EP1595135A1

EP1595135A1 - Method of performing optical measurement on a sample

Info

Publication number: EP1595135A1
Application number: EP04706394A
Authority: EP
Inventors: David Beaglehole
Original assignee: Beaglehole Instruments Ltd
Current assignee: Beaglehole Instruments Ltd
Priority date: 2003-02-03
Filing date: 2004-01-29
Publication date: 2005-11-16
Also published as: JP4555900B2; WO2004070365A1; EP1595135A4; JP2006516731A

Abstract

The invention relates to a method of performing an optical measurement on a sample, such as an ellipticity measurement. The sample is irradiated with a polarized irradiation beam and a return beam is linearly polarized. The irradiation or return beam is modulated with a birefringence modulator, such as a photoelastic modulator, in accordance with a primary modulation signal. The return beam is directed onto a multichannel detector. Typically the detector is a slow detector, such as a CCD, having a response time greater than a period of the primary modulation signal. Detection values are generated simultaneously at each detection element and processed to determine a plurality of measurements. Various measurement techniques are described, including detector signal averaging over gated intervals; a design employing coherent modulation of the gain of an ICCD, and a modulator-coherent flash lamp design.

Description

METHOD OF PERFORMING OPTICAL MEASUREMENT ON A SAMPLE

FIELD OF THE INVENTION

The invention relates to a method of perfoπning an optical measurement on a sample, such as an ellipticity measurement.

BACKGROUND OF THE INVENTION

EUipsometers have been used for a number of years in measurements of thin films. In particular, ellipsometers have been used in the measurement of oxide and other layers on semiconductors. EUipsometers analyse the ellipticity induced by reflection from a surface, measuring two parameters. This technique enables much more precise measurements than are possible using reflectometry measurements, for example.

A simple ellipsometer includes a light source which produces a beam of light which passes through a polarizer, forming a beam of plane-polarized light. The light source may be a laser or LED for single wavelength measurements, or a white light source for spectroscopic measurements. The beam passes through a retarder (sometimes referred to as a compensator) before striking the surface of a sample. The reflected light passes through a second polarizer (usually called the analyser) and enters a light detector. The light detector is usually a photodiode or a photomultiplier. An ellipsometer with a single photodiode or photomultiplier detector is a single channel ellipsometer.

The retarder may rotate. Alternatively, a birefringence modulator may be used. This modulator is typically a photoelastic modulator which includes an element with a birefringence dependent on the strain applied to it. A periodic strain is applied by a piezoelectric transducer, so that the b efringence is modulated at a high frequency (angular frequency ω₀) usually in a mechanical resonance mode

A single channel birefringence-modulator ellipsometer has a sensitivity which is typically 100 times more than that of a common rotating-component ellipsometer. The ellipsometer has one detector. It achieves its very high sensitivity by using coherent lock-in amplifier detection operating at α>o and 2ωo. This puts the electronics into a low noise region and the coherent detection of the lock-in with both frequency and phase eliminates noise signals which are not coherent with the modulator. Further, the modulation element undergoes mechanical resonance without motion of the centre of mass, and this eliminates motion of the light beam on the detector which often causes residual stray signals in the rotating-component design.

The usual configuration for a birefringence-modulator ellipsometer is Source P M Sample A Detector, where P, M, and A are respectively the Polariser, Modulator and Analyser (sometimes it is used with the modulator following the sample). In the usual configuration the Polariser and Analyser are oriented at 45° and the modulator is parallel or perpendicular to the s direction (the s direction being parallel to the. surface of the sample and perpendicular to the plane of incidence). Then / = I₀ r_s ² {1 + p¹ + 2ρ cos(Δ .+ δ)} (1)

Here I₀ is the incident intensity, I the intensity following the Analyser, r_s the magnitude of the s amplitude reflectivity, p and Δ are the parameters of the reflected polarisation ellipse, p the magnitude and Δ the phase angle, δ the modulator phase shift which varies with time as δ = δ₀ sin ω₀t . The expression can be expanded to read

/ oc 1 + p ² + 2p cos Δ cos δ - 2p sin Δ sin δ

I °c 1 + p ² + 2p cos Δ {J₀ (δ₀ ) + 2J- (δ₀ ) cos 2ω₀t + ..} - 2/7 sin Δ {2J_X (δ₀ ) sin ω₀t + 2J₃ (δ₀ ) sin 3ω . + ••}

(2) Here J₀, Ji, J₂..are integer Bessel Functions dependent on the amplitude of the modulator phase shift δo and theseries sums continue to higher order. The three lowest frequency terms are: the dc component I_dc ∞ 1 + p ² + 2p cos Δ J₀ (δ₀ ) (3) the ac component at angular frequency ω₀ 1_^ oc 2p sin Δ J. (δ₀ ) sin ω₀t (4) the ac component at angular frequency 2ω₀ 1_2m oc 2p cos Δ J₂ (δ₀ ) cos 2ω_ύt (5)

Lock-in amplifiers tuned to ωo and 2ωo output the amplitudes of the con and 2ωo signals. The ratio of the ac/dc signals provides two expressions involving p and Δ from which these two parameters can be derived. Parameters (x,y) can then be derived from p and Δ , where

_ 2/3 cos Δ _ 2 sinΔ ^{X ~} l + p^{2 , y ~} 1 + p^{2 ■}

EUipsometers may be used in an imaging mode, where a multichannel array detector such as a CCD is used. In this case a rotating modulator has been used and a set of CCD images are recorded at different orientations of the retarder, which can then be analysed to form images of x and y, or p and Δ, over the illuminated sample area.

It would be desirable to preserve the beneficial features of a birefringence modulator (high stability modulation and little or no motion of the centre of mass) in such an ellipsometer The frame rate of multichannel CCD detectors is typically in the range 20 to 200 frames per second, while the modulation frequency con of a typical birefringence modulator is around 50 kHz. It is not possible to follow the rapidly changing modulated signal using an otherwise suitable detector.

A multi-detector ellipsometer is described in US5757671. The detectors used are photodiodes, with the signals from all detectors being multiplexed to a single analog/digital converter. The signal is subsequently Fourier decomposed. This method is not readily extendable to a large number of channels.

A spectroscopic ellipsometer based on a birefringence modulator is an example of another desirable instrument. Here multichannel detectors could measure all colours at the same time. A straight forward method to achieve this would consist of many single channels detectors each with their associated two lock-in amplifiers. Such an instrument would be very bulky. Multichannel CCD detectors are again too slow to follow the modulation signals.

SUMMARY OF THE INVENTION

A first aspect of the invention provides a method of performing a measurement on a sample including: irradiating the sample with a polarized irradiation beam; linearly polarizing a return beam from the sample; modulating the irradiation or return beam with a birefringence modulator in accordance with a primary modulation signal; generating a secondary modulation signal which has a predetermined phase relationship with the primary modulation signal; directing the return beam onto a multichannel detector, the multichannel detector having a plurality of detection elements; simultaneously generating a detection value at each detection element; processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam; and modulating the irradiation or return beam in accordance with the secondary modulation signal, or controlling the generation or processing of the detection values in accordance with the secondary modulation signal.

A second aspect of the invention provides measurement apparatus including: a radiation source; a polarizer; a birefringence modulator configured to modulate an irradiation or return beam in accordance with a primary modulation signal; an analyzer; means for generating a secondary modulation signal which has a predetermined phase relationship with the primary modulation signal; a multichannel detector having a plurality of detection elements configured to simultaneously generate a detection value at each detection element; a processor for processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam; and means for modulating the irradiation or return beam in accordance with the secondary modulation signal, or controlling the generation or processing of the detection values in accordance with the secondary modulation signal. By processing a set of simultaneously generated detection values, the invention provides a truly parallel system which is fast, and is readily extendable to a large number of channels. This can be contrasted with the system of US5757671 in which each detector value is generated at a different time.

In imaging or spectroscopic configurations this enables studies of a substrate to be analysed in a short time. This aspect of the invention is particularly valuable in time-critical processes such as semiconductor manufacture or situations where surface features are changing with time.

The use of a birefringence modulator brings the advantages of relatively high stability modulation and little or no motion of the centre of mass.

Furthermore, the invention performs synchronous illumination or detection using a secondary modulation signal. This enables the modulator and detector/processor to operate synchronously, even when their respective frequencies of operation are different. For instance it enables a

"slow" detector to be used, which cannot follow the primary modulation signal, but can integrate the detection signals over portions of the modulator cycle. Such a detector typically has a response time greater than a period of the primary modulation signal, and is typically also an integrating detector. However it should be noted that a "fast" detector may also be employed, and the detection values integrated not by the detector itself, but in subsequent electronics.

The invention also typically avoids the need for conventional lock-in amplifier detector which would be prohibitively bulky and expensive in the number required for say 500 parallel channels.

The use of a secondary modulation signal also provides flexibility, enabling a variety of detection schemes to be employed. Typically the secondary modulation signal switches in turn between two or more measurement modes, although it is possible that the measurement of some useful parameters might be achieved by using only a single measurement mode. However in the preferred schemes described below there are at least three modes including a DC measurement mode. In some preferred measurement procedures the secondary modulation signal has a first phase relationship with the primary modulation signal during a first measurement mode, and a second phase relationship with the primary modulation signal during a second measurement mode. For example the secondary modulation signal may include a series of pulses having a first phase relationship with the primary modulation signal during the first measurement mode, and a series of pulses having a second phase relationship with the primary modulation signal during the second measurement mode. Alternatively the secondary modulation signal may include a series of pulses with a first pulse width during the first measurement mode, and a series of pulses with a second pulse width during the second measurement mode.

In other preferred measurement procedures the secondary modulation signal has a first frequency content during a first measurement mode,and a second frequency content during a second measurement mode. For example the secondary modulation signal may contain a first set of one or more harmonics of the frequency of the primary modulation signal during the first measurement mode, and a second set of one or more harmonics of the frequency of the primary modulation signal during the second measurement mode. Alternatively the secondary modulation signal may contain a square-wave pulse train at a first frequency during the first measurement mode, and a square-wave pulse train at a second frequency during the second measurement mode.

The secondary modulation signal may be used to control a variety of hardware elements, in order to perform the desired coherent detection. For instance the irradiation or return beam may be modulated by opening and closing a gate in the path of the irradiation beam or the return beam. In a preferred embodiment this is achieved by using an intensified charge-coupled device (ICCD), although any controllable gate (such as a chopper coherent with the modulator) may be used. Alternatively the irradiation beam may be modulated in accordance with the secondary modulation signal by turning on and off a radiation source such as a flash lamp. This has the advantage that the source is only on for some of the time, thus reducing power requirements and extending the life of the source. Alternatively the irradiation beam may be modulated in accordance with the secondary modulation signal by varying the intensity of a radiation source such as a light emitting diode or LED. Alternatively the generation or processing of the detection values may be controlled by varying a gain of the multichannel detector, or controlling subsequent electronics in accordance with the secondary modulation signal.

In the case where the radiation source is turned on and off to produce a series of radiation pulses, and the spectrum of the pulse varies with time during heating and cooling effects, the method may further include the step of closing a gate in the path of the irradiation or return beam during each radiation pulse, or reducing the gain of the detector during each radiation pulse. This provides a "spectral clean-up" of the radiation pulses by discarding unwanted signal.

Although generated in parallel, the detection values are typically read out serially from the multichannel detector.

In the preferred hardware examples described below the multichannel detector is a Charge Coupled Device (CCD) detector. Alternatively the detector may be a Complementary Metal Oxide Semiconductor (CMOS) detector or a Photo Diode Array (PDA) detector, with suitable gating features.

A variety of birefringence modulators may be used. In the preferred hardware examples described below a resonant modulator such as a photoelastic modulator is used. However, other non-resonant types of birefringence modulator may be used, such as a liquid crystal variable retarder, or Faraday or Kerr effect retarders.

The method may be employed in an imaging device, in which a two dimensional image representative of a property of the sample is provided. Alternatively the apparatus may be used in a spectroscopic mode, where the light incident on the detector is dispersed using a grating (or other wavelength dispersive element) and the measurements are made as a function of wavelength.

The method may be employed to perform a variety of measurements where the measured property is associated with transmission through a sample as well as reflection from a sample. Examples include ellipticity, circular transmission dichroism, stress birefringence and surface optical anisotropy. BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described by way of example with reference to the accompanying drawings, in which:

Figure 1 shows a spectroscopic ellipsometer;

Figure 2 shows the timing for a first measurement process;

Figure 3 shows the timing for a second measurement process; Figure 4 shows the timing for a third measurement process;

Figure 5 shows a spectroscopic ellipsometer with a triggered flash lamp;

Figure 6 shows the timing for a fourth measurement process;

Figure 7 is a graph showing preliminary data;

Figure 8 is a graph showing normalised data; and Figure 9 is a graph showing spectroscopic raw data using a triggered flash lamp method.

DESCRIPTION OF THE INVENTION

Various embodiments of the invention will now be described with reference to a first hardware example (Figure 1) and a second hardware example (Figure 5).

1 First Hardware Example: Modulator-coherent detector signal integrating over gated intervals of a modulator cycle

1.1 Hardware

Figure 1 shows a spectroscopic ellipsometer. Light from a white light source 1 passes through a polarizer 2, forming a beam of plane-polarized light. The polarized beam is modulated by a photoelastic birefringence modulator which comprises a fused silica modulator portion 3 which is driven into resonance by a piezoelectric drive element 4. A piezoelectric gauge element 5 generates a signal in response to the vibration of the modulator portion, and feeds the signal back into the drive element via a feedback path 6. An example of a suitable modulator is the High Stability Birefringence Modulator manufactured by Beaglehole Instruments Limited of 32 Salamanca Road, Wellington, New Zealand.

The beam passes through the modulator and a condenser lens 16, before striking the surface of a sample 7. The reflected light passes through an objective lens 8, a second polarizer 9 (usually called the analyser) and is focused onto the entrance slit of a spectrograph 20 which has an intensified charge-coupled device (ICCD) camera at the exit plane. The ICCD camera has a CCD 10, and a gate in front of the CCD which can be opened and closed in a time ~ 5ns (depending upon the manufacturer). The gate comprises an intensifier 11 and phosphor screen 12. The intensifier operates in a similar way to a photomultiplier, and the gain of the intensifier 11 can be controlled via an input line 13. An example of a suitable ICCD camera is the PI_MAX1024 manufactured by Roper Scientific, 3660 Quakerbridge Road, Trenton, NJ 08619.

In some ICCD cameras, the phosphor screen 12 and CCD 10 are coupled by optical-fibre cables (not shown). In an alternative arrangement, the birefringence modulator may be placed between the sample and the analyser 9.

A gate controller 14 controls the gate, and in turn is controlled by a computer 15 which also receives and processes data from the CCD 10. The gate controller 14 derives modulator- coherent pulses each cycle from a positive-going zero crossing of the primary modulation signal received from the gauge element 5, and opens and closes the gate at specified points during the modulator oscillation. For instance it can be held open for one full period T of the modulator, in

T which case we measure \I_dcdt , the ac terms averaging to zero. Other intervals for instance 0 - o

T/2, 0 - 5T/8 give functions of pcosΔ and psinΔ, from which p and Δ can be derived. When shot noise limited, the noise of the detector is proportional to the square root of the number of photons falling on the detector during the measurement time, so this number is a measure of the design efficiency. In the present case about V* of the photons incident onto the detector are not used, and measurements for three separate intervals are required to determine I₀ and the two ellipsometry parameters. The. CCD 10 is read out by computer 15 which processes the data to calculate a set of ellipticity values. The computer 15 may process data from each individual CCD pixel, or may only process summed values taken from blocks of pixels (a technique commonly known as "binning"). Also, the computer may process data taken from the entire CCD, or from only a specified region of interest (ROI) within the field of view of the CCD.

The hardware of Figure 1 can be operated using a variety of measurement procedures. An ellipsometry analysis is given below for three measurement procedures followed by an example of the measurement procedure.

1.2.1 Ellipsometry Analysis (First Measurement Procedure)

The signal measured in a single channel of a modulation ellipsometer is:

I = I₀ r² {l + p² +2 p cos(A + δ)} (6)

I₀ r_ { 1 + p² + 2 p cos Δ cos δ-2p sin Δ sin δ}

where Δ is the optical phase shift due to the sample, and δ is the optical phase-shift of the modulator, and δ = δ₀ sin -at.

In the first measurement procedure the signal is integrated between times ti and t₂:

cos δ = J₀ (δ₀) + 2J₂ ( δ₀ ) cos 2ω t + 2J₄ (δ₀ ) cos 4ω t + .. (7)

(2 (2 .2 jdtcosδ =J₀(δ₀)(t₂ -t.) + 2J₂(δ_g) jdt cos2ωt+2J₄(δ₀) jdt cos4_»t+.

.1 .1 .1

= J _ (δ₀ ) (t₂ - 1. ) + (2J₂ (δ₀ ) 12ω)(sin 2ω t₂ - sin 2ωt.)+ (2J₄ ( δ₀ ) 14ω)(sin 4_u t₂ - sin 4ωt.) + . (8)

smJ=2J₁(£₀)sinωt+2J₃(£-)sin3-yt+. (9)

(2J ( δ₀ ) I _y)(cos o t. - cos -o t₂ ) + (2J₃ (δ_a ) 13-»)(cos 3ω t. - cos 3ω t₃ ) + .

.2

\dtl=l₀r² {l+p²+J₀(δ₀)2pcosA(t₂ -t,)

.1 -sin4-at_x) + ..]

+ 4p sin Δ [Jj (^_ ) / _y)(cos ω t_t - cos ω t₂ ) + (J₃ (δ₀ ) 13<»)(cos 3ω t. - cos 3ω t₂ ) + .] }

(11) The following table presents the values of the three terms normalised byl₀r² integrated from time tl = 0 to time t2: T equals the modulator period 2π/ω.

t2 = T/2

Term 2 (even J)

Term 3 (oddj) 4.sinΔ[2J₁( ₀) + 2J₃( ₀)/3+2J₅

(12) t2 = 5T/8

Term2 4p cos Δ [J₂ (δ₀)/2-J₆ (δ₀ )/6](T/ π)

Term3 4p sin Δ [J. (δ₀ ) 1.707 + J₃ (δ₀ )0.293 / 3 + J₅ (δ₀ )0.293 / 5 + .] (T 12π)

(13) t2 = 3T/4

Term 1 [l+ ²+J-( ₀)2 cosΔ](3r/4) Term 2 0 Term 3 4 sinΔ

(14) t2 = 7T/8

Term 1 [l+p²+J_Q(δ₀)2pcosA-(lTI ) Term 3 4p sin Δ [J. (δ₀ ) 0.293 + J₃ (δ₀ )1.707 / 3 + J₅ ( δ₀ )0.293 / 5 + .] (T 12π)

(15) t2 = T

Terml [l+p² + J₀(δ₀)2pcosA] T Term 2 0

Term 3 0 (16)

The terms psinΔ and pcosΔ are the real and imaginary parts of the complex amplitude reflectivity ratio, which fully determine the ellipticity. These can be seen to depend upon δ₀, which in turn depends upon the amplitude of the modulator birefringence, which in turn varies inversely with the optical wavelength. The lowest order Bessel functions dominate the expressions, but the higher orders contribute a little at large δ₀.

To remove the dependence on the intensity we take the ratio of two measurements made for different integration periods. If we take the total signal for t2 = 3T/4 and divide this by the total signal for t2 = T we have the ratio:

I(tl = 0,t2 = 3T/4) 4 sinΔ α

(17)

/(tl = 0,t2 = T) (l+p² +J₀(δ₀)2pcosA)β

where , β are simple functions of δ₀ and T.

With a choice of different periods we can similarly get a ratio proportional to ^^ . (18)

1 + p + J₀2 ->cosΔ

From these ratios the ellipticity parameters can be derived.

1.2.2 Example of First Measurement Procedure

Figure 2 is a timing diagram of an example of the first measurement procedure. The primary modulation signal is shown in Figure 2 at (a) as a sine wave at angular frequency ω₀. The gate controller 14 generates a pulse from each positive-going zero crossing of the primary modulation signal, which is used to control the phase of the gate control signal, shown at (b), (c) and (d). The procedure is as follows:

Exposure 1 Fully expose the CCD for ni cycles of the primary modulation signal. The value ni is selected so that the CCD is almost fully exposed (pixel wells near full). The gate control signal on input line 13 during Exposure 1 is shown in Figure 2 at (b). In the example of Figure 2, ni is shown with a value of two, so the gate is opened in this case for two cycles Readout 1 Read out the CCD.

Exposure 2 Expose the CCD for n₂ cycles of the primary modulation signal, for T/2 seconds per cycle. The value n₂ is selected so that the CCD is almost fully exposed, and may be different to the value ni for Exposure 1. The gate control signal on input line 13 during Exposure 2 is shown in Figure 2 at (c). In the example of Figure 2, n₂ is shown with a value of two, so the gate is opened in this case for two cycles

Readout 2 Read out the CCD.

Exposure 3 Expose the CCD for n₃ cycles of the primary modulation signal, for 5T/8 seconds per cycle. The value n₃ is selected so that the CCD is almost fully exposed, and may be different to the value ni for Exposure 1 and/or the value n₂ for Exposure 2. The gate control signal on input line 13 during Exposure 3 is shown in Figure

2 at (d). In the example of Figure 2, n₃ is shown with a value of two, so the gate is opened in this case for two cycles Readout 3 Read out the CCD.

The above steps are then repeated until the noise in the data is as small as desired. The CCD frame readouts are then processed according to the equations above, taking into account appropriately the cycle-exposure numbers ni _s n_{2 ,} n₃.

1.3.1 Ellipsometry Analysis (Second Measurement Procedure)

In the second measurement procedure, the gain G is switched between off and G=l as a square wave as follows: • Odd modulation G₀dd = 1 for interval t/T = 0 to 1/2, G₀dd = 0 for interval t/T = Yz to 1.

• Even modulation G_eVen = 0 for intervals t/T = 0 to 1/8, 3/8 to 5/8, 7/8 to 1.

= 1 for intervals t/T = 1/8 to 3/8, 5/8 to 7/8

The total on-time is T/2 each full cycle in both cases.

The signal that is measured is the time-averaged product G I over many cycles. Even and odd modulating functions have different averages, classified by their symmetry about T/2.

S = I₀ G {l + _yσ² +2_/σcos(Δ + )} = I₀G {l + ?² + 2 ? cos Δ cos ^-2 ? sin Δ sin ^} (19)

We expand the time variation of the modulator optical phase δ: cos δ = cos (£₀snuy₀t) = J₀ ( δ₀ ) + ∑ 2J_m (δ₀ ) cos(mω₀t) m=2,4.. sinδ = sin(δ₀smω₀t) = 2J_m(δ₀)άn(mω₀t) (20) m=l,3.. If we average the time-independent terms over one cycle we obtain S_d0 given by

S,- = /- [l + /?² + 2/. cosΔJ T . If we average the even time-dependent terms for the G_eVe_n ⁼ 1 on-time, we have

Se_ven = (δ_Q ) C0S(m^β?-t)

Changing the time variable to θ = ω₀t = 2πt/T we have

S_eveM = I₀2pcosA ^- ∑2J_m (δ₀)Sdθcos(mθ)

2τt _{m =} Λ

Similarly we find using G₀dd

^Sodd = ^Jo ²P sin Δ jdt ∑ 2J_m sin mω₀t

1,3.. • _ T - -i - _Ύ cosmθ i

S_oa, = -/₀2 _?smΔ— ∑2J_m ~- - |_Goda=1 M=1,3 . "*

S_odrf = I₀2p sin Δ T Sum_odd with Swm.^ = (Ji + J₃ / 3 + J₅ / 5..)2 / (22)

In our measurements we measure the time integrated signal for ni full periods with no modulation and obtain the A = 'dc' signal. We measure with odd modulation and record B - de'- Odd'. We measure with even modulation andrecord C - dc' + 'even'.

„. _, _ A -B 2 -»sinΔ Sum_odd , C -A 2pcos A Sum_even

We then have = — —. — — = v , = — —. — — = x

A 1 + p² + 2pcosAJ₀ A 1 + p² + 2pcosAJ₀

The parameters x, y can be derived from (x',y'): _y ^, ₌_ yy SSuumm_oodddd ^ _χ ^, ₌_ xxSSuumm_eevvee^_{n rø} y — ? *^* —

1 + xJ - 1 + xJ -

x' _y . _y^ + ^θ ) x = ι S Suumm_eevvee ^: _nn --xx' τ'JJτ₀--'- y =?^ SS,uumm_oodddd - ^• (2

1.3.2 Example of Second Measurement Procedure

Figure 3 is a timing diagram of an example of the second measurement procedure. The procedure is as follows:

Exposure 1 Fully expose the CCD for ni cycles of the primary modulation signal. The value n is selected so that the CCD is almost fully exposed. The gate control signal on input line 13 during Exposure 1 is shown in Figure 3 at (b). In the example of Figure 3, m is shown with a value of two, so the gate is opened in this case for two cycles Readout 1 Read out the CCD. Exposure 2 Expose the CCD for n₂ cycles of the primary modulation signal, with a square wave at frequency ω₀, odd about t=T/2. The value n₂ is selected so that the CCD is almost fully exposed, and may be different to the value ni for Exposure 1. The gate control signal on input line 13 during Exposure 2 is shown in Figure 3 at (c). In the example of Figure 3, n₂ is shown with a value of two, so the gate is opened in this case for two cycles

Readout 2 Read out the CCD. Exposure 3 Expose the CCD for n₃ cycles of the primary modulation signal, with a square wave at frequency 2ω₀, even about t-T/2. The value n₃ is selected so that the CCD is almost fully exposed, and may be different to the value ni for Exposure 1 and/or the value n₂ for Exposure 2. The gate control signal on input line 13 during Exposure 3 is shown in Figure 3 at (d). In the example of Figure 3 n₃ is shown with a value of two, so the gate is opened in this case for two cycles

Readout 3 Read out the CCD.

The above steps are then repeated as before until the signal fluctuations are as small as desired.

1.3.3 Experimental Data

Figure 7 shows some preliminary measurements of the parameters x,y using the second measurement procedure.. Note that the polariser and analyzer are only efficient in the range 420 to 800nm. y ~ l, x ~ 0 at 630nm.

Figure 8 is a graph showing normalised data. The solid upper curve shows the even data divided by dc and the lower solid curve shows the odd data divided by dc. The broken lines show calculated values for comparison purposes.

1.4.1 Ellipsometry Analysis (Third Measurement Procedure)

Rather than using a square modulation gate, the intensifier can be used to modulate the gain G of the detector, with the Gain varying in time as the sum of even and odd harmonic sine waves.

If the gain is modulated as ^lA G₀{ l+cos(ω_gt + φ_g)}, the signal becomes

I=l/2 GJ₀r ²{l + cos(ω_gt + _g)}{l + p² + 2 σcos(Δ + δ)} (25) When the equation is expanded, one half the intensity takes the same dc and ac expressions as before, the other half involves sum and difference terms with angular frequency ω_g ± ω₀ , ω_g ± 2ω₀. Thus if ω_g is set to 0, ω₀, 2ω₀ in turn, the difference frequency becomes zero for each of the dc and ac, and time averaged measurements of the three zero-frequency 5 signals can be made. Note the gain-modulation signal is derived from the modulation oscillation amplitude so that it is exactly coherent. The efficiency is about 1/3. The gain phase-shift φ_g can be adjusted for maximum zero-frequency signal. The third measurement procedure effectively turns the detector into a self-operating lock-in amplifier.

10 The gain-modulating function can also be generated to have equal amplitudes of even and odd higher harmonics:

G_odd = 1/2 G₀{(l + cosβ>₀t + cos3β.₀t + cos5β.₀t..}

(26) G_even = 1/2 G-{(l + cos2β.₀t + cos4ω₀t + cos6β. _t..}

The zero-frequency terms will then be derived from the even and odd harmonics in the ac, dc terms in equations 3, 4, 5 above, giving the zero- frequency signals proportional to _{i g} odd = 2psmA{J. (δ₀)+J₃(δ₀) + ...} even = 2 7 cos Δ{J₂ (£₀ ) + J₄ (e>₀ ) + ...}

At fixed modulator amplitude δ₀ is a function of light wavelength, and if a wide spectral range is used, zeros in the Ji, J₂,..Bessel functions in equations 3, 4 cause low sensitivity to p, Δ in these regions. The sum of the Bessel functions in equation 8 has no zeros, and the "dead" regions can 0 be eliminated. The efficiency is again about 1/3.

Instead of varying the gain of the detector, one can equivalently vary the intensity of the light source. An LED is a bright and essentially incoherent source and can provide suitably narrow band source for imaging ellipsometry applications. Laser diodes can also be modulated at high 5 frequency, but the longer coherence length makes these less suitable for imaging applications. LED illumination does not have the same coherence.

1.4.2 Example of Third Measurement Procedure Figure 4 give an example of the third measurement procedure. The procedure is as follows:

Exposure 1 Fully expose the CCD for ni cycles of the primary modulation signal. The value ni is selected so that the CCD is almost fully exposed. The gate control signal on input line 13 during Exposure 1 is shown in Figure 2 at (b). In the example of

Figure 4, ni is shown with a value of two, so the gate is modulated in this case for two cycles Readout 1 Read out the CCD.

Exposure 2 Expose the CCD for n₂ cycles of the primary modulation signal, with the gain modulated with the sum of three odd sines, odd about t=T/2 as shown at (c) in

Figure 4. The value n₂ is selected so that the CCD is almost fully exposed, and may be different to the value m for Exposure 1. In the example of Figure 4, n₂ is shown with a value of two, so the gate is opened in this case for two cycles Readout 2 Read out the CCD. Exposure 3 Expose the CCD for n₃ cycles of the primary modulation signal, with the gain modulated with the sum of three even sines, even about t=T/2 as shown at (d) in Figure 4. The value n₃ is selected so that the CCD is almost fully exposed, and may be different to the value ni for Exposure 1 and/or the value n₂ for Exposure 2. In the example of Figure 4, n₃ is shown with a value of two, so the gate is modulated in this case for two cycles

Readout 3 Read out the CCD.

The above steps are then repeated.

2 Second Hardware Example: Coherent short flash lamp pulse illumination

2.1 Hardware

An alternative spectroscopic ellipsometer is shown in Figure 5. Much of the hardware is identical to the hardware shown in Figure 1, so reference numbers are repeated for identical components. The conventional light source 1 is replaced by a flash lamp 21 such as a Hamamatsu Super-quiet 15W Xe Flash tube that generates a pulse with width ~ 1.75μs at full width half maximum (FWHM). Each flash provides 0.15J of energy. The lamp can provide 100 flashes per second. The lamp has an arc size of 1.5mm. The period of the modulator T is 20 μs, so we will assume in the following analysis that as a first approximation the pulse width is small compared with the period. A more detailed analysis can take into account the finite width.

The xenon arc lamp 21 can be operated in a triggered pulse mode, producing pulses with a maximum repetition frequency ~ 100Hz. For instance, if we take measurements at four different points during the cycle, at t/T = 0, ^lA, Vi , % , then I₀, δ₀, p and Δ can be derived. The time- averaged intensity of the flash lamp is less than a 75 W CW Xe lamp through most of the visible spectrum, but has more deep UV light. The efficiency is higher than the averaging mode in the first embodiment described above.

2.1.1 Ellipsometry analysis

The signal measured in a single channel of a modulation ellipsometer is:

I = I₀ r ² {l+p² + 2pcos(A+ δ)}

(28)

{1+p² + 2 ?cosΔcos J - 2/? sin Δ sine))

where Δ is the optical phase shift due to the sample, and δ is the optical phase-shift of the modulator, and δ = δ₀ sin ω t (which varies with wavelength as ~C/λ).

If we measure for short times, then we record / at specific values of ω t, for instance as shown in the following Table.

If we take 4 measurements of the intensity at ωt = 0, π/2, π and 3π/2, we can determine the following ratios:

(D-B) _ 2 sinΔsinJ- y'= (29)

(D + B) 1 + p² +2 cosΔcosJ₀

(A + C)-(B + D) 2pcosΔ(l-cosJ₀) C' = (30)

(D + B) 1 + p + 2 cosΔcosc>-

Note the denominators could be A+C which removes the cosδ₀ term, but makes the linear contribution larger. It is best to work with δ₀ = π/2 and cosδ_σ = 0, but the wavelength variation of δ₀ prevents this for all wavelengths.

(D-B) (l-cos ₀) (D-B)

Note tanΔ = -

(A+C)-(B + D) sin£₀ (A + C) - (B + D) tan(< 2) (31)

The functions (x',y') are close to the usual modulation ellipsometry functions (x, y) and the latter can be derived directly from (x',y') , the scaling depending on δ₀ and ' .

/tan(A/2) x =^■

1- cos y=- (32) -(! + ;<;*) l-cos ₀(l + x')

Note resonances occur when cos<->₀(l+x') = 1, and for y also when δ₀ = π. Between these resonances there is a range of a factor of three where the x',y' measured parameters could be accurately corrected.

Note the B and D measurements can be made at other phases, eg π/4; the value of δ would then be δ₀1 2 , and the range of sensitivity will be correspondingly altered. 2.1.2 Spectral Clean-up

The intensity that is emitted by the flash lamp is a pulse of light of short duration, set-off by an electric trigger pulse. There is usually a tail which decays slowly following the main flash. This tail has a light spectrum which differs from the spectrum emitted by the main flash. Optical signals which depend upon the spectrum thus will have a time dependence due to changes in the spectrum as well as the primary change associated with the time-varying intensity.

The spectrum changes can be eliminated if only the main portion of the flash is studied. A relatively simple way to eliminate the effects of the tail is to use a gated detector under the control of the same trigger that sets off the flash. There is usually some steady delay between the generation of the flash trigger pulse and the occurrence of the flash. This same trigger pulse can therefore be used to open and close the gate to the detector.

The gate controller 14 opens the intensifier 11 before the flash occurs. The intensifier can then be closed after a time interval chosen so that the intensifier is closed immediately following the main flash, thus eliminating the detection of the tail. This method has been shown to work well in practice. The gating interval was adjusted for the particular delays associated with the flash- intensifier combination by recording the integrated detector signal due to the flash, and then shortening the interval to gate closure until the integrated signal started to fall. We observed a clean-up of signal occurring when the integrated intensity was reduced by a factor of- 10% by shortening the time to the closure of the intensifier.

Adding an intensifier to a CCD is an expensive option, since intensifier technology depends upon high speed switching of high voltages. Some CCDs (eg interline transfer) are able to perform exposure control down to time intervals as short as lOmicroseconds. Therefore, instead of using the ICCD shown in Figure 5, these cameras can therefore be used without requiring an intensifier, if the electronics has accurate timing to (i) start the exposure, (ii) send the flash trigger, (iii) stop the exposure at the appropriate time to cut off the tail. The timing will need careful adjustment to match the particular flash/camera combination but the adjustment so that the flash occurs in the final portion of the exposure interval should be readily achieved. 2.1.3 Example Procedure

Figure 6 gives an illustrative example of the operation of the system of Figure 5. The gate controller 14 controls the phase of the flash lamp and gate control signals as shown at (b) to (e).

The procedure is as follows:

Exposure 1 Expose the CCD with n flashes of the flash lamp at phase point A. The flash lamp can typically be flashed at a rate in the range of 100-300 Hz. The value n is selected so that the CCD is almost fully exposed. The output of the flash lamp during only one of the flashes of Exposure 1 is shown at (b), and the gate control signal is shown at (c). The value n might typically take a value of two or three.

Readout 1 Read out the CCD.

Exposure 2 Expose the CCD with n flashes of the flash lamp at phase point B. The output of the flash lamp during only one of the flashes of Exposure 2 is shown at (d), and the gate control signal is shown at (e).

Readout 2 Read out the CCD.

Exposure 3 Expose the CCD with n flashes of the flash lamp at phase point C. The flash lamp output and gate control signal during Exposure 3 are not shown in Figure 6. Readout 3 Read out the CCD.

Exposure 4 Expose the CCD with n flashes of the flash lamp at phase point D. The flash lamp output and gate control signal during Exposure 4 are not shown in Figure 6.

Readout 4 Read out the CCD.

The above steps are then repeated.

2.1.4 Experimental Data

Figure 9 is a graph showing spectroscopic raw data using the triggered flash lamp method.

Applications 3.1 Spectroscopic Ellipsometer

In the examples previously described, the invention is employed in a spectroscopic ellipsometer. The spectroscopic ellipsometer included a spectrograph 20 which disperses the return beam across the surface of the ICCD, so that each pixel records intensity at its associated wavelength.

3.2 Imaging Ellipsometer

In this application the sample is illuminated by a condenser, and an objective lens then forms an image of the sample on the multichannel CCD or ICCD. The ellipticity parameters may then be found for each point in the image using one or other of the procedures described above The computer can calculate the ellipticity parameters in a desired region of interest (ROI) or over the whole image field, and display the ellipticity parameters in a desired format. For example an ellipticity parameter x or y may be represented in a gray scale image, with the brightness of each pixel in the image being representative of the value of the parameter at that point on the sample surface.

4 Summary

While the present invention has been illustrated by the description of the embodiments thereof, and while the embodiments have been described in detail, it is not the intention of the Applicant to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, representative apparatus and method, and illustrative examples shown and described. Accordingly, departures may be made from such details without departure from the spirit or scope of the Applicant's general inventive concept.

Claims

1. A method of performing a measurement on a sample including: irradiating the sample with a polarized irradiation beam; linearly polarizing a return beam from the sample; modulating the irradiation or return beam with a birefringence modulator in accordance with a primary modulation signal; generating a secondary modulation signal which has a predetermined phase relationship with the primary modulation signal; directing the return beam onto a multichannel detector, the multichannel detector having a plurality of detection elements; simultaneously generating a detection value at each detection element; processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam; and modulating the irradiation or return beam in accordance with the secondary modulation signal, or controlling the generation or processing of the detection values in accordance with the secondary modulation signal.

2. A method according to claim 1 wherein the secondary modulation signal alternates in turn between two or more measurement modes.

3. A method according to claim 2 wherein the secondary modulation signal has a first phase relationship with the primary modulation signal during a first measurement mode; and a second phase relationship with the primary modulation signal during a second measurement mode.

4. A method according to claim 3 wherein the secondary modulation signal includes a series of pulses having a first phase relationship with the primary modulation signal during the first measurement mode; and a series of pulses having a second phase relationship with the primary modulation signal during the second measurement mode.

5. A method according to claim 2 wherein the secondary modulation signal includes a series of pulses with a first pulse width during the first measurement mode; and a series of pulses with a second pulse width during the second measurement mode.

6. A method according to claim 2 wherein the secondary modulation signal has a first frequency content during a first measurement mode; and a second frequency content during a second measurement mode.

7. A method according to claim 6 wherein the secondary modulation signal contains a first set of one or more harmonics of the frequency of the primary modulation signal during the first measurement mode; and a second set of one or more harmonics of the frequency of the primary modulation signal during the second measurement mode.

8. A method according to claim 6 wherein the secondary modulation signal contains a square- wave pulse train at a first frequency during the first measurement mode; and a square-wave pulse train at a second frequency during the second measurement mode.

9. A method according to any of claims 2 to 8 wherein the secondary modulation signal switches in turn between three or more measurement modes.

10. A method according to any of claims 2 to 9 wherein one of the measurement modes is a DC measurement mode.

11. A method according to any of the preceding claims wherein the irradiation or return beam is modulated in accordance with the secondary modulation signal by opening and closing a gate in the path of the beam.

12. A method according to any of the preceding claims wherein the irradiation beam is modulated in accordance with the secondary modulation signal by turning on and off a radiation source.

13. A method according to claim 12 wherein the radiation source is a flash lamp source.

14. A method according to claim 12 wherein the radiation source is a gas discharge lamp.

15. A method according to claim 12, 13 or 14 wherein the radiation source is turned on and off to produce a series of radiation pulses, and the method further includes the step of closing a gate in the path of the irradiation or return beam during each radiation pulse, or reducing the gain of the detector during each radiation pulse.

16. A method according to any of claims 1 to 11 wherein the irradiation beam is modulated in accordance with the secondary modulation signal by varying the intensity of a radiation source.

17. A method according to claim 16 wherein the radiation source is a light emitting diode.

18. A method according to any of the preceding claims wherein the generation or processing of the detection values is controlled by varying a gain of the multichannel detector in accordance with the secondary modulation signal.

19. A method according to any of the preceding claims wherein the multichannel detector is an integrating detector.

20. A method according to any of the preceding claims further including serially reading out the detection values from the multichannel detector.

21. A method according to any of the preceding claims wherein the multichannel detector is a charge coupled device.

22. A method according to any of the preceding claims wherein the multichannel detector has a response time greater than a period of the primary modulation signal.

23. A method according to any of the preceding claims further including: generating a plurality of sets of detection values, each set of detection values corresponding to a different predetermined phase of the birefringence modulator.

24. A method according to any of the preceding claims wherein the birefringence modulator is a photoelastic modulator.

25. A method according to any of the preceding claims wherein the birefringence modulator is a resonant modulator.

26. A method according to any of the preceding claims further including displaying a two dimensional image representative of the measurements.

27. A method according to any of the preceding claims further including directing the return beam onto a wavelength dispersive element

28. A method according to any of the preceding claims wherein each measurement includes an ellipticity measurement.

29. Measurement apparatus including: a radiation source; a polarizer; a birefringence modulator configured to modulate an irradiation or return beam in accordance with a primary modulation signal; an analyzer; means for generating a secondary modulation signal which has a predetermined phase relationship with the primary modulation signal; a multichannel detector having a plurality of detection elements configured to simultaneously generate a detection value at each detection element; a processor for processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam; and means for modulating the irradiation or return beam in accordance with the secondary modulation signal, or controlling the generation or processing of the detection values in accordance with the secondary modulation signal.

30. Apparatus according to claim 29 configured to perform a method according to any of claims 1 to 28.

31. A method of performing a measurement on a sample including: irradiating the sample with a polarized irradiation beam; linearly polarizing a return beam from the sample; modulating the irradiation or return beam with a photoelastic modulator; directing the return beam onto a multichannel detector, the multichannel detector having a plurality of detection elements; simultaneously generating a detection value at each detection element; and processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam.

32. A method according to claim 31 and any one of claims 1 to 28.

33. Measurement apparatus including: a radiation source; a polarizer; a photoelastic modulator; an analyzer; a multichannel detector having a plurality of detection elements configured to simultaneously generate a detection value at each detection element; and a processor for processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam.

34. Apparatus according to claim 33 configured to perform a method according to any of claims 1 to 28, 31 or 32.

35. A method of performing a measurement on a sample including: irradiating the sample with a polarized irradiation beam; linearly polarizing a return beam from the sample; modulating the irradiation or return beam with a birefringence modulator in accordance with a primary modulation signal; directing the return beam onto a multichannel detector, the multichannel detector having a plurality of detection elements and having a response time greater than a period of the primary modulation signal; simultaneously generating a detection value at each detection element; and processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam.

36. A method according to claim 35 and any of claims 1 to 28, 31 or 32.

37. Measurement apparatus including: a radiation source; a polarizer; a birefringence modulator configured to modulate an irradiation or return beam in accordance with a primary modulation signal; an analyzer; a multichannel detector having a plurality of detection elements configured to simultaneously generate a detection value at each detection element, the detector having a response time greater than a period of the primary modulation signal; and a processor for processing the simultaneously generated detection values to determine a plurality of measurements, each measurement corresponding with a respective detection element and being indicative of a change induced by the sample on the irradiation beam.

38. Apparatus according to claim 37 configured to perform a method according to any of claims 1 to 28, 31, 32, 35 or 36.