Patent Publication Number: US-2023144331-A1

Title: Systems and methods for semiconductor chip surface topography metrology

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 16/910,667, filed on Jun. 24, 2020, which is a continuation of International Application No. PCT/CN2020/076432, filed on Feb. 24, 2020, both of which are hereby incorporated by reference in their entireties. 
    
    
     BACKGROUND 
     Embodiments of the present disclosure relate to metrology systems and methods in semiconductor manufacturing. 
     Surface topography is an important surface property, and it affects the performance of semiconductor products as well as their fabrication processes. For example, the wafer bonding process has been increasingly used to achieve innovative stacking structures in semiconductor devices. Topography, which defines the flatness of the wafer surface, is one of the most key factors to achieve a good bonding result. A successful bonding process requires ultra-precise alignment of two wafers, as well as planarization of the bonding interface. For example, interface topographic defects can cause wafer edge die open issues during the bonding processes, thereby causing serious yield loss or downgrade ratio. 
     SUMMARY 
     Embodiments of systems and methods for measuring a surface topography of a semiconductor chip are disclosed herein. 
     In one example, a method for measuring a surface topography of a semiconductor chip is disclosed. A plurality of interference signals and a plurality of spectrum signals are received by at least one processor. Each of the interference signals and spectrum signals corresponds to a respective one of a plurality of positions on a surface of the semiconductor chip. The spectrum signals are classified by the at least one processor into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. A surface height offset between a surface baseline and at least one of the categories is determined by the at least one processor based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. The surface topography of the semiconductor chip is characterized by the at least one processor based, at least in part, on the surface height offset and the interference signals. 
     In another example, a system for measuring a surface topography of a semiconductor chip includes an interferometer, a spectrometer, a scanning probe microscopy (SPM) or an electron microscope, and at least one processor. The interferometer is configured to provide a plurality of interference signals each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip. The spectrometer is configured to provide a plurality of spectrum signals each corresponding to a respective one of the plurality of positions on the surface of the semiconductor chip. The SPM or the electron microscope is configured to provide a plurality of calibration signals. The at least one processor is configured to classify the spectrum signals into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. The at least one processor is also configured to determine a surface height offset between a surface baseline and at least one of the categories based, at least in part, on at least one of the calibration signals associated with the region corresponding to the at least one of the categories. The at least one processor is also configured to characterize the surface topography of the semiconductor chip based, at least in part, on the surface height offset and the interference signals. 
     In still another example, a tangible computer-readable device has instructions stored thereon that, when executed by at least one computing device, causes the at least one computing device to perform operations. The operations include receiving a plurality of interference signals and a plurality of spectrum signals. Each of the interference signals and spectrum signals corresponds to a respective one of a plurality of positions on a surface of a semiconductor chip. The operations also include classifying the spectrum signals into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. The operations further include determining a surface height offset between a surface baseline and at least one of the categories based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. The operations further include characterizing a topography of the semiconductor chip based, at least in part, on the surface height offset and the interference signals. 
     In yet another example, a method for training a model is disclosed. A model for classifying spectrum signals is provided by at least one processor. A plurality of training samples each including a spectrum signal and a labeled category of the spectrum signal are obtained by the at least one processor. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. A parameter of the model is adjusted by the at least one processor based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
     In yet another example, a system for training a model includes a memory and at least one processor operatively coupled to the memory. The at least one processor is configured to provide a model for classifying spectrum signals. The at least one processor is also configured to obtain a plurality of training samples each including a spectrum signal and a labeled category of with the spectrum signal. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. The at least one processor is further configured to adjust a parameter of the model based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
     In yet another example, a tangible computer-readable device has instructions stored thereon that, when executed by at least one computing device, causes the at least one computing device to perform operations. The operations include providing a model for classifying spectrum signals. The operations also include obtaining a plurality of training samples each including a spectrum signal and a labeled category of with the spectrum signal. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. The operations further include adjusting a parameter of the model based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate embodiments of the present disclosure and, together with the description, further serve to explain the principles of the present disclosure and to enable a person skilled in the pertinent art to make and use the present disclosure. 
         FIG.  1    illustrates a schematic diagram of an exemplary system for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  2 A  illustrates a cross-section of an exemplary semiconductor chip without a transparent layer and an interference signal obtained therefrom, according to some embodiments of the present disclosure. 
         FIG.  2 B  illustrates a cross-section of another semiconductor chip with a transparent layer and another interference signal obtained therefrom, according to some embodiments of the present disclosure. 
         FIG.  3 A  illustrates a diagram of an exemplary interferometer, according to some embodiments of the present disclosure. 
         FIG.  3 B  illustrates a diagram of another exemplary interferometer with a spectrometer, according to some embodiments of the present disclosure. 
         FIG.  4 A  illustrates exemplary constituent lights of a white light source, according to some embodiments of the present disclosure. 
         FIG.  4 B  illustrates an exemplary interference signal generated by the constituent lights of the white light source in  FIG.  4 A , according to some embodiments of the present disclosure. 
         FIG.  5 A  illustrates exemplary constituent lights of a Xenon (Xe) lamp, according to some embodiments of the present disclosure. 
         FIG.  5 B  illustrates an exemplary interference signal generated by the constituent lights of the Xe lamp in  FIG.  5 A , according to some embodiments of the present disclosure. 
         FIG.  6    illustrates a schematic diagram of an exemplary computing device of the system in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  7 A  illustrates exemplary eight interference signals, according to some embodiments of the present disclosure. 
         FIG.  7 B  illustrates the exemplary eight interference signals in  FIG.  7 A  classified into four categories, according to some embodiments of the present disclosure. 
         FIGS.  8 A and  8 B  illustrate exemplary processes of surface height offset calibration and calibrated surface height calculation, according to some embodiments of the present disclosure. 
         FIG.  9    is a flowchart of an exemplary method for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  10    is a flowchart of an exemplary method for calculating a calibrated surface height, according to some embodiments of the present disclosure. 
         FIG.  11    is a flowchart of an exemplary method for generating a calibrated height map, according to some embodiments of the present disclosure. 
         FIG.  12    illustrates exemplary original height map, classification map, and calibrated height map, according to some embodiments of the present disclosure. 
         FIG.  13    illustrates a schematic diagram of another exemplary computing device of the system in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  14 A  illustrates exemplary  12  interference signals, according to some embodiments of the present disclosure. 
         FIG.  14 B  illustrates  12  spectrum signals transformed from the exemplary  12  interference signals in  FIG.  14 A , according to some embodiments of the present disclosure. 
         FIG.  15    is a flowchart of another exemplary method for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  16    is a flowchart of another exemplary method for generating a calibrated height map, according to some embodiments of the present disclosure. 
         FIG.  17    illustrates a schematic diagram of still another exemplary computing device of the system in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  18    is a flowchart of still another exemplary method for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. 
         FIG.  19    is a flowchart of still another exemplary method for generating a calibrated height map, according to some embodiments of the present disclosure. 
         FIG.  20    illustrates exemplary semiconductor chip surface pattern, original height map, spectrum signals, and classification map, according to some embodiments of the present disclosure. 
         FIG.  21    illustrates a schematic diagram of an exemplary system for training a model for surface topography characterization, according to some embodiments of the present disclosure. 
         FIG.  22    a flowchart of an exemplary method for training a model for surface topography characterization, according to some embodiments of the present disclosure. 
         FIG.  23    a flowchart of another exemplary method for training a model for surface topography characterization, according to some embodiments of the present disclosure. 
         FIG.  24    illustrates a block diagram of an exemplary computing device, according to some embodiments of the present disclosure. 
     
    
    
     Embodiments of the present disclosure will be described with reference to the accompanying drawings. 
     DETAILED DESCRIPTION 
     Although specific configurations and arrangements are discussed, it should be understood that this is done for illustrative purposes only. A person skilled in the pertinent art will recognize that other configurations and arrangements can be used without departing from the spirit and scope of the present disclosure. It will be apparent to a person skilled in the pertinent art that the present disclosure can also be employed in a variety of other applications. 
     It is noted that references in the specification to “one embodiment,” “an embodiment,” “an example embodiment,” “some embodiments,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. Further, when a particular feature, structure or characteristic is described in connection with an embodiment, it would be within the knowledge of a person skilled in the pertinent art to effect such feature, structure or characteristic in connection with other embodiments whether or not explicitly described. 
     In general, terminology may be understood at least in part from usage in context. For example, the term “one or more” as used herein, depending at least in part upon context, may be used to describe any feature, structure, or characteristic in a singular sense or may be used to describe combinations of features, structures or characteristics in a plural sense. Similarly, terms, such as “a,” “an,” or “the,” again, may be understood to convey a singular usage or to convey a plural usage, depending at least in part upon context. In addition, the term “based on” may be understood as not necessarily intended to convey an exclusive set of factors and may, instead, allow for existence of additional factors not necessarily expressly described, again, depending at least in part on context. 
     As used herein, the term “substrate” refers to a material onto which subsequent material layers are added. The substrate itself can be patterned. Materials added on top of the substrate can be patterned or can remain unpatterned. Furthermore, the substrate can include a wide array of semiconductor materials, such as silicon, germanium, gallium arsenide, indium phosphide, etc. Alternatively, the substrate can be made from an electrically non-conductive material, such as a glass, a plastic, or a sapphire wafer. 
     As used herein, the term “layer” refers to a material portion including a region with a thickness. A layer can extend over the entirety of an underlying or overlying structure or may have an extent less than the extent of an underlying or overlying structure. Further, a layer can be a region of a homogeneous or inhomogeneous continuous structure that has a thickness less than the thickness of the continuous structure. For example, a layer can be located between any pair of horizontal planes between, or at, a top surface and a bottom surface of the continuous structure. A layer can extend horizontally, vertically, and/or along a tapered surface. A substrate can be a layer, can include one or more layers therein, and/or can have one or more layer thereupon, thereabove, and/or therebelow. A layer can include multiple layers. For example, an interconnect layer can include one or more conductor and contact layers (in which interconnect lines and/or via contacts are formed) and one or more dielectric layers. 
     Atomic force microscopy (AFM) is one of the common methods for topography measurement. However, it suffers from low throughput, which severely constrains AFM&#39;s inline usage and also limits troubleshooting efficiency and learning cycle frequency. Another category of topography metrology includes electron microscopy, such as scanning electron microscopy (SEM) or transmission electron microscopy (TEM), which suffers from long cycle time and wafer consumption. Also because of the actual topography can be within 100 nm in some situations, but the measurement range can be at the micrometer level, SEM/TEM is not reliable due to more than 1,000 times of X/Y ratio. 
     Compared with AFM and SEM/TEM, white light interferometry (WLI) is a more practical and efficient method for topography characterization, of whose throughput can be more than 100 times higher than AFM, and it also enables die-level large area measurement. WLI, unlike laser-based interferometry, is featured of a signal envelope in the spatial domain to show the exact and resolvable height information from a certain reflective surface. However, the accuracy and precision of the conventional WLI approach for wafer surface topography measurements are lower than those of AFM. 
     Various embodiments in accordance with the present disclosure provide efficient systems and methods of inline surface topography metrology with high throughput suitable for semiconductor chip mass production while still maintaining sufficient accuracy and precision. According to some aspects of the present disclosure, signals from optical measurements, such as interference signals or spectrum signals, combined with machine learning models, can enable high throughput, inline measurement of semiconductor chip surface topography without the necessity of opaque film deposition and consumption of product wafers. In some embodiments, interference signals, such as low coherent interference infringes, are classified into several categories (e.g., using machine learning), each of which is added with a respective surface height offset calibrated from another measurement, for example, AFM or SEM/TEM. As a result, calibrated surface heights (and a calibrated height map therefrom in some cases) of a semiconductor chip having multiple layers can be readily attained with high accuracy and precision. In some embodiments, spectrum signals, such as reflectance spectrums which contain the sample&#39;s material and structure information, are obtained either directly from a spectrometer or indirectly from interference signals (e.g., using Fourier transform) can be similarly classified into several categories (e.g., using another machine learning model), each of which is added with its intrinsic surface height offset calibrated from, for example, AFM or SEM/TEM measurement. 
     According to some aspects of the present disclosure, the light source spectrum can be manipulated, such as being extending to a wider range (e.g., using a Xe lamp), with minimum or no change to the optical elements and detector of the system. A larger range of spectrum would yield narrower signals. The width of the low coherent interference fringe can thus be reduced, thereby improving the signal-to-noise ratio (SNR) and repeatability of the surface topography measurement. As a result, the overlap-free zone (i.e., film thickness) of the test sample can be extended since the thickness requirement can be reduced by the extended light source spectrum. 
       FIG.  1    illustrates a schematic diagram of an exemplary system  100  for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. System  100  can include a computing device  102  having at least one processor that implements the various functions disclosed herein for measuring surface topography  116  of a semiconductor chip, such as classification using machine learning models, surface height derivation and calibration, and signal transformation. System  100  can also include one or more optical measuring instruments that can provide one or more types of signals sampled from the surface of a semiconductor chip, which are used as the input signals for surface topography characterization by computing device  102 . In some embodiments, the optical measuring instruments of system  100  include an interferometer  104  configured to provide a plurality of interference signals  110  each corresponding to a respective one of a plurality of positions on the surface of a semiconductor chip. In some embodiments, the optical measuring instruments of system  100  also include a spectrometer  106  configured to provide a plurality of spectrum signals  112  each corresponding to a respective one of the plurality of positions on the surface of the semiconductor chip. That is, a plurality of positions on the surface of a semiconductor chip can be sampled, and interference signals  110  and spectrum signals  112  sampled from those positions can be obtained by interferometer  104  and spectrometer  106 , respectively. It is understood that in some embodiments, spectrometer  106  may not be included in system  100 . In one example, interference signals  110 , but not spectrum signals  112 , may be used as the input signals of computing device  102 . In another example, interference signals  110  may be transformed into spectrum signals  112 , and both interference signals  110  and spectrum signals  112  may be used as the input signals of computing device  102 . 
       FIG.  2 A  illustrates a cross-section of an exemplary semiconductor chip  202  without a transparent layer and an interference signal obtained therefrom, according to some embodiments of the present disclosure. The interference signal can be obtained by, for example, interferometer  104  of system  100  in  FIG.  1    using interferometry. Interferometry is a family of techniques in which waves, usually electromagnetic waves, are superimposed, causing the phenomenon of interference, which is used to extract information. Interferometers are widely used in science and industry for the measurement of small displacements, refractive index changes, and surface irregularities. In interferometers, light from a single source can be split into two beams that travel in different optical paths, which are then combined again to produce interference. The resulting interference signals, such as interference fringes, can provide information about the difference in optical path lengths. As one type of interferometry, low coherent interferometry is a non-contact optical method for surface topography measurement that relies on spectrally-broadband, such as visible-wavelength light (i.e., white light). Low coherent interferometry technology employs low coherence characteristics of for example, white light to generate interference waves by reflecting light from the sample surface and a reference surface through a beam splitter which, in turn, is used to get the surface profile based on the optical path difference. 
     As shown in  FIG.  2 A , the sample is semiconductor chip  202 , and a white light  206  is illuminated at a position on the surface of semiconductor chip  202  and is reflected from the surface of semiconductor chip  202 . Semiconductor chip  202  can include a logic device chip, such as a central processing unit (CPU), a graphics processing unit (GPU), an application processor (AP), a programmable logic device (PLD), or a microcontroller unit (MCU), a memory device chip, such as Flash memory, dynamic random-access memory (DRAM), or static random-access memory (SRAM), or any other suitable semiconductor chips. It is understood that semiconductor chip  202  is not limited to the final product and may include any intermediate structures during the fabrication processes or a bare wafer. For example, semiconductor chip  202  may include wafers to be bonded before a bonding process, such as hybrid bonding. As used herein, a “wafer” is a piece of a semiconductor material for semiconductor devices to build in and/or on it and that can undergo various fabrication processes before being separated into dies. A bare wafer is a wafer in its original form before undergoing any fabrication process. The wafer can include silicon (e.g., single crystalline silicon), silicon germanium (SiGe), gallium arsenide (GaAs), germanium (Ge), silicon on insulator (SOI), or any other suitable materials. In one example, the wafer may be a silicon wafer. Nevertheless, the surface topography of semiconductor chip  202  needs to be measured for quality control before, during, or after the fabrication process, according to some embodiments. 
     In some embodiments, the position at which white light  206  is illuminated in  FIG.  2 A  is in an opaque layer, such as the surface of a silicon substrate or any layers formed on the silicon substrate with opaque materials including, for example, metals (e.g., copper, tungsten, cobalt, etc.), polysilicon, to name a few. An interference signal corresponding to the position in an opaque layer at the surface of semiconductor chip  202  includes an interference fringe  208  (also known as a “signal envelope”) of low coherent interferometry, which shows how the superimposed signals for the constituent wavelengths result in high fringe contrast at the point where all the patterns agree in phase—the so-called stationary phase position, according to some embodiments. The surface height at the position can thus be resolved and derived from interference fringe  208  of the interference signal. In other words, the interference signal is associated with the original surface height at the position, according to some embodiments. 
     A more challenging case is a sample coated with transparent thin-film layers.  FIG.  2 B  illustrates a cross-section of another exemplary semiconductor chip  203  with a transparent layer  204  and another interference signal obtained therefrom, according to some embodiments of the present disclosure. It is understood that in some embodiments, semiconductor chip  203  may be the same chip as semiconductor chip  202 , while white light  206  is illuminated at a different position in transparent layer  204 , such as the surface of a glass substrate or any layers formed on a silicon or glass substrate with transparent materials including, for example, silicon oxide or silicon nitride. 
     As shown in  FIG.  2 B , white light  206  is reflected at various interfaces, such as the top surface of transparent layer  204 , the top surface of the opaque layer (e.g., the substrate surface), as well as an echo resulting from the internal reflection between the top surface and the substrate surface, according to some embodiments. As a result, another interference signal corresponding to the position in transparent layer  204  at the surface of semiconductor chip  203  includes another interference fringe  210  of low coherent interferometry. Different from interference fringe  208  in  FIG.  2 A , interference fringe  210  can include three components: a top surface reflection component  212  corresponding to the top surface of transparent layer  204 , a substrate component  214  corresponding to the substrate of semiconductor chip  203 , and an internal reflection component  216  corresponding to the echo resulting from the internal reflection. Compared with the interference signal corresponding to a position in an opaque layer, the interference signal corresponding to a position in a transparent layer has a more complex interference fringe from which a surface height may not be accurately and precisely resolved. That is, for semiconductor chips with multiple layers, in particular one or more transparent layers, the incoherent superposition interference signal includes summing the interference contributions of light intensity from multiple layers, which may not be suitable for direct derivation of surface height information therefrom. As described below in detail, machine learning models run by computing device  102  can filter the complication of the input signals, such as interference signals having multi-component interference fringe, into categories without knowing the actual structure, thereby improving the accuracy and precision of surface topography measurement. 
       FIG.  3 A  illustrates a diagram of an exemplary interferometer  300 , according to some embodiments of the present disclosure. Interferometer  300  may be one example of interferometer  104  in  FIG.  1   , such as a low coherent interferometer. Interferometer  300  can include a light source  302 , a detector  304 , a sample holder  306  holding a sample  308 , and a scanner  310 . In some embodiments, interferometer  300  is a white-light interferometric microscope, which combines an interferometer with the optics of a microscope including, for example, tube lens, condenser lens, beam splitter, objective lens mirrors, etc. Scanner  310  can be an accurate positioning stage (e.g., a piezoelectric actuator) configured to move the objective (e.g., a Mirau objective) vertically. The interference signal of a pixel has maximum modulation when the optical path length of light impinging on the pixel is the same for the reference and the object beams, according to some embodiments. As such, the surface height of the position on the surface of sample  308  by this pixel corresponds to the z-value of scanner  310  when the modulation of the correlogram is the greatest. It is understood that although interferometer  300  is illustrated as a Mirau interferometer having a Mirau objective, interferometer  300  may be any other suitable types of interferometers, such as a Twyman—Green interferometer having a Twyman—Green objective. It is further understood that in some embodiments, a database  312  may be connected to detector  304  to store the interference signals or any other information associated with the interference signals, such as the original surface heights derived from the interference signals, for future processing. 
     Light source  302  can include any suitable light sources for low coherent interferometry. In some embodiments, light source  302  includes a white light source including, but not limited to incandescent lamps (e.g., tungsten-halogen lamps), fluorescent lamps, and white light light-emitting diodes (LEDs). The range of wavelengths of the spectrum of light source  302  can be between about 400 nm and about 900 nm, such as between 400 nm and between 900 nm. In some embodiments, the range of wavelengths of the spectrum of light source  302  is the same range of wavelengths of the spectrum of white light (also known as “visible spectrum”), e.g., between about 400 nm and about 700 nm, such as between 400 nm and 700 nm.  FIG.  4 A  illustrates exemplary constituent lights of a white light source, according to some embodiments of the present disclosure. The constituent lights of a white light source can include red, green, and blue lights as shown in  FIG.  4 A . In some embodiments, the constituent lights may further include violet, cyan, yellow, and orange lights. 
       FIG.  4 B  illustrates an exemplary interference signal generated by the constituent lights of the white light source in  FIG.  4 A , according to some embodiments of the present disclosure. In this example, the range of wavelengths of the spectrum of the white light source is between 400 nm and 900 nm, and the x-axis and y-axis represent the z-value of the scanner and the interference signal strength, respectively. As shown in  FIG.  4 B , the interference signal includes an interference fringe having the width w of about 2 μm. It is understood that when the interference signal corresponds to a position in a transparent layer at the sample surface, multiple components of the interference fringe may be overlapped (superposition) to increase the width of the interference fringe and/or have multiple peaks (e.g.,  210  in  FIG.  2 B ), which lowers the SNR compared to theoretical Gaussian distribution. For both direct derivation of surface height and classification using machine learning, a narrower and simpler interference fringe (e.g., having a single narrow peak) in an interference signal is preferred as it has the higher SNR, vertical resolution, and repeatability, which in turn can be used to measure the surface topography of a semiconductor chip having a thinner transparent layer. 
     Referring back to  FIG.  3 A , the spectrum of light source  302  can be extended to a wider range in order to reduce the width of the interference fringe of the interference signal as the width of the interference fringe depends on the spectrum width of light source  302 , thereby improving the SNR, vertical resolution, and repeatability of the interference signal. Moreover, the overlap-free zone (e.g., transparent layer thickness) can be in turn extended since the thickness requirement can be reduced accordingly. In some embodiments, the spectrum of light source  302  is greater than the spectrum of white light. For example, the spectrum of light source  302  may further include at least one of ultraviolet (UV) light or infrared (IR) light. In some embodiments, the range of wavelengths of the spectrum of light source  302  is greater than the range between about 400 nm and about 700 nm (e.g., visible spectrum), such as greater than the range between 400 nm and 700 nm. That is, the wavelengths of the spectrum of light source  302  can be smaller than 400 nm and/or larger than 700 nm. In some embodiments, the range of wavelengths of the spectrum of light source  302  is greater than the range between about 400 nm and about 900 nm, such as greater than the range between 400 nm and 900 nm. That is, the wavelengths of the spectrum of light source  302  can be smaller than 400 nm and/or larger than 900 nm. In one example, the range of wavelengths of the spectrum of light source  302  may be between about 190 nm and about 1,100 nm, such as between 190 nm and 1,100 nm. Light source  302  can include any suitable light sources that can emit lights having a broader spectrum wavelength range than the white light, for example, metal halide lamps. In some embodiments, light source  302  includes a Xe lamp, such as a Xe arc lamp or a Xe flash lamp. 
     Accordingly, the interference signal can include an interference fringe having the width not greater than about 2 μm, such as not greater than 2 μm (e.g., 2 μm, 1.9 μm, 1.8 μm, 1.7 μm, 1.6 μm, 1.5 μm, 1.4 μm, 1.3 μm, 1.2 μm, 1.1 μm, 1 μm, 0.9 μm, 0.8 μm, 0.7 μm, 0.6 μm, 0.5 μm, 0.4 μm, 0.3 μm, 0.2 μm, 0.1 μm, any range bounded by the lower end by any of these values, or in any range defined by any two of these values). In some embodiments, the width of the interference fringe is about 1.2 μm, such as 1.2 μm. Consequently, the minimum thickness of the transparent layer on the sample (e.g., a semiconductor device) is not greater than about 2 μm, such as not greater than 2 μm (e.g., 2 μm, 1.9 μm, 1.8 μm, 1.7 μm, 1.6 μm, 1.5 μm, 1.4 μm, 1.3 μm, 1.2 μm, 1.1 μm, 1 μm, 0.9 μm, 0.8 μm, 0.7 μm, 0.6 μm, 0.5 μm, 0.4 μm, 0.3 μm, 0.2 μm, 0.1 μm, any range bounded by the lower end by any of these values, or in any range defined by any two of these values). In some embodiments, the minimum thickness of the transparent layer is about 1.2 μm, such as 1.2 μm. 
       FIG.  5 A  illustrates exemplary constituent lights of a Xe lamp, according to some embodiments of the present disclosure. The constituent lights of a Xe lamp can include red, green, and blue lights in the white light, as well as UV and IR lights not in the white light.  FIG.  5 B  illustrates an exemplary interference signal generated by the constituent lights of the Xe lamp in  FIG.  5 A , according to some embodiments of the present disclosure. In this example, the range of wavelengths of the spectrum of the Xe lamp is between 190 nm and 1,100 nm, and the x-axis and y-axis represent the z-value of the scanner and the interference signal strength, respectively. As shown in  FIG.  5 B , the interference signal includes an interference fringe having the width w of about 1.2 μm. That is, compared with the example shown in  FIG.  4 B , by extending the wavelength range of the light source spectrum, a narrower interference fringe can be obtained in the interference signal in  FIG.  5 B , which has the higher SNR, vertical resolution, and repeatability. 
     Referring back to  FIG.  3 A , besides spectrum extension at light source  302  to narrow the interference fringe of the interference signal, the interference signal can be manipulated in any other suitable manners, e.g., by combining or subtracting spectrums, to create the desired signal shape for future processing, such as signal classification or direct surface height derivation. In some embodiments, interferometer  300  further includes one or more optical elements configured to manipulate the spectrum of light source  302 . The optical elements include at least one of a filter or an antireflection film, according to some embodiments. 
     In some embodiments, interferometer  300  includes detector  304  suitable for low coherent interferometry. Interference occurs at detector  304  if the optical path lengths of the two arms differ less than half the coherence length of light source  302 , according to some embodiments. Each pixel of detector  304  can sample a different position within the image of the surface of sample  308 . In some embodiments, detector  304  includes a white light charge-coupled device (CCD) or a white light charge complementary metal-oxide-semiconductor (CMOS) image sensor. The white light CCD or white light CMOS image sensor can be used for detecting light source  302  having a white light spectrum as well as having a Xe lamp spectrum (e.g., between 190 nm and 1,100 nm). That is, the same white light CCD or white light CMOS image sensor can be used as detector  304  regardless of whether light source  302  is a white light source or a Xe lamp. 
     As described above with respect to  FIG.  1   , spectrum signals are another type of signals obtained from optical measurements, which can reveal the surface structure and material information.  FIG.  3 B  illustrates a diagram of another exemplary interferometer  301  with a spectrometer  316 , according to some embodiments of the present disclosure. Spectrometer  316  may be one example of spectrometer  106  in  FIG.  1   , such as an optical spectrometer (also known as “spectrophotometer” or “spectroscope”). Compared with interferometer  300  shown in  FIG.  3 A , another beam splitter  318  and spectrometer  316  can be added interferometer  301  to be able to provide both interference signals and spectrum signals each corresponding to a respective one of a plurality of positions on the surface of sample  308  (e.g., a semiconductor chip). As shown in  FIG.  3 B , the reference light and reflected object light are split by beam splitter  318  to be transmitted to both detector  304  and spectrometer  316 . Spectrometer  316  can include any suitable optical spectrometers that show the intensity of light as a function of wavelength or frequency. An optical spectrometer is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum. In some embodiments, the variable measured by spectrometer  316  includes reflectance or reflectivity, and each spectrum signal provided by spectrometer  316  includes a reflectance spectrum. The reflectance of the surface of sample  308  is its effectiveness in reflecting radiant energy, which is the fraction of incident electromagnetic power that is reflected at an interface. The reflectance spectrum can represent the reflectance as a function of wavelength, which is associated with the surface structure and material. It is understood that in some embodiments, the spectrum signals provided by spectrometer  316  may be stored in database  312  as well. 
     Referring back to  FIG.  1   , the input signals (e.g., interference signals  110  and spectrum signals  112 ) from the optical measuring instruments (e.g., interferometer  104  and spectrometer  106 ) of system  100  can be sampled at a higher throughput than the input signals from conventional surface topography measuring instruments, such as AFM and SEM/TEM, without damaging the sample (e.g., a semiconductor chip). To compensate for the low accuracy and precision of surface topography measurement associated with the optical measurements, system  100  can further include a scanning probe microscopy (SPM) or an electron microscope (EM)  108  configured to provide a plurality of calibration signals  114  to computing device  102  for surface height calibration. SPM can include, but not limited to, an AFM or a scanning tunneling microscope (STM). EM can include, but not limited to an SEM or a TEM. SPM/EM 108 can provide surface topography information at higher accuracy and precision, but with lower throughput, which is suitable as the calibration signals instead of the input signals. By combining the input signals (e.g., interference signals  110  or spectrum signals  112 ) with higher throughput and calibration signals  114  with higher accuracy and precision, system  100  can provide surface topography  116  of a semiconductor chip efficiently and effectively. 
       FIG.  6    illustrates a schematic diagram of an exemplary computing device  600  of system  100  in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Computing device  600  may be one example of computing device  102  in  FIG.  1   . Computing device  600  can include a plurality of functional modules and units implemented by at least one processor. In some embodiments, computing device  600  includes an interference signal classifier  602 , a calibration module  604 , a characterization module  606 , and a surface height calculation unit  610 . A model  608  for classifying interference signals, run by computing device  600 , is used by interference signal classifier  602 , according to some embodiments. As described below in detail, model  608  can be a machine learning model trained for classifying interference signals. A plurality of interference signals  612  sampled by interferometer  104  (shown in  FIG.  1   ) are provided as inputs of computing device  600  for classification and surface height calculation, according to some embodiments. In some embodiments, a plurality of calibration signals  614  sampled by SPM/EM 108 (shown in  FIG.  1   ) are also provided as inputs of computing device  600  for post-classification calibration. 
     In some embodiments, interference signal classifier  602  is configured to receive a plurality of interference signals  612  each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip. As described above, the surface of a semiconductor chip (e.g., the top surface on which semiconductor devices are formed) can be sampled at various positions at any suitable interval or pitch in a sampling field (e.g., the entire die or a portion thereof) to obtain interference signals  612 . As such, each interference signal  612  can correspond to a respective sampling position on the surface. The surface height at each sample position (referred to herein as the “original surface height”) can be resolved and derived from respective interference signal  612  as described above. That is, each interference signal  612  is associated with an original surface height at the respective sampling position in the sampling field, according to some embodiments. In some embodiments, each interference signal  612  includes an interference fringe of low coherent interferometry (e.g.,  208  in  FIG.  2 A and  210    in  FIG.  2 B ). The semiconductor chip can include multiple layers. In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer or a silicon nitride layer. In some embodiments, the sampling field includes the transparent layer. Thus, at least one of interference signals  612  can include a multi-component interference fringe of low coherent interferometry (e.g.,  210  in  FIG.  2 B ), i.e., an incoherent superposition signal having interference contributions of light intensity from multiple layers. 
     In some embodiments, interference signal classifier  602  is further configured to classify interference signals  612  into a plurality of categories using model  608 . Each of the categories corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. Model  608  can include a classification model. Classification is the process of predicting the categories (also known as “classes”) of given data points, according to some embodiments. In some embodiments, a classification model, implemented by a classification algorithm, includes a mapping function (f) from input variables (e.g., interference signals  612 ) to discrete output variables (e.g., the categories). Model  608  can include, but not limited to, k-nearest neighbor (KNN), case-based reasoning, decision tree, naive Bayes, artificial neural network (ANN), logistic regression, Fisher&#39;s linear discriminant, support vector machine (SVM), or perceptron. In some embodiments in which model  608  includes a classification model, as part of the supervised learning, the categories are known and predetermined. For example, each category may correspond to a region having the same material on the surface of the semiconductor chip. That is, based on the design of the semiconductor chip, e.g., the structures and materials in the sampling field, a plurality of categories can be identified and used as the labels for the training as well as the output variables for classification. In one example, a first category may correspond to a first region of silicon oxide (a transparent layer), a second category may correspond to a second region of tungsten (an opaque layer), and a third category may correspond to a third region of silicon substrate (an opaque layer) in the sampling field on the surface of the semiconductor chip. 
     In some embodiments, model  608  includes a clustering model. Clustering is the task of grouping a set of objects in such a way that objects in the same group (known as a “cluster”) are more similar to each other than to those in other clusters. Model  608  can include, but not limited to, linkage clustering, k-means clustering, Gaussian mixture model clustering, or density-based clustering. In some embodiments in which model  608  includes a clustering model, as part of the unsupervised learning, the categories used by interference signal classifier  602  are not predetermined. In some embodiments, interference signal classifier  602  is configured to cluster interference signals  612  into a plurality of clusters using model  608  (e.g., a clustering model) and adjust the clusters to become the categories used by interference signal classifier  602  based, at least in part, on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material. In other words, clusters can be learned first in an unsupervised manner, and the categories can be determined from the clusters in a supervised manner based on, for example, the structures and materials in the sampling field. In one example, a cluster that does not correspond to a region having the same material in the sampling field may be disregarded. In another example, multiple clusters that correspond to the same region having the same material or correspond to different regions have the same material may be merged. 
     In some embodiments, any suitable feature selection and feature extraction approaches can be applied to interference signals  612  by interference signal classifier  602  to select and/or extract features (e.g., feature vectors), either latent features or patent features, from each interference signal  612  to reduce the complexity and improve the efficiency of the classification process. In one example, model  608  may include KNN, and 10-dimensional feature vectors may be extracted from each interference signal  612  for classification using the KNN model by interference signal classifier  602 . 
       FIG.  7 A  illustrates exemplary eight interference signals, according to some embodiments of the present disclosure. As shown in  FIG.  7 A , each of the eight interference signals includes a multi-component interference fringe, which corresponds to a respective position in a transparent layer in the sampling field on the sample surface.  FIG.  7 B  illustrates the exemplary eight interference signals in  FIG.  7 A  classified into four categories, according to some embodiments of the present disclosure. Each of the four categories corresponds to a respective region in the sampling field having the same material. The categories can be predetermined or adjusted from a number of clusters determined using a clustering model. The eight interference signals are classified into the four categories using model  608  by interference signal classifier  602 , according to some embodiments. As shown in  FIG.  7 B , each category includes interference signals that have substantially similar interference fringes, which indicates the same material and/or structure at the respective sampling positions. 
     Referring back to  FIG.  6   , in some embodiments, calibration module  604  is configured to determine a surface height offset between a surface baseline and at least one of the categories based, at least in part, on a calibration signal  614  associated with the region corresponding to the at least one of the categories. That is, a respective surface height offset can be added to each category based on the same surface baseline for calibration to increase the accuracy and precision of the surface topography. As the first type of inputs, the categories and interference signals  612  classified into each category can be provided by interference signal classifier  602  to calibration module  604 . As the second type of inputs, calibration signals  614  can be provided by, for example, SPM/EM 108 (shown in  FIG.  1   ), to calibration module  604 . Calibration signals  614  are signals that presumably can provide higher accuracy and precision than interference signals  612  in terms of indicating the surface height information of the sample, but with lower throughput or may damage the sample. In some embodiments, each calibration signal  614  is associated with a topographic height determined by an SPM or an electron microscopy. Depending on the specific instrument providing calibration signals  614 , calibration signals  614  can include AFM signals from an AFM, SEM signals from an SEM, or TEM signals from a TEM. 
     In some embodiments, a third type of inputs—original surface heights are provided to calibration module  604  by surface height calculation unit  610  based on interference signals  612 . As described above, each interference signal  612  is associated with an original surface height at the respective position, and surface height calculation unit  610  is configured to derive the original surface height at the respective position in the sampling field by resolving corresponding interference signal  612 , according to some embodiments. For example, the z-value (representing the original surface height) for the position on the surface imaged by this pixel may correspond to the z-value of the positioning stage (e.g., scanner  310  in  FIGS.  3 A and  3 B ) when the modulation of the correlogram is the greatest (represented by the peak in the interference fringe). 
     The surface baseline can be preset to any suitable value, such as 0. In some embodiments, to determine the surface height offset, calibration module  604  is configured to designate the surface baseline to a baseline region corresponding to one of the categories. In one example, calibration module  604  may select a region in the sampling field that corresponds to the category having the largest number of interference signals  612  as the baseline region and may designate the surface baseline, e.g., 0, as the surface height offset of the baseline region. In another example, calibration module  604  may select the largest region having the same material in the sampling field as the baseline region and designate the surface baseline, e.g., 0, as the surface height offset of the baseline region. In still another example, calibration module  604  may select the region having a specific material (e.g., silicon substrate region) in the sampling field and designate the surface baseline, e.g.,  0 , as the surface height offset of the baseline region. 
     In some embodiments, to determine the surface height offset, calibration module  604  is configured to receive calibration signal  614  and a baseline signal corresponding to the baseline region. In some embodiments, the baseline signals are those calibration signals  614  that are obtained from the baseline region, e.g., the largest region or the silicon substrate region, in the sampling field. For example, SPM/EM 108 may measure calibration signals  614  across multiple regions, including the baseline region, in the sampling field on the surface of a semiconductor chip, and one or more calibration signals  614  corresponding to the baseline region may be used as the baseline signals. The calibration can be performed following a calibration pattern in the sampling field. That is, calibration signals  614 , including the baseline signals, can be measured in the calibration pattern, for example, a line or an area across multiple regions, including the baseline region, in the sampling field. Similar to other calibration signals  614 , each baseline signal is associated with a topographic height determined by an SPM or an electron microscopy, according to some embodiments. 
     In some embodiments, to determine the surface height offset, calibration module  604  is configured to determine the surface height offset based, at least in part, on calibration signal  614 , the baseline signal, and interference signals  612 . In case more than one baseline signal or more than one calibration signal  614  are received, the mean value of multiple baseline signals or the mean value of multiple calibration signals  614  can be used for determining the surface height offset of the corresponding region (and the category associated with the region). It is understood that any other suitable values determined based on multiple baseline signals or calibration signals  614 , such as the median value, the maximum value, or the minimum value, may be used for determining the surface height offset of the corresponding region as well. Interference signals  612  that correspond to the positions in the calibration pattern are used for calibration, e.g., determining the surface height offsets. Similarly, in case more than one interference signal  612  is received, the mean value of multiple interference signals  612  can be used for determining the surface height offset of the corresponding region (and the category associated with the region). It is understood that any other suitable values determined based on multiple interference signals  612 , such as the median value, the maximum value, or the minimum value may be used for determining the surface height offset of the corresponding region as well. 
       FIGS.  8 A and  8 B  illustrate exemplary processes of surface height offset calibration and calibrated surface height calculation, according to some embodiments of the present disclosure. As shown in  FIG.  8 A , interference signals  612  may be classified into two categories A and B, each corresponding to a respective region  802  or  804  in the sampling field on the surface of a semiconductor device. Category A may be designated as the baseline region since region  802  is larger than region  804  and/or since region  802  is a silicon substrate region. Calibration may be performed following a calibration pattern  806 , e.g., a straight line across both regions  802  and  804 , for example, using AFM. Multiple positions in calibration pattern  806  may be sampled to obtain multiple AFM signals, including the baseline signals in region  802 . The AFM signals in region  804  may be averaged to obtain a calibration signal of region  804  (category B), and the AFM signals in region  802  may be averaged to obtain a baseline signal of region  802  (category A). The topographic height A of region  802  and the topographic height B of region  804  may be determined based on the average calibration signal and the average baseline signal, respectively. 
     As shown in  FIG.  8 B , the difference between topographic height A and topographic height B, i.e., the topographic step height HA, then may be obtained. The difference between original surface height A and original surface height B, i.e., the interference step height HI may be determined based on the interference signals corresponding to the positions in calibration pattern  806 , for example, by surface height calculation unit  610  in  FIG.  6   . By setting region  802  as the baseline region with the surface baseline equal to 0, the surface height offset O of region  804  may be determined according to the equation: O═HA—HI. Accordingly, the surface height offset associated with category B is HA—HI, and the surface height offset associated with category A is 0 (i.e., the value of surface baseline). It is understood that if more than two categories are classified, the surface height offsets of each other category may be determined in the same manner. 
     Referring back to  FIG.  6   , characterization module  606  is configured to characterize the surface topography of the semiconductor chip based, at least in part, on the surface height offset and interference signals  612 . In some embodiments, to characterize the surface topography of the semiconductor chip, characterization module  606  is further configured to calculate a calibrated surface height at one of the positions on the surface of the semiconductor chip based, at least in part, on the corresponding original surface height and the surface height offset. That is, for any specific position on the surface of the semiconductor chip, its original surface height can be derived from corresponding interference signal  612  by surface height calculation unit  610 , and can be classified into one of the categories by interference signal classifier  602  as described above. The surface height offset of the category in which the specific position is classified can be determined by calibration module  604  as described above. Accordingly, the calibrated surface height of the specific position, which presumably has higher accuracy and precision, can be calculated by adding the surface height offset to its original surface height. The calibrated surface heights of any desired number of positions on the surface of the semiconductor chip can be calculated in the same manner to characterize the surface topography of the semiconductor chip in any suitable forms, such as a calibrated height map of the semiconductor chip surface described below in detail. As a result, by using interference signal classifier  602  based on interference signals  612  and model  608 , the surface topography of the semiconductor chip can be characterized with high throughput. By using calibration module  604  based on calibration signals  614 , the accuracy and precision of the surface topography of the semiconductor chip can be maintained at the desired level. 
       FIG.  9    is a flowchart of an exemplary method  900  for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Examples of the device that can perform operations of method  900  include computing device  600  depicted in  FIG.  6   . It is understood that the operations shown in method  900  are not exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than shown in  FIG.  9   . 
     Referring to  FIG.  9   , method  900  starts at operation  902 , in which a plurality of interference signals each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip are received. For example, interference signals  612  may be received by interference signal classifier  602  of computing device  600 . In some embodiments, each interference signal includes an interference fringe of low coherent interferometry and is associated with an original surface height at the respective position. In some embodiments, the semiconductor chip includes multiple layers, and at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer or a silicon nitride layer. 
     Method  900  proceeds to operation  904 , as illustrated in  FIG.  9   , in which the interference signals are classified into a plurality of categories using a model. Each of the categories can correspond to a region having the same material on the surface of the semiconductor chip. For example, interference signals  612  may be classified into multiple categories using model  608  by interference signal classifier  602  of computing device  600 . In some embodiments, the model includes a classification model, and the categories are predetermined based on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material. In some embodiments, the model further includes a clustering model, and the interference signals are first clustered into a plurality of clusters using the clustering model. The clusters are then adjusted to become the categories based, at least in part, on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material, according to some embodiments. 
     Method  900  proceeds to operation  906 , as illustrated in  FIG.  9   , in which a surface height offset between a surface baseline and at least one of the categories is determined based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. For example, surface height offsets of each category classified by interference signal classifier  602  may be determined based on calibration signals  614  by calibration module  604  of computing device  600 . Method  900  proceeds to operation  908 , as illustrated in  FIG.  9   , in which the surface topography of the semiconductor chip is characterized based, at least in part, on the surface height offset and the interference signals. For example, the surface topography of the semiconductor chip may be characterized by characterization module  606  of computing device  600  based on the surface height offsets determined by calibration module  604  and interference signals  612 . In some embodiments, to characterize the surface topography of the semiconductor chip, a calibrated surface height is calculated at one of the positions on the surface of the semiconductor chip. 
       FIG.  10    is a flowchart of an exemplary method  1000  for calculating a calibrated surface height, according to some embodiments of the present disclosure. Referring to  FIG.  10   , method  1000  starts at operation  1002 , in which the surface baseline is designated to a baseline region corresponding to one of the categories. The baseline region is the largest region, according to some embodiments. Method  1000  proceeds to operation  1004 , as illustrated in  FIG.  10   , in which the calibration signal and a baseline signal corresponding to the baseline region are received. Each of the calibration and baseline signals is associated with a topographic height determined by an SPM or an electron microscopy in a calibration pattern across the regions, according to some embodiments. Method  1000  proceeds to operation  1006 , as illustrated in  FIG.  10   , in which the surface height offset is determined based, at least in part, on the calibration signal, the baseline signal, and the interference signals corresponding to the positions in the calibration pattern. Method  1000  proceeds to operation  1008 , as illustrated in  FIG.  10   , in which the calibrated surface height at one of the positions on the surface of the semiconductor chip is calculated based, at least in part, on the corresponding original surface height derived from the corresponding interference signal and the surface height offset of the category in which the corresponding interference signal is classified. 
     As described above, the characterization of the surface topography of a semiconductor chip may be presented in any suitable forms, such as a calibrated height map.  FIG.  11    is a flowchart of an exemplary method  1100  for generating a calibrated height map, according to some embodiments of the present disclosure. Referring to  FIG.  11   , method  1100  starts at operation  1102 , in which an original height map is generated based, at least in part, on the received interference signals. For example, as shown in  FIG.  12   , an original height map  1202  may be generated based on interference signals  612 . Original height map  1202  represents the original surface heights (e.g., between −10 nm and 10 nm) in a sampling field (in an area of 300 μm by 300 μm) on the surface of a semiconductor chip. The original surface height at each position in the sampling field may be resolved and derived from respective interference signal  612  by surface height calculation unit  610 . Original height map  1202  may be generated with high throughput but low accuracy and precision. 
     Referring to  FIG.  11   , method  1100  proceeds to operation  1104 , in which the original height map is transformed into a classification map based, at least in part, on the classified interference signals and the categories. For example, as shown in  FIG.  12   , original height map  1202  may be transformed into a classification map  1204  by interference signal classifier  602  based on classified interference signals  612  and the categories. Classification map  1204  represents  8  categories (e.g.,  1  to  8 ) in the sampling field on the surface of a semiconductor chip. The category of each position in the sampling field may be the category in which interference signal  612  corresponding to the respective position is classified. A category may correspond to a region having the same material on the surface of the semiconductor chip. For example, category  4  may be the silicon substrate, which is also the largest region in the sampling field. Some categories may be merged as they correspond to regions having the same material. For example, categories 5-8 may be consolidated into one category. 
     Referring to  FIG.  11   , method  1100  proceeds to operation  1106 , in which a calibrated height map is generated from the original height map based, at least in part, on the surface height offset and the classification map. For example, as shown in  FIG.  12   , a calibrated height map  1206  may be generated from original height map  1202  by calibration module  604  and characterization module  606  based on the surface height offsets and classification map  1204 . Calibrated height map  1206  represents the calibrated surface heights (e.g., between −10 nm and 10 nm) in the sampling field on the surface of a semiconductor chip. One of the regions may be selected as the baseline region, and the surface baseline (e.g., 0) may be designated to the corresponding category. For example, surface baseline 0 may be designated to category  4 . The surface height offsets of each category in classification map  1204  may be determined with respect to the surface baseline and used for generating calibrated height map  1206  by adding the corresponding surface height offset to the respective original surface height at each position in original height map  1202 . Compared with original height map  1202 , calibrated height map  1206  have higher accuracy and precision. 
       FIG.  13    illustrates a schematic diagram of another exemplary computing device  1300  of system  100  in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Computing device  1300  may be another example of computing device  102  in  FIG.  1   . Computing device  1300  can include a plurality of functional modules and units implemented by at least one processor. Different from computing device  600  in  FIG.  6    including interference signal classifier  602  configured to classify interference signals  612 , computing device  1300  includes a domain transform unit  1304  configured to transform interference signals  612  into spectrum signals  1306  and also includes a spectrum signal classifier  1302  configured to classify spectrum signals  1306  using a model  1308  for classifying spectrum signals  1306 , according to some embodiments. Similar to computing device  600  in  FIG.  6   , computing device  1300  further includes calibration module  604 , characterization module  606 , and surface height calculation unit  610 , according to some embodiments. It is understood that the details of the similar modules or units (e.g., the inputs, outputs, functions, etc.) in both computing devices  600  and  1300  may not be repeated below. 
     In some embodiments, spectrum signal classifier  1302  is configured to receive a plurality of spectrum signals  1306  each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip. As described above, spectrum signals  1306  are another type of signals that can be classified using a machine learning process with high throughput for surface topography characterization, according to some embodiments. Spectrum signals  1306  can be transformed from interference signals  612  by domain transform unit  1304  as shown in  FIG.  13   . Domain transform unit  1304  can transform signals between two domains, such as the temporal domain, time domain, spatial domain, frequency domain, etc. In some embodiments, domain transform unit  1304  is configured to transform interference signals  612  (in the spatial domain) into spectrum signals  1306  (in the frequency domain) each corresponding to the respective one of the positions on the surface of the semiconductor. In one example, interference signals  612  may be transformed into spectrum signals  1306  using Fourier transform by domain transform unit  1304 . Fourier transform can decompose a function of time (a signal) into its constituent frequencies. Consequently, each position in the sampling field can be associated with respective interference signal  612  as well as respective spectrum signal  1306 . Spectrum signals  1306  can contain the sample&#39;s material and structure information. Each spectrum signal  1306  includes a reflectance spectrum, according to some embodiments. 
       FIG.  14 A  illustrates exemplary  12  interference signals, according to some embodiments of the present disclosure. Each of the  12  interference signals may include an interference fringe of low coherent interferometry. At least some of the interference fringes may be multi-components interference fringes corresponding to one or more transparent layers in the sampling field on the sample surface.  FIG.  14 B  illustrates  12  spectrum signals transformed from the exemplary  12  interference signals in  FIG.  14 A , according to some embodiments of the present disclosure. Each of the  12  spectrum signals may include a reflectance spectrum, which represents the reflectivity change in the wavelength range of the light source spectrum of the interferometer providing the  12  interference signals. As described above, the wavelength range of the light source spectrum of the interferometer may be suitable for any low coherent interferometry, such as in the white light range or extended beyond the white light range, which may affect the transformed reflectance spectrums as well. 
     Referring back to  FIG.  13   , model  1308  for classifying spectrum signals, run by computing device  1300 , is used by spectrum signal classifier  1302 , according to some embodiments. As described below in detail, model  1308  can be a machine learning model trained for classifying spectrum signals. It is understood that model  1308  for classifying spectrum signals and model  608  in  FIG.  6    for classifying interference signals may be the same type of machine learning models including a classification model (e.g., a KNN), but trained with different types of training samples, i.e., spectrum signals as the training samples for model  1308  and interference signals as the training samples for model  608 . 
     In some embodiments, spectrum signal classifier  1302  is further configured to classify spectrum signals  1306  into a plurality of categories using model  1308 . Each of the categories corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. Model  1308  can include a classification model, such as KNN, case-based reasoning, decision tree, naive Bayes, ANN, logistic regression, Fisher&#39;s linear discriminant, SVM, or perceptron. In some embodiments in which model  1308  includes a classification model, as part of the supervised learning, the categories are known and predetermined. For example, each category may correspond to a region having the same material on the surface of the semiconductor chip. That is, based on the design of the semiconductor chip, e.g., the structures and materials in the sampling field, a plurality of categories can be identified as the labels for the training as well as the output variables for classification. In one example, a first category may correspond to a first region of silicon oxide (a transparent layer), a second category may correspond to a second region of tungsten (an opaque layer), and a third category may correspond to a third region of silicon substrate (an opaque layer) in the sampling field on the surface of the semiconductor chip. 
     In some embodiments, model  1308  includes a clustering model, such as linkage clustering, k-means clustering, Gaussian mixture model clustering, or density-based clustering. In some embodiments in which model  1308  includes a clustering model, as part of the unsupervised learning, the categories used by spectrum signal classifier  1302  are not predetermined. In some embodiments, spectrum signal classifier  1302  is configured to cluster spectrum signals  1306  into a plurality of clusters using model  1308  (e.g., a clustering model) and adjust the clusters to become the categories used by spectrum signal classifier  1302  based, at least in part, on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material. In other words, clusters can be learned first in an unsupervised manner, and the categories can be determined from the clusters in a supervised manner based on, for example, the structures and materials in the sampling field. In one example, a cluster that does not correspond to a region having the same material in the sampling field may be disregarded. In another example, multiple clusters that correspond to the same region having the same material or correspond to different regions have the same material may be merged. 
     In some embodiments, any suitable feature selection and feature extraction approaches can be applied to spectrum signals  1306  by spectrum signal classifier  1302  to select and/or extract features (e.g., feature vectors), either latent features or patent features, from each spectrum signal  1306  to reduce the complexity and improve the efficiency of the classification process. In one example, model  1308  may include KNN, and 10-dimensional feature vectors may be extracted from each spectrum signal  1306  for classification using the KNN model by spectrum signal classifier  1302 . 
     In some embodiments, calibration module  604  is configured to determine a surface height offset between a surface baseline and at least one of the categories from spectrum signal classifier  1302  based, at least in part, on calibration signal  614  associated with the region corresponding to the at least one of the categories, as described above in detail with respect to  FIG.  6   . That is, a respective surface height offset can be added to each category based on the same surface baseline for calibration to increase the accuracy and precision of the surface topography. 
     In some embodiments, characterization module  606  is configured to characterize the surface topography of the semiconductor chip based, at least in part, on the surface height offset and interference signals  612 , as described above in detail with respect to  FIG.  6   . In some embodiments, to characterize the surface topography of the semiconductor chip, characterization module  606  is further configured to calculate a calibrated surface height at one of the positions on the surface of the semiconductor chip based, at least in part, on the corresponding original surface height and the surface height offset. That is, for any specific position on the surface of the semiconductor chip, its original surface height can be derived from corresponding interference signal  612  by surface height calculation unit  610 , and can be classified into one of the categories by spectrum signal classifier  1302  as described above in detail. As a result, by using spectrum signal classifier  1302  based on transformed spectrum signals  1306  and model  1308 , the surface topography of the semiconductor chip can be characterized with high throughput. By using calibration module  604  based on calibration signals  614 , the accuracy and precision of the surface topography of the semiconductor chip can be maintained at the desired level. 
       FIG.  15    is a flowchart of another exemplary method  1500  for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Examples of the device that can perform operations of method  1500  include computing device  1300  depicted in  FIG.  13   . It is understood that the operations shown in method  1500  are not exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than shown in  FIG.  15   . It is understood that some operations in method  1500  are substantially the same as their counterparts in method  900  in  FIG.  9    and thus, the details of the substantially same operations in both methods  900  and  1500  may not be repeated below. 
     Referring to  FIG.  15   , method  1500  starts at operation  902 , in which a plurality of interference signals each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip are received. For example, interference signals  612  may be received by domain transform unit  1304  of computing device  1300 . In some embodiments, each interference signal includes an interference fringe of low coherent interferometry and is associated with an original surface height at the respective position. In some embodiments, the semiconductor chip includes multiple layers, and at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer or a silicon nitride layer. 
     Method  1500  proceeds to operation  1502 , as illustrated in  FIG.  15   , in which the interference signals are transformed into a plurality of spectrum signals each corresponding to the respective one of the positions on the surface of the semiconductor chip. For example, interference signals  612  may be transformed into spectrum signals  1306  by domain transform unit  1304  of computing device  1300 . In some embodiments, each of the spectrum signals includes a reflectance spectrum. In some embodiments, the interference signals are transformed into the spectrum signals using Fourier transform. 
     Method  1500  proceeds to operation  1504 , as illustrated in  FIG.  15   , in which the spectrum signals are classified into a plurality of categories using a model. Each of the categories can correspond to a region having the same material on the surface of the semiconductor chip. For example, spectrum signals  1306  may be classified into multiple categories using model  1308  by spectrum signal classifier  1302  of computing device  1300 . In some embodiments, the model includes a classification model, and the categories are predetermined based on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material. In some embodiments, the model further includes a clustering model, and the interference signals are first clustered into a plurality of clusters using the clustering model. The clusters are then adjusted to become the categories based, at least in part, on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material, according to some embodiments. 
     Method  1500  proceeds to operation  906 , as illustrated in  FIG.  15   , in which a surface height offset between a surface baseline and at least one of the categories is determined based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. For example, surface height offsets of each category classified by spectrum signal classifier  1302  may be determined based on calibration signals  614  by calibration module  604  of computing device  1300 . Method  1500  proceeds to operation  908 , as illustrated in  FIG.  15   , in which the surface topography of the semiconductor chip is characterized based, at least in part, on the surface height offset and the interference signals. For example, the surface topography of the semiconductor chip may be characterized by characterization module  606  of computing device  1300  based on the surface height offsets determined by calibration module  604  and interference signals  612 . In some embodiments, to characterize the surface topography of the semiconductor chip, a calibrated surface height is calculated at one of the positions on the surface of the semiconductor chip. One example of calculating a calibrated surface height is described above with respect to  FIG.  10    and thus, is not repeated for ease of description. 
     As described above, the characterization of the surface topography of a semiconductor chip may be presented in any suitable forms, such as a calibrated height map.  FIG.  16    is a flowchart of another exemplary method  1600  for generating a calibrated height map, according to some embodiments of the present disclosure. It is understood that some operations in method  1600  are substantially the same as their counterparts in method  1100  in  FIG.  11    and thus, the details of the substantially same operations in both methods  1100  and  1600  may not be repeated below. 
     Referring to  FIG.  16   , method  1600  starts at operation  1102 , in which an original height map is generated based, at least in part, on the received interference signals. Method  1600  proceeds to operation  1602 , as illustrated in  FIG.  16   , in which a spectrum map is generated based, at least in part, on the transformed spectrum signals. Method  1600  proceeds to operation  1604 , as illustrated in  FIG.  16   , in which the spectrum map is transformed into a classification map based, at least in part, on the classified spectrum signals and the categories. Method  1600  proceeds to operation  1106 , as illustrated in  FIG.  16   , in which a calibrated height map is generated from the original height map based, at least in part, on the surface height offset and the classification map. 
       FIG.  17    illustrates a schematic diagram of still another exemplary computing device  1700  of system  100  in  FIG.  1    for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Computing device  1700  may be still another example of computing device  102  in  FIG.  1   . Computing device  1700  can include a plurality of functional modules and units implemented by at least one processor. Different from computing device  1300  in  FIG.  13    in which spectrum signals  1306  are transformed from interference signal  612  by domain transform unit  1304 , spectrum signals  1702  in  FIG.  17    are received from a spectrometer (e.g.,  106  in  FIGS.  1  and  316    in  FIG.  3 B ) by spectrum signal classifier  1302 , according to some embodiments. That is, computing device  1700  may not include domain transform unit  1304 . Similar to computing device  1300  in  FIG.  13   , computing device  1700  further includes spectrum signal classifier  1302 , model  1308  for classifying spectrum signals, calibration module  604 , characterization module  606 , and surface height calculation unit  610 , according to some embodiments. It is understood that the details of the similar modules or units (e.g., the inputs, outputs, functions, etc.) in both computing devices  1300  and  1700  may not be repeated below. 
     In some embodiments, spectrum signal classifier  1302  is configured to receive a plurality of spectrum signals  1702  each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip. As described above, spectrum signals  1702  are another type of signals that can be classified using a machine learning process with high throughput for surface topography characterization, according to some embodiments. Spectrum signals  1702  can be obtained directly from a spectrometer, such as an optical spectrometer. Spectrum signals  1702  can contain the sample&#39;s material and structure information. Each spectrum signal  1702  includes a reflectance spectrum, according to some embodiments. 
     In some embodiments, spectrum signal classifier  1302  is further configured to classify spectrum signals  1702  into a plurality of categories using model  1308 . Each of the categories corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. Model  1308  can include a classification model, such as KNN, case-based reasoning, decision tree, naive Bayes, ANN, logistic regression, Fisher&#39;s linear discriminant, SVM, or perceptron. In some embodiments, model  1308  includes a clustering model, such as linkage clustering, k-means clustering, Gaussian mixture model clustering, or density-based clustering. Any suitable feature selection and feature extraction approaches can be applied to spectrum signals  1702  by spectrum signal classifier  1302  to select and/or extract features (e.g., feature vectors), either latent features or patent features, from each spectrum signal  1702  to reduce the complexity and improve the efficiency of the classification process. In one example, model  1308  may include KNN, and 10-dimensional feature vectors may be extracted from each spectrum signal  1702  for classification using the KNN model by spectrum signal classifier  1302 . 
     In some embodiments, calibration module  604  is configured to determine a surface height offset between a surface baseline and at least one of the categories from spectrum signal classifier  1302  based, at least in part, on calibration signal  614  associated with the region corresponding to the at least one of the categories, as described above in detail with respect to  FIG.  6   . That is, a respective surface height offset can be added to each category based on the same surface baseline for calibration to increase the accuracy and precision of the surface topography. 
     In some embodiments, characterization module  606  is configured to characterize the surface topography of the semiconductor chip based, at least in part, on the surface height offset and interference signals  612 , as described above in detail with respect to  FIG.  6   . For any specific position on the surface of the semiconductor chip, its original surface height can be resolved and derived from corresponding interference signal  612  by surface height calculation unit  610 , and can be classified into one of the categories by spectrum signal classifier  1302  as described above in detail. As a result, by using spectrum signal classifier  1302  based on received spectrum signals  1702  and model  1308 , the surface topography of the semiconductor chip can be characterized with high throughput. By using calibration module  604  based on calibration signals  614 , the accuracy and precision of the surface topography of the semiconductor chip can be maintained at the desired level. 
       FIG.  18    is a flowchart of still another exemplary method  1800  for measuring the surface topography of a semiconductor chip, according to some embodiments of the present disclosure. Examples of the device that can perform operations of method  1800  include computing device  1700  depicted in  FIG.  17   . It is understood that the operations shown in method  1800  are not exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than shown in  FIG.  18   . It is understood that some operations in method  1800  are substantially the same as their counterparts in method  1500  in  FIG.  15    and thus, the details of the substantially same operations in both methods  1800  and  1500  may not be repeated below. 
     Referring to  FIG.  18   , method  1800  starts at operation  1802 , in which a plurality of interference signals and a plurality of spectrum signals are received. Each of the interference signals and spectrum signals can correspond to a respective one of a plurality of positions on a surface of the semiconductor chip. That is, a pair of an interference signal and a spectrum signal can be sampled from the same position in the sampling field. For example, spectrum signals  1702  may be received by spectrum signal classifier  1302 , and interference signals  612  may be received by surface height calculation unit  610  of computing device  1700 . In some embodiments, each interference signal includes an interference fringe of low coherent interferometry and is associated with an original surface height at the respective position, and each spectrum signal includes a reflectance spectrum. In some embodiments, the semiconductor chip includes multiple layers, and at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer or a silicon nitride layer. 
     Method  1800  proceeds to operation  1504 , as illustrated in  FIG.  18   , in which the spectrum signals are classified into a plurality of categories using a model. Each of the categories can correspond to a region having the same material on the surface of the semiconductor chip. For example, spectrum signals  1702  may be classified into multiple categories using model  1308  by spectrum signal classifier  1302  of computing device  1700 . In some embodiments, the model includes a classification model, and the categories are predetermined based on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material. In some embodiments, the model further includes a clustering model, and the interference signals are first clustered into a plurality of clusters using the clustering model. The clusters are then adjusted to become the categories based, at least in part, on the design of the semiconductor chip, such that each category corresponds to the respective region having the same material, according to some embodiments. 
     Method  1800  proceeds to operation  906 , as illustrated in  FIG.  18   , in which a surface height offset between a surface baseline and at least one of the categories is determined based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. For example, surface height offsets of each category classified by spectrum signal classifier  1302  may be determined based on calibration signals  614  by calibration module  604  of computing device  1700 . Method  1800  proceeds to operation  908 , as illustrated in  FIG.  18   , in which the surface topography of the semiconductor chip is characterized based, at least in part, on the surface height offset and the interference signals. For example, the surface topography of the semiconductor chip may be characterized by characterization module  606  of computing device  1700  based on the surface height offsets determined by calibration module  604  and interference signals  612 . In some embodiments, to characterize the surface topography of the semiconductor chip, a calibrated surface height is calculated at one of the positions on the surface of the semiconductor chip. One example of calculating a calibrated surface height is described above with respect to  FIG.  10    and thus, is not repeated for ease of description. 
     As described above, the characterization of the surface topography of a semiconductor chip may be presented in any suitable forms, such as a calibrated height map.  FIG.  19    is a flowchart of still another exemplary method  1900  for generating a calibrated height map, according to some embodiments of the present disclosure. It is understood that some operations in method  1900  are substantially the same as their counterparts in method  1600  in  FIG.  16    and thus, the details of the substantially same operations in both methods  1900  and  1600  may not be repeated below. 
     Referring to  FIG.  19   , method  1900  starts at operation  1102 , in which an original height map is generated based, at least in part, on the received interference signals. For example, as shown in  FIG.  20   , an original height map  2008  may be generated based on the received interference signals corresponding to a semiconductor chip surface pattern  2002 . Referring to  FIG.  19   , method  1900  proceeds to operation  1902 , as illustrated in  FIG.  19   , in which a spectrum map is generated based, at least in part, on the received spectrum signals. For example, as shown in  FIG.  20   , spectrum signals  2004  corresponding to semiconductor chip surface pattern  2002  may be received from an optical spectrometer, which may be used to generate a spectrum map. Referring to  FIG.  19   , method  1900  proceeds to operation  1604 , as illustrated in  FIG.  19   , in which the spectrum map is transformed into a classification map based, at least in part, on the classified spectrum signals and the categories. For example, as shown in  FIG.  20   , a classification map  2006  may be transformed from the spectrum map based on the classified spectrum signals and the categories. Classification map  2006  represents  3  categories each corresponding to a region having the same material in semiconductor chip surface pattern  2002 , such as a tungsten vertical interconnect access (VIA), a copper layer, and a silicon substrate. Referring to  FIG.  19   , method  1900  proceeds to operation  1106 , as illustrated in  FIG.  19   , in which a calibrated height map is generated from the original height map based, at least in part, on the surface height offset and the classification map. 
       FIG.  21    illustrates a schematic diagram of an exemplary system  2100  for training a model  2104  for surface topography characterization, according to some embodiments of the present disclosure. Model  2104  may be any machine learning models disclosed herein, such as model  608  for classifying interference signals or model  1308  for classifying spectrum signals. System  2100  can include a plurality of functional modules and units implemented by at least one processor. In some embodiments, system  2100  includes a model training module  2102  configured to train model  2104  for classifying either interference signals or spectrum signals over a set of training samples  2106  (including interference signals or spectrum signals) based on an objective function  2110  (also known as a “loss function”) using a training algorithm  2108 . Model training module  2102  can provide model  2104  for classifying either interference signals or spectrum signals depending on the types of training samples  2106  (either interference signals or spectrum signals). Model  2104  can include a classification model, such as KNN, case-based reasoning, decision tree, naive Bayes, ANN, logistic regression, Fisher&#39;s linear discriminant, SVM, or perceptron. 
     To train model  2104  for classifying interference signals, model training module  2102  can also obtain training samples each including an interference signal and a labeled category of the interference signal. The interference signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. For example, each training interference signal may be manually, automatically, or semi-automatically labeled with one of multiple predetermined categories each corresponding to a region having the same material on the surface of the semiconductor chip, such as silicon substrate, copper layer, tungsten VIA, silicon oxide layer, silicon nitride layer, to name a few. In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer, and at least one of the categories corresponds to the transparent layer. In some embodiments, a training interference signal includes an interference fringe of low coherent interferometry, which may be used as the signature for labeling the training interference signal. 
     To train model  2104  for classifying spectrum signals, model training module  2102  can also obtain training samples each including a spectrum signal and a labeled category of the spectrum signal. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. For example, each training spectrum signal may be manually, automatically, or semi-automatically labeled with one of multiple predetermined categories each corresponding to a region having the same material on the surface of the semiconductor chip, such as silicon substrate, copper layer, tungsten VIA, silicon oxide layer, silicon nitride layer, to name a few. In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer, such as a silicon oxide layer, and at least one of the categories corresponds to the transparent layer. In some embodiments, a training spectrum signal includes a reflectance spectrum, which may be used as the signature for labeling the training spectrum signal. 
     To train model  2104  for classifying interference signals or spectrum signals, model training module  2102  can further adjust one or more parameters of model  2104  based, at least in part, on a difference between the labeled category and a classified category of the interference signal or the spectrum signal in each of training samples  2106 . In some embodiments, model  2104  includes one or more parameters (e.g., the “k” in KNN) that can be jointly adjusted by model training module  2102  when being fed with training samples  2106 . Model training module  2102  can jointly adjust the parameters of model  2104  to minimize objective function  2110  over training samples  2106  using training algorithm  2108 . Any suitable objective function  2110  and training algorithm  2108  can be selected based on the specific type of model  2104  to be trained. For example, for a KNN model, a mean square error (MSE)-based objective function may be used by model training module  2102  in combination with a KNN classification training algorithm. It is understood that the training of model  2104 , e.g., the adjustment of the parameter, may be performed in an iterative manner. 
       FIG.  22    a flowchart of an exemplary method  2200  for training a model for surface topography characterization, according to some embodiments of the present disclosure. Examples of the system that can perform operations of method  2200  include system  2100  depicted in  FIG.  21   . It is understood that the operations shown in method  2200  are not exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than shown in  FIG.  22   . 
     Referring to  FIG.  22   , method  2200  starts at operation  2202 , in which a model for classifying interference signals is provided. The model can include a classification model. For example, model  2104  may be provided to model training module  2102  of system  2100 . Method  2200  proceeds to operation  2204 , as illustrated in  FIG.  22    in which a plurality of training samples each including an interference signal and a labeled category of the interference signal are obtained. The interference signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. The interference signal can include an interference fringe of low coherent interferometry, and at least part of the surface of the semiconductor chip includes a transparent layer. For example, training samples  2106  may be obtained by model training module  2102 . Method  2200  proceeds to operation  2206 , as illustrated in  FIG.  22    in which a parameter of the model is adjusted based, at least in part, on a difference between the labeled category and a classified category of the interference signal in each of the training samples. For example, one or more parameters of model  2104  may be adjusted by model training module  2102  over training samples  2106 . 
       FIG.  23    a flowchart of another exemplary method  2300  for training a model for surface topography characterization, according to some embodiments of the present disclosure. Examples of the system that can perform operations of method  2300  include system  2100  depicted in  FIG.  21   . It is understood that the operations shown in method  2300  are not exhaustive and that other operations can be performed as well before, after, or between any of the illustrated operations. Further, some of the operations may be performed simultaneously, or in a different order than shown in  FIG.  23   . 
     Referring to  FIG.  23   , method  2300  starts at operation  2302 , in which a model for classifying spectrum signals is provided. The model can include a classification model. For example, model  2104  may be provided to model training module  2102  of system  2100 . Method  2300  proceeds to operation  2304 , as illustrated in  FIG.  23    in which a plurality of training samples each including a spectrum signal and a labeled category of the spectrum signal are obtained. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having the same material on the surface of the semiconductor chip, according to some embodiments. The spectrum signal can include a reflectance spectrum, and at least part of the surface of the semiconductor chip includes a transparent layer. For example, training samples  2106  may be obtained by model training module  2102 . Method  2300  proceeds to operation  2306 , as illustrated in  FIG.  23    in which a parameter of the model is adjusted based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. For example, one or more parameters of model  2104  may be adjusted by model training module  2102  over training samples  2106 . 
     Various embodiments can be implemented, for example, using one or more computing devices, such as a computing device  2400  shown in  FIG.  24   . One or more computing devices  2400  can be an example of computing device  102  in  FIG.  1    and can be used, for example, to implement method  900  of  FIG.  9   , method  1000  of  FIG.  10   , method  1100  of  FIG.  11   , method  1500  of  FIG.  15   , method  1600  of  FIG.  16   , method  1800  of  FIG.  18   , and method  1900  of  FIG.  19   . For example, computing device  2400  can perform various functions in surface topography metrology, such as interference signals and/or spectrum signals classification, surface height offset calibration, calibrated surface height calculation, as well as calibrated height node generation. One or more computing devices  2400  can also be an example of system  2100  in  FIG.  21    and can be used, for example, to implement method  2200  of  FIG.  22    and method  2300  of  FIG.  23   . For example, computing device  2400  can perform various functions in model training. Computing device  2400  can be any computer capable of performing the functions described herein. 
     Computing device  2400  can include one or more processors (also called central processing units, or CPUs), such as a processor  2404 . Processor  2404  is connected to a communication infrastructure or bus  2406 , according to some embodiments. One or more processors  2404  can each be a GPU. In some embodiments, a GPU is a processor that is a specialized electronic circuit designed to process mathematically intensive applications. The GPU may have a parallel structure that is efficient for parallel processing of large blocks of data, such as mathematically intensive data common to computer graphics applications, images, videos, etc. 
     Computing device  2400  can also include user input/output device(s)  2403 , such as monitors, keyboards, pointing devices, etc., which communicate with communication infrastructure or bus  2406  through user input/output interface(s)  2402 . 
     Computing device  2400  can also include a main or primary memory  2408 , such as random-access memory (RAM). Main memory  2408  can include one or more levels of cache. Main memory  2408  has stored therein control logic (i.e., computer software) and/or data, according to some embodiments. 
     Computing device  2400  can also include one or more secondary storage devices or memory  2410 . Secondary memory  2410  can include, for example, a hard disk drive  2412  and/or a removable storage device or drive  2414 . Removable storage drive  2414  can be a floppy disk drive, a magnetic tape drive, a compact disk drive, an optical storage device, tape backup device, and/or any other storage device/drive. 
     Removable storage drive  2414  can interact with a removable storage unit  2418 . Removable storage unit  2418  includes a computer usable or readable storage device having stored thereon computer software (control logic) and/or data, according to some embodiments. Removable storage unit  2418  can be a floppy disk, magnetic tape, compact disk, DVD, optical storage disk, and/any other computer data storage device. Removable storage drive  2414  can read from and/or writes to removable storage unit  2418  in a well-known manner. 
     According to some embodiments, secondary memory  2410  can include other means, instrumentalities or other approaches for allowing computer programs and/or other instructions and/or data to be accessed by computing device  2400 . Such means, instrumentalities or other approaches may include, for example, a removable storage unit  2422  and an interface  2420 . Examples of removable storage unit  2422  and interface  2420  can include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an EPROM or PROM) and associated socket, a memory stick and USB port, a memory card and associated memory card slot, and/or any other removable storage unit and associated interface. 
     Computing device  2400  can further include a communication or network interface  2424 . Communication interface  2424  enables computing device  2400  to communicate and interact with any combination of remote devices, remote networks, remote entities, etc. (individually and collectively referenced by reference number  2428 ), according to some embodiments. For example, communication interface  2424  may allow computing device  2400  to communicate with remote devices  2428  over communications path  2426 , which may be wired and/or wireless, and which may include any combination of LANs, WANs, the Internet, etc. Control logic and/or data may be transmitted to and from computing device  2400  via communication path  2426 . 
     In some embodiments, a tangible apparatus or article of manufacture comprising a tangible computer useable or readable medium having control logic (software) stored thereon is also referred to herein as a computer program product or program storage device. This includes, but is not limited to, computing device  2400 , main memory  2408 , secondary memory  2410 , and removable storage units  2418  and  2422 , as well as tangible articles of manufacture embodying any combination of the foregoing. Such control logic, when executed by one or more data processing devices (such as computing device  2400 ), causes such data processing devices to operate as described herein. 
     Based on the teachings contained in this disclosure, it will be apparent to persons skilled in the relevant art(s) how to make and use embodiments of the present disclosure using data processing devices, computer systems and/or computer architectures other than that shown in  FIG.  24   . In particular, embodiments may operate with software, hardware, and/or operating system implementations other than those described herein. 
     According to one aspect of the present disclosure, a method for measuring a surface topography of a semiconductor chip is disclosed. A plurality of interference signals and a plurality of spectrum signals are received by at least one processor. Each of the interference signals and spectrum signals corresponds to a respective one of a plurality of positions on a surface of the semiconductor chip. The spectrum signals are classified by the at least one processor into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. A surface height offset between a surface baseline and at least one of the categories is determined by the at least one processor based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. The surface topography of the semiconductor chip is characterized by the at least one processor based, at least in part, on the surface height offset and the interference signals. 
     In some embodiments, each of the interference signals includes an interference fringe of low coherent interferometry, and each of the spectrum signals includes a reflectance spectrum. 
     In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer. 
     In some embodiments, each of the interference signals is associated with an original surface height at the respective position. 
     In some embodiments, to characterize the surface topography of the semiconductor chip, a calibrated surface height at one of the positions on the surface of the semiconductor chip is calculated based, at least in part, on the corresponding original surface height and the surface height offset. 
     In some embodiments, the model includes a classification model. 
     In some embodiments, to classify the plurality of spectrum signals, the plurality of spectrum signals are clustered into a plurality of clusters, and the plurality of clusters are adjusted to become the plurality of categories based, at least in part, on a design of the semiconductor chip, such that each of the categories corresponds to the respective region having the same material. 
     In some embodiments, to determine the surface height offset, the surface baseline is designated to a baseline region corresponding to one of the categories, the calibration signal and a baseline signal corresponding to the baseline region are received, and the surface height offset is determined based, at least in part, on the calibration signal, the baseline signal, and the interference signals. 
     In some embodiments, each of the calibration and baseline signals is associated with a topographic height determined by a SPM or an electron microscope. 
     In some embodiments, an original height map is generated based, at least in part, on the received interference signals, a spectrum map is generated based, at least in part, on the received spectrum signals, the spectrum map is transformed into a classification map based, at least in part, on the classified spectrum signals and the categories, and a calibrated height map is generated from the original height map based, at least in part, on the surface height offset and the classification map. 
     According to another aspect of the present disclosure, a system for measuring a surface topography of a semiconductor chip includes an interferometer, a spectrometer, a scanning probe microscopy (SPM) or an electron microscope, and at least one processor. The interferometer is configured to provide a plurality of interference signals each corresponding to a respective one of a plurality of positions on a surface of the semiconductor chip. The spectrometer is configured to provide a plurality of interference spectrum each corresponding to a respective one of the plurality of positions on the surface of the semiconductor chip. The SPM or the electron microscope is configured to provide a plurality of calibration signals. The at least one processor is configured to classify the spectrum signals into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. The at least one processor is also configured to determine a surface height offset between a surface baseline and at least one of the categories based, at least in part, on at least one of the calibration signals associated with the region corresponding to the at least one of the categories. The at least one processor is also configured to characterize the surface topography of the semiconductor chip based, at least in part, on the surface height offset and the interference signals. 
     In some embodiments, the interferometer includes a low coherent interferometer, and each of the interference signals includes an interference fringe of low coherent interferometry, and the spectrometer includes a reflectance spectrometer, and each of the spectrum signals includes a reflectance spectrum. 
     In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer. 
     In some embodiments, each of the interference signals is associated with an original surface height at the respective position. 
     In some embodiments, to characterize the surface topography of the semiconductor chip, the at least one processor is further configured to calculate a calibrated surface height at one of the positions on the surface of the semiconductor chip based, at least in part, on the corresponding original surface height and the surface height offset. 
     In some embodiments, the model includes a classification model. 
     In some embodiments, to classify the plurality of spectrum signals, the at least one processor is further configured to cluster the plurality of spectrum signals into a plurality of clusters, and adjust the plurality of clusters to become the plurality of categories based, at least in part, on a design of the semiconductor chip, such that each of the categories corresponds to the respective region having the same material. 
     In some embodiments, to determine the surface height offset, the at least one processor is further configured to designate the surface baseline to a baseline region corresponding to one of the categories, receive the calibration signal and a baseline signal of the calibration signals corresponding to the baseline region, and determine the surface height offset based, at least in part, on the calibration signal, the baseline signal, and the interference signals. 
     In some embodiments, each of the calibration signals is associated with a topographic height. 
     In some embodiments, the at least one processor is further configured to generate an original height map based, at least in part, on the received interference signals, generate a spectrum map based, at least in part, on the received spectrum signals, transform the spectrum map into a classification map based, at least in part, on the classified spectrum signals and the categories, and generate a calibrated height map from the original height map based, at least in part, on the surface height offset and the classification map. 
     According to still another aspect of the present disclosure, a tangible computer-readable device has instructions stored thereon that, when executed by at least one computing device, causes the at least one computing device to perform operations. The operations include receiving a plurality of interference signals and a plurality of spectrum signals. Each of the interference signals and spectrum signals corresponds to a respective one of a plurality of positions on a surface of a semiconductor chip. The operations also include classifying the spectrum signals into a plurality of categories using a model. Each of the categories corresponds to a region having a same material on the surface of the semiconductor chip. The operations further include determining a surface height offset between a surface baseline and at least one of the categories based, at least in part, on a calibration signal associated with the region corresponding to the at least one of the categories. The operations further include characterizing a topography of the semiconductor chip based, at least in part, on the surface height offset and the interference signals. 
     According to yet another aspect of the present disclosure, a method for training a model is disclosed. A model for classifying spectrum signals is provided by at least one processor. A plurality of training samples each including a spectrum signal and a labeled category of the spectrum signal are obtained by the at least one processor. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. A parameter of the model is adjusted by the at least one processor based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
     In some embodiments, the interference signal includes a reflectance spectrum. 
     In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer. 
     In some embodiments, the model includes a classification model. 
     According to yet another aspect of the present disclosure, a system for training a model includes a memory and at least one processor operatively coupled to the memory. The at least one processor is configured to provide a model for classifying spectrum signals. The at least one processor is also configured to obtain a plurality of training samples each including a spectrum signal and a labeled category of with the spectrum signal. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. The at least one processor is further configured to adjust a parameter of the model based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
     In some embodiments, the interference signal includes a reflectance spectrum. 
     In some embodiments, at least part of the surface of the semiconductor chip includes a transparent layer. 
     In some embodiments, the model includes a classification model. 
     According to yet another aspect of the present disclosure, a tangible computer-readable device has instructions stored thereon that, when executed by at least one computing device, causes the at least one computing device to perform operations. The operations include providing a model for classifying spectrum signals. The operations also include obtaining a plurality of training samples each including a spectrum signal and a labeled category of with the spectrum signal. The spectrum signal corresponds to a position on a surface of a semiconductor chip, and the labeled category corresponds to a region having a same material on the surface of the semiconductor chip. The operations further include adjusting a parameter of the model based, at least in part, on a difference between the labeled category and a classified category of the spectrum signal in each of the training samples. 
     The foregoing description of the specific embodiments will so reveal the general nature of the present disclosure that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present disclosure. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance. 
     Embodiments of the present disclosure have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. 
     The Summary and Abstract sections may set forth one or more but not all exemplary embodiments of the present disclosure as contemplated by the inventor(s), and thus, are not intended to limit the present disclosure and the appended claims in any way. 
     The breadth and scope of the present disclosure should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.