Inspection apparatus and method, lithographic apparatus and lithographic processing cell

An “angle-resolved” version of FD-OCT is used to measure reflectance properties. An inspection apparatus comprises an illumination source configured to provide an illumination beam, an interferometer configured to use the illumination beam to illuminate a target on a substrate at an incidence angle and to use radiation reflected from the substrate with a reference beam derived from the illumination beam to produce an output beam, a sampling device arranged to select a portion of the output beam, a spectrometer configured to receive the selected portion of the output beam and to measure a spectrum of the received selected portion of the output beam, and a processor configured to determine from the measured spectrum reflectance properties of the target such as raw spectrometer spectral data, the Fourier transformed data, the extracted intensity components or carrier phase or the calculated complex reflectance.

FIELD OF THE INVENTION

The present invention relates to inspection apparatus and methods of inspection usable, for example, in the manufacture of devices by lithographic techniques.

BACKGROUND

In order to monitor the lithographic process, parameters of the patterned substrate are measured. Parameters may include, for example, the overlay error between successive layers formed in or on the patterned substrate and critical linewidth of developed photosensitive resist. This measurement may be performed on a product substrate and/or on a dedicated metrology target. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. By comparing the properties of the beam before and after it has been reflected or scattered by the substrate, the properties of the substrate can be determined. This can be done, for example, by comparing the reflected beam with data stored in a library of known measurements associated with known substrate properties. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.

Critical Dimension (CD) metrology using scatterometry is done in the following ways:

1. Angle-Resolved using a selectable wavelength, however measuring on small in-die targets is challenging since the angular divergence of the light limits the angular resolution.

2. Spectroscopic using a fixed angle of incidence, however it is difficult to underfill a small target with a well-defined angle of incidence.

In both cases all measurement light must be focused into the target which is usually referred to as “underfilling the target”

SUMMARY

According to an embodiment of the present invention, there is provided an inspection apparatus comprising an illumination source configured to provide an illumination beam of broadband radiation, an interferometer configured to use the illumination beam to illuminate a target on a substrate at an incidence angle and to use radiation reflected from the substrate with a reference beam derived from the illumination beam to produce an output beam, a sampling device arranged to select a portion of the output beam, a spectrometer configured to receive the selected portion of the output beam and to measure a spectrum of the received selected portion of the output beam, and a processor configured to determine reflectance properties of the target at the incidence angle from the measured spectrum.

According to another embodiment of the present invention, there is provided an inspection method comprising the following steps. Providing an illumination beam of broadband radiation. Using the illumination beam to illuminate a target on a substrate at an incidence angle and using radiation reflected from the substrate with a reference beam derived from the illumination beam to produce an output beam. Selecting a portion of the output beam. Measuring a spectrum of the received selected portion of the output beam. Determining reflectance properties of the target at the incidence angle from the measured spectrum.

According to a further embodiment of the present invention, there is provided a lithography apparatus comprising an exposure system and an inspection apparatus comprising: an illumination source configured to provide an illumination beam of broadband radiation, an interferometer configured to use the illumination beam to illuminate a target on a substrate at an incidence angle and to use radiation reflected from the substrate with a reference beam derived from the illumination beam to produce an output beam, a sampling device arranged to select a portion of the output beam, a spectrometer configured to receive the selected portion of the output beam and to measure a spectrum of the received selected portion of the output beam, and one or more processor configured to determine reflectance properties of the target at the incidence angle from the measured spectrum and to control the exposure system using the determined reflectance properties.

According to a still further embodiment of the present invention, there is provided lithographic cell comprising a lithographic apparatus comprising an exposure system and an inspection apparatus. The inspection apparatus comprises an illumination source configured to provide an illumination beam of broadband radiation, an interferometer configured to use the illumination beam to illuminate a target on a substrate at an incidence angle and to use radiation reflected from the substrate with a reference beam derived from the illumination beam to produce an output beam, a sampling device arranged to select a portion of the output beam, a spectrometer configured to receive the selected portion of the output beam and to measure a spectrum of the received selected portion of the output beam, and one or more processor configured to determine reflectance properties of the target at the incidence angle from the measured spectrum and to control the exposure system using the determined reflectance properties.

DETAILED DESCRIPTION

Before describing such embodiments in more detail, however, it is instructive to present an example environment in which embodiments of the present invention may be implemented.

As shown inFIG. 2, the lithographic apparatus LA forms part of a lithographic cell LC, also sometimes referred to a lithocell or cluster, which also includes apparatus to perform pre- and post-exposure processes on a substrate. Conventionally these include spin coaters SC to deposit resist layers, developers DE to develop exposed resist, chill plates CH and bake plates BK. A substrate handler, or robot, RO picks up substrates from input/output ports I/O1, I/O2, moves them between the different process apparatus and delivers then to the loading bay LB of the lithographic apparatus. These devices, which are often collectively referred to as the track, are under the control of a track control unit TCU which is itself controlled by the supervisory control system SCS, which also controls the lithographic apparatus via lithography control unit LACU. Thus, the different apparatus can be operated to maximize throughput and processing efficiency.

In order that the substrates that are exposed by the lithographic apparatus are exposed correctly and consistently, it is desirable to inspect exposed substrates to measure properties such as overlay errors between subsequent layers, line thicknesses, critical dimensions (CD), etc. If errors are detected, adjustments may be made to exposures of subsequent substrates, especially if the inspection can be done soon and fast enough that other substrates of the same batch are still to be exposed. Also, already exposed substrates may be stripped and reworked—to improve yield—or discarded, thereby avoiding performing exposures on substrates that are known to be faulty. In a case where only some target portions of a substrate are faulty, further exposures can be performed only on those target portions which are good.

An inspection apparatus is used to determine the properties of the substrates, and in particular, how the properties of different substrates or different layers of the same substrate vary. The inspection apparatus may be integrated into the lithographic apparatus LA or the lithocell LC or may be a stand-alone device. To enable most rapid measurements, it is desirable that the inspection apparatus measure properties in the exposed resist layer immediately after the exposure. However, the latent image in the resist has a very low contrast—there is only a very small difference in refractive index between the parts of the resist which have been exposed to radiation and those which have not—and not all inspection apparatus have sufficient sensitivity to make useful measurements of the latent image. Therefore measurements may be taken after the post-exposure bake step (PEB) which is customarily the first step carried out on exposed substrates and increases the contrast between exposed and unexposed parts of the resist. At this stage, the image in the resist may be referred to as semi-latent. It is also possible to make measurements of the developed resist image—at which point either the exposed or unexposed parts of the resist have been removed—or after a pattern transfer step such as etching. The latter possibility limits the possibilities for rework of faulty substrates but may still provide useful information.

FIG. 3depicts a scatterometer which may be used in the present invention. It comprises a broadband (white light) radiation projector2which projects radiation onto a substrate W. The reflected radiation is passed to a spectrometer detector4, which measures a spectrum10(intensity as a function of wavelength) of the specular reflected radiation. From this data, the structure or profile giving rise to the detected spectrum may be reconstructed by processing unit PU, e.g., by Rigorous Coupled Wave Analysis and non-linear regression or by comparison with a library of simulated spectra as shown at the bottom ofFIG. 3. In general, for the reconstruction the general form of the structure is known and some parameters are assumed from knowledge of the process by which the structure was made, leaving only a few parameters of the structure to be determined from the scatterometry data. Such a scatterometer may be configured as a normal-incidence scatterometer or an oblique-incidence scatterometer.

Another scatterometer that may be used with the present invention is shown inFIG. 4. In this device, the radiation emitted by radiation source2is collimated using lens system12and transmitted through interference filter13and polarizer17, reflected by partially reflected surface16and is focused onto substrate W via a microscope objective lens15, which has a high numerical aperture (NA), preferably at least 0.9 and more preferably at least 0.95. Immersion scatterometers may even have lenses with numerical apertures over 1. The reflected radiation then transmits through partially reflecting surface16into a detector18in order to have the scatter spectrum detected. The detector may be located in the back-projected pupil plane11, which is at the focal length of the lens system15, however the pupil plane may instead be re-imaged with auxiliary optics (not shown) onto the detector. The pupil plane is the plane in which the radial position of radiation defines the angle of incidence and the angular position defines azimuth angle of the radiation. The detector is preferably a two-dimensional detector so that a two-dimensional angular scatter spectrum of a substrate target30can be measured. The detector18may be, for example, an array of CCD or CMOS sensors, and may use an integration time of, for example, 40 milliseconds per frame.

A reference beam is often used for example to measure the intensity of the incident radiation. To do this, when the radiation beam is incident on the beam splitter16part of it is transmitted through the beam splitter as a reference beam towards a reference mirror14. The reference beam is then projected onto a different part of the same detector18or alternatively on to a different detector (not shown).

A set of interference filters13is available to select a wavelength of interest in the range of, say, 405-790 nm or even lower, such as 200-300 nm. The interference filter may be tunable rather than comprising a set of different filters. A grating could be used instead of interference filters.

The detector18may measure the intensity of scattered light at a single wavelength (or narrow wavelength range), the intensity separately at multiple wavelengths or integrated over a wavelength range. Furthermore, the detector may separately measure the intensity of transverse magnetic- and transverse electric-polarized light and/or the phase difference between the transverse magnetic- and transverse electric-polarized light.

Using a broadband light source (i.e., one with a wide range of light frequencies or wavelengths—and therefore of colors) is possible, which gives a large etendue, allowing the mixing of multiple wavelengths. The plurality of wavelengths in the broadband preferably each has a bandwidth of Δλ and a spacing of at least 2 Δλ (i.e., twice the bandwidth). Several “sources” of radiation can be different portions of an extended radiation source which have been split using fiber bundles. In this way, angle resolved scatter spectra can be measured at multiple wavelengths in parallel. A 3-D spectrum (wavelength and two different angles) can be measured, which contains more information than a 2-D spectrum. This allows more information to be measured which increases metrology process robustness. This is described in more detail in EP1,628,164A.

The target30on substrate W may be a 1-D grating, which is printed such that after development, the bars are formed of solid resist lines. The target30may be a 2-D grating, which is printed such that after development, the grating is formed of solid resist pillars or vias in the resist. The bars, pillars or vias may alternatively be etched into the substrate. This pattern can be sensitive to lens aberrations of the project system PL in the lithographic projection apparatus, and illumination symmetry and the presence of these effects will manifest themselves in a variation in the printed grating. Accordingly, the scatterometry data of the printed gratings is used to reconstruct the gratings. The parameters of the 1-D grating, such as line widths and shapes, or parameters of the 2-D grating, such as pillar or via widths or lengths or shapes, may be input to the reconstruction process, performed by processing unit PU, from knowledge of the printing step and/or other scatterometry processes.

U.S. Patent Application publication number US 2004/0085544 (A1), incorporated by reference herein in its entirely, discloses an example method including: imaging test light emerging from a test object over a range of angles to interfere with reference light on a detector, wherein the test and reference light are derived from a common source; for each of the angles, simultaneously varying an optical path length difference from the source to the detector between interfering portions of the test and reference light at a rate that depends on the angle at which the test light emerges from the test object; and determining an angle-dependence of an optical property of the test object based on the interference between the test and reference light as the optical path length difference is varied for each of the angles. However, that approach is that susceptible to vibration because the reference mirror is sequentially stepped and the “phase steps need to be accurately known. This implies the need for a very stable set-up. Any mechanical vibration may introduce phase errors. That approach may not be suitable for measuring small in-die targets since it measures in the back-focal plane of a lens

Embodiments of the present invention relate to using an “angle-resolved” version of FD-OCT (Fourier Domain Optical Coherence Tomography).

FD-OCT is used in medical imaging applications and is described for example in the publication “Ultrahigh resolution Fourier domain optical coherence tomography”, R. A. Leitgeb et al, 17 May 2004, Vol. 12, No. 10, Optics Express 2156, which is incorporated by reference herein in its entirety.

FIG. 5shows an embodiment using angle-resolved FD-OCT. A low-divergence broadband illumination beam IB2from an illumination source IS is directed into an interferometer IF and split in two parts by beam splitter BS. The reflected part (measurement beam) is sent to a high NA (Numerical Aperture) objective L1and is projected on the target30at a certain incidence angle. The transmitted part (reference beam) is projected on a reference mirror RM via lens L2. The lenses L1and L2should preferably be equal. If they are not equal then the different dispersion properties of L1and L2have to be accounted for. In that case the OPD gets an extra wavelength-dependent term that may be eliminated through a calibration.

The beams that are reflected by the reference mirror and reflected by the target are recombined by the beam splitter BS into an interferometer output beam. Lens L3is used to make an image of the overlapping object and reference mirror on the input facet of a multimode detection fiber, thus serving as a sampling device. The size of the image of the target is larger than the fiber core diameter. In this way, the fiber acts as an aperture that only selects and collects radiation from the area of interest and blocks all other parts of the image, thus selecting a portion of the output beam. In practice the image on the fiber is a strongly magnified version of the object. As a result, the angle-of-incidence on the fiber input is well within the NA of the fiber (typically 0.22). For example, if the target size is 10×10 μm2and the fiber core diameter is 200 μm then a magnification factor of 40 will create an image of the target of 400×400 μm2which is larger than the core diameter. The NA of the light incident on the fiber will be NAobj/40≈0.024 which is much smaller than the NA of standard multimode fibers.

The light that is captured by the fiber is sent to a spectrometer and the detected spectrum is given by:

In this equation Robjand Rrefare, respectively, the DC intensity of the target object and reference arm waves, φobj, and φrefare the phase of the object and reference waves and OPD is the Optical Path Difference between the object and reference waves. In FD-OCT this OPD is deliberately set to a relatively large value. As a result of the large OPD, the intensity varies periodically as a function of 1/λ so that a high-frequency fringe pattern on the spectrometer spectral output is observed. In order to explain the subsequent signal processing more clearly we can also rewrite the measured spectrum in a slightly different form:
I(ν)=Robj+Rref+2√{square root over (RobjRref)} cos(2πντ+φobj−φref)

In this equation ν and τ are, respectively, the optical frequency of the light and the time-of-flight difference between the object and reference waves. This equation shows that the phase information of the object (φobj) is encoded on a high-frequency carrier. The principle of FD OCT relies on the fact that the spectral amplitude of the reflected light equals the Fourier transform of the longitudinal sample structure.

An FFT (Fast Fourier Transform) of I(ν), for example performed by processing unit PU, yields a frequency spectrum consisting a DC term Robj+Rrefand a signal on a high frequency carrier. By demodulating the high frequency components with a Fourier Transform two signal intensity components can be extracted:
IC(θ,λ)=√{square root over (Robj(θ,λ)Rref)} cos(φobj(θ,λ)−φref)
IS(θ,λ)=√{square root over (Robj(θ,λ)Rref)} sin(φobj(θ,λ)−φref)

The component ICthat is in phase with the original carrier is referred to as the in-phase component. The other component IS, which is 90° (π/2 radians) “out-of-phase”, is referred to as the quadrature component. The dependence of the phase φobjon wavelength and incidence angle (θ) is explicitly shown in the equations. From this signal processing the complex reflectance of the object can be determined for a given angle of incidence for example using processor unit PU. Processor unit PU may be incorporated into the spectrometer or outside it.

Beyond specular reflection from the target, higher orders diffracted from other areas of the target may end up being selectively collected by the fiber facet aperture. These higher diffraction orders will normally not interfere with the reference beam and as a result they will not contribute to the signal formation of the high-frequency carrier term.

The carrier frequency depends on the actual OPD so the actual frequency can be used for focus control. By including the phase of the carrier fine-focus control can be performed as well. This technique may therefore also be used as a level sensor. Level sensing can be implemented by simply putting an inspection apparatus such as described with reference toFIG. 5in a lithography apparatus and using the phase of the measured high frequency carrier to measure the height of the substrate.

“Reflectance properties” referred to herein may be for example the raw spectrometer spectral data, the Fourier transformed data, the extracted intensity components or carrier phase or the calculated complex reflectance. The reflectance properties implicitly relate to a range of frequencies and may be representative of one or more incidence angles, as described below.

If the two lenses L1and L2are not identical, additional calibrations will be necessary to calibrate the different dispersion properties of the two lenses.

The incident light is normally polarized and it is also possible to measure the polarization state of the scattered light with a slight modification of the set-up. This can be performed by including an ellipsometry extension to the scatterometer such as described in U.S. Pat. No. 7,701,577, which is incorporated by reference herein in its entirety.

A series of signals may be measured for different angles of incidence. This can be done by scanning the illumination beam in the back-focal plane of L1. This scanning may be performed as described below with reference toFIG. 6.

The illumination source unit IS is shown in more detail inFIG. 6. The source unit provides illumination for two modes of operation of the scatterometer. The first mode is as an angle-resolved scatterometer using IB1and measurement in the pupil plane, similar to as described with reference toFIG. 4. The second mode uses the FD-OCT approach using IB2similar to as described with reference toFIG. 5.

The source includes a first source module21, which may include for example a xenon lamp and provides a first illumination beam IB1, and a second source module22, which provides a second illumination beam IB2. The second source module22may include a supercontinuum laser to provide a broadband (white light) output to form the second illumination beam IB2. A beam selection unit25directs the illumination beams to the remainder of the inspection apparatus, depicted MS inFIG. 6.

The supercontinuum laser may include a pulsed laser source whose output is fed into a non-linear medium, e.g., a photonic crystal fiber. The pulsed source emits very short pulses, e.g., of femtosecond or picosecond duration, of a narrow band of wavelengths which are spread by the non-linear medium into a broadband beam of radiation. This type of source can provide a powerful beam with a low etendue and a suitable range of wavelengths. Other sources are suitable, for example, a Xenon gas discharge (either electrical discharge or laser-produced plasma) or a Deuterium source in case of a broadband UV wavelength range.

Outputs of the first and second sources21,22are conveniently led to the beam selection unit25by optical fibers23and24. Fiber23may include a multimode fiber and fiber24may include an endlessly single-mode PM fiber.

The beam selection unit in this embodiment includes a tilting mirror254driven by actuator255to select one of the illumination beams IB1, IB2for the output to the remainder of the inspection apparatus. The tilting mirror is positioned in a back-projected substrate plane, which is a plane conjugate with the substrate having the target being measured, created by an optical system including a first condensing lens256. A second condensing lens253creates a back-projected pupil plane, which is a plane that is a Fourier transform of the back-projected substrate plane, in which is positioned an aperture plate252. The aperture plate252has two apertures separated by a small distance. In one aperture, a secondary source is formed by a third condensing lens251which collects light from the first source21output by fiber23. In the other aperture, the output of the fiber24, carrying light from second source22, is located.

With the above arrangement, the two illumination beams are brought together on the tilting mirror254, but have different angle of incidence. Thus, by changing the angle of the tilting mirror254by only a small amount, e.g., less than 50 mrad in an embodiment, one of the illumination beams can be selected and directed along the axis of first condensing lens256. The other beam is directed off-axis and blocked by an aperture stop257provided on a further back-projected pupil plane. Aperture stop257is preferably provided in a turret or carousel driven by actuator258so that a selected one of a plurality of apertures can be interposed into the optical path, in accordance with the illumination beam chosen.

It will appreciated that the above embodiment can readily be extended to encompass more than two light sources to provide additional flexibility. The spacing of the multiple sources in the aperture plate252, the focal lengths of condenser lenses256and253and the range of movement of the tiltable mirror can be chosen to accommodate the desired number of sources.

Furthermore, as well as switching between illumination beams IB1, IB2, the tiltable mirror can be used, in combination with an appropriate aperture stop257, to control the incidence angle of illumination at the wafer. The tiltable mirror may be tiltable about one or two axes. Preferably, to avoid positioning errors, the tiltable mirror pivots about the point of incidence of the illumination beams IB1, IB2.

The basic illumination arrangement of the metrology device is Kohler illumination so that the source size and angular distribution in the back-projected pupil plane at aperture plate252respectively determine the angular distribution of illumination and spot size on the substrate. Thus, the illustrated arrangement allows for rapid switching between a mode with illumination of a small area from a wide range of angles, using the first source module, and mode with illumination of a larger area from a narrow range of angles, using the second source module. In the latter mode, by use of a sufficiently powerful source and a rapidly tiltable mirror, a large number of FD-OCT measurements using the second illumination beam IB2at different angles of illumination can be taken in a short period of time.

In an embodiment, a small measurement spot may be provided to underfill relatively large targets, e.g., in the scribe line, for accurate measurements as an angle-resolved scatterometer using IB1and measurement in the pupil plane, similar to as described with reference toFIG. 4, and whilst a larger spot with a well defined illumination incidence angle may be provided for measurements using IB2of relatively small targets, e.g., in-die markers, using the FD-OCT method similar to as described with reference toFIG. 5.

The two sources may both be kept on during use of the apparatus to allow rapid selection between them or selectively energized as required.

FIG. 7is a flow chart of a method according to an embodiment. The method has the steps as follows:

702: Provide a broadband illumination beam.

704: Split the illumination beam into measurement and reference beams.

706: Illuminate the target with the measurement beam at the incidence angle and the reference mirror with the reference beam.

708: Recombine the reflected portion of the measurement beam and the reference beam into an output beam.

710: Select a portion of the output beam, for example using an aperture.

712: Measure spectrum of the selected portion of the output beam to extract spectral information from it.

714: Fourier transform and calculate complex reflectance and/or carrier phase.

716: Determine CD by reconstruction using complex reflector or determine the wafer surface height using carrier phase.

A processor such as PU inFIG. 5may be used to control for example focus or dose settings of an exposure system of a lithographic apparatus by using the determined reflectance properties and reconstructed CD and/or level sensing measurements. The inspection apparatus may be incorporated in a lithographic apparatus or lithographic cell.

As described above, the target is on the surface of the substrate. This target will often take the shape of a series of lines in a grating or substantially rectangular structures in a 2-D array. The purpose of rigorous optical diffraction theories in metrology is effectively the calculation of a diffraction spectrum that is reflected from the target. In the embodiments described herein, the reflectance properties of the target are similarly calculated. Target shape information can be obtained for CD (critical dimension) uniformity and overlay metrology. Overlay metrology is a measuring system in which the overlay of two targets is measured in order to determine whether two layers on a substrate are aligned or not. CD uniformity is simply a measurement of the uniformity of the grating on the spectrum to determine how the exposure system of the lithographic apparatus is functioning. Specifically, CD, or critical dimension, is the width of the object that is “written” on the substrate and is the limit at which a lithographic apparatus is physically able to write on a substrate.

Using an inspection apparatus as described with reference toFIG. 5in combination with modeling of a target structure such as the target30and its reflectance properties, measurement of the shape and other parameters of the structure can be performed in a number of ways. In a first type of process, represented byFIG. 8, reflectance properties based on a first estimate of the target shape (a first candidate structure) is calculated and compared with the observed reflectance properties. Parameters of the model are then varied systematically and the reflectance properties re-calculated in a series of iterations, to generate new candidate structures and so arrive at a best fit. In a second type of process, represented byFIG. 9, reflectance properties for many different candidate structures are calculated in advance to create a ‘library’ of sets of reflectance properties. Then the reflectance properties observed from the measurement target is compared with the library of calculated reflectance properties to find a best fit. Both methods can be used together: a coarse fit can be obtained from a library, followed by an iterative process to find a best fit.

Referring toFIG. 8in more detail, the way the measurement of the target shape and/or material properties is carried out will be described in summary. The target will be assumed for this description to be periodic in only 1 direction (1-D structure). In practice it may be periodic in 2 directions (2-dimensional structure), and the processing will be adapted accordingly.

802: The reflectance properties of the actual target on the substrate are measured using a scatterometer such as described above with reference toFIG. 5. This measured reflectance properties are forwarded to a calculation system such as a computer. The calculation system may be the processing unit PU ofFIG. 5referred to above, or it may be a separate apparatus.

803: A ‘model recipe’ is established which defines a parameterized model of the target structure in terms of a number of parameters pi(p1, p2, p3and so on). These parameters may represent for example, in a 1D periodic structure, the angle of a side wall, the height or depth of a feature, the width of the feature. Properties of the target material and underlying layers are also represented by parameters such as refractive index (at a particular wavelength present in the scatterometry radiation beam). Importantly, while a target structure may be defined by dozens of parameters describing its shape and material properties, the model recipe will define many of these to have fixed values, while others are to be variable or ‘floating’ parameters for the purpose of the following process steps. Further below we describe the process by which the choice between fixed and floating parameters is made. Moreover, we shall introduce ways in which parameters can be permitted to vary without being fully independent floating parameters. For the purposes of describingFIG. 8, only the variable parameters are considered as parameters pi.

804: A model target shape is estimated by setting initial values pi(0)for the floating parameters (i.e., p1(0), p2(0), p3(0)and so on). Each floating parameter will be generated within certain predetermined ranges, as defined in the recipe.

806: The parameters representing the estimated shape, together with the optical properties of the different elements of the model, are used to calculate the reflectance properties, for example using a rigorous optical diffraction method such as RCWA or any other solver of Maxwell equations. This gives estimated or model reflectance properties of the estimated target shape.

808,810: The measured reflectance properties and the model reflectance properties are then compared and their similarities and differences are used to calculate a “merit function” for the model target shape.

812: Assuming that the merit function indicates that the model needs to be improved before it represents accurately the actual target shape, new parameters p1(1), p2(1), p3(1), etc. are estimated and fed back iteratively into step806. Steps806-812can be repeated.

In order to assist the search, the calculations in step806may further generate partial derivatives of the merit function, indicating the sensitivity with which increasing or decreasing a parameter will increase or decrease the merit function, in this particular region in the parameter space. The calculation of merit functions and the use of derivatives is generally known in the art, and will not be described here in detail.

814: When the merit function indicates that this iterative process has converged on a solution with a desired accuracy, the currently estimated parameters are reported as the determined shape parameters of the actual target structure.

The computation time of this iterative process is largely determined by the forward diffraction model used, i.e., the calculation of the estimated model reflectance properties using a rigorous optical diffraction theory from the estimated target structure. If more parameters are required, then there are more degrees of freedom. The calculation time increases in principle with the power of the number of degrees of freedom. The estimated or model reflectance properties calculated at806can be expressed in various forms. Comparisons are simplified if the calculated pattern is expressed in the same form as the measured reflectance properties generated in step802. For example, a modeled spectrometer output spectrum can be compared easily with a raw spectrometer spectrum measured by the spectrometer ofFIG. 5or a modeled complex reflectance can be compared easily with a complex reflectance output from the processing unit PU ofFIG. 5.

FIG. 9illustrates an alternative example process in which plurality of model reflectance properties for different estimated target shapes (candidate structures) are calculated in advance and stored in a library for comparison with a real measurement. The underlying principles and terminology are the same as for the process ofFIG. 8. The steps of theFIG. 9process are:

902: The process of generating the library begins. A separate library may be generated for each type of target structure. The library may be generated by a user of the measurement apparatus according to need, or may be pre-generated by a supplier of the apparatus.

903: A ‘model recipe’ is established which defines a parameterized model of the target structure in terms of a number of parameters pi (p1, p2, p3and so on). Considerations are similar to those in step803of the iterative process.

904: A first set of parameters p1(0), p2(0), p3(0), etc. is generated, for example by generating random values of all the parameters, each within its expected range of values.

906: Sets of model reflectance properties are calculated and stored in a library, representing the reflectance properties expected from a target shape represented by the parameters.

908: A new set of shape parameters p1(1), p2(1), p3(1), etc. is generated. Steps906-908are repeated tens, hundreds or even thousands of times, until the library which comprises all the stored modeled sets of reflectance properties is judged sufficiently complete. Each stored pattern represents a sample point in the multi-dimensional parameter space. The samples in the library should populate the sample space with a sufficient density that any real set of reflectance properties will be sufficiently closely represented.

910: After the library is generated (though it could be before), the real target30is placed in the scatterometer and its reflectance properties are measured.

912: The measured reflectance properties are compared with the modeled sets of reflectance properties stored in the library to find the best matching pattern. The comparison may be made with every sample in the library, or a more systematic searching strategy may be employed, to reduce computational burden.

914: If a match is found then the estimated target shape used to generate the matching library reflectance properties can be determined to be the approximate object structure. The shape parameters corresponding to the matching sample are output as the determined shape parameters. The matching process may be performed directly on the model reflectance properties, or it may be performed on substitute models which are optimized for fast evaluation.

916: Optionally, the nearest matching sample is used as a starting point, and a refinement process is used to obtain the final parameters for reporting. This refinement process may comprise an iterative process very similar to that shown inFIG. 8, for example.

Whether refining step916is needed or not is a matter of choice for the implementer. If the library is very densely sampled, then iterative refinement may not be needed because a good match will always be found. On the other hand, such a library might be too large for practical use. A practical solution is thus to use a library search for a coarse set of parameters, followed by one or more iterations using the merit function to determine a more accurate set of parameters to report the parameters of the target substrate with a desired accuracy. Where additional iterations are performed, it would be an option to add the calculated reflectance properties and associated refined parameter sets as new entries in the library. In this way, a library can be used initially which is based on a relatively small amount of computational effort, but which builds into a larger library using the computational effort of the refining step916. Whichever scheme is used, a further refinement of the value of one or more of the reported variable parameters can also be obtained based upon the goodness of the matches of multiple candidate structures. For example, the parameter values finally reported may be produced by interpolating between parameter values of two or more candidate structures, assuming both or all of those candidate structures have a high matching score.

The computation time of this iterative process is largely determined by the forward reflectance properties model at steps806and906, i.e., the calculation of the estimated model reflectance properties using a rigorous optical diffraction theory from the estimated target shape.

Embodiments of the present invention provides several advantages:

1. Fast CD metrology on small grating is enabled.

2. Stray light that may occur in the sensor optics is effectively suppressed since it will have a significantly different OPD than the nominal OPD of the object. As a result it is effectively suppressed in the demodulation of the carrier frequency.

4. The measured signal also contains focus information that can be used for focus control (it obviates the need for an extra focus measuring branch).

5. This technique can also be used a level sensor.

6. Mixing with a strong reference wave of the object is also beneficial for measuring on objects with a low reflectance like a-C (amorphous carbon) films.