System and method for characterizing three-dimensional structures

A metrology system for characterizing three-dimensional structures and methods for manufacturing and using same. The metrology system includes a measurement system that preferably comprises an energy source and energy detector and that is in communication with a processing system. Under control of the processing system, the metrology system rotates the measurement system relative to a structure while the energy source directs a beam of incident energy toward the structure. The incident energy rebounds from the structure as scattered energy, at least a portion of which propagates toward the energy detector. Due to the relative rotation, the energy detector receives scattered energy from the structure at a plurality of angles, and the measurement system produces data signals therefrom, which data signals are provided to the processing system. The processing system analyzes the data signals to determine whether the structure has any defects, such as yield limiting deviations or other processing defects.

FIELD OF THE INVENTION

The present invention relates generally to metrology and/or process monitoring systems and more particularly, but not exclusively, to optical metrology and/or process monitoring systems for characterizing yield limiting deviations and defects during semiconductor processing.

BACKGROUND OF THE INVENTION

Semiconductor processing is a well established technology for making microelectronic devices. This technology involves depositing thin films of insulator (dielectric) and metallic materials on the surface of semiconductor wafer. These films vary in thickness from a few Angstroms to a few microns depending on what function they serve in the structure of an electronic device. The device is built layer by layer starting from the surface of the semiconductor. The transistors, which are the active part of the device, are formed in the semiconductor and film stacks consisting of alternating metal-dielectric structures are built on top of the semiconductor. These thin films are etched at specific lithographically defined locations to form vias or contact holes. These vias or contacts are filled with conducting materials such as metals so that connections can be made from upper layer interconnects to lower layer interconnects. Interconnects connect different points of the device to each other within one plane.

There are tight tolerances for film thicknesses and lateral dimensions of the structures involved. Any deviation or excursion from a set of predefined design rules can be a serious yield limiting issue in the manufacturing of these devices. For example, if the thickness of a given layer deviates from the required specification, there would be a severe penalty on yield—a wrong film thickness is therefore a yield limiting deviation or defect. These issues have only become more important as integrated circuit processing technology advances to allow smaller device geometries. For this reason, film characterization has proven to be an important part of monitoring the yield and the operation of the device. Current technologies for film characterization include spectroscopic ellipsometry and reflectometry. Both these techniques rely on reflection of light from planar interfaces and they take advantage of changes in Fresnel reflectivity with wavelength and angle of illumination and their application to semiconductor processing is covered under U.S. Pat. Nos. 4,999,014; 5,042,951; 5,181,080; 5,329,357; 5,412,473; 5,596,411; 5,608,526; 5,771,094; 5,747,813; 5,917,594; and 6,323,946. It is important to note that for film characterization, reflectometry and ellipsometry rely on reflection of light from two-dimensional (2D) planes of film interfaces. Recently, a technology called scatterometry, covered under U.S. Pat. Nos. 6,429,943, 6,433,878, 6,483,580, 6,451,621 has emerged which can use the same hardware as an ellipsometer or a reflectometer for dimensional measurements. For example with these techniques the smallest dimension (critical dimension) printed, may be measured. As the world of microelectronics is moving toward nanotechnology, both critical dimension (CD) metrology and film thickness measurement are playing an increasingly vital role in high performance device fabrication. The devices of the future will require an increasing numbers of lithography masking steps, thereby increasing and accelerating the number of corresponding CD and film measurement steps.

Many structures, and their corresponding yield limiting deviations and defects are, in general, three-dimensional (3D). This is true for both the at the transistor level and also at the subsequent metal layers. At the transistor level one would be interested in measuring the sidewall angle, height, and profile of a feature with minimum dimensions. A wrong CD, profile, or sidewall angle would also be a yield limiting deviation or defect.

For interconnects, recently, the copper Damascene process has become the preferred technology. In this technology a layer of diffusion barrier material such as TaN is deposited on the walls of the trench and via. This process step is followed by depositing a seed layer of copper on top of the barrier layer. And finally through electroplating a thicker layer of copper fills up the trenches and vias. This process then is followed by the Chemical Mechanical Planarization (CMP).FIGS. 1A-Bshow the top and side views, respectively, of this structure after CMP.FIG. 1Ashows the copper lines, the diffusion barrier layer and the inter-metal dielectric (IMD) layer separating the conductor lines from each other. InFIG. 1B, the side view additionally shows the trench etch stop, interlayer dielectric (ILD) and the dielectric diffusion barrier and the via for making connection to the lower layer. InFIG. 1C, some of the problems associated with the copper Damascene are captured and some typical thicknesses for the films involved are given. Firstly, the dishing and erosion of the copper is shown. Since copper is a soft material during CMP, the material loses planarity and the surface becomes bowed. This can make lithography of the subsequent steps complicated and can lead to a reduction in yield.

The side wall coverage with the barrier material is another major problem. This is because vacuum deposition, while effective on flat surfaces, can be problematic when it comes to high aspect ratio trenches and vias. Proper coverage of the sidewalls with the barrier material can cause the diffusion of the copper and can lead to serious problems, ultimately limiting the fabrication yield. Formation of voids within the copper is another major problem that arises during the electroplating process. Voids such as the one shown inFIG. 2increase the electrical resistance of the trench and via and can lead to high current densities and heating. As is clear, these problems usually are in three dimensions. Prior art ellipsometry and reflectometry fail to characterize such yield limiting deviations. Therefore, a need clearly exists for characterizing these three-dimensional deviations in conjunction with film characterization and film thickness measurement.

In view of the foregoing, a need exists for an improved metrology and/or process monitoring system that overcomes the aforementioned obstacles and deficiencies of currently-available systems.

SUMMARY OF THE INVENTION

The various embodiments disclosed herein are directed toward a metrology and/or process monitoring system (herein referred to, separately and collectively, as a “metrology system”) that is configured to characterize three-dimensional structures to determine whether the structures have any defects, such as yield limiting deviations or other processing defects.

Each of the embodiments comprises a metrology system including a measurement system that is in communication with a processing system. Being configured to characterize a three-dimensional structure formed on a specimen, the metrology system can rotate the measurement system relative to the specimen while the measurement system directs a beam of incident energy toward the specimen. The rotation of the measurement system relative to the specimen is performed along an axis of rotation that preferably is substantially perpendicular to a surface of the specimen and intersects the structure. Propagating toward the specimen substantially at an angle of illumination relative to the axis of rotation, the incident energy rebounds from the specimen as scattered energy, at least a portion of which propagates toward the measurement system.

The measurement system also is configured to receive the scattered energy and to produce data signals therefrom, providing the data signals to the processing system. As the relative rotation continues, the measurement system receives scattered energy associated with each of a plurality of rotation angles and produces additional data signals, which likewise are provided to the processing system. Thereby, a spectrum of data signals is produced with respect to the plurality of rotation angles. Receiving the spectrum of data signals from the measurement system, the processing system is configured to perform an analysis of the data signals to determine whether the structure has any defects, such as yield limiting deviations or other processing defects.

Other aspects and features of the various embodiments disclosed herein will become apparent from consideration of the following description taken in conjunction with the accompanying drawings.

It should be noted that the figures are not drawn to scale and that elements of similar structures or functions are generally represented by like reference numerals for illustrative purposes throughout the figures. It also should be noted that the figures are only intended to facilitate the description of the preferred embodiments of the present invention. The figures do not describe every aspect of the present invention and do not limit the scope of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Since current metrology and/or process monitoring systems (herein referred to, separately and collectively, as “metrology systems”) are inadequate for complex structures, can be destructive, and can prove difficult and costly to implement, a metrology system for characterizing three dimensional structures that is configured to rotate relative to the three dimensional structures during characterization can prove much more desirable and provide a basis for a wide range of industrial applications, such as the characterization of yield limiting deviations and defects during semiconductor processing. This result can be achieved, according to one embodiment disclosed herein, by employing a metrology system100as shown in FIG.2.

The exemplary metrology system100includes a measurement system200that is coupled with, and configured to communicate with, a processing system300. Being configured to characterize a three-dimensional structure410formed on a specimen400, the metrology system100can rotate the measurement system200relative to the specimen400while the measurement system200directs a beam of incident energy500toward the specimen400. As illustrated inFIG. 2, the rotation of the measurement system200relative to specimen400is performed along an axis of rotation AR that preferably is substantially perpendicular to an external surface420of the specimen400and intersects the structure410. Propagating toward the specimen400substantially at an angle of illumination (or angle of incidence) θ relative to the axis of rotation AR, the incident energy500rebounds from the specimen400as scattered energy520. The scattered energy520rebounds from the specimen400in a plurality of directions as illustrated in FIG.2. At least a portion of the scattered energy520propagates toward the measurement system200.

The measurement system200also is configured to receive the portion of the scattered energy520and to produce data signals (not shown) therefrom, providing the data signals to the processing system300. As the relative rotation continues, the measurement system200receives scattered energy520associated with each of a plurality of rotation angles (or azimuthal angles) φ and produces additional data signals, which likewise are provided to the processing system300. Thereby, a spectrum of data signals is produced with respect to the rotation angle φ. Receiving the spectrum of data signals, in whole or in part, from the measurement system200, the processing system300is configured to perform an analysis of the data signals to determine whether the structure410has any defects, such as yield limiting deviations or other processing defects. The processing system300can analyze the data signals in any suitable manner, such as by comparing the data signals with one or more mathematical models (not shown) of the structure410and/or by using a neural network that has been trained to identify structural defects.

Turning toFIG. 3, the metrology system100is shown as having a measurement system200′ that comprises an energy source210and an energy detector220. Typically being coupled and preferably being substantially fixedly coupled, the energy source210and the energy detector220are approximately uniformly disposed about, and substantially in axial alignment with, the axis of rotation AR. Thereby, the energy source210and the energy detector220are configured to rotate substantially as a unit around the axis of rotation AR relative to the specimen400.

As will be discussed in more detail below with reference toFIGS. 6A-B, the energy source210and the energy detector220can be provided in any appropriate configuration such that the energy detector220is configured to receive the scattered energy520(shown in FIG.2). The suitability of a particular configuration may depend, at least in part, upon the nature of the specific application for which the metrology system100is to be utilized. Illustrative factors for identifying suitable configurations include the dimensions and complexity of the structure410being characterized, the materials from which the structure410is formed, and the desired precision of the characterization results. The measurement system200′ as shown inFIG. 3is provided in the manner discussed in more detail below with reference to FIG.6B and is configured to receive the incident energy500that reflects from the specimen400as reflected energy500′.

The energy source210can be any type of energy source that can provide a suitable beam of incident energy500, which preferably comprises electromagnetic radiation. Illustrative energy sources include monochromatic light sources, such as a gas laser or a solid state laser diode, and broadband sources, such as a xenon-arc lamp, as well as x-ray, ultraviolet, infra-red, and/or microwave energy. Being configured to direct the beam of incident energy500toward the specimen400in the manner discussed above with reference to the measurement system200(shown in FIG.2), the energy source210can be coupled with, and can communicate with, the processing system300as illustrated in FIG.3. The processing system300, for example, can be configured to activate and deactivate the energy source210and/or to control the angle of illumination θ relative to the axis of rotation AR. The angle of illumination θ can comprise any suitable angle for directing the incident energy500toward the specimen400. Therefore, the angle of illumination θ can be a substantially-fixed predetermined angle or can be adjustable among a plurality of predetermined angles within a predetermined range of angles.

Similarly, the processing system300can control a predetermined wavelength λ of the incident energy500provided by the energy source210. The incident energy500has at least one predetermined wavelength λ that preferably is substantially within a predetermined range of wavelengths. Stated somewhat differently, the wavelength λ of the incident energy500can comprise a substantially-fixed predetermined wavelength or can vary among a plurality of predetermined wavelengths, such as a sweep of successive wavelengths, each being substantially within the predetermined range. The incident energy500also can be polychromatic energy, such as white light, simultaneously comprising a plurality of wavelengths λ. Although the incident energy500generally is shown and described herein as comprising optical waves and/or microwaves for purposes of illustration, it is understood that the wavelength λ of the incident energy500can be any suitable wavelength within any predetermined range and is not limited to the illustrated embodiments.

For example, the incident energy500can comprise radio waves having a frequency of up to approximately three gigahertz (<3 GHz) or microwaves having a frequency in a range substantially between three hundred megahertz and three hundred gigahertz (300 MHz-300 GHz). Likewise, the frequency of the incident energy500can be substantially within the infrared band having a wavelength between approximately seven hundred nanometers and one hundred micrometers (700 nm-100 μm), the visible band having a wavelength between approximately four hundred and seven hundred nanometers (400 nm-700 nm), the ultraviolet band having a wavelength between approximately four and four hundred nanometers (4 nm-400 nm), or the soft or hard x-ray band having a wavelength between approximately one picometer and ten nanometers (1 pm-10 nm). The selection of the predetermined wavelength λ and/or the predetermined range may depend, at least in part, upon the nature of the specific application for which the metrology system100is to be utilized in the manner discussed above. If comprising polychromatic light energy, the incident energy500can have a plurality of wavelengths λ within a range of between approximately one hundred and ninety nanometers and one and one-half microns (190 nm-1.5 microns), or a portion thereof, simultaneously.

It will be appreciated that the energy source210can include a beam-formation system (or beam-conditioning system)215as shown inFIGS. 4A-B. Being disposed substantially between the energy source210and the specimen400, the beam-formation system215is configured to receive output energy510(shown inFIG. 4B) from the energy source210and to convert the output energy510into the beam of incident energy500. As illustrated inFIG. 14B, for example, the beam-formation system215can include one or more polarization systems215A, beam-splitting systems215B, modulation systems215C,215G, mirrors215D,215F, wave plates215E, beam-combining systems215H, and/or any other suitable components. Exemplary modulation systems include phase or intensity modulation systems, such as an acousto-optic modulation (AOM) system. The beam-formation system215can be disposed substantially within the energy source210as illustrated inFIG. 4Aor can be separate from the energy source210as shown in FIG.4B.

FIGS. 5A-Billustrate the energy detector220for the measurement system200′ (shown in FIG.3). The energy detector220can comprise any type of energy detector that is suitable for detecting and/or receiving the reflected energy500′. If the energy source210is a laser or light emitting diode system, for example, one or more photomultiplier tubes (PMT) and/or photodiodes can be used as the energy detector220. Likewise, the energy detector220can comprise a wavelength dispersive element, such as a prism or grating, and a charge-coupled device (CCD) or photodiode array when the energy source210is a broadband or polychromatic source. Furthermore, the energy detector220can include one or more polarization elements, such as a polarization system215A (shown inFIG. 14B) and/or a wave plate215E (shown in FIG.14B). The energy detector220likewise can comprise demodulator circuitry after the reflected energy500′ has been detected. The energy detector220also is coupled with, and can communicate with, the processing system300. For example, preferably being configured to produce data signals from the reflected energy500′, the energy detector220configured to provide the data signals to the processing system300in the manner discussed above with regard to the measurement system200(shown in FIG.2).

As desired, an energy-collection system (or collection system)225can be disposed substantially between the specimen400and the energy detector220as illustrated inFIGS. 5A-B. The energy-collection system225is configured to receive the reflections of the incident energy500from the specimen400and to convert these reflections into the reflected energy500′. In the manner discussed above with regard to the beam-formation system215(shown in FIGS.4A-B), the energy-collection system225can include any number of additional systems such as one or more polarization systems215A (shown inFIG. 14B) and/or wave plates215E (shown in FIG.14B). As shown inFIG. 5A, the energy-collection system225can be disposed substantially within the energy detector220, or the energy-collection system225can be separate from the energy detector220as shown in FIG.5B.

One configuration of the energy source210and the energy detector220of the measurement system200′ (shown inFIG. 3) is shown inFIGS. 6A-B. As illustrated inFIG. 6A, the beam of incident energy500propagates from the energy source210, defining an axis of incidence AI. The energy detector220can be displaced from the axis of incidence AI by an angular offset α. By being displaced from the axis of incidence AI by the angular offset α, the energy detector220is configured to detect and/or receive non-specular scatterings of the incident energy500from the specimen400as the scattered energy520. It will be appreciated that the angular offset α can comprise any suitable angular offset and preferably is selected to enhance the sensitivity of the metrology system100to one or more preselected features, such as the structure410(shown inFIGS. 2 and 3) of the specimen400to be characterized. This configuration sometimes is referred to as a dark field detection configuration.

It will be appreciated that, if the surface420of the specimen400is substantially smooth, no significant dark field scattering with result from the reflection of the incident energy500from the surface420. As such, when the measurement system200′ is provided in the dark field detection configuration, the scattered energy520primarily comprises energy scattered from the three-dimensional structure410formed on the specimen400. The structure410therefore can be characterized by the scattered energy520rebounded from the structure410, and any defects in the structure410can be detected.

When the angular offset α is substantially equal to zero, the energy detector220is substantially in axial alignment with the axis of incidence AI. In contrast to the dark field detection configuration of the measurement system200′, the energy detector220is configured to detect and/or receive specular scattering or reflection of the incident energy500from the specimen400as the reflected energy500′. This configuration may be referred to as a bright field detection configuration and is illustrated in FIG.6B. The energy source210and the energy detector220preferably are substantially fixedly coupled such that the angular offset α is approximately maintained during the rotation of the measurement system200′ relative to the specimen400. As illustrated inFIGS. 6B, the energy source210and the energy detector220are substantially fixedly coupled via a coupling system230, which can comprise any type of mechanical coupling system, including one or more brackets and/or platforms, such as the rotatable platform710shown in FIG.7B.

Since the energy source210and the energy detector220are substantially axially aligned, the incident energy500from the energy source210and the reflected energy500′ received by the energy detector220define a plane of incidence PI as shown inFIGS. 6B and 8. Since the axis of rotation AR preferably is substantially perpendicular to the surface420of the specimen400, the plane of incidence PI likewise preferably is substantially perpendicular to the surface420as illustrated in FIG.9. Therefore, when the energy source210and the energy detector220rotate about the axis of rotation AR (shown in FIG.9), the plane of incidence PI likewise rotates about the axis of rotation AR.

Further, the phase of the incident energy500can be measured when the energy source210and the energy detector220are in the bright field detection configuration. For example, the metrology system100can include one or more beam-splitting systems215B (shown inFIG. 14B) and/or beam-combining systems215H (shown inFIG. 14B) for branching off a portion of the incident energy500to form a reference beam of incident energy (not shown). The reference beam can be directed toward the energy detector220such that the reference beam interferes with the reflected energy500′ Similarly, when the reflected energy500′ includes at least two components, such as a S-polarized component and a P-polarized component, the components of the reflected energy500′ can be interfered to provide a phase difference between the two components. It is understood that, as desired, the metrology system100can include a second energy source (not shown) that is configured to provide the reference beam.

One embodiment of a processing system300′ for metrology systems100′ is illustrated in FIG.7A. The processing system300′ is configured to receive the data signals from the measurement system200′ and to analyze the data signals to determine whether the structure410(shown inFIG. 2) formed on the specimen400has any defects. As shown inFIG. 7A, the processing system300′ comprises a data acquisition system310′, a central processing system320′, and a memory system330′. The data acquisition system310′ is configured to receive the data signals and, as desired, to convert the data signals into digital data (not shown). In a preferred embodiment, the data acquisition system310′ includes at least one analog-to-digital conversion (ADC) system for digitizing the data signals.

Being configured to perform the analysis of the digital data, the central processing system320′ can comprise any type of processing system, such as one or more central processing units (CPUs) and/or digital signal processors (DSPs), and is configured to communicate with the data acquisition system310′ and the memory system330′. The central processing system320′ thereby can receive the digital data from acquisition system310′ and/or the memory system330′. In other words, the central processing system320′ can perform the analysis of the digital data in real-time and/or can store the digital data in the memory system330′ for later retrieval and analysis. The digital data preferably is stored in the memory system330′ such that the association between the digital data and the rotation angle φ is substantially maintained. If each rotation angle φ is associated with a memory register (not shown), for example, the digital data for each rotation angle φ can be stored in the relevant memory register. Similarly, the digital data and the associated rotation angle φ can be stored in the memory system330′ in the form of a look-up table.

Comprising any suitable type of memory system, the memory system330′ can include volatile memory and/or non-volatile memory of any kind and can be configured to store and provide other types of information. For example, the central processing system320′ can perform the data analysis by receiving and executing a series of instructions, which can be provided in the form of instruction code, such as software or firmware, that is stored in the memory system330′. The partial and/or complete results of the analysis likewise can be stored in, and retrievable from, the memory system330′. As desired, the central processing system320′ can analyze the digital data as the data signals are successively received by the processing system300′, and/or the analysis can be delayed until substantially the complete spectrum of data signals has been received.

The central processing system320′ can perform the analysis of the digital data in any suitable manner. For example, the analysis of the digital data can be performed via a neural network (not shown). The neural network can be trained to identify preferred spectra of digital data by examining a plurality of sample specimens400. By analyzing a wide range of good and bad sample specimens400, the neural network can “learn” to identify spectra associated with preselected structural defects.

In another embodiment, the central processing system320′ is configured to perform the data analysis by comparing the digital data with one or more mathematical models (not shown) of the structure410as illustrated by the processing system300″ of the metrology system100″ shown in FIG.7B. Being provided substantially in the manner discussed above with reference to the processing system300′ (shown in FIG.7A), the processing system300″ comprises a data acquisition system310″, a central processing system320″, and a memory system330″ and further includes a modeling system340″. As desired, the modeling system340″ can be combined with, or substantially separate from, the memory system330″.

The modeling system340″ is configured to provide at least one mathematical model of the structure410. Each mathematical model typically is calculated based upon input parameters regarding ideal dimensions of the structure410as well as other information, such as user-provided information. Upon receiving the digital data, the central processing system320″ is configured to compare the digital data with the mathematical model in any suitable manner, such as by performing a minimization procedure, such as a minimization procedure involving nonlinear regression. Similarly, model data (not shown) can be precalculated for each mathematical model and stored in the modeling system340″, preferably in the form of a look-up table. The central processing system320″ thereby can perform the data analysis by comparing the digital data with the model data. The processing system300(shown inFIG. 2) is shown and described herein as comprising the processing system300′ in FIG.7A and the processing system300″ inFIG. 7Bfor purposes of illustration only. The processing system300can be any suitable type of processing system and is not limited to the illustrated embodiments. Likewise, it is understood that the measurement system200(shown inFIG. 2) can comprise any suitable type of measurement system and is not limited to the exemplary measurement systems200′,200″ shown and described with reference toFIGS. 3 and 6AandFIG. 7B, respectively.

It also will be appreciated that the incident energy500and/or the reflected energy500′ can propagate between the measurement system200′ substantially directly as illustrated inFIG. 7Aor via one or more intermediate systems, such as the focusing system800shown in FIG.7B. Being disposed substantially between the measurement system200′ and the specimen400, the focusing system800is configured to focus the incident energy500, the reflected energy500′ and/or the scattered energy520(shown in FIGS.2and8). Illustrative focusing system800are disclosed in U.S. Pat. No. 5,604,334, issued to Finarov, and U.S. Pat. No. 6,124,924, issued to Feldman et al., each of which are hereby expressly incorporated herein by reference.

If the energy source210is a monochromatic light source, such as a laser, for example, the focusing system800can be a lens or a lens system, such as a microscope objective; whereas, the focusing system800can comprise radiation-reflective focusing optics when the energy source210is a broadband source. Likewise, the focusing system800can include a bent crystal if the energy source210emits incident energy500with a preselected wavelength λ that is substantially in the x-ray band. As desired, the focusing system800can include the beam-formation system215discussed in more detail above with regard toFIGS. 4A-Band/or the energy-collection system225discussed in more detail above with reference toFIGS. 5A-B.

Returning toFIG. 3, the metrology system100can further include a platform600for supporting the specimen400. The platform600can comprise any suitable type of platform, such as a vacuum chuck or an electrostatic chuck, such that the specimen400is secured substantially in place. In the manner described above, depending, at least in part, upon the nature of the specific application for which the metrology system100is to be utilized, the platform600can be a motorized translation platform, or any other suitable mechanical device or system known in the art. Specifically, a motorized translation stage can be employed such that different portions, such as multiple structures410, of the specimen400can be characterized by the metrology system100. Although illustrated inFIG. 3as being uncoupled from the measurement system200′ and the processing system300, it is understood that the platform600can be coupled with, and configured to communicate with, the measurement system200′ and/or the processing system300as desired.

The relative rotation between the measurement system200′ and the specimen400can be achieved in any manner such as by rotating the measurement system200′. For example,FIG. 7Billustrates a rotation system700that is configured to rotate the measurement system200′ substantially about the axis of rotation AR to achieve the relative rotation between the measurement system200′ and the specimen400. As shown inFIG. 7B, the rotation system700comprises a rotatable platform710and a control system720. The rotatable platform710is fixedly coupled with the energy source210and the energy detector220of the measurement system200′. The control system720can comprise any suitable type of control system, such as a motor, and, as shown inFIG. 7B, can be coupled with the processing system300″. Thereby, the operation of the control system720, and therefore the rotation of the measurement system200′, is controllable via the processing system300″.

The control system720can further include an encoding system (not shown) that is configured to produce a rotational data signal (not shown) that represents the rotation angle φ of the rotatable platform710and to provide the rotational data signal to the processing system300″. The rotational data signal can provide feedback to the processing system300″ when the processing system300″ is configured to control the rotation of the measurement system200′. Further, the processing system300″ can utilize the rotational data signal to associate the relevant rotation angle φ with the relevant data signal and/or the digital data produced therefrom, for example, when storing the digital data in the memory system330″ in the manner discussed in more detail above with reference to the processing system300″.

Although shown and described as comprising the rotation system700inFIG. 7Bfor purposes of illustration, it is understood that the relative rotation between the measurement system200and the specimen400can be achieved by way of any suitable rotation system and is not limited to the illustrated embodiment. For example, the relative rotation can be carried out electronically, such as by employing a measurement system200as shown inFIG. 8that comprises an array210′ of energy sources210A-F and an array220′ of energy detectors220A-F. The array210′ can comprise any number of energy sources210A-F, each being provided in the manner set forth in more detail above with reference to FIGS.3and4A-B; Likewise, the array220′ can include any number of energy detectors220. Each of the energy detectors220A-F in the array220′ are provided in the manner set forth in more detail above with reference to FIGS.3and5A-B. Each of the arrays210′,220′ can be disposed, partially or substantially completely, around the specimen400in substantially any suitable arrangement or configuration, and each energy source210in the array210′ is associated with at least one energy detector220in the array220′.

As shown inFIG. 8, the arrays210′,220′ are provided in the bright field detection configuration (shown inFIG. 6B) and are partially disposed around the specimen400. Energy source210A is configured to direct incident energy500A toward the specimen400and is associated with energy detector220A. The energy detector220A is configured to receive a portion of the incident energy500A that reflects from the specimen400as reflected energy500A′. Being associated with energy detector220B, energy source210B can direct incident energy500B toward the specimen400at a predetermined angle φABrelative to the incident energy500A provided by the energy detector220A. A portion of the incident energy500B that reflects from the specimen400is received by the energy detector220B as reflected energy500B′. Similarly, energy sources210C-F respectively direct incident energies500C-F toward the specimen400at predetermined angles φBC, φCD, φDE, and φEFrelative to the incident energies500B-E, respectively. The incident energies500C-F reflect from the specimen400as reflected energies500C-F′, a portion of which is received by energy detectors220C-F, respectively.

The predetermined angles φAB, φBC, φCD, φDE, and φEFcan comprise any suitable angle and preferably are substantially equal. Similarly, the energy detectors220A-F preferably are configured to provide the incident energies500A-F with substantially the same characteristics. Thereby, when the energy detectors220A-F are successively activated, the incident energies500A-F are successively directed toward the specimen400, and the energy detectors220A-F successively receive the reflected energies500A-F′ such that the measurement system200is virtually rotated relative to the specimen400.

Upon receiving the reflected energies500A-F′, the measurement system200can produce the spectrum of data signals therefrom and provide the spectrum of data signals to the processing system300(shown inFIG. 3) in the manner discussed in more detail above. Likewise, the processing system300can perform an analysis of the spectrum of data signals in the manner set forth above to determine whether the structure410has any defects. Electronic rotation can reduce the time required to produce the spectrum of data signals, which time reduction is highly desirable for in line metrology and process monitoring of semiconductor wafers during processing.

It will be appreciated that electronic rotation likewise can be performed with the arrays210′,220′ in the dark field detection configuration discussed above with reference to FIG.6A. Furthermore, by associating more than one energy detector220with an energy source210, the measurement system200is configured to be in both the bright field and the dark field detection configurations. If the energy detectors220A,220C are associated with the energy source210A, for example, the measurement system200is configured to receive and analyze the reflected energy500A′ via the energy detector220A and the scattered energy520(shown in FIG.2) via the energy detector220C. Thereby, the metrology system100substantially simultaneously receive and analyze bright field and dark field data signals.

The details of the operation of the metrology system100″ will be presently discussed with reference toFIGS. 6B,7B,8, and9. Although a bright field detection configuration of the energy source210and the energy detector220as shown inFIG. 6Bis assumed for purposes of illustration, it is understood that the present discussion can equally apply to a dark field detection configuration of FIG.6A.FIG. 9is a three-dimensional view of an exemplary structure410formed on the specimen400. For purposes of simplicity, the exemplary structure410is illustrated inFIG. 9as a plurality of substantially parallel trenches430formed in the specimen400and defined by internal surfaces440. It is understood, however, that any surface in which the reflectivity or impedance is a function of angle can be characterized by the metrology system100″. In the manner discussed in more detail above with reference toFIG. 7B, the metrology system100″ is configured to rotate the measurement system200along the axis of rotation AR, which preferably is substantially perpendicular to the external surface420of the specimen400and intersects the structure410.

In operation, the energy source210provides the beam of incident energy500, which propagates toward the specimen400substantially at the angle of illumination θ relative to the axis of rotation AR. Upon reaching the specimen400, the incident energy500reflects from the specimen400. As shown inFIG. 9, some of the incident energy500rebounds from the specimen400in various directions as scattered energy520; whereas, a portion of the incident energy500reflects toward the energy detector220as reflected energy500′ in the manner discussed in more detail above with reference to FIG.2. The energy detector220receives and detects the reflected energy500′ and produces data signals therefrom. Although the data signals can be any suitable type of information regarding the reflected energy500′, such as an amplitude, a frequency, a phase change, and/or a power level, the data signals are shown and described as comprising a power level of the reflected energy500′ for purposes of this example.

As the metrology system100″ rotates the energy source210and the energy detector220about the axis of rotation AR, the incident energy500propagates toward, and therefore reflects from, the external and internal surfaces420,440from different rotation angles φ. The power level of the reflected energy500′ as received by the energy detector220therefore can vary as a function of the rotation angle φ. For instance, when the energy source210and the energy detector220are substantially perpendicular to the trenches430, a relatively large portion of the incident energy500is reflected by the internal surfaces440as scattered energy520, and the power level of the reflected energy500′ as measured by the energy detector220is relatively low. In contrast, a lesser portion of the incident energy500is reflected by the internal surfaces440as scattered energy520when the energy source210and the energy detector220are substantially in parallel with the trenches430. The energy detector220therefore measures reflected energy500′ with a higher power level.

In the manner described in more detail above with reference toFIG. 3, the measurement system200′ produces a spectrum of measured power data signals from the measured power levels. The measurement system200′ provides the spectrum of measured power data signals as well as the rotational data signals produced by the rotation system700to the processing system300″. Upon receiving the spectrum of measured power data signals and the rotational data signals, the processing system300″ produces digital measured power data therefrom, which digital measured power data is associated with the relevant rotation angles φ, in the manner discussed in more detail above with reference to FIG.7A. Thereby, the measured power spectrum PS comprises the measured power level as a function of rotation angles φ and is illustrated inFIG. 10is produced.

The modeling system340″ of the processing system300″ preferably includes at least one mathematical model of the structure410of FIG.9. Since the measurement system200′ is configured to measure the power level of the reflected energy500′ in this example, the relevant mathematical model likewise comprises the measured power level as a function of rotation angles φ and is illustrated as a model power spectrum MS in FIG.10. The processing system300″ performs an analysis of the exemplary structure410ofFIG. 9by comparing the measured power spectrum PS with the model power spectrum MS. Thereby, the metrology system100″ can determine whether the structure410has any defects.

It will be appreciated that the operation of the metrology system100″ can be modified in accordance with the nature of the specific application for which the metrology system100″ is to be utilized. Illustrative factors for identifying suitable configurations include the dimensions and complexity of the structure410being characterized, the materials from which the structure410is formed, and the desired precision of the characterization results. By the adjusting the operation of the metrology system100″, the metrology system100″ can be configured to analyze more complex structures410, to increase the precision of the characterization results, to more quickly characterize the structure410, and to yield additional information with regard to the structure410.

For example, the metrology system100″ can be configured to analyze a different number of data signals when characterizing the structure410. The number of data signals can be adjusted by modifying the range of the rotation angle φ by which the metrology system100″ rotates the measurement system200″ relative to the specimen400and/or by changing the number of measurement that measurement system200″ makes per revolution relative to the specimen400. The range of rotation angles φ can comprise any suitable range of angles, including ranges that exceed a complete revolution of the revolution of the measurement system200″ relative to the specimen400. Stated somewhat differently, the range of rotation angles φ can be greater than, less than, or substantially equal to a complete revolution of three hundred and sixty degrees (360°). By increasing the number of data signals, the metrology system100″ can be configured to analyze more complex structures410and/or increase the precision of the characterization results.

The operation of the metrology system100″ likewise can be modified by permitting other operational parameters of the metrology system100″, such as the angle of illumination θ, the polarization of the incident energy500, and/or the wavelength λ (shown inFIG. 3) of the incident energy500, to be adjustable. Although each was presumed to be substantially constant in the above example, the angle of illumination θ and/or the wavelength λ of the incident energy500can be adjustable. In the manner discussed in more detail above with reference toFIG. 3, the angle of illumination θ can be adjustable within a predetermined range of angles. Likewise, when the incident energy500comprises electromagnetic radiation, for example, the wavelength λ of the incident energy500can vary among a plurality of predetermined wavelengths, such as a sweep of successive wavelengths, each being substantially within a predetermined range in the manner discussed above with regard to FIG.3.

The angle of illumination θ and/or the wavelength λ of the incident energy500can be adjustable via the processing system300″ and/or independently of the processing system300″. In addition to receiving the data signals and the rotational data signal, the processing system300″ also can receive one or more control signals (not shown) that represent the angle of illumination θ and/or the wavelength λ of the incident energy500. These control signals can be provided, and associated with the data signals, substantially in the manner discussed above with regard to the rotational data signals. Furthermore, the control signals can provide feedback to the processing system300″ when the processing system300″ is configured to control the angle of illumination θ and/or the wavelength λ of the incident energy500.

The angle of illumination θ and/or the wavelength λ of the incident energy500can be adjustable relative to the rotation angle φ. Stated somewhat differently, the metrology system100″ can be configured to adjust the rotation angle φ, the angle of illumination θ, and/or the wavelength λ either in isolation or substantially simultaneously in any combination. For example, the angle of illumination θ and/or the wavelength λ of the incident energy500can be held substantially fixed for a substantially complete revolution of the measurement system200″ relative to the specimen400. The angle of illumination θ and/or the wavelength λ of the incident energy500likewise can be varied as the measurement system200″ rotates relative to the specimen400.FIGS. 11A-Bprovide exemplary three-dimensional measured power spectrum characterizations PS′, PS″ of the structure410shown in FIG.9. By permitting other operational parameters of the metrology system100″ to be adjustable, the metrology system100″ can be configured to analyze more complex structures410and/or increase the precision of the characterization results.

FIG. 11illustrates an electric field E of the incident energy500incident on the surface420and is discussed with reference to the metrology system100shown in FIG.3. As shown inFIG. 12, the surface420includes a grating450. The incident energy500comprises a propagating wave with a S-type polarization such that the electric field E is substantially perpendicular to the plane of incidence PI (shown inFIG. 9) defined by the incident energy500and the reflected energy500′. As the energy source210rotates though the rotation angle φ relative to the specimen400, the electric field E on the surface420of the specimen400forms an angle φ′ relative to the grating450, which angle φ′ is approximately equal to the rotation angle φ. It will be appreciated that, for each angle φ′, the surface420can have a different impedances at microwave frequencies and a different reflectivities at optical and/or X-ray wavelengths λ.

For surfaces420that are substantially smooth and isotopic, the field boundary conditions are approximately the same for each rotation angle φ at which these surfaces420are being interrogated. The field boundary conditions however can differ for each rotation angle φ if the surface420, such as the grating450shown inFIG. 12, is not substantially smooth and isotopic. These differences in the field boundary conditions can result in a different reflectivity for the surface420for each rotation angle φ. Since these differences exist in the phase and/or the amplitude of the complex reflection coefficient, the term “reflectivity” can refer to the usage of the phase and/or the intensity. As such, intensity and/or phase spectra can be obtained with respect to the angle φ′, and, furthermore, such spectra can be obtained with different input polarizations.

It will be appreciated that the grating450can be viewed as a plurality of closely-spaced, coupled electromagnetic waveguides. When the incident energy500reaches the surface420, a wave (not shown) is launched in these waveguides, and any associated coupling and resonances can be a function of the characteristics of the incident energy500. The characteristics of the incident energy500include the angle of illumination θ, rotation angle φ, and the polarization of the incident energy500. Further, in spectroscopic reflectometry and ellipsometry, a change in the angle of illumination θ and/or the wavelength λ (shown inFIG. 3) of the incident energy500can produce a change in the spectrum even if the surface420is substantially smooth and isotopic. Here, on the other hand, a change in the spectrum with respect to the rotation angle φ will result only if the surface420includes the grating450or any other three-dimensional structure, such as structure410(shown in FIG.2). The three-dimensional properties of the grating450therefore are being analyzed rather than the two-dimensional properties of the surface420.

FIGS. 13A-Dillustrate the polarization of the electric field E of the incident energy500and is discussed with reference to the metrology system100shown in FIG.3. As illustrated inFIGS. 13A-D, the surface420includes the grating450, which comprises a plurality of substantially parallel grating lines450′. Turning toFIG. 13A, the incident energy500is shown as having the electric field E with S-polarization and as propagating toward the grating450at an rotation angle φ that is substantially equal to zero degrees (0°). In other words, the incident energy500is substantially perpendicular to the grating lines450′. The electric field E of the incident energy500therefore is substantially parallel to the grating lines450′. The incident energy500illustrated inFIG. 13Blikewise has the electric field E with the S-polarization but propagates toward the grating450at an rotation angle φ that is substantially equal to ninety degrees (90°). Since the incident energy500is substantially in parallel with the grating lines450′, the electric field E is substantially perpendicular to the grating lines450′ as shown in FIG.13B.

Similarly,FIGS. 13C-Dillustrate the incident energy500with the electric field E having P-polarization. In the P-polarization, the electric field E is substantially in the plane of incidence PI (shown inFIG. 9) and has a tangential component and a perpendicular component. The tangential component is substantially parallel to the surface420; whereas, the perpendicular component is substantially perpendicular to the surface420. InFIG. 13C, the incident energy500is shown as propagating toward the grating450at an rotation angle φ that is substantially equal to zero degrees (0°). Since the incident energy500is substantially perpendicular to the grating lines450′, the electric field likewise is substantially perpendicular to the grating lines450′ and has a field component E′ that is substantially normal to the surface450. The incident energy500that propagates toward the grating450at an rotation angle φ that is substantially equal to ninety degrees (90°) is illustrated in FIG.13D. Here, the incident energy500is substantially parallel to the grating lines450′ such that the electric field E also is substantially parallel to the grating lines450′. In the manner discussed above with reference toFIG. 13C, the field component E′ of the electric field E is substantially normal to the surface450.

Another embodiment of the metrology system100(shown inFIG. 2) is illustrated as the metrology system100″ inFIGS. 14A-B. In the manner discussed in more detail above with reference to the metrology system100′ (shown in FIG.7), the metrology system100″ includes a measurement system200″ that is coupled with, and configured to communicate with, a processing system300″ as shown in FIG.14A. Being configured to characterize a three-dimensional structure410(shown inFIG. 2) formed on a specimen400, the metrology system100″ can rotate the measurement system200″ relative to the specimen400while the measurement system200″ directs a beam of incident energy500toward the specimen400. As illustrated inFIG. 14A, the rotation of the measurement system200″ relative to specimen400is performed along an axis of rotation AR that preferably is substantially perpendicular to an external surface420of the specimen400and intersects the structure410. Propagating toward the specimen400substantially at an angle of illumination θ relative to the axis of rotation AR, the incident energy500reflects from the surface420as reflected energy500′, at least a portion of which propagates toward the measurement system200″.

The measurement system200″ also is configured to receive the reflected energy500′ and to produce data signals (not shown) therefrom, providing the data signals to the processing system300″. As the relative rotation continues, the measurement system200″ receives reflected energy500′ associated with each of a plurality of rotation angles φ and produces additional data signals, which likewise are provided to the processing system300″. Thereby, a spectrum of data signals is produced with respect to the rotation angle φ. Receiving the spectrum of data signals, in whole or in part, from the measurement system200″, the processing system300″ is configured to perform an analysis of the data signals to determine whether the structure410has any defects, such as yield limiting deviations or other processing defects. The processing system300″ can analyze the data signals in any suitable manner, such as by comparing the data signals with one or more mathematical models (not shown) of the structure410.

As shown inFIG. 14A, the measurement system200″ comprises an energy source210, an energy detector220, and a rotation system700, each being provided in the manner discussed in more detail above with reference toFIGS. 3,4A-B,5A-B, and7. Typically being coupled and preferably being substantially fixedly coupled, the energy source210and the energy detector220are approximately uniformly disposed about, and substantially in axial alignment with, the axis of rotation AR. Thereby, the rotation system700is configured to rotate the energy source210and the energy detector220around the axis of rotation AR relative to the specimen400.

The measurement system200″ further includes a beam-formation system215″ and an energy-collection system225. In the manner described above with reference toFIGS. 4A-B, the beam-formation system215″ is disposed substantially between the energy source210and the specimen400and is configured to receive output energy510from the energy source210and to convert the output energy510into the beam of incident energy500. The energy-collection system225is provided in the manner described above with reference toFIGS. 5A-Band is disposed substantially between the specimen400and the energy detector220. The energy-collection system225is configured to receive the reflections of the incident energy500from the specimen400and to convert these reflections into the reflected energy500′ in the manner described above with reference toFIGS. 5A-B. Being shown inFIG. 14Aas being separate from the energy source210and the energy detector220, respectively, for purposes of illustration, it will be appreciated that the beam-formation system215″ can be disposed substantially within the energy source210as illustrated inFIG. 4A, and/or the energy-collection system225can be disposed substantially within the energy detector220as illustrated in FIG.5A.

Upon receiving the output energy510from the energy source210, the beam-formation system215″ is configured to divide the output energy510into a plurality of components and to modulate each component at a preselected frequency. The modulated components then are recombined to form the beam of incident energy500. One embodiment of the beam-formation system215″ is illustrated in FIG.14B. As shown inFIG. 14B, the beam-formation system215″ is configured to divide the output energy510into two components. If the output energy510comprises electromagnetic energy, for example, the components can be a S-polarized component and a P-polarized component of the output energy510.

The beam-formation system215″ includes a polarization system215A that is configured to receive the output energy510to provide polarized output energy510A. A beam-splitting system215B is coupled with the polarization system215A and can receive the polarized output energy510A, dividing the polarized output energy510A into first and second polarized output energy510B,510C. The first polarized output energy510B is provided to a first modulation system215C, which is configured to modulate the first polarized output energy510B at a first preselected modulation frequency F1, and then is provided to a beam-combining system215H via a mirror215D.

The polarized output energy510C is provided to a wave plate215E. Preferably comprising a one-half wave plate, the wave plate215E is configured to modify the polarization of the polarized output energy510C, such as by approximately ninety degrees (90°). The polarized output energy510C, as modified, is provided to a second modulation system215G via a mirror215F. The second modulation system215G is configured to modulate the second polarized output energy510C at a second preselected modulation frequency F2and to provide the second polarized output energy510C, as modified and modulated, to the beam-combining system215H. The beam-combining system215H combines the modulated first polarized output energy510B with the second polarized output energy510C, as modified and modulated, to form the resultant beam of incident energy500.

Returning toFIG. 14A, the resultant beam of incident energy500is directed toward the specimen400in the manner described in more detail above. The reflected energy500′ is received by the energy-collection system225, which analyzes the polarization of the reflected energy500′ before providing the reflected energy500′ to the energy detector220. Since the beam of incident energy500includes two polarization states, each being modulated at a different preselected frequency, the reflected energy500′ received by the energy detector220substantially comprises two sets of information. In other words, each polarization state may be processed by the measurement system200as two separate operands.

Many operations therefore can be performed on the reflected energy500′ to produce the data signals. For example, the two polarization states can be interfered to derive interference signals (not shown) that comprise a difference in phase between the signals comprising the two polarization states. To interfere the two polarization states of the reflected energy500′, the energy-collection system225can analyze the reflected energy500′ at an angle of substantially forty-five degrees (45°). Thereby, the interference signals are provided with frequencies that are substantially equal to the sum and/or the difference of the first and second preselected modulation frequencies F1, F2. Once produced, the interference signals can be provided to the processing system300″ as the data signals. It will be appreciated that any suitable one-operand and/or two-operand operation can be performed on the two polarization states of the reflected energy500′. Illustrative two-operand operations include addition, subtraction, ratio, and/or logic operations, such as AND, OR, NAND, NOR, and/or XOR.

In the manner discussed in more detail above with reference toFIGS. 7A-B, the processing system300″ can be provided in any suitable manner and, as shown inFIG. 14A, is provided substantially in the manner described above with reference to FIG.7B. The processing system300″ is configured to receive the data signals from the measurement system200″ and includes a data acquisition system310″, a central processing system320″, a memory system330″ and a modeling system340″. Each of the data acquisition system310″, the central processing system320″, the memory system330″ and the modeling system340″ are provided in the manner described in more detail above with regard to FIG.7B.

The processing system300″ further includes first and second frequency generators350,360. The first and second frequency generators350,360can comprise any suitable type of frequency generator and are configure to generate the first and second preselected modulation frequencies F1, F2, respectively. Although illustrated as being disposed within the processing system300″, the first and second frequency generators350,360can be separate from the processing system300″ and, as desired, may be disposed within the measurement system200″. The first and second frequency generators350,360are coupled with, and configured to provide the first and second preselected modulation frequencies F1, F2to, the beam-formation system215″ and the data acquisition system310″.

The processing system300″ can process the interference signals and/or the data signals provided by the measurement system in the manner discussed in more detail above with reference to FIG.7B. Preferably, the data acquisition system310″ comprises a synchronous data acquisition system and is configured to lock the interference signals and/or the data signals to any of the frequencies that correspond to the interference signals and/or the data signals. The frequencies that correspond to the interference signals and/or the data signals include the first modulation frequency F1, the second modulation frequency F2, a sum of the first and second modulation frequencies F1, F2, and a difference between the first and second preselected modulation frequencies F1, F2. Such a method for acquiring the interference signals and/or the data signals sometimes is referred to as “lock-in detection.”

Although the metrology system100″ is shown and described as being in the bright field detection configuration in the manner discussed above with reference toFIG. 6B, it will be appreciated that the metrology system100″ likewise can be provided in the dark field detection configuration in the manner described in more detail above with reference to FIG.6A. Furthermore, if the beam of incident energy500was not modulated in the manner described above with reference toFIG. 14B, the metrology system100″ is configured to analyze simple reflectivity data as a function of the rotation angle φ when provided in the bright field detection configuration. Likewise, when provided in the dark field detection configuration, the metrology system100″ is configured to analyze simple scattering data as a function of the rotation angle φ if the beam of incident energy500was not modulated.

Radio or microwaves have a substantially long wavelength λ relative to the structures comprising the metrology system100and/or to any aperture or lens with reasonable size. As such, the directivity of the incident energy500can become lost such that the incident energy500appears to be coming from a point source. For this reason, the metrology system100can further include a near field cavity system900as shown in FIG.15. An exemplary near field cavity system900is disclosed by Ash et al in 1974, in Nature, the disclosure of which is hereby expressly incorporated herein by reference. The near field cavity system900forms a microwave cavity910that is configured to communicate with a sub-wavelength hole (or aperture)920defined by the near field cavity system900.

The near field cavity system900is configured to provide radiation signals930. These radiation signals930preferably are evanescent and decay substantially exponentially. In operation, the metrology system100can detect the presence of defects in the structure410by measuring an input impedance (not shown) of the cavity910. The input impedance of the cavity910can be readily measured. When the structure410includes a defect (not shown), the near field cavity system900can detect the defect, indicating the detection of the defect via a change in the input impedance.

When the specimen400is vibrated at a preselected frequency and axially relative to the axis of rotation AR, the input impedance of the cavity910can be modulated at the preselected frequency. The measurement system200and/or the energy detector220of the metrology system100can be locked on the preselected frequency. Since the direction of the electric field E outside of the cavity900is a function of the modes within the cavity900. As a result, when the cavity900is rotated about the axis of rotation AR, a spectrum of input impedances can be obtained with respect to the rotation angle φ.

Although the various embodiments have been described with reference to optical waves and microwaves, it will be appreciated that the various embodiments apply to energy with any wavelength, such as x-rays. When the incident energy500comprises x-rays, for example, the angle of illumination θ should approach an angle of approximately ninety degrees (90°). If the angle of illumination θ is too large, the reflected energy500′ is approximately six orders of magnitude down. Therefore, the range of suitable angles of illumination θ comprises a range of very shallow angles when the incident energy500comprises x-rays. To increase the range of suitable angles of illumination θ when the incident energy500comprises x-rays, the beam of incident energy500can be modulated at a preselected frequency and synchronous detection can be performed on the incident energy in the manner described above with reference to the dark field detection configuration of the metrology system100shown in FIG.6A. Thereby, a signal-to-noise ratio of the incident energy500can be improved for angles of illumination θ that approach approximately ninety degrees (90°) such that the range of suitable angles of illumination θ can be expanded when the incident energy500comprises x-rays.

The various embodiments disclosed herein are susceptible to various modifications and alternative forms, and specific examples thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the subject matter disclosed herein is not to be limited to the particular forms or methods disclosed, but to the contrary, the all modifications, equivalents, and alternatives are covered that fall within the spirit and scope of the claims.