FIELD OF THE INVENTION

The present invention relates to a method and an apparatus for reflectance anisotropy spectroscopy, and particularly to a method and apparatus having high sensitivity.

BACKGROUND ART

Reflectance Anisotropy Spectroscopy (RAS) is a technique for non-destructive optical surface analysis, The RAS technique measures the difference in reflectance (AR) in a sample for light that is linearly polarized along two mutually orthogonal directions x and y in a surface plane (x,y) of the sample, normalized to its average reflectance (R). The reflectance anisotropy signal, hereinafter referred to as spectroscopic measurement signal or, in short, RAS signal, is defined as follows:

AR R - R _v

— = 2— ^y - (1)

R R _x + R _y where R _x and R _y are the reflectances for the light polarized along the directions x and y respectively.

An overview of the RAS technique is given by P. Weightman et al, in "Reflection Anisotropy Spectroscopy", published in Reports on Progress in Physics vol. 68 (2005), pages 1251- 1341.

The RAS technique has been often used for measuring the anisotropy of monocrystalline surfaces, e.g. for in situ and real-time measurement of the epitaxial growth of a monocrystalline layer of semiconductor material.

The epitaxial growth of 6-thiophene thin films by ultrahigh-vacuum organic molecular beam deposition has been studied in situ using the RAS technique in "Highly sensitive optical monitoring of molecular film growth by organic molecular beam deposition", published in Applied Physics Letters vol. 83 (2003), pages 4146-4148, by Goletti etal. The authors found that the measured intensity scales with film thickness and estimated a RAS sensitivity to deposition of less than 1/50 of the monolayer. Patent DE 198 25 390 CI discloses a method of correcting the signs of measurement results in RAS measurements as used for in situ crystalline layer growth characterization on rotating samples to obtain a layer having homogeneous thickness and composition.

Many organic gas sensors are composed of a detection layer and a transducer that can convert the presence of molecules on the detection layer into a detectable signal. Controlled absorption of volatile compound molecules on porphyrin films deposited by means of the Lamgmuir-Blodgett (LB) technique on quartz has been studied by G. Bussetti et al. in "Site- Sensitive Gas Sensing and Analyte Discrimination in Langmuir-Blodgett Porphyrin Films", published in J. Phys. Chem. C 115 (2011), pages 8189-8194. In this paper, the changes in optical anisotropy of films have been measured by RAS .

The Applicant has observed that high sensitivity is required to measure small anisotropy signals, |AR/R|, e.g. of less than 10 ^"4 , which can often be only partially obtained or after relatively complex optimization of parameters that can be only accessed by an expert user of the system, such as, for example, optical alignments, signal integration times and change in the applied voltage value.

The Applicant has understood that a high-performance RAS technique can be obtained by reducing the non-linearity effects of the optical detector, while ensuring high stability of the photocurrent output of the optical detector. Particularly, a stable photocurrent signal can be produced by controlling the supply voltage to the detector in constant photocurrent mode. The Applicant has realized that high photocurrent stability may be obtained by a system for controlling the supply voltage to the optical detector, wherein such system performs its control function at a relatively low voltage, preferably a voltage lower than or equal to 10 V, more preferably lower than or equal to 5 V.

The present disclosure relates to a method of stabilizing output signals from an optical detector in an optical spectroscopy apparatus, the method comprising:

- detecting an optical signal modulated at a modulation frequency, by an optical detector which is configured to convert the received optical signal into an electrical photocurrent signal and is operatively connected to a voltage generator, configured to provide an input supply voltage to the detector;

- converting and amplifying the detected photocurrent signal into an analog electric voltage signal proportional to the photocurrent signal, wherein the analog voltage signal comprises a component modulated at said modulation frequency, and a direct- current component; - providing the analog voltage signal to an electrical control line and to an electrical acquisition line,

- converting the analog voltage signal provided to the control line into a digital voltage signal and providing said digital voltage signal as input data to a control algorithm, - by using the control algorithm calculating the error between the input data and a target digital voltage value corresponding to a target output photocurrent value from the optical detector and executing an error function, thereby obtaining a digital control voltage value, and

- adjusting the supply voltage for the optical detector based on the feedback of the digital control voltage value, if the input data is determined to deviate from the target digital voltage value.

The input data for the control algorithm is the measurement parameter to be controlled. The control algorithm is a feedback loop algorithm.

Preferably, the method comprises, after executing an error function to obtain a digital control voltage value and prior to adjusting the supply voltage:

- converting the digital control signal into an analog control signal and

- propagating the analog control signal along a signal propagation delay line, wherein adjusting the supply voltage comprises acquiring the analog control signal propagated along the delay line, generating a supply voltage feedback signal proportional to the analog control signal and supplying said supply voltage feedback signal to the optical detector.

Preferably, the delay line has a time constant ranging from 1 to 10 seconds.

Preferably, the analog control signal is a direct-current signal.

Preferably, the error function is a proportional-integral-derivative control function.

In some embodiments, the steps of determining whether the digital voltage signal deviates from a target digital voltage value and executing an error function is implemented by a proportional-integral-derivative (PID) controller, which implements the control algorithm. Preferably, the method comprises, after converting an analog voltage signal into a digital voltage signal:

- sampling a plurality of digital voltage signals for a predetermined interval of sampling time and calculating the average value of the plurality of digital voltage signals, wherein providing a digital voltage signal is providing said average value as input data for the control algorithm. In this embodiment, and preferably, the input digital voltage value to the control algorithm has a DC component only and the output analog control voltage signal from the control algorithm is a direct-current signal.

Preferably, the sampling time ranges from 10 ms to 1 s.

In the preferred embodiments, the optical spectroscopy apparatus is a reflectance anisotropy spectroscopy apparatus.

Preferably, the method further comprises:

- acquiring the analog voltage signal along the acquisition line and extracting the modulated component of the analog voltage signal by phase locking the analog voltage signal to said modulation frequency, and

- processing the modulated component of the analog voltage signal by calculating a differential reflectance variation proportional to the modulated component.

Preferably, the step of extracting is carried out by a lock-in amplifier, which is operatively connected to the acquisition line and phase-locked to said modulation frequency.

Preferably, the method comprises, before receiving an optical signal:

- irradiating a surface of a sample with a polarized optical beam, whose polarization state is modulated at a modulation frequency, thereby causing reflection of the incident optical signal to obtain a reflected optical signal modulated at said modulation frequency, and

selecting a wavelength range in the optical signal reflected from the sample, comprising at least one wavelength,

wherein detecting a modulated optical signal is detecting an optical signal modulated at the polarization modulation frequency, the detected optical signal containing information about the reflectance difference in the sample, particularly along two mutually orthogonal directions in a plane that passes through the surface of the sample.

In certain preferred embodiments, the modulated component is processed by calculating a reflectance difference in the sample at the at least one wavelength of the selected wavelength range.

Preferably, after converting an analog voltage signal into a digital voltage signal, the method comprises:

- sampling a plurality of digital voltage signals for a predetermined interval of sampling time and calculating the average value of the signals of the plurality of digital voltage signals, thereby averaging the modulated component to zero, wherein providing a digital voltage signal is providing said average value as input data for the control algorithm,

- processing the average value of the digital signals and calculating an average reflectance, and

calculating the ratio of reflectance differential variation to average reflectance, thereby obtaining a spectroscopic measurement signal.

The optical detector is preferably a cascade detector, more preferably a photomultiplier or an avalanche photodiode.

In the preferred embodiments, the step of converting and amplifying the photocurrent signal is carried out in a single amplification stage.

Preferably, converting the photocurrent signal into an electrical analog voltage signal proportional to the at least one photocurrent signal is performed by means of a transimpedance amplifier.

Preferably, the transimpedance amplifier has a gain parameter ranging from 3xl0 ⁴ to IxlO ⁶ . In certain preferred embodiments, the transimpedance amplifier is configured to have an output analog voltage signal with an average value of the modulated signal ranging from 0.1 V to 2.0 V, preferably from 0.3 V to 1.0 V, such average voltage signal corresponding to the DC component of the output photocurrent signal of the optical detector.

Preferably, the transimpedance amplifier has a feedback resistance ranging from 10 ⁴ Ω to 10 ⁶ Ω.

The present disclosure also relates to an optical spectroscopy apparatus comprising:

- an optical detector which is configured to receive optical signals modulated at a modulation frequency and to convert the optical signals into electrical photocurrent signals and a voltage generator, the optical detector being powered by the voltage generator;

a transimpedance amplifier operatively connected with the optical detector to receive electrical photocurrent signals, convert and to amplify the received signals into voltage signals proportional to the received signals, the transimpedance amplifier comprising a first output and a second output;

an analog-to-digital converter operatively connected to the first output of the transimpedance amplifier and configured to convert output voltage signals from the transimpedance amplifier into digital voltage signals; - a feedback loop control algorithm implemented by firmware execution in a microcontroller, which is operatively connected to the analog-to-digital converter and is configured to acquire digital voltage signals and input said digital voltage signals as input data for the control algorithm, wherein the control algorithm is configured to compute the error between respective input data and a target digital voltage value corresponding to a target output photocurrent value of the optical detector, and to execute an error function, thereby obtaining respective digital control voltage values as output signals of the microcontroller,

- a digital-to-analog converter, which is operatively connected to the microcontroller and is configured to convert the digital control voltage values into analog control signals, and

a signal propagation delay line, which is operatively connected to the digital-to- analog converter and is adapted to introduce a delay in the propagation of an analog control signal, the delay being equal to a time constant,

wherein the supply voltage generator is operatively connected to the delay line and is configured to convert the analog control signal into a voltage signal proportional thereto as a supply voltage feedback for the optical detector.

Preferably, the voltage generator is a DC/DC electric generator. In certain embodiments, the electric generator has a conversion ratio N of the supply voltage value to the control analog voltage value that ranges from 100 to 300.

Preferably, the microcontroller is configured to instruct the A/D converter to sample the digital voltage signals at sampling time intervals, and to calculate the average value of the signals acquired in each sampling interval. The signals acquired and integrated over sampling intervals are input data input to the control algorithm.

Preferably, the delay line has a time constant ranging from 1 to 10 seconds.

In certain preferred embodiments, the apparatus also comprises, upstream from the optical detector:

- a radiation source which is configured to emit a radiation beam,

- a first polarizer which is arranged so as to receive the radiation beam emitted by the radiation source and is configured for linear polarization of the radiation beam, a photoelastic modulator arranged so as to receive the polarized output beam from the first polarizer, and is configured to cause a modulation of the polarization state of the polarized beam and generate an optical beam modulated at a polarization modulation frequency,

- a support for a sample to be analyzed, which is arranged so as to receive the modulated optical beam along a first optical path and, a sample being present, to cause a reflected optical beam along a second optical path,

- a monochromator which is arranged along the first optical path or the second optical path and is configured to perform a wavelength scan in a spectral region of the reflected optical beam or to select a predetermined wavelength in such spectral region,

wherein the optical detector is placed downstream from the monochromator, to receive an output optical signal from the monochromator.

Preferably, the apparatus also comprises:

a lock-in amplifier which is connected to the second output of the transimpedance amplifier and is phase locked to said modulation frequency to extract the modulated component of the received analog voltage signal, and

a processor, which is operatively connected to the lock-in amplifier to receive and process the spectroscopic measurement signals by calculating a reflectance differential variation AR as a function of the wavelength or of time, if the monochromator selects a wavelength in the spectral region, the processor being operatively connected to the microcontroller to receive the average value R of reflectance therefrom and to calculate the value AR/R, thereby producing a spectroscopic measurement signal.

BRIEF DESCRIPTION OF THE FIGURES

Figure 1 is a block diagram of a typical RAS measurement apparatus.

Figure 2 shows the electronic portion downstream from the optical detector in the RAS system of Figure 1.

Fig. 3 is a block diagram of a RAS measurement apparatus according to one embodiment of the present invention.

Figure 4 is a block diagram of the electronic portion of the apparatus of Figure 3.

Figure 5 is a flowchart of a method of automatically controlling the supply voltage of an optical detector according to one embodiment of the present invention. Figure 6 is a time (t) chart of the RAS signal of a constant signal acquired by a traditional RAS apparatus as shown in Figures 1 and 2 (thin solid line and empty circles) and by a RAS apparatus according to one embodiment of the present invention (thick solid line).

Figure 7 is a wavelength spectrum of the RAS signal from a crystalline silicon sample with a surface lying on the crystallographic plane (110) for a RAS apparatus as shown in Figures 1 and 2 (empty circles) and a RAS apparatus according to one embodiment of the present invention (solid circles).

Figure 8 is the RAS signal acquired from a rotating polycarbonate sample, versus rotation speed, using a RAS apparatus according to one embodiment of the present invention.

DETAILED DESCRIPTION

Figure 1 is a block diagram of a RAS apparatus, whose optical part as shown in the figure represents a typical configuration

The RAS apparatus 10 comprises a radiation source 11, which is configured to emit a beam of (unpolarized) radiation within a spectral wavelength range. Preferably, the light source is configured to emit light within a spectral range from the near ultraviolet (UV) to the near infrared (IR), i.e. a wavelength range from 200 nm to 1700 nm, or a subrange of such spectral range. For instance, the light source 11 is a xenon arc lamp.

The radiation beam emitted from the source, optionally after being deviated by a mirror (not shown), passes through a first polarizer 12, e.g. a Glan-Taylor prism, which linearly polarizes the beam. The linearly polarized radiation is directed into a photoelastic modulator (PEM) 13, which is positioned to receive the radiation from the first polarizer 12, such that the polarization axis of the incoming beam is at a certain non-zero angle relative to the modulation axis of the PEM. The PEM produces a modulation of the polarization state of the radiation beam that passes therethrough, and causes the incoming beam to switch between two mutually orthogonal directions. The component of the incident radiation along the modulation axis incurs a predetermined phase delay with respect to the component perpendicular to the modulation axis. In the system configuration of Figure 1, the beam that enters the PEM has a polarization axis at an angle of +45° relative to the modulation axis of the PEM, and the phase delay is set to π such that the modulator operates as a half-wave plate on the incoming optical beam. Therefore, the PEM produces a modulation of the polarization direction ranging from -45° to +45° (modulation axes). In many applications, the photoelastic modulator, such as a commercial modulator PEM- 100 manufactured by Hinds Instruments, comprises a piezoelectric crystal, which has an electric field applied thereto to generate mechanical stresses in known directions of the crystal, and an optical head coupled to the crystal and made of a transparent isotropic material, such as silica or CaF ₂ . The modulation axis of the PEM is the crystallographic direction of the stress induced by the electric field and the modulation frequency is given by the resonance frequency of the crystal, typically 50 kHz.

The polarizer 12 and the PEM 13 are placed along the optical path 21 of the beam emitted by the radiation source 11. A sample 14 to be analyzed is placed in the optical path 21, downstream of the PEM, and the modulated radiation beam impinges perpendicular to its surface. The incident optical beam interacts with the material and the structure of the sample, which causes reflection of the incident optical beam, to thereby obtain a reflected optical signal, represented by an optical reflection signal, which is modulated at a polarization modulation frequency,

In usual ways, the sample 14 is placed on a sample holder (not shown in Figures 1 and 3) along the optical path 21, such that the beam emitted by the source, which passes through the PEM, impinges upon the sample.

The sample may be placed in such position that the axes along which anisotropy occurs, e.g. particular crystallographic axes if the sample is a crystalline material or stress axes if mechanical measurements are made, are aligned along the axes x and y (i.e. the modulation axes at +45° and -45° respectively).

The beam reflected from the sample enters a monochromator 16, which is configured to perform a wavelength scan of the sample spectrum or select a wavelength of interest in the sample spectrum, e.g. a wavelength associated with the response caused by a particular optical transition or particular structural properties of the sample under analysis. Preferably, the monochromator is a dispersive optical element, for example a rotating reflection diffraction grating. In certain embodiments, the monochromator may be configured to select a wavelength range comprising at least one wavelength of interest.

A second polarizer 15, or analyzer, is placed along the optical path 22 of the beam reflected from the sample, between the sample 14 and the monochromator 16. The analyzer 15 prevents the optical reflection signal from the sample (ΔΡν) from being altered (for example by reflections inside the monochromator) if it is aligned at 0°, i.e. at 45° relative to the axis of the polarizer. Preferably, the second polarizer is of the same type as the first polarizer, e.g. a Glan-Taylor prism.

As an alternative to the arrangement as shown in Figure 1 , the monochromator may be placed downstream from the light source and upstream from the polarizer 12.

In some system configurations, by simply making use of the reversibility of the optical path of light, and differently from the arrangement of the figure, the PEM is placed downstream the sample and upstream the monochromator, namely the polarization of the radiation reflected from the sample is analyzed by the PEM. Therefore, the optical configuration described with reference to Figure 1 shall be intended without limitation.

The radiation modulated by the PEM and selected according to wavelength is detected by an optical detector 17.

Optionally, once the beam reflected from the sample has passed through the second polarizer, it is focused in an optical fiber (not shown) which guides it to the monochromator 16. If an optical fiber is used, then a focusing lens and a fiber-optic coupler downstream from the latter are arranged downstream from the second polarizer and along the optical path of the beam reflected from the sample. Radiation propagates through the optical fiber to the entrance slit of the monochromator to be detected by the optical detector 17.

In spectroscopy apparatus operating in the spectral range between the near UV and the near IR, the optical detector is generally a photomultuplier tube.

The photomultiplier typically has a frequency response higher than the frequency of the PEM, i.e. the modulation frequency, ω, which is for example 50 kHz. The output analog photocurrent signal of the photomultiplier is composed of an alternating-current (AC) component, which comprises a ω frequency component and a 2ω frequency component, which is superimposed on a direct-current component (DC). The AC component is detected by a lock-in amplifier 19, which is locked to the polarization modulation frequency such that only the component at the modulation frequency, ω or 2ω, will be extracted from the signal, and the DC signal component, as well as any contribution to the signal associated with noise not related to the analysis, will be eliminated. The lock to the resonance frequency of the PEM is implemented as is known in the art by an electrical connection, typically a digital connection, if the PEM and the lock-in amplifier are electronic devices having a digital operation, indicated with 39 in Figure 1. Therefore, the output signal of the lock-in amplifier contains information about reflectance variations in the sample, particularly in the surface region of the sample. The RAS signal is proportional to the quantity according to the following equation:

R DC where Δν _ω , ₂ ω is the voltage signal that corresponds to the modulated output photocurrent signal from the photomultiplier, which is read by the lock-in amplifier, and VDC is the average value of this modulated signal, which corresponds to the average reflectance, R, on which the modulation Δν _ω ,2ω is superimposed.

In a lock-in amplifier operating in current mode, the output analog photocurrent signal from the photomultiplier is converted into an analog voltage signal for amplification. The output signal of the photomultiplier cannot be directly introduced at the input of the lock-in amplifier due to the difference between the output impedance of the photomultiplier and the input impedance of the lock-in amplifier. For example, a typical photomultiplier has an impedance of the order of 50 Ω, whereas a typical commercial lock-in amplifier as used in RAS spectroscopy apparatus has an impedance of the order of Ω, when it operates in current mode.

The output analog photocurrent signal is proportional to the intensity of the detected radiation. Since the typical output photocurrents of the photomultiplier are of the order of a few μΑ, there is a minor difference between R _x and R _y , AR, of the equations (1) and (2), typically a few pA. When this (modulated) current signal is converted into a voltage signal with an impedance of 50 Ω, it will correspond to a voltage signal of less than one nV. The value of this voltage signal is smaller than the sensitivity of usual lock-in amplifiers, which is typically 2 nV. In these test configurations, it becomes necessary to amplify the signal from the detector. A frequent solution in prior art RAS apparatus is to provide a preamplification device, including a plurality of serially-connected commercially available low-noise preamplifiers. In the RAS apparatus of Figure 1, a pre-amplification device 18 is operatively connected to the photomultiplier and disposed between the latter and the lock-in amplifier. The electronic chain downstream from the detector of the apparatus of Figure 1 is shown in greater detail in the diagram of Figure 2. The preamplification device 18, which receives the output photocurrent from the photomultiplier 17, converts the analog photocurrent signal into an analog voltage signal, for easier signal processing, and adapts the low impedance of the photomultplier to the high impedance of the lock-in amplifier 19. The output AC signals of the lock-in amplifier are transmitted to a processor 20, such as a personal computer, which receives the signals, calculates the quantity AR/R from the equation (2) for each wavelength signal and stores it in a spectrum, which expresses the reflectivity differential variation according to the wavelength or the photon energy is expressed, the latter being generally expressed in eV. The spectral extension of a RAS apparatus generally ranges from 200 nm to 1700 nm. These values depend both on the material of the optical parts and on the selected source and detection system. The spectrum AR/R may be displayed in a display connected to the processor (which is shown as integrated in the PC).

The measuring sensitivity of a RAS apparatus is given by the lowest measurable value \AR/R\ and in traditional apparatus is typically of the order of 10 ^"4 -10 ^"3 . For example, a typical average photocurrent of 10 μΑ (R) is converted into voltage and amplified by a preamplification device, to obtain an output signal ranging from 10 mV to 100 mV. The modulated signal AR is of the order of 5 pA and this value, after the conversion and amplification chain in the preamplification device, corresponds to a voltage value generally ranging from 5 μν to 50 μν, i.e. a range of values that allow RAS signal measurement. As is generally known, a photomultiplier tube is supplied with an externally applied voltage, which increases from the anode to the cathode. In Figures 1 and 2, a direct-current voltage generator 25 is shown, which is connected to the photomultiplier 17. The multiplication process generally occurs through pairs of dynodes, i.e. secondary collection and amplification emitters interposed between the anode and the cathode. The voltage applied between the anode and the cathode, i.e. total polarization, has a relatively high value, typically from 500 Volt to 1500 Volt, to obtain photocurrents in which the AC component is clearly discernible from the noise caused, for example, by dark current and/or current generated by photons produced by scintillation of photoelectrons not associated with external photon absorption A photomultiplier, as well as an avalanche photodiode (APD), which uses cascade amplification, is a detector having a response which, to a first approximation, may be considered linear. Nevertheless, if very high sensitivity is desired, its inherent non-linearity may alter signal measurement.

The Applicant has observed that high sensitivity is required for measuring small reflectance anisotropy signals |AR/R|, for instance originating from a few organic molecules on a surface, which can often be only partially obtained with a RAS apparatus as shown in Figures 1 and 2, and in many cases of interest only after optimization of parameters that can be only accessed by an expert user of the system, such as optical alignments, signal integration times, change in the applied voltage value, etc.

The Applicant has realized that a high performance RAS apparatus may be obtained by reducing the non-linearity effects of cascade detectors, which is mostly inherent in the amplification of the individual collection and emission elements that compose the detector, and that these effects are reduced while ensuring high stability of the output photocurrent of the photodetector.

Particularly, the Applicant has understood that a stable photocurrent signal can be obtained by controlling the supply voltage to the photodetector in constant photocurrent mode. Supply voltage control is implemented in such a manner as to maintain a constant voltage value VDC (Eq. (2)), which, in many test conditions, is of the order of a few hundreds of mV at the output of the photodetector and is generally less than 1 V.

The Applicant has realized that high photocurrent stability may be obtained by a system for adjusting the supply voltage to the photodetector, wherein such system performs its control function at low voltage, preferably a voltage of 10 V or less, more preferably of 5 V or less. Fig. 3 is a block diagram of a RAS measurement apparatus according to one embodiment of the present invention. Equal reference numerals designate equal elements or elements having the same functions as those described with reference to Figure 1. Particularly, the pre- detection portion of the apparatus of Figure 3 may be equal to that of Figure 1 or have the characteristics described with reference to such figure.

While reference is made hereinbelow to a photomultiplier tube, in short photomultiplier or PM, the present invention shall not be intended to be limited to a photomultiplier tube as a system for optical detection of the radiation reflected from the sample, but may generally apply to spectroscopy apparatus having cascaded optical detectors, such as photomultiplier tubes and avalanche photodiodes.

The measurement apparatus of Figure 3 comprises a photomultiplier (PM) 17 whose output is connected to the input of an electronic control and amplification unit 23, briefly referred to hereinafter as control unit. The PM is powered by a voltage generator 36, as described in greater detail below, which provides a supply voltage V _SU ppiy. A first output 26 of the control unit is connected to the input of a lock-in amplifier 29, whereas a second output 27 of the control unit 23 is operatively connected to a processor 20, such as a personal computer or a workstation connected to a server. The output 28 of the lock-in amplifier is operatively connected to the processor 20.

The control unit 23 is described in greater detail with reference to Figure 4 which shows the electronic portion of the RAS apparatus of Figure 3 downstream from the photodetector 17. The control unit 23 comprises a transimpedance amplifier 31, whose input 38 is electrically connected to the photomultiplier to receive the output photocurrent signal. The photocurrent signal is modulated at the polarization modulation frequency that has been set in the PEM 13. Preferably, the modulation frequency ω ranges from 50 kHz to 100 kHz.

The transimpedance amplifier is configured to convert and amplify the photocurrent signal into a voltage signal proportional to the input current signal. The output analog voltage signal of the transimpedance amplifier is modulated at the modulation frequency and is composed of an alternating-current (AC) component, which comprises a ω frequency component and a 2ω frequency component, and is superimposed on a direct-current component (DC), VDc(t). In most cases of interest, the direct-current component VDC of the output voltage of the transimpedance amplifier corresponds to the average value of the output modulated signal.

The gain parameter, i.e. the ratio of the open-circuit output voltage to the input voltage, of the transimpedance amplifier preferably ranges from 3x10 ⁴ to lxl 0 ⁶ , more preferably from 2x10 ⁵ to 6xl0 ⁵ , and for example is 5xl0 ⁵ . Preferably, the transimpedance amplifier has a feedback resistance that ranges from 10 ⁴ Ω to 10 ⁶ Ω such that, with a gain parameter ranging from 3x10 ⁴ to lxlO ⁶ , a VDC signal can obtained at the output of the amplifier ranging from about 0.1 Volt to 2.0 Volt.

For example, if the feedback resistance is 10 ⁵ Ω, the VDC at the output of the transimpedance amplifier will range from 0 V to 1.0 V for input signals ranging from about 0 μΑ (corresponding to zero reflectivity of the sample, or more generally to a reflectivity of less than 10 ^"6 ) to 10 μΑ. Preferably, the average value of the output modulated signal of the transimpedance amplifier is of from 0.1 Volt to 2.0 Volt, more preferably from 0.3 Volt to 1.0 Volt.

Preferably, the sensitivity of the transimpedance amplifier is of 1 nA or less.

Preferably, the transimpedance amplifier has a gain-to-band ratio of the order of 1 GHz. For example, it is a video amplifier as used in analog video signal-carrying systems. For example, the amplifier is a high-speed transimpedance amplifier OP A 380 manufactured by Texas Instruments, which exhibits a linear current-voltage conversion over a range of 5 decades.

The transimpedance amplifier 31 has a first output 37 and a second output 26 for the output voltage signal. The first output 37 is connected to an analog-to-digital (A/D) converter 32, comprised in the control unit, whereas the second output 26 is connected to the lock-in amplifier 29, which is external to the control unit 23, as also schematically shown in Figure 3. The electrical connection between the first output and the A/D converter is referred to as the control line (reference numeral 24 in Figure 4), whereas the electrical connection between the second output and the lock-in amplifier is referred to as acquisition line (24'). The A/D converter 32 is a linear converter and is configured to convert output voltage signals from the transimpedance amplifier into digital voltage signals. The A/D converter is operatively connected, at its output, to a microcontroller 33, for instance by a serial connection, e.g. a SPI port, in such a way that it is configured to be controlled by the microcontroller.

In preferred embodiments, the microcontroller instructs the A/D converter, as is usual by exchanging electronic control signals therewith, to sample the analog voltage signals over time intervals, indicated with sampling intervals, to obtain respective digital signals, and is configured to acquire the digital signals and integrate the digital signals sampled over each sampling interval to average the modulated signal to zero, and hence obtain a digital voltage signal that only contains the DC component. In practice and according to one embodiment, the A/D converter is controlled to accomplish the following tasks: acquiring a plurality of analog voltage signals at a sampling frequency over a sampling time interval, converting the plurality of analog signals into a respective plurality of digital voltage signals and outputting the plurality of signals.

The microcontroller 33 calculates the average value of the plural digital voltage signals as acquired by the A D converter 32, thereby obtaining a digital voltage signal, V , 1=0, 1, 2, which is a number proportional to the DC component of the input signal, Voc(t). Preferably, the A/D converter 32 has a resolution of 12 bit or more, more preferably ranging from 12 bit to 24 bit.

In one embodiment, the A/D converter has a resolution of 12 bit, which means that it encodes the input analog signal into 2 ¹² =4096 discrete values. For example, with an average modulated voltage signal of 1.0 Volt at the output of the transimpedance amplifier, which corresponds to a value IDC-10 μΑ at the output of the photomultiplier, the conversion resolution equals to a voltage difference of 244 μΥ between two adjacent discrete levels. A feedback loop control algorithm for stabilization of the output photocurrent from the photomultiplier, IDC, is implemented on the microcontroller for controlling the supply voltage of the photomultiplier (Vsuppiy), so as to maintain a constant average value of the output photocurrent from the optical detector, as described in greater detail below.

Upon acquisition of a first digital voltage value, the control algorithm is initialized. The digital voltage values, W, corresponding to the output photocurrents of the photomultiplier as detected at time t, IDC ¹ , constitute the input data for the control algorithm, i.e. the actual measurement parameter to be controlled.

In one embodiment, upon initialization of the control algorithm, the measured photocurrent, which corresponds to an initial digital signal Vi°, is associated with an initial supply voltage value Vsuppiy ⁰ . Particularly, during the initialization step, the optical signal reaches the photomultiplier, which is supplied with a voltage V _SU ppiy ⁰ , and produces an initial digital signal Vi°, to be inputted by the microcontroller into the control algorithm as input data. Such voltage value Vi° is compared by the control algorithm with a predetermined target digital voltage signal value, VT, which corresponds to a target photocurrent value. Assuming the case of a photomultiplier having a maximum output photocurrent I _ma x = 30μΑ, the target digital voltage signal value is selected to a value of about 3 V or less.

In preferred embodiments, acquisition of an input digital voltage signal comprises sampling the digital voltage signals over sampling time intervals and calculating the average value of the sampled digital signals over each sampling time interval. Preferably, the average value of the plurality of signals that have been sequentially acquired in a sampling time interval is obtained by calculating the root mean square of the sum of squared signals of the plurality of signals, and provides an input digital signal as an average value of the plurality of digital voltage signals that have been sampled. Therefore, in such preferred embodiments, the average value of the samples acquired by the microcontroller over a sampling interval constitutes the input data of the control algorithm. In certain embodiments, signal integration improves the signal-to-noise ratio and preferably the number of samples, i.e. the number of the plurality of signals that have been sequentially acquired in the sampling interval, is at least 100, and more preferably ranges from 200 to 500, to allow processing of reflectance anisotropy signals to a few parts by 10 ^"6 .

Preferably, the sampling time interval is selected to range from 10 ms to 500 ms.

It should be noted that the acquisition of a relatively large number of samples affects the input data acquisition time. The sampling interval is preferably selected according to the sampling rate of the A/D converter and the processing speed of the microcontroller. The sampling rate is, for example, a few MHz and generally depends on the converter in use, whereas the typical processing speed of a microcontroller is of the order of some ten MHz, for example 20 MHz. According to one embodiment, the control algorithm acquires 300 samples with a sampling rate of 0.5 Msample/s and the sampling interval is selected to be 100 ms.

The input value of the control algorithm shall be designated below as the photocurrent value at a time t, V? (including the initial value Vi ⁰ a t=0 acquired once the algorithm has been initialized), whether it represents a single value acquired by the microcontroller at a given time or, in preferred embodiments, the average value of a plurality of digital voltage signals acquired over an acquisition time interval, namely the time "t" designates either a given time or, in certain preferred embodiments, an acquisition time interval corresponding to the sampling time interval.

After the acquisition of the input data, the control algorithm executes an error function, f(X), which quantifies how the input voltage value is close to a target digital voltage value VT, which is set by the operator in the algorithm, and corresponds to a target output photocurrent value of the detector. In certain embodiments, the target voltage value is introduced into the control algorithm as a single input data value. In certain embodiments, the target voltage value is preferably selected such that the output voltage values from the transimpedance amplifier are high enough as to be at least equal to the input sensitivity of the lock-in amplifier, while falling within the operating range of the photodetector (and hence generally being relatively low).

If the input value VV is determined to deviate from the target value, VT, by an error value X=(VV - VT) other than zero, a positive or negative value, the algorithm operates to bring the measured voltage back to the target voltage value by varying a control quantity. The control quantity is a control voltage (Vc ^l )dig, which adjusts the supply voltage of the photomultiplier. Particularly, the algorithm calculates the control voltage value according to the error value X that has been determined, i.e. (Vc ^t )di _g =f(X).

The control voltage value so calculated represents the output result of the algorithm. Such result is transmitted to a digital-to-analog (D/A) converter 34, which is operatively connected to the microcontroller 33 and is configured to convert the digital control voltage value (Vc ^l )dig into an analog control voltage value (Vc^an. It shall be noted that, in the embodiments that include signal sampling, the input data value for the control algorithm is a digital voltage value that contains only the direct-current component. Therefore, the analog control voltage signal (Vc^an is a direct-current signal (with no modulated component).

Preferably, the D/A converter 34 has a resolution of 14 bit or more, more preferably ranging from 14 bit to 24 bit. In one embodiment, the D/A converter has a resolution of 16 bit, which means that it encodes the input analog signal into 2 ¹⁶ =65536 discrete values. For example, when the maximum output voltage of the transimpedance amplifier is 1.0 Volt, this conversion resolution is equal to 15 μν voltage difference between adjacent discrete levels. Generally, the average analog output voltage value of the converter D/A depends on the resolution of the latter. In certain embodiments, the D/A converter is configured to obtain an analog output voltage value ranging from 1 to 10 V, preferably from 0.5 to 5.0 Volt.

The analog control voltage signal is inputted into a DC/DC electric generator 36 adapted to convert the control direct-current voltage at the output of the algorithm, which is a low voltage (after D/A conversion), into a higher direct-current voltage, Vsuppiy ¹ . The conversion ratio, i.e. the ratio of the output voltage of the DC/DC converter to the input voltage of the DC/DC converter is selected such that the converted voltage value is of the same order of magnitude as the supply voltage V _SU p _P iy ⁰ of the detector, typically of the order of kilo volt. To a first approximation, the DC/DC conversion may be expressed as V _suP piy -Ν*(νο η, with N being the conversion ratio. The conversion ratio depends on the type of the photodetector of the RAS apparatus. If the detector is a photomultiplier, the conversion ratio N preferably ranges from 100 to 300.

The Applicant has noted that the response of the photomultiplier to a supply voltage change is practically instantaneous, and hence any supply voltage change implies a quasi- instantaneous change of the output photocurrent from the photomultiplier. Furthermore, the Applicant noted that in the embodiments in which the control algorithm calculates the derivative of the error X versus time, if the response time tends to zero, then the derivative value will tend to infinity.

The Applicant has realized that it is advantageous to insert a delay line for propagation of the analog signal between the output of the D/A converter and the input of the DC/DC generator so as to prevent the control algorithm from becoming instable, which would possibly lead to the presence of undamped oscillations in the control algorithm. Preferably, the delay line has a time constant ranging from 1 to 10 seconds, more preferably from 2 to 4 seconds. For example, the time constant is about 3 seconds. In Figure 4, the analog output control voltage of the D/A converter 34 is transmitted to a delay line 35 which is operatively connected to the DC/DC generator 36. The analog control voltage signal propagates along the delay line, which is for example an RC electric circuit, and exits the line with a delay that is equal to the time constant.

Then, the analog signal exiting the delay line 35 is introduced into the DC/DC generator 36 which is operatively connected to the detector input, such that the value Vsu piy ¹ may be introduced as a supply voltage of the detector.

In one embodiment, the initial supply voltage value, V _SU ppiy°, is set in the DC/DC generator such that the real quantity that initializes the control algorithm, i.e. (Vc°)dig, is derived from the photocurrent as measured at Vsuppiy ⁰ .

In a preferred embodiment, the microcontroller 33 is a proportional-integral-derivative controller, PID, designed for negative feedback control. In a PID controller, the PID control function, f(X), which is known per se, may be expressed as: where the first term is proportional to the error X, the second term is proportional to the time derivative of the error and the third term is proportional to the integral of the error in an integration time tint. -Preferably, the integration time value tint ranges from 10 ms to 1 s, more preferably from 50 to 500 ms, and is, for example, 200 ms. The parameters K _p , Kd and Ki are constant proportionality factors that may be empirically or theoretically determined according to the particular detection system, to the supply to the detector and the processing time delays of the whole apparatus.

Since the digital microcontroller processes discrete quantities, in a known manner, the algorithm uses a discretized form of Eq. (3) to calculate f(X). The control algorithm may be implemented as a software program installed on the microcontroller firmware.

Typically, the supply voltage to a photomultiplier tube ranges from about 300 V to 1500 V.

It shall be noted that the process for stabilizing the output photocurrent from the photomultiplier is conducted at a low voltage, preferably not exceeding 5 V, and is followed by the conversion of the control voltage into a supply voltage value that is high enough to control the photomultiplier outside the control algorithm. This will make possible to obtain an accurate stabilization for it is performed at relatively small analog voltage values with a corrective action having a minimum step, i.e. a minimum error value (Vc ^l ) _d ig, which is very small as compared with the input supply voltage value.

In preferred embodiments, the ratio of the minimum error value (Vc^ _d ig, corresponding to the conversion resolution of the D/A converter, to the input supply value to the photomultiplier, is of the order of 10 ^" 0 ^"4 .

The output voltage signal from the transimpedance amplifier 31 (output 26) enters a lock-in amplifier 29, which thus receives an analog voltage signal, particularly a low voltage value, corresponding to the output photocurrent from the photomultiplier, i.e. a voltage-converted and amplified signal. The signal introduced in the lock-in amplifier consists of an AC component superimposed on a DC component. The DC and AC components of the analog voltage signal are separated by the lock-in amplifier 29, which is phase-locked to the resonance frequency ω of the PEM 13 by an electrical connection 39. The output signal from the lock-in amplifier is the modulated component of the analog signal and constitutes the spectroscopic measurement signal containing the information about reflectance variation of the surface region of the analyzed sample 14, i.e. |AR|.

In certain preferred embodiments, the lock-in amplifier is only used for phase-locking of the signal to the frequency that has been set by the PEM 13, and not for amplification of the signal that has already been inputted into the lock-in amplifier with such an amplitude as to allow RAS signal analysis, without requiring any further amplification stages. In practice, and in one embodiment, the lock-in amplifier is set up to only operate in AC mode, and to be locked to the phase of the PEM, without amplifying the signals received at its input. In preferred embodiments, the output photocurrent of the detector is amplified for RAS signal generation in a single amplification stage, preferably by a single transimpedance amplifier.

The microcontroller 33 transmits the average value of the digital voltage signal obtained at its input by the A/D converter 32, to the processor 20; such average value represents the average reflectance to which the reflectance variation shall be normalized, see equations (1) and (2).

The AC signal as measured by the lock-in amplifier is sent to the processor 20, which also receives the DC signal from the microcontroller 33 and records the whole measurement by software means. Particularly, the processor 20 calculates the quantity AR/R from the equation (2) for each signal and stores it in a spectrum, which expresses the differential reflectance variation as a function of the photon energy. If the monochromator 16 is configured to perform a wavelength scan of the sample spectrum in a spectral region of interest, the processor 20 will calculate the quantity AR/R from the equation (2) for each wavelength signal of the spectral region of interest and stores it in a spectrum, which expresses the reflectance differential variation as a function of the wavelength normalized to the value R, which has been calculated from the average value VDC controlled by the control algorithm.

If the monochromator 16 is configured to select a particular wavelength of interest in the sample spectrum, then the processor will calculate the quantity AR/R from the equation (2) for the selected wavelength as a function of time.

It shall be noted that, since the value VDC of the equation (2) is stabilized by means of the control system of the present disclosure (and hence the output photocurrent from the detector is stabilized), a high measurement sensitivity may be obtained, even on samples that produce a low anisotropy signal, e.g. lower than 10 ^"4 .

Figure 5 is a flowchart of a method of automatically controlling the output photocurrent from a cascade optical detector contained in a spectroscopy apparatus, according to one embodiment of the present invention. In the method of Figure 5 the control function f(X) is a PID function and the method comprises the steps of:

setting the parameters K _p , Kd and Ki of a PID control function, f(X), which is included in a control algorithm implemented in a microprocessor of a control unit (step 40). Such parameters may be set as is usual, e.g. by a user entering numerical parameters through a user interface of a computer that is operatively connected to the microprocessor (e.g. the computer 20 of Figures 3 and 4);

setting an initial supply voltage value, Vsuppiy ⁰ (step 41). It shall be understood that steps (40) and (41) may be exchanged in order;

- detecting an output photocurrent signal from a cascade optical detector (step 42); converting and amplifying the output photocurrent signal thereby generating an analog voltage signal (step 43). Preferably the step of converting and amplifying is carried out by a transimpedance amplifier;

converting the amplified analog input voltage signal into a digital voltage signal and sampling a plurality of digital voltage signals over a sampling time interval so as to obtain a digital input voltage value, Vi° (step 44);

- initializing a control algorithm (step 45) that implements a PID control function, f(X), as defined by the parameters K , Kd and Ki that have been previously set. It shall be understood that the control algorithm may be initialized after any one of steps 42 to 44;

- after generation of a digital input voltage value, Vi°, and initialization of the control algorithm, such algorithm acquires the value Vi° and calculates, from the error between the input value and a target voltage value, X=(Vi° - VT), a digital control voltage signal using the control function f(X), i.e. (fase 46);

- converting the digital control voltage signal (Vc°)di _g into an analog control voltage signal, (V _c °)an (step 47);

- propagating the analog control voltage signal along a delay line having a time constant (step 48);

- generating a supply voltage feedback signal by converting the analog control voltage signal into an analog signal whose amplitude is proportional to the amplitude of the control voltage signal (step 49);

supplying the supply feedback signal to the optical detector (step 50), and

- repeating the preceding steps from 42 to 50 to form a feedback loop to maintain the output photocurrent of the detector constant (51).

Figure 6 shows a time constant measurement of a RAS signal RAS, AR/R, by a traditional RAS apparatus as shown in Figures 1 and 2 (empty circles joined by a thin solid line) and by a RAS apparatus according to one embodiment of the present invention and shown in Figures 3 and 4 (thick solid line). The total measurement time interval was 360 seconds. The constant signal was acquired at a fixed wavelength of 360 ran on the surface (110) of a silicon crystal. The two RAS apparatus being compared are identical in their optical pre- detection portion, and particularly the optics of the instrument and the measurement conditions are the same for the two RAS signals being compared. The detector was a photomultiplier Hamamatsu series R Head-on 1463P. The PEM frequency was 50 kHz and the lock-in amplifier, for both apparatus, was a digital amplifier Stanford SR-850. In the RAS apparatus of Figures 3-4, the transimpedance amplifier was an OPA 380 with an average output voltage of 0.7 V, the A/D converter had a resolution of 12 bit, the D/A converter had a resolution of 16 bit, the delay line had a time constant of 3 seconds and the DC/DC generator had a conversion ratio, N, of 250 for generating a supply voltage of about 1000 Volt.

Figure 6 shows that the signal acquired by the traditional RAS apparatus is much more noisy than the signal acquired by the apparatus according to one embodiment of the present invention. Particularly, while signal acquisition has been conducted at a constant optical anisotropy value, a number of signal spikes are observed in the thin continuous line, which might distort the determination of an actual, significant variation of the RAS signal with time.

Conversely, the signal acquired by the apparatus of the present invention is much more stable or exhibits "inherent" variations that are 50-fold smaller than those of the output signal of the traditional RAS system. Signal variations for the apparatus according to one embodiment of the present invention are about 5xl0 ^"6 , i.e. about equal to the thickness of the line that represents the signal, in the figure. Without wishing to be bound by any particular explanation, the oscillations observed in the signal of the apparatus of the present disclosure, which have a duration of a few seconds and an amplitude of about 10 ^"5 , should be imputed to mechanical instabilities of the workbench.

Figure 7 shows a spectrum of the RAS signal, AR/R, versus the wavelength, from a crystalline silicon sample with a surface lying on the plane (110). The empty circles connected by a solid line represent experimental measurements taken by a traditional RAS apparatus as shown in Figures 1 and 2, whereas the solid circles joined by a solid line represent experimental measurements taken by a test apparatus as described with reference to Figures 3 and 4, The test conditions are the same as those for the acquisition of the spectra of Figure 6.

In the traditional apparatus, calibration was required to optimize all the parameters of the optical apparatus (selection of the operating conditions for lock-in, alignment of optical elements, selection of signal integration times, etc.) by an expert user, who could understand which elements might introduce an effect on the stability of the RAS apparatus. Several test days and calibrations are required to obtain the curve of values with empty circles, as shown in Figure 7. Conversely, in the case of the apparatus as described with reference to Figures 3 and 4, the optical signal could be acquired soon after turning on the apparatus, i.e. after a few minutes, with no further calibration.

According to some preferred embodiments of the present invention, the control method allows to obtain high measurement sensitivity readily after turning on the instrument and initializing the control algorithm. This allows to extend the RAS technique to a larger number of users and application fields, as it does not require the skills of expert operators for start-up and optimization of the apparatus. Figure 8 shows the RAS signal obtained from measurements taken from a polycarbonate disk rotating at various rotation speeds. The RAS signal, i.e. the optical anisotropy as defined by the equation (2), originates frpm the mechanical anisotropy (stress) induced in the disk by rotation, which changes according to rotation speed. Due to the stability of the RAS signal, the apparatus may be also used by operators with no expertise in spectroscopy and optical instruments, who might require information about the mechanical properties of a sample, e.g. a hard-disk of a computer or a CD during operation, moving blades or turbines, etc.

In certain preferred embodiments, the apparatus and method of the present invention might be used to obtain test results with high accuracy, without requiring complex calibrations of the instruments of the apparatus, for the apparatus to be also used by users that have no particular expertise.