiple waves overlapped and averaged. The result is two 18-point waves, one wave each for Va and Vb. 3) Fourier Transform-The DFT is applied to the two 18-point waves to yield the desired coefficients Va n and Vbn corresponding to the DC, 50, 100, 150 and 200 kHz PM harmonics. 4) Calculate-The values of the modulation amplitude
Mo, |
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4.1. Tests of Self-Calibration
The Hinds PEM-90 Photoelastic Modulator (PEM) incorporated into the present instrument displays a precalibrated measurement of the modulation amplitude Mo during operation. We compared this display to the SCME measurement of the modulation. The graph below, obtained without signal averaging, shows the results of this test with four important features: 1) the SCME determined that the PEM calibration was incorrect by 6%, but within the expected accuracy considering the PEM had not been recalibrated in over three years; 2) The calculated modulation amplitude Mo was linear in the displayed amplitude to well above Mo = 2 radians (1/3 wave); 3) There is significant systematic error at large modulation amplitude (Mo > 1 radian) when the approximate power series in Mo solutions (instead of the exact solutions used in the in the present instrument); and 4) the signal-to-noise ratio becomes rather poor as the modulation amplitude falls below 0.75 radians due to digitizer resolution, as mentioned above.
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4.2. Correction for Alignment Errors
Equations 8-10 show that small misalignments (<4°) of
the Modulator Angle error em and Analyzer Angle error ea about
the optical axis are corrected in the analysis. The analysis returns
accurate values of the sample parameters and as well as the modulation
amplitude Mo and when em and ea are within the specified
range.
Figure 4 show how successful the SCME is in correcting for-and
calculating-the alignment errors. The measurements were made with
14.8 nm silicon dioxide on a silicon wafer at a 75° incidence
angle. These tests of the alignment correction and calculation
algorithms were conducted by varying em and ea near 0°. Note
from the following graphs that misalignment of the analyzer within
±5° has little or no effect on the values of any of
the quantities; the largest systematic error is in the measurement
of
which varies by 0.05°. Misalignment of the modulator results
in larger deviations, as shown in the graphs.
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The small value of Å 7° in this test is particularly sensitive
to misalignment of the modulator because the silicon wafer is
set near Brewster's angle (where = 0) because the polarization modulator
varies the ellipticity, but not the orientation of the ellipse,
and therefore has difficulty distinguishing orientation changes.
This is in contrast to the RAE which modulates the orientation
of the polarization, but leaves the ellipticity fixed at zero;
the RAE has difficulty measuring under some circumstances.
4.3. Signal-to-Noise Ratio
The precision of measurements recorded at high data rates is
limited by noise and the resolution of the ADC. The ADC has 12-bit
resolution so that the maximum resolution for one cycle (one period
of the PM frequency), when the signal spans the full range of
the ADC, is 0.06°. Noise will further degrade the precision.
But errors due to noise and ADC resolution decrease with signal
averaging as illustrated in the following graphs (recorded using
an early prototype that did not benefit from the noise-reducing
amplitude modulation). A series of measurements of , each consisting of the
average of N cycles (requiring time N/(50 kHz) to collect), and
repeating 100 times to determine the standard deviation. We see
that collecting N = 100 cycles, which takes 2 ms, ensures that
the value of
are precise to 0.03° or better. The time required to calculate
the FFT,
and
is dependent upon the main computer processor or DSP chip and
should not add considerable delay. The SCME modulation amplitude
was 0.095 radians. The use of amplitude modulation in the present
instrument reduces the signal-to-noise ratio even further.
4.4. Standards
4.4.1. Variable Wave Plate-Testing
The figure at right demonstrates the instrument's accuracy
in measuring
. The 'sample' used was a commercial Babinet-Soliel Variable Retarder
(Optics for Research model RC-10) which could be set to a fixed
retardation with accuracy of 0.3°. The rms deviation of the
measured values the calibrated values was <1° without signal
averaging or amplitude modulation. The rms error is significantly
improved by signal averaging and the addition of amplitude modulation
to the instrument. The absolute disagreement between the SCME
and the retarder was only 0.25%.
The conditions for this test similar to the previous test except
with a high-quality (1:105) Glan-Thompson
polarizer (Karl Lambrecht MGT25S5) functioning as a test sample
instead of the variable compensator. As noted previously, the
SCME does not distinguish between the 0-45° and 45-90°
ranges in
and therefore the measured values of are folded into the 0-45° range
in the data at right. The test polarizer introduced negligible
retardance and therefore the instrument measured = 0.
4.5. Special Samples
4.5.1. Silicon with Native Oxide
The prototype ellipsometer was used to measure the optical
constants
and
for silicon. The data shown in the figure were collected without
signal averaging using a modulation amplitude of 0.628 radians
(1/4 wave). The angle of incidence resolution of the prototype
ellipsometer was approximately 0.5° and was the major source
of systematic and random errors. The ellipsometer data (points)
are in excellent agreement with reference data (lines) generated
from optical constants obtained from the literature.
4.5.2. Gallium Arsenide
Measurements performed on a GaAs wafer as described in the previous section.
4.5.3. Iridium Mirror
Measurements of and on iridium at approximately 75° angle of incidence
show the wide operating range of the modulation amplitude Mo.
In this example, where is well below 45°, the usable range of modulations
extends from 0.75 radians to 3.5 radians.
4.6. In Situ Demonstrations
In-situ etching measurements were performed by mounting the SCME source and detector head assembly on optical ports of two different atomic oxygen etching systems: and electron-cyclotron-resonance apparatus and an 'asher' RF plasma. Photographs of these installations are shown in Appendix F. Mounting and alignment were quick and easy with the aid of the built-in alignment and help facilities of the User Interface of the computer controller. Once mounted and aligned, the SCME recorded and displayed data in real time and continuously log it for future reference.
4.6.1. ECR Oxygen Plasma Etch (Film 1)
A highly-absorbing film of diamond-like carbon (DLC) on silicon
was etched in an Electron-Cyclotron-Resonance (ECR) oxygen plasma
apparatus operated by Professor Natale Ianno and graduate student
Brian in the UNL Department of Electrical Engineering. The and in-situ
data below show clearly the interference effects, etch rate, and
the etch endpoint, labeled 'Stop'. A film of "diamond-like
carbon" (DLC, actually amorphous hydrogenated carbon) about
270 nm thick was placed in a chamber equipped with an electron
cyclotron resonance (ECR) plasma source. When running with pure
oxygen as the source gas the ECR produces atomic oxygen, which
readily etches the DLC.
4.6.2. Atomic Oxygen Asher (Film 2)
SCME data were obtained during the etch, then modeled to obtain
the etch rate. Because the analysis software used is set up to
model growth rather than etching, the data were time-reversed
before analysis. The following graphs show the measured and data,
reversed in time. The far right of the graphs is actually the
start of the etch, and it reaches the silicon substrate at the
left of the graph. The data were analyzed using optical constants
found previously from ex situ spectroscopic ellipsometry
analysis of the film, and reference data for the silicon and its
native oxide. The real time data near the start of the etch were
first fit for the starting thickness and the angle of incidence.
During the rest of the analysis the angle was kept fixed to the
best fit value. Model data were generated assuming uniform growth
of a DLC layer. The "growth" rate (actually the etch
rate) was fit to the data.
A couple of details are worth noting. First, the signal to
noise ratio of the measured data is high. Second, the ellipsometry
data do not lose sensitivity as the layer thickness approaches
zero, as reflectivity data would. The slopes of and remain high right up to
the point at which the film is completely removed, and then sharply
change to zero. Because of the high signal-to-noise ratio and
high sensitivity to film thickness right down to zero, these data
could be used in real time to precisely determine when the film
was completely etched away, simply by monitoring the slopes of
and/or
.
A low-absorption 500-nm film of diamond-like carbon (DLC) on
silicon was etched in an atomic oxygen asher apparatus operated
by Professor Paul Snyder and graduate student Cory in the UNL
Department of Electrical Engineering. The and in-situ data below show
clearly the interference effects, etch rate, and the etch endpoint.
(Note: the time scale has been reversed; etching starts at the
right and proceeds to the left) Since the absorption was low,
the interference fringes are more pronounced. The model fit using
known optical constants of DLC and silicon was used to calculate
the etching rate. The data show that the etch rate was lower during
the first minute of etch, resulting in the disagreement between
the model and the data between 4.4 min (start) and 3.8 min). Both
and
fit
well to the model except in the critical range Å 45° where is less
accurate, as discussed in the following section. Note the unshielded
RF plasma generated large amplitude noise producing a S/N Å
1 in the raw data, but the Fourier Analysis filtered this noise
very well.
4.7. Accuracy and Sources of Error
The prototype SCME achieves a basic accuracy of 0.2° in
and
0.2° in
(except for the critical range of 43° < < 47°) without need
for external calibration. There are four different classes of
sources of error: Environmental, Operational, Component,
and Sample. Design considerations affect all three, though
to different degrees. This section describes these sources of
error, their relative severity, and methods to reduce or eliminate
their effects.
4.7.1. Environmental Sources of Error
Many environmental influences contribute noise to the raw instrument data, including: electrical emissions, vibration, temperature variations, and dust and turbulence in the beam path. The double modulation (polarization PM and amplitude AM) design and signal averaging combine to make greatly reduce noise even in inherently noisy environments like the RF 'asher' experiment described above.
Accuracy can be effected by environmental conditions which affect all ellipsometers. Air turbulence and ambient dust primarily affect optical throughput, adding intensity noise and decreasing the signal. Dust and severe air turbulence can also partially depolarize the light, a small effect in the forward-scattered signal reaching the detectors.
Temperature changes do not greatly affect accuracy as the instrument is inherently calibration free. Thermal or mechanical stress can cause misalignment of the laser beam, correctable by the operator as part of the sample alignment procedure. Misalignment the polarization axes of the optical elements is corrected automatically by the analysis software as discussed above.
Ambient light does not significantly affect ellipsometer operation because of the low acceptance f/number of the detector system and the AM operation. Likewise the instrument design-especially the detector head assembly and signal cabling, are well shielded from electrical interference. Ambient light and electrical interference can have a significant effect on accuracy if they drive the optical detectors, electronic amplifiers, or the ADC to saturation, a condition that is detected by the operating software and displayed to the user.
4.7.2. Operational Sources of Error
The instrument operator has the responsibility of ensuring proper alignment of the sample to direct the laser beam through the analyzer onto the detectors. As described earlier, the instrument guides the operator through this procedure. The operator can also control many of the environmental factors discussed in the previous section.
Certain applications of the instrument will require inserting optical elements, such as vacuum chamber windows, into the beam path. These elements must be made polarization-neutral or independently characterized to ensure overall measurement accuracy. (High-quality neutral vacuum chamber windows specifically designed for ellipsometry and polarimetry are readily available.)
Though the SCME is designed to make accurate measurements of
and
,
proper interpretation of these measurements to extract, e.g.,
film thickness and refractive index, require accurate control
and measurement of the angle of incidence. The SCME source and
detector head assemblies have been designed to mount on, e.g.,
precision theta-two-theta goniometer systems which can ensure
sufficient angle-of-incidence precision.
While the SCME automatically corrects for small (<4°) misalignment of the polarization modulator and analyzer polarization axes with respect to the sample plane, it cannot compensate for a misalignment of the input polarizer axis with respect to the polarization modulator. This alignment can be adjusted carefully, according to procedures we have prepared, during instrument assembly to a tolerance of 0.2°, sufficiently precise to maintain specified instrument accuracy. The present instrument is aligned to this tolerance and the rigid polarizer-modulator assembly (see section 2.3) should prevent misalignment; no operator intervention is required to check or correct misalignment of these components under ordinary operating conditions. Damage, servicing, or other operations which disturb this assembly will require realigning these components.
4.7.3. Component Sources of Error
Accuracy is dependent on the quality and performance optical and electronic components. We have selected commercially-available components of the highest quality and constructed custom printed circuitry according to sound engineering principles. Of these components, the polarization modulator, photodetectors, detector amplifiers and ADC are the primary sources of error.
The fused silica Photoelastic polarization modulator (PEM)
was chosen for the SCME because it has nearly zero residual static
retardance. However, the small residual retardance of approximately
0.1° that does exist will produce like error in measurements
of
. Two recent papers have analyzed in detail the effects of residual
birefringence on PEM performance in modulation ellipsometers [J.
Badoz, M. P. Silverman, and J. C. Canit, J. Opt. Soc. Am. B
7, 672 (1990); and F. A. Modine and G. E. Jellison, Applied
Physics Communications 12, 121 (1993)]. The specific
PEM used in the SCME shows no more than 0.15° residual retardance
over its entire ~1" aperture, and some regions of size ~2
mm (large enough for the laser beam) have less than 0.1° residual
retardance. In order to correct for residual retardance in the
PEM, a procedure necessary only for the most accurate measurements,
this residual retardance must be measured by placing the instrument
in the transmission (straight-through) configuration without any
object in the beam path. The value of (residual) measured in this manner
is then subtracted from all subsequent measurements of . The measurement of he
value of
(residual) should be made again if the ambient temperature changes
by more than 5° C because the residual retardance of the PEM
depends somewhat on ambient temperature. The PEM supplier, Hinds
Instruments does offer selected PMs with much reduced residual
retardances, a consideration for future SCME instruments.
The desired signal components Va0-4 and Vb0-4 (Eqns. 8) are contained in the lower sidebands of the signal spectrum ranging from 25 kHz to 225 kHz (see section 2.6). It is assumed in Eqns. 8 that the combined photodetector-amplifier-ADC circuitry have a flat frequency response over this range of frequencies. These components must also have linear response to input signals. The components in the present instrument do not significantly affect the accuracy of the present instrument.
The present instrument employs a relatively strong laser light source and therefore presents strong, low noise, optical signals to the photodetector-amplifier-ADC circuitry. Alternate configurations of the instrument designed for spectroscopic use will handle significantly lower optical intensities and will benefit from a higher resolution ADC and increased amplification.
The polarization purity of the input polarizer and output analyzer is critical to instrument accuracy. The Jones matrix analysis given in section 2.2 assumes ideal polarizers. The high quality Glan-Laser input polarizer and Wollaston Prism output analyzer both have extinction ratios exceeding 105:1, far exceeding the minimum 103:1 extinction ratio necessary to achieve the accuracy of the present instrument.
4.7.4. Sample
Nonuniform or highly deformed samples can also introduce considerable error in the ellipsometric measurements. Surface roughness can also introduce error. An optional configuration of the SCME characterizes the surface roughness by measuring the total scattered light incident on the Quad detectors. This option may be particularly useful in in-situ film growth, degradation, or etching experiments.
4.8. Evaluation of Strengths and Weaknesses
4.8.1. Simplicity
Since the alignment and analysis are straightforward, and outside calibration is unnecessary, the SCME is an inherently simple device to use, simpler in optical design than an ordinary monochrometer and comparable operational complexity to a modern spectrophotometer.
4.8.2. Ruggedness
The SCME design is inherently rugged because it has no moving parts and is constructed entirely from solid-state optical and electronic components. The robustness of the present instrument is limited primarily by the (excellent) major vendor-supplied components: the laser, the polarization-modulator system, and the portable computer.
The present instrument has been constructed for use in common laboratory and industrial environments. However, it should not be operated outside of the specified temperature range or subjected to severe shocks or temperature gradients. Caustic and corrosive environments should also be avoided.
4.8.3. Stability
The SCME has no moving parts. Once constructed and bolted in place, the optical elements require little or no additional alignment. Small errors in alignment of the sample, modulator or analyzer are automatically corrected by the analysis algorithms. Detector, source, or beam pointing drift have virtually no effect on accuracy provided the drift is slow compared to the collection time of one wave (> 20 ms).
4.8.4. Versatility
The Source and Detector Head Assemblies are compact and can be mounted in a variety of locations and configurations where there is optical access to the surface under study: vacuum chambers, process systems, storage facilities, etc.
4.8.5. Noise
Modulation techniques are inherently insensitive to noise. In the basic form, without amplitude modulation, the SCME accuracy and stability are limited primarily by the dc offsets in the optical and electronic signals. With amplitude modulation and demodulation the accuracy is limited primarily by the quality of the optical components and electronic circuitry.
5.1. Degradation Monitoring
The SCME will be useful in monitoring degradation and contamination of surfaces and thin films. These changes typically occur slowly over long periods of time. Examples include contamination of mirror surfaces by physisorbed hydrocarbons or chemisorbed species permeation of thin films by water vapor, and salt corrosion. Ellipsometry is inherently very sensitive to small changes in surface overlayers, thin film optical constants, and layer thicknesses. In addition the monitor must have low noise to detect small changes, and must have minimal drift over time, since such drifts might be misinterpreted as real changes in the sample.
5.2. In Situ Monitoring and Process Control
The SCME is also useful for real time monitoring of thin film deposition and etching processes. Its high speed and rugged laser source are especially suited for the fast deposition and etch rates (and noisy conditions) often encountered in industrial settings. Its ruggedness has been demonstrated by taking data during etching in an rf plasma system (section 3.6.2). This system was so noisy that a conventional ellipsometer was unable to take data while the plasma was on, yet the SCME seemed unaffected by it. The bright laser light source and four-quadrant alignment system allows for easy alignment, and the laser can be focused if necessary. This small, rugged, self calibrating instrument is well suited for nonideal industrial applications such as this.
Applications of real time monitoring include any type of thin film deposition or etching. This may occur in a vacuum, atmospheric, or liquid environment. Common examples include sputter deposition, plasma etching, electrochromic deposition, and wet chemical etching. The former two are done in vacuum environments, while the latter are in liquid ambients. In both cases optical windows on the chamber are the only system requirements. Examples of dry etch monitoring with the SCME were given in section 3.6.
5.3. Quality Control
The SCME can be applied directly to quality control in manufacturing of semiconductor devices, magnetic and magneto-optic data storage media, flat-panel displays, and other surface-critical technologies. SCME systems can be located on processing equipment to monitor contamination, film and oxide growth, etching steps, etc. In addition, Q. C. functions can combine with process control functions in the same process line to reduce the Q. C.-process modification cycle time. Samples can be spot-checked or whole-surface profiles can be obtained by moving samples on two-dimensional steppers; the high data acquisition rate of the SCME will permit rapid 2-D profiling and high overall throughput. The noncontact nature of ellipsometry, as opposed to conductance and other electrical probes, will help maintain sample integrity.
6.1. Space Qualification of the Optical components
Most of the optical components of the SCME can be obtained in space-qualified form from these vendors.
High quality crystal polarizers (like the Glan-Thompson) and dual-beam analyzers (like the Wollaston) modified for use in space can be obtained from Karl Lambrecht and CVI, among other vendors. In addition, Corning Glass produces Polarcor, an efficient glass-matrix embedded polarizer that is suitable for space environments, though with slightly lower performance than the prism polarizers. Polarcor does have an advantage that it is thinner than prism polarizers but.
Laser Max informs us that they can make space qualified versions of laser models used in the SCME. Laser Max has previously made space qualified versions of other laser models in their product line, thus demonstrating their abilities in this area. The Laser Max lasers are rugged and can be potted with stable low-outgassing cements.
The Hinds PEM-90 Polarization Modulator System incorporated into the SCME will require substantial rebuilding for space qualification. Besides rebuilding the control and power electronic circuits, the important modulator head assembly requires some changes. The cements and plastic mounts in the head assembly can be changed to materials suitable for space. Though the vendor has not made a space-qualified Polarization Modulator System, they have made head assemblies for use in high vacuum systems, addressing some of the challenges of space qualification.
6.2. Spectroscopic And Variable Angle Capabilities
The optical system presently takes data at a single fixed angle of incidence. It could instead be coupled with a variable angle of incidence base, so that data could be measured over a wide range of angles. This would increase the expense and complexity of the system. Another option would be to modify the optical system so that data were obtained simultaneously or sequentially at several discrete angles. In principle, obtaining data at more than one angle of incidence increases the amount of information about the sample that can be extracted. In practice however, data measured at different angles are usually highly correlated in information content and do not present much additional information over a single-angle measurement. Furthermore, for in situ applications where the system is mounted externally to a chamber with fixed windows, multiple angle measurements could not be made because the limited field of view through the windows fixed the incidence angle. Another issue concerning the incidence angle is sensitivity. For a static sample, there is an optimum angle for maximum sensitivity to film thickness and other parameters of interest. However, in most applications of this instrument the sample will not be static but changing (as a film is deposited or etched, for example), so that the optimum angle is not fixed but varies in time. Therefore a variable/multiple angle capability is probably not warranted for most applications.
The optical system currently uses a single wavelength solid state laser source. Multiple (two or more) wavelength data would provide useful additional information content, at relatively little increase in complexity and expense. Different wavelengths have different penetration depths, especially for semiconductor sample. A shorter (above-gap) wavelength would be more sensitive to surface changes, while a longer (below-gap) wavelength would penetrate to underlying interfaces and be sensitive to overall layer thickness. Several laser sources could be simply integrated through fiber optics. A fully spectroscopic system would provide a great deal more information, but at the cost of a much bigger, more complex and expensive system, and the need for more elaborate data analysis. A broadband lamp source would be needed, which would have significantly lower signal to noise than laser sources. Either a scanning monochromator (which would be slow) or a polychromator with detector array (with higher electronic complexity) could be used to select wavelengths. Development of such a system would be a major undertaking. While spectroscopic capability would be very valuable in a research instrument, it is probably not necessary for most monitoring applications.
In summary, the greatest return in information content for the least additional complexity and expense would be obtained by adding one or two more wavelengths, while keeping the fixed angle of incidence configuration.
This work was supported by NASA Small Business Innovation Research contract #NAS8-39920. The Ellipsometer is protected by U.S. patent #5,657,126 issued 12 August 1997 and assigned to the University of Nebraska.
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