In an embodiment, a method comprises fitting a spectroscopic data of a layer in a layered structure to a dielectric function having a real part and an imaginary part; confirming that the dielectric function is physically possible; based on the dielectric function not being physically possible, repeating the fitting the spectroscopic data, or, based on the dielectric function being physically possible, defining an n degree polynomial to the dielectric function; determining a second derivative and a third derivative of the n degree polynomial; equating the second derivative to a first governing equation and the third derivative to a second governing equation and determining a constant of the first governing equation and the second governing equation; and based on the key governing equations, determining one or more of a band gap, a thickness, and a concentration of the layer.

A method for detecting an internal crack in a wafer includes a first image recording step of applying near infrared light having a transmission wavelength to a reference wafer having the same configuration as a target wafer to be subjected to the detection of the internal crack, thereby obtaining a first image of the reference wafer having no internal crack and then recording the first image, a processing step of processing the target wafer, a second image recording step of applying the near infrared light to the target wafer, thereby obtaining a second image of the processed target wafer and then recording the second image, and an internal crack detecting step of removing the same image information between the first image and the second image from the second image to obtain a residual image, thereby detecting the residual image as the internal crack in the target wafer.

In a first measuring process, P-polarized infrared light is emitted onto a substrate at a first incident angle at which an interference signal becomes smaller than a change by light absorption by the substrate, and light transmitted through or reflected from the substrate is measured. In a substrate processing process, substrate processing is performed on the substrate after the first measuring process. In a second measuring process, after substrate processing, P-polarized infrared light is emitted onto the substrate at a second incident angle at which an interference signal becomes smaller than a change caused by light absorption by the substrate, and light transmitted through or reflected from the substrate is measured. In an extraction process, a difference spectrum between the spectrum of the transmitted light or reflected light measured in the first measuring process and the transmitted light or reflected light measured in the second measuring process is extracted.

The present invention addresses the problem of providing a novel technology for measuring an etching amount in heat treatment in which growth and etching proceed simultaneously. The present invention includes: a first substrate thickness measuring step S10 for measuring the thickness 10D of a to-be-heat-treated semiconductor substrate 10; a second substrate thickness measuring step S20 for measuring the thickness 20D of a heat-treated semiconductor substrate 20; a growth layer thickness measuring step S30 for measuring the thickness 21D of a growth layer 21 which has gone through crystal growth by heat treatment; and an etching amount calculating step S40 for calculating the etching amount ED on the basis of the thickness 10D of the to-be-heat-treated semiconductor substrate 10, the thickness 20D of the heat-treated semiconductor substrate 20, and the thickness 21D of the growth layer 21.

Systems and methods for non-contact characterization of semiconductor devices. Systems may include: an infrared radiation source directing radiation towards the semiconductor device; a radiation directing device positioned proximal the infrared radiation source to direct radiation towards an opposing side of the semiconductor device, the semiconductor device receivable between the radiation directing device and the infrared radiation source; and a radiation detector proximal to the infrared radiation source to sense radiation associated with a plurality of infrared wavebands from the semiconductor device for determining a dopant profile property of the semiconductor device. The sensed radiation may include radiation originating from the infrared radiation source reflected from the semiconductor device. The sensed radiation may include radiation originating from the radiation directing device and emerging from the semiconductor device. The dopant profile properties may be based on infrared reflectance or infrared transmittance associated with the plurality of respective infrared wavebands.

Systems and methods for measuring or inspecting semiconductor structures using broadband infrared radiation are disclosed. The system may include an illumination source comprising a pump source configured to generate pump light and a nonlinear optical (NLO) assembly configured to generate broadband IR radiation in response to the pump light. The system may also include a detector assembly and a set of optics configured to direct the IR radiation onto a sample and direct a portion of the IR radiation reflected and/or scattered from the sample to the detector assembly.

A method of inspecting a silicon article includes irradiating a silicon article with infrared radiation, transmitting a portion of the infrared radiation through the silicon article, and filtering the infrared radiation transmitted through the silicon article. Image data is acquired from the filtered infrared radiation and an image of the silicon article reconstructed from the image data. Based on the reconstructed image of the silicon article, one or more anomalies defined within the silicon article are identified.

After determining the precipitated oxygen concentration and the residual oxygen concentration in a silicon wafer after heat treatment performed in a device fabrication process; the critical shear stress .sub.cri at which slip dislocations are formed in the silicon wafer in the device fabrication process is determined based on the obtained precipitated oxygen concentration and residual oxygen concentration; and the obtained critical shear stress .sub.cri and the thermal stress applied to the silicon wafer in the heat treatment of the device fabrication process are compared, thereby determining that slip dislocations are formed in the silicon wafer in the device fabrication process when the thermal stress is equal to or more than the critical shear stress .sub.cri, or determining that slip dislocations are not formed in the silicon wafer in the device fabrication process when the thermal stress is less than the critical shear stress .sub.cri.

In one aspect, a spectrometer insert is provided. The spectrometer insert includes: an enclosed housing; a first transparent window on a first side of the enclosed housing; a second transparent window on a second side of the enclosed housing, wherein the first side and the second side are opposing sides of the enclosed housing; and a sample mounting and heating assembly positioned within an interior cavity of the enclosed housing in between, and in line of sight of, the first transparent window and the second transparent window. A method for using the spectrometer insert to locally heat a sample so as to measure temperature-dependent optical properties of the sample is also provided.

A method of determining the carbon content in a silicon sample may include: generating electrically active polyatomic complexes within the silicon sample. Each polyatomic complex may include at least one carbon atom. The method may further include: determining a quantity indicative of the content of the generated polyatomic complexes in the silicon sample, and determining the carbon content in the silicon sample from the determined quantity.