Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
  • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
  • G01N21/21—Polarisation-affecting properties
  • G01N21/211—Ellipsometry

Definitions

• the invention relates to a method of perfo ⁇ ning an optical measurement on a sample, such as an ellipticity measurement.
• EUipsometers have been used for a number of years in measurements of thin films.
• 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.
• 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 ⁇ 0 ) 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 ⁇ >o and 2 ⁇ o. 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).
• P, M, and A are respectively the Polariser, Modulator and Analyser (sometimes it is used with the modulator following the sample).
• I 0 is the incident intensity
• I the intensity following the Analyser
• r s the magnitude of the s amplitude reflectivity
• p and ⁇ are the parameters of the reflected polarisation ellipse
• p the magnitude and ⁇ the phase angle
• the three lowest frequency terms are: the dc component I dc ⁇ 1 + p 2 + 2p cos ⁇ J 0 ( ⁇ 0 ) (3) the ac component at angular frequency ⁇ 0 1 ⁇ oc 2p sin ⁇ J. ( ⁇ 0 ) sin ⁇ 0 t (4) the ac component at angular frequency 2 ⁇ 0 1 2m oc 2p cos ⁇ J 2 ( ⁇ 0 ) cos 2 ⁇ ⁇ t (5)
• Lock-in amplifiers tuned to ⁇ o and 2 ⁇ o output the amplitudes of the con and 2 ⁇ o signals.
• the ratio of the ac/dc signals provides two expressions involving p and ⁇ from which these two parameters can be derived. Parameters (x,y) can then be derived from p and ⁇ , where
• EUipsometers may be used in an imaging mode, where a multichannel array detector such as a CCD is used.
• 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 ⁇ , over the illuminated sample area.
• 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.
• 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.
• 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.
• the invention 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.
• 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.
• birefringence modulator brings the advantages of relatively high stability modulation and little or no motion of the centre of mass.
• 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.
• a detector typically has a response time greater than a period of the primary modulation signal, and is typically also an integrating detector.
• 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.
• 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.
• 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.
• 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.
• 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.
• the secondary modulation signal has a first frequency content during a first measurement mode,and a second frequency content during a second measurement mode.
• 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.
• 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.
• 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.
• ICCD intensified charge-coupled device
• 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.
• 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.
• 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.
• 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.
• the detection values are typically read out serially from the multichannel detector.
• the multichannel detector is a Charge Coupled Device (CCD) detector.
• the detector may be a Complementary Metal Oxide Semiconductor (CMOS) detector or a Photo Diode Array (PDA) detector, with suitable gating features.
• CMOS Complementary Metal Oxide Semiconductor
• PDA Photo Diode Array
• birefringence modulators may be used.
• a resonant modulator such as a photoelastic modulator is used.
• 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.
• 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.
• 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
• Figure 9 is a graph showing spectroscopic raw data using a triggered flash lamp method.
• 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.
• the phosphor screen 12 and CCD 10 are coupled by optical-fibre cables (not shown).
• 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/2, 0 - 5T/8 give functions of pcos ⁇ and psin ⁇ , from which p and ⁇ can be derived.
• 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 I 0 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.
• ROI region of interest
• 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.
• the signal measured in a single channel of a modulation ellipsometer is:
• ⁇ the optical phase shift due to the sample
• ⁇ the optical phase-shift of the modulator
• the signal is integrated between times ti and t 2 :
• T the modulator period 2 ⁇ / ⁇ .
• psin ⁇ and pcos ⁇ are the real and imaginary parts of the complex amplitude reflectivity ratio, which fully determine the ellipticity. These can be seen to depend upon ⁇ 0 , 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 ⁇ 0 .
• ⁇ are simple functions of ⁇ 0 and T.
• 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 ⁇ 0 .
• 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).
• 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 n 2 cycles of the primary modulation signal, for T/2 seconds per cycle.
• the value n 2 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).
• n 2 is shown with a value of two, so the gate is opened in this case for two cycles
• Exposure 3 Expose the CCD for n 3 cycles of the primary modulation signal, for 5T/8 seconds per cycle.
• the value n 3 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 n 2 for Exposure 2.
• the gate control signal on input line 13 during Exposure 3 is shown in Figure
• n 3 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 , n 3 .
• 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.
• Se ven ( ⁇ Q ) C0S(m ⁇ ?-t)
• 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).
• 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.
• the value n 2 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).
• n 2 is shown with a value of two, so the gate is opened in this case for two cycles
• Exposure 3 Expose the CCD for n 3 cycles of the primary modulation signal, with a square wave at frequency 2 ⁇ 0 , even about t-T/2.
• the value n 3 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 n 2 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 n 3 is shown with a value of two, so the gate is opened in this case for two cycles
• 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.
• 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.
• 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 ⁇ g can be adjusted for maximum zero-frequency signal.
• the third measurement procedure effectively turns the detector into a self-operating lock-in amplifier.
• the gain-modulating function can also be generated to have equal amplitudes of even and odd higher harmonics:
• G odd 1/2 G 0 ⁇ (l + cos ⁇ > 0 t + cos3 ⁇ . 0 t + cos5 ⁇ . 0 t.. ⁇
• G even 1/2 G- ⁇ (l + cos2 ⁇ . 0 t + cos4 ⁇ 0 t + cos6 ⁇ . _t.. ⁇
• ⁇ 0 is a function of light wavelength, and if a wide spectral range is used, zeros in the Ji, J 2 ,..Bessel functions in equations 3, 4 cause low sensitivity to p, ⁇ 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.
• 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.
• 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
• 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.
• n 2 is selected so that the CCD is almost fully exposed, and may be different to the value m for Exposure 1.
• n 2 is shown with a value of two, so the gate is opened in this case for two cycles Readout 2 Read out the CCD.
• the value n 3 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 n 2 for Exposure 2.
• n 3 is shown with a value of two, so the gate is modulated in this case for two cycles
• FIG. 5 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 ⁇ 1.75 ⁇ s 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 ⁇ s, 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 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.
• the signal measured in a single channel of a modulation ellipsometer is:
• I I 0 r 2 ⁇ l+p 2 + 2pcos(A+ ⁇ ) ⁇
• ⁇ is the optical phase shift due to the sample
• ⁇ is the optical phase-shift of the modulator
• ⁇ ⁇ 0 sin ⁇ t (which varies with wavelength as ⁇ C/ ⁇ ).
• the intensity that is emitted by the flash lamp is a pulse of light of short duration, set-off by an electric trigger pulse.
• 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.
• FIG. 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).
• 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).
• 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.
• Figure 9 is a graph showing spectroscopic raw data using the triggered flash lamp method.
• 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.
• 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.
• ROI region of interest
• 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.

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