JP2005233733A - Method, instrument, and program for measuring carrier concentration and stress in semiconductor device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for spectroscopically finding carrier concentration and stress in a semiconductor device. <P>SOLUTION: According to this stress measuring method, a half-value width and a peak position of an emission spectrum are obtained in a portion under test of a specimen under test. The carrier concentration of the specimen under test is calculated from the half-value width of the mission spectrum of the specimen under test based on a relation between the half-value width of the emission spectrum and carrier concentration previously determined by means of a plurality of standard specimens different in carrier concentration having the same composition ratio as the specimen under test. The peak position of the mission spectrum of the standard specimen at the carrier concentration of the specimen under test is calculated from a relation between the peak position of the mission spectrum and the carrier concentration determined by means of a plurality of standard specimens different in carrier concentration having the same composition ratio as the specimen under test. A difference value (a peak position movement amount) is determined between the calculated peak position of the emission spectrum of the standard specimens and the measured peak position of the emission spectrum of the specimen under test. Stress acting on the portion under test is calculated from the movement amount and the stress sensitivity coefficient of the specimen under test. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a stress measurement method by emission spectral analysis of a semiconductor device.

  In general, a strain generated in a member in a manufacturing process of a precision device, a fine device, or the like affects the characteristics and reliability of the device itself. For example, in a fine LSI or the like, stress concentration occurs around various thin film patterns formed during the manufacturing process. In particular, a large stress concentration is likely to occur in the periphery of a device isolation film having a structure in which a thick oxide film such as a wiring using a silicide having a large internal stress, a LOCOS (Local oxidation of silicon) structure, or a trench structure is embedded. For example, near the LOCOS boundaries and trenches, the value of stress generated in the Si substrate is also equal to or greater than 100 MPa. Such a large stress causes strain and dislocation in the element region, thereby deteriorating device characteristics and reducing reliability. In order to avoid such a problem, it is necessary to perform device design in consideration also the local stress distribution. As a technique for measuring stress, spectral analysis such as Raman emission analysis or emission spectral analysis is currently used (see Non-Patent Document 1).

  Measurement of stress in materials by emission spectroscopy including photoluminescence and cathodoluminescence methods uses the piezospectroscopic (PS) effect that the peak position of the emission spectrum shifts when stress is applied to the material. Done. In general, the peak position of the emission spectrum shifts to the high energy side under compressive stress and to the low energy side under tensile stress. It is known that the relationship between the strain of a substance due to stress (σ) and the peak shift amount (Δν) of the emission spectrum can be linearly approximated (Δν = Πσ: Π is the stress sensitivity coefficient) in the range of stress up to several GPa. (See Non-Patent Document 2).

  The semiconductor material, even by a change in not without carrier concentration and composition stresses only, the peak position of the emission spectrum of the material changes. Therefore, when the stress acting on the material is estimated from the peak shift amount of the emission spectrum of the semiconductor device, the carrier concentration and composition of the semiconductor material must be taken into consideration.

Non-Patent Document 3, the peak position of the emission spectrum, with half-width, and peak intensity, to be able to derive the carrier concentration and the stress of the GaAs MESFET (Me tal S emiconductor F ield E ffect T ransistor) It has been suggested. However, Non-Patent Document 3, specific derivation method is not disclosed.
ITOCHU, outside two people, "analysis of LSI of local stress by Raman spectroscopy", Toyota Central R & D Labs R & D Review, December 1994, Vol. 29, no. 4, p. 43-52 Hiroyuki Suenaga, “Analysis of Strengthening Mechanism in Ceramic / Metal Composite Materials”, 1999 Master's Thesis, Kyoto Institute of Technology M.M. Yoshikawa, 2 others, J. Appl. Phys. , Vol. 84, no. 3, 1 August 1998, p. 1693-1696

  Therefore, the first object of the present invention is to specifically provide a method for determining the carrier concentration of semiconductor materials or semiconductor devices and the stress acting on them using a spectroscopic technique.

  Further, Non-Patent Document 3 teaches that the peak position, half-value width, and peak intensity of the emission spectrum are used to obtain the stress acting on the semiconductor device and its carrier concentration. It is also taught that the peak intensities of these are highly variable depending on the type of stress (compression or tension) and / or carrier concentration. Therefore, there is a problem that the stress or carrier concentration of the semiconductor device obtained based on the peak intensity lacks accuracy and reliability.

  Accordingly, a second object of the present invention is to provide a method for accurately and reliably determining the carrier concentration of a semiconductor device or semiconductor material and the stress acting on the semiconductor device or semiconductor material by spectroscopic techniques. That is.

  In order to solve the above-mentioned problems, in the present invention, the carrier concentration of the test sample and the stress acting on the test site are obtained from only the peak position and half-value width of the emission spectrum without using the peak intensity of the spectrum. The method of the present invention is based on the knowledge found by the present inventors that the “half width” of the emission spectrum does not change with stress.

  The invention, in one aspect, provides an apparatus for determining the stress acting on the test sample. This apparatus includes a spectrum measurement unit for measuring an emission spectrum at a test site of a test sample, a storage unit, a calculation unit, and an output unit.

  The storage unit includes data including an algorithm representing a relationship between a half value width of an emission spectrum and a carrier concentration obtained in advance using a plurality of standard samples having different carrier concentrations and having the same composition ratio as the test site of the test sample. And data including an algorithm representing the relationship between the peak position of the emission spectrum and the carrier concentration for a plurality of standard samples having the same composition ratio as the test site of the test sample and having different carrier concentrations, and the test sample And stress sensitivity coefficient data. The calculation unit calculates the half width and peak position of the emission spectrum from the emission spectrum measured at the test site of the test sample, and the relationship between the half width of the emission spectrum of the standard sample and the carrier concentration And calculating the carrier concentration at the test site of the test sample from the half-value width of the emission spectrum of the test sample, and the peak position of the emission spectrum of the standard sample and the carrier concentration Based on the algorithm representing the relationship, the peak position of the emission spectrum of the standard sample at the carrier concentration of the test sample, the calculated peak position of the emission spectrum of the standard sample, and the measured above by obtaining a difference value between the peak position of the emission spectrum of the test sample, the target From obtaining a peak position movement amount due to the stress of the emission spectrum of the sample, and the peak position movement amount, the stress sensitivity coefficient of the test sample, wherein:

Δν = Πσ
Based on (Δν: peak position movement amount of emission spectrum of test site of test sample, Π: stress sensitivity coefficient, σ: stress acting on test site of test sample), the test of the test sample performing including processing and calculating the stress acting on site. The output unit outputs the calculated stress value.

  In a preferred embodiment of the stress determination apparatus according to the present invention, the output unit further outputs the calculated carrier concentration of the test sample.

  In another aspect, the present invention also provides an apparatus for determining the carrier concentration of a test sample. This apparatus includes a spectrum measurement unit for measuring an emission spectrum at a test site of a test sample, a storage unit, a calculation unit, and an output unit.

  The storage unit includes data including an algorithm representing a relationship between a half-value width of an emission spectrum and a carrier concentration obtained in advance using a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample. Is stored. The calculation unit calculates a half-value width of the emission spectrum from the emission spectrum measured at the test site of the test sample, and an algorithm representing the relationship between the half-value width of the emission spectrum of the standard sample and the carrier concentration And calculating the carrier concentration of the standard sample in the half-value width of the emission spectrum of the test sample. The output unit outputs the calculated carrier concentration.

  In a preferred embodiment of the stress-determining device or carrier concentration determination apparatus of the present invention, the test sample is a semiconductor device.

  In a preferred embodiment of the stress determination device or carrier concentration determination device of the present invention, the emission spectrum is obtained by irradiating a sample with an arbitrary electromagnetic wave in a wavelength range from electron beams, ions, or γ rays to visible light. Is.

  The invention, in yet another aspect, provides a computer program for determining the stress acting on the test sample.

The computer program for determining the stress acting on the test sample of the present invention comprises the step of determining the half-value width and peak position of the emission spectrum from the emission spectrum measured at the test site of the test sample, Based on an algorithm representing the relationship between the half-value width of the emission spectrum obtained using a plurality of standard samples having the same composition ratio as the test site of the sample and different carrier concentrations and the carrier concentration, the emission spectrum of the test sample The step of calculating the carrier concentration at the test site of the test sample from the half width, the peak position of the emission spectrum obtained in advance using a plurality of standard samples having the same composition ratio as the test sample and having different carrier concentrations based on an algorithm representing the relationship between the carrier concentration and, the standard in the carrier concentration of the test sample Calculating the peak position of the emission spectrum of the sample, obtaining the difference value between the calculated peak position of the emission spectrum of the standard sample and the measured peak position of the emission spectrum of the test sample. From the step of obtaining the peak position shift amount due to the stress of the emission spectrum of the test sample, and the peak position shift amount and the stress sensitivity coefficient of the test sample, the formula:
Δν = Πσ
Based on (Δν: peak position shift amount of the emission spectrum of the test site of the test sample, Π: stress sensitivity coefficient, σ: stress acting on the test site of the test sample), the stress acting on the test sample is Cause the computer to perform processing including the step of calculating.

  The invention, in yet another aspect, provides a computer program for determining the carrier concentration of the test sample.

  The computer program for determining the carrier concentration of the test sample of the present invention includes a step of determining a half width of the emission spectrum from the emission spectrum measured at the test site of the test sample, and the test sample in advance. Based on the algorithm representing the relationship between the half-value width of the emission spectrum and the carrier concentration obtained for the standard sample having the same composition ratio as the test site, the half-value width of the emission spectrum of the test sample A computer is caused to perform a process including a step of calculating a carrier concentration at a test site.

  In a preferred embodiment of the program for determining the stress acting on the test sample of the present invention or the program for determining the carrier concentration, the test sample is a semiconductor device.

  In a preferred embodiment of the program for determining the stress acting on the test sample of the present invention or the program for determining the carrier concentration, the emission spectrum is in the wavelength range from electron beam, ion, or γ-ray to visible light. It was obtained by irradiating a sample with an arbitrary electromagnetic wave.

  The present invention also provides, in another aspect, provides a method of determining the stress acting on the test sample. This method includes a step of measuring an emission spectrum at a test site of a test sample and obtaining a half width and a peak position of the spectrum, a plurality of different carriers having the same composition ratio as the test site of the test sample in advance. Based on the relationship between the half-value width of the emission spectrum determined using a standard sample having a concentration and the carrier concentration, the carrier concentration at the test site of the test sample is calculated from the half-value width of the emission spectrum of the test sample. The test, based on the relationship between the peak position of the emission spectrum and the carrier concentration determined in advance using a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample. calculating a peak position of the emission spectrum of the standard sample in the carrier concentration of the sample, the emission of the standard samples the calculated spectrum Determining the peak position movement amount due to the stress of the emission spectrum of the test sample by obtaining a difference value between the peak position of the test sample and the peak position of the emission spectrum of the test sample measured above, and the peak position A step of calculating a stress acting on the test site of the test sample from the movement amount and the stress sensitivity coefficient of the test sample is included.

  In a preferred embodiment of the method for determining the stress acting on the test sample of the present invention, the relationship between the half-value width of the emission spectrum of the standard sample and the carrier concentration is the same composition ratio as the test site of the test sample. Is obtained by measuring the emission spectra of a plurality of standard samples having a plurality of different carrier concentrations with known carrier concentrations and deriving the relationship between the half-value width of the emission spectra of the standard samples and the carrier concentration.

  In a preferred embodiment of the method for determining the stress acting on the test sample of the present invention, an algorithm representing the relationship between the peak position of the emission spectrum of the standard sample and the carrier concentration is the test site of the test sample. It is obtained by measuring the emission spectra of a plurality of standard samples having the same composition ratio and having a plurality of different carrier concentrations with known carrier concentrations and deriving the relationship between the peak positions of the emission spectra of the standard samples and the carrier concentration.

In a preferred embodiment of the method for determining a stress acting on a test sample of the present invention, in the step of calculating the stress, an equation:
Δν = Πσ
(Δν: peak position shift amount of emission spectrum of test site of test sample, Π: stress sensitivity coefficient, σ: stress acting on test site of test sample)
Is used.

  The invention, in yet another aspect, provides a method of determining the carrier concentration of the test sample. This method includes a step of measuring an emission spectrum at a test site of a test sample to obtain a half width of the emission spectrum, and a plurality of carrier concentrations having the same composition ratio as the test site of the test sample in advance. Calculating the carrier concentration at the test site of the test sample from the half-value width of the emission spectrum of the test sample based on the relationship between the half-value width of the emission spectrum and the carrier concentration obtained for different standard samples. Include.

  In a preferred embodiment of the method for determining the carrier concentration of the test sample of the present invention, the relationship between the half-value width of the emission spectrum of the standard sample and the carrier concentration has the same composition ratio as the test site of the test sample. It is obtained by measuring the emission spectra of a plurality of standard samples having a plurality of different carrier concentrations with known carrier concentrations and deriving the relationship between the half-value width of the emission spectra of the standard samples and the carrier concentration.

(Explanation of terms)
As used herein, the term “standard sample” is a reference sample made of a semiconductor material having the same composition as the semiconductor material of the test sample, and is configured to be homogeneous so that a zero stress state can be assumed. It refers to the sample. The carrier concentration of the standard sample may be different from the carrier concentration of the test sample. Examples of typical standard sample, for example, such as a wafer having the same composition as the test sample. Incidentally, the standard sample size, shape, thickness, etc. does not necessarily have to match the test sample.

  As used herein, the term “test sample” means a semiconductor material or semiconductor device that is the subject of stress measurement and carrier concentration measurement by the method of the present invention. “Test site” refers to a site for measuring stress (or composition, carrier concentration, etc.) in a test sample. For example, an arbitrary site on a thin film or substrate in a semiconductor device is the test site. Can be.

  As used herein, the term “carrier concentration” is used in the ordinary sense used in the art, and means the concentration per unit volume of electrons and holes that contribute to electrical conduction in a semiconductor material. . In the examples of this specification, the carrier concentration generated by doping impurities (Si, Zn, etc.) in the semiconductor device corresponds to this.

  According to the present invention, the measurement of the stress of a semiconductor material or a semiconductor device by a spectroscopic technique is specifically (or quantitatively) realized.

  Furthermore, according to the present invention, it is possible to easily and accurately evaluate the movement amount of the peak position due to the carrier concentration and the stress from only the peak position and half width of the emission spectrum.

  The present invention is very useful as an analysis / evaluation technique for high-quality crystal growth in a semiconductor device manufacturing process and high-quality device fabrication.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
(Method for determining carrier concentration and stress of test sample)
FIG. 1 is a flowchart showing a procedure for obtaining the carrier concentration and peak position movement amount of the test sample and the stress acting on the test site of the test sample from the emission spectrum of the test sample by the method of the present invention. Hereinafter, with reference to FIG. 1, a description is given of the procedure of stress measurement in the carrier concentration measurement and the measurement site of the test sample.

  First, start by preparing a test sample. In this embodiment, the peak position shift amount due to the carrier concentration and the stress is obtained from the emission spectrum at the test site of the two-element compound semiconductor material whose carrier concentration is unknown (hereinafter referred to as the two-element test sample).

  In step S1, the elemental composition at the test site of the test sample is determined. In the case of a two-element compound semiconductor such as GaAs or GaN, particularly in the case of a single crystal, two elements exist stably in a 1: 1 composition. To do. Therefore, the composition ratio at the test site can be assumed to be 1: 1.

Next, in step S2, a plurality of compound semiconductor standard samples having the same composition as the test site of the two-element test sample and different carrier concentrations are prepared, the emission spectra of these standard samples are measured, and the half-value width w _std And determine the peak position ν _std . Here, the carrier concentration can be appropriately selected by those skilled in the art. For example, different carrier concentrations are prepared in the range of 0 to 1.0 × 10 ¹⁹ atoms / cm ³ . The carrier concentration of the standard sample, for example, can be determined using four-point probe method, C-V (capacitance-voltage) method, scanning probe microscopy, and spectroscopic techniques. As the scanning probe microscopy, a scanning capacitance microscope (SCM), a scanning spreading resistance microscope (SSRM), or the like is preferable. In particular, SSRM is preferable because quantification of the carrier concentration is better. As a spectroscopic technique, cathodoluminescence spectroscopy, photoluminescence spectroscopy, Raman spectroscopy, or the like can be used. In addition, although not a method for directly obtaining the carrier concentration, secondary ion mass spectrometry (SIMS) can be used as a method for obtaining with high accuracy the concentration of impurities intentionally added to the semiconductor to generate carriers.
Next, in step S3 and step S4, from the emission spectrum of the standard sample, an equation 1: representing the dependence of the peak position ν _std and the half width w _{std on} the carrier concentration c
ν _std = f (c)
And Formula 2:
w _std = g (c)
Ask for. Here, f (c) and g (c) is a function related to carrier concentration c. Incidentally, steps S3 and S4 may be performed either order.

Next, in step S5, 2-element by measuring the emission spectrum in a test site of the test sample and calculate the peak position [nu _e and the half-width w _e. Then, in step S6, the half-value width of the emission spectrum is not changed by the stress, by utilizing the change depends only on the carrier concentration, applying the half-width w _e obtained in w _std of formula 2. As a result, the carrier concentration c _e is obtained in the measurement site of the compound semiconductor material.

Next, in step S7, by fitting the c _e obtained in Equation 1, the peak position [nu ₀ of emission spectrum at a carrier concentration c _e is calculated at zero stress. By subtracting the value of ν ₀ obtained in this way from the value of the emission spectrum ν _e obtained for the two-element test sample in step S8, the stress at the test site of the two-element test sample is determined. it can be determined peak position movement amount .DELTA..nu _e of the emission spectrum due.

The emission spectrum gives rise to a peak position shift proportional to the stress value.
Δν = Πσ
It is known that this relationship holds (supra). Here, Δν represents the peak position movement amount due to stress, σ represents the stress applied to the sample, and Π represents the stress sensitivity coefficient of the sample.

Therefore, in step S9, if the stress sensitivity coefficient の of the compound semiconductor having the same composition as that of the two-element test sample and having a carrier concentration c _e is known, the value of Δν _e obtained above is used as the stress sensitivity coefficient Π. in by dividing, it is possible to obtain a stress value σ acting on the measurement site of the 2-element test sample. This is the end of the stress measurement at the measurement site of the test sample.

で近似することができる（但し、σ：亀裂の先端から当該亀裂の中心線の延長線上を当該亀裂先端前方への微小距離ｒの位置に働く応力、Ｋ：臨界応力拡大係数）。また、応力拡大係数Ｋは、下記式：

（ｘ：試料の亀裂の先端から当該亀裂の中心線上を当該亀裂の内部に向かう方向への距離、２ｕ：距離ｘでの開口変位量、Ｅ’：平面ひずみヤング率）から求められる（但し、Ｅ’は、下記式：

（Ｅ：ヤング率、ν：ポアソン比）で表される）。ヤング率Ｅおよびポアソン比νは物質に固有の値である。上記のように表される応力分布σと、測定したスペクトルのピークシフト量Δνとの関係から、応力感度係数Πを求めることができる。 Incidentally, the stress sensitivity coefficient of the test sample can be determined by the stress measuring method described in the specification of Japanese Patent Application No. 2004-42068 copending by the present applicant. Specifically, in the standard sample having a crack formed by pressing an indenter (for example, a Vickers indenter) or the like against a plane of a standard sample (for example, a wafer having a flat surface) having the same composition as the test sample. The stress distribution σ near the crack tip and the shift amount Δν due to the stress at the peak position of the spectrum obtained from the emission spectrum or Raman spectrum of the standard sample obtained near the crack tip are obtained, and the relationship between them is obtained. By analyzing, the stress sensitivity coefficient Π is derived. Here, the stress distribution of the crack tip is represented by the following formula:

(Where σ is the stress acting on the extension of the center line of the crack from the crack tip to the front of the crack tip at a position of a minute distance r, and K is the critical stress intensity factor). Further, the stress intensity factor K is expressed by the following formula:

(X: distance from the tip of the crack of the sample toward the inside of the crack on the center line of the crack, 2u: opening displacement at distance x, E ′: plane strain Young's modulus) E 'is represented by the following formula:

(E: Young's modulus, ν: Poisson's ratio)). The Young's modulus E and Poisson's ratio ν are values inherent to the substance. The stress sensitivity coefficient Π can be obtained from the relationship between the stress distribution σ expressed as described above and the measured peak shift amount Δν of the spectrum.

  The stress sensitivity coefficient measurement method is particularly useful when obtaining a stress sensitivity coefficient of a minute test object or obtaining a stress sensitivity coefficient of a coating film such as a thin film.

  Further, the stress sensitivity coefficient can be measured by other known methods, such as 4-point bending method. The 4-point bending method is particularly effective when the test object has a size that can be fixed to the jig of the 4-point bending apparatus.

(Apparatus and program for determining carrier concentration and stress of test sample)
In another aspect, the present invention provides an apparatus for performing the above-described method and an operation for determining carrier concentration or stress of a test sample in a computer mounted on (or used in conjunction with) such an apparatus. A program for performing the processing is also provided. Figure 2 is a block diagram showing the overall configuration of an apparatus for determining such carrier concentration and stress.

  In FIG. 2, an apparatus 20 according to an embodiment of the present invention includes a sample stage (where a sample is placed), various probe sources that irradiate the sample, a spectroscope for spectroscopically analyzing light emitted from the sample, and spectroscopic light. A spectrum measuring unit 21 composed of a detector or the like (not shown) for detecting a signal, a storage unit 22 composed of a ROM, RAM, hard disk, FD, or MO disk, and a computation composed of a CPU or the like Unit 23, an input unit 24 configured by an external storage device such as a keyboard or an FD, and an output unit 25 configured by an output unit such as a terminal or a display unit such as a liquid crystal display. Yes.

In the apparatus 20 of FIG. 2, the spectrum measurement unit 21 measures the emission spectrum at the spectrum measurement site of the test sample or standard sample, and outputs the result to the storage unit 22 or the calculation unit 23. The storage unit 22 is the spectrum data measured by the spectrum measurement unit 21, the data input from the input unit 24 (for example, the relational expression of ν _std = f (c) and w _std = g (c)), or The result of the arithmetic processing in the arithmetic unit 23 is stored. The calculation unit 23 includes an algorithm necessary for calculation processing, a program for executing calculation processing, and the like. The calculation unit 23 stores in advance data in the spectrum of the test sample or the standard sample measured by the spectrum measurement unit 21 or the storage unit 22. Data on the spectrum of the stored test sample or standard sample is acquired, the carrier concentration of the test sample or the stress acting on the test site is calculated according to the above algorithm or program, and the result is stored in the storage unit 22. Record or output to the output unit 25. The CPU that constitutes the calculation unit 23 also serves as a control unit (not shown) that controls the entire device 20 including each unit. Terminal, an output unit 25 composed of such as a liquid crystal display or display monitor, data or operation result from the arithmetic unit 23 or the storage unit 22, or output to the outside under the control of the CPU, or display.

  On the other hand, FIG. 3 is a flowchart showing the operation process performed by the calculating unit 23 of the device 20 shown in FIG. Hereinafter, each step will be described with reference to FIG.

Processing performed by the arithmetic unit 23 shown in FIG. 3, the operation of such pressing operation processing start key by the user is initiated, such as by transferring from the input unit 24 a start signal to the arithmetic unit 23. First, in step S11, the emission spectrum at the test site of the test sample measured by the spectrum measurement unit 21 is acquired directly from the spectrum measurement unit 21 or from the storage unit 22, and the half width and peak position are obtained from the spectrum. Determine using a commercially available peak fitting program. Next, in step S12, the relationship between the half-value width w _std of the standard sample stored in advance in the storage unit 22 and the carrier concentration (w _std = g (c)) is acquired, and the above-described relational expression is used. The carrier concentration corresponding to the half-value width of the test sample obtained in step 1 is calculated.

Next, in step S13, similarly, the relationship (ν _std = f (c)) between the peak position ν _std of the standard sample and the carrier concentration stored in advance in the storage unit 22 is obtained, and based on the relational expression. Te, and calculates the peak positions corresponding to the carrier concentration of the test samples obtained above.

  Next, in step S14, by obtaining a difference value between the peak position of the spectrum of the test sample obtained in step S11 and the peak position of the spectrum of the standard sample obtained in step S13, the test site of the test sample is obtained. The peak position movement amount Δν due to the working stress is calculated.

  Next, in step S15, the stress sensitivity coefficient Π of the test sample stored in advance in the storage unit 22 is acquired, and together with the peak position movement amount Δν at the test site of the test sample obtained above, the formula: Δν = by fitting the Paishiguma, after calculating the stress sigma, the process ends.

  In this way, the apparatus 20 according to an embodiment of the present invention allows the half-value width of the emission spectrum at the test site not to depend on the stress acting on the test site, so that only the half-value width and the peak position are used. The carrier concentration of the test sample and the stress acting on the test site can be obtained. Incidentally, Step S11 in FIG. 3, instead of performing the calculating unit 23 may perform the spectrum measuring section 21 in advance.

  Examples of the two-element compound semiconductor to which the present invention can be applied include AlN, GaN, GaAs, GaSb, InP, InAs, InSb, and II-VI group elements of ZnO, ZnS, ZnSe, and ZnTe, which are composed of III-V group elements. , CdS, CdSe, HgS, and SnTe, PbS, PbSe, PbTe, etc., which are further composed of IV-VI group elements.

  In addition, the emission spectrum of the test sample or standard sample is obtained by irradiating the sample with an electromagnetic wave in a wavelength range from electron beam, ion, or γ-ray to X-ray, ultraviolet light, and visible light, and the light emitted from the sample is spectroscope. It can be obtained by detecting with.

(Embodiment 2)
In this embodiment, the peak position shift amount due to the carrier concentration and the stress is obtained from the emission spectrum of the compound semiconductor material composed of three or more elements of unknown stress, unknown carrier concentration, and unknown composition. Procedure is similar to that shown in FIG. 1, hereinafter, be described with reference to FIG. When there are three or more elements, the composition changes due to differences in the production environment, and the peak wavelength and half width of the emission spectrum also change. Therefore, it is necessary to first determine the composition at the site to be examined.

  First, in step S1, the composition at the test site of a compound semiconductor material (hereinafter referred to as “multi-element test sample”) composed of three or more elements whose stress is unknown, whose carrier concentration is unknown, and whose composition is unknown is set to the wavelength. It is determined using an analysis method such as a dispersion X-ray microanalyzer method (WDS method), a wavelength dispersion X-ray microanalyzer method, or a wavelength dispersion X-ray fluorescence X-ray method.

Next, in step S2, a plurality of compound semiconductor standard samples having the same composition as the test site of the multi-element test sample and having different carrier concentrations are prepared, and the emission spectra of these standard samples are measured. Here, the carrier concentration can be appropriately selected by those skilled in the art. For example, different carrier concentrations are prepared in the range of 0 to 1.0 × 10 ¹⁹ atoms / cm ³ . Carrier concentration of the standard sample can be determined as described in the first embodiment.

Then determined in step S3 and step S4, the peak position [nu _std and the half-width w _std relation formula showing a carrier concentration dependence of the (see above Equations 1 and 2).

Next, in step S5, by measuring the emission spectra at the measurement site of the multi-element system the test sample and calculate the peak position [nu _e and the half-width w _e. As long as the composition of the compound semiconductor material is constant, it may be assumed that the full width at half maximum of the emission spectrum does not change with stress, but changes only depending on the carrier concentration. Thus, the half-width w _e of the emission spectra at the measurement site of a multi-element system test sample obtained can be applied to w _std equation 2, whereby in step S6, the measurement site of the compound semiconductor material The carrier concentration c _e can be obtained.

Next, in step S7, the peak position ν ₀ of the emission spectrum of the multi-element test sample having the above composition at zero stress and carrier concentration c _e can be calculated by applying the determined c _e to Equation 1. it can. Next, in step S8, by subtracting this ν ₀ from the emission spectrum ν _e at the test site of the multi-element test sample, the peak of the emission spectrum due to the stress at the test site of the multi-element test sample. The movement amount Δν _e can be obtained.

Here, if the stress sensitivity coefficient の of the compound semiconductor having the same composition as the multi-element test sample is known at the carrier concentration c _e , by dividing Δν _e by the stress sensitivity coefficient に お い て in step S9, it is possible to obtain the stress value σ acting on the measurement site of the multi-element system the test sample.

  Incidentally, the stress sensitivity coefficient of the test sample can be obtained in a manner similar to that described in the first embodiment.

  Also, if the test object has a uniform composition at each site and a uniform carrier concentration, such as a thin film uniformly formed on a semiconductor wafer, for example, Even if the stress sensitivity coefficient is unknown, the present invention makes it possible to more accurately evaluate the magnitude of “relative” stress between the test sites of the test object. is there.

  The compound semiconductor consisting of three elements or more which the present invention may be applied, AlGaAs is three element system, GaAsP, GaInAs, GaInP, AlInAs, AlGaN, HgCdTe, PbSnTe, the like are also four-element based PbSnTe AlGaAsSb, GalnPAs, AlGaInAs AlGaInP, InPAsSb, and the like. Other compounds of the 5-element system and 6-element semiconductor is also applicable.

  In addition, the emission spectrum of a test sample or standard sample is obtained by irradiating the sample with electromagnetic waves in the energy region from electron beams, ions, or γ rays to X-rays, ultraviolet rays, and even visible light, and the light emitted from the sample is spectroscope. It can be obtained by detecting with.

  In still another aspect, the present invention provides a carrier concentration measuring device and a stress measuring device similar to those described in the first embodiment for a compound semiconductor composed of three or more elements, and a computer program that can be mounted on them. To do. Its description is substantially the same as that described in the first embodiment, and a description thereof will be omitted.

  As described above, in the first and second embodiments, the present invention has been described using the compound semiconductor material. However, the scope of the present invention is not limited to these, and a single semiconductor material (for example, silicon (Si), germanium ( against the carrier concentration and stress measurement of Ge), etc.), the present invention can be applied.

  Further, the present invention includes a substrate in a semiconductor device, the thermal oxide film can be applied to the stress measurement and carrier concentration measurement of any site, such as a thin film. The semiconductor device includes an optical semiconductor device (for example, a light receiving device made of a semiconductor, a light emitting device, a device including both of them, typically including a semiconductor laser, an avalanche photodiode, a phototransistor, etc.), an electronic device. (Eg, transistors), and other semiconductor devices.

  Specific examples of semiconductor devices to which the present invention can be applied are given below, but the scope of the present invention is not limited thereto. The present invention relates to a semiconductor device of stress such as the following may be applied to the carrier concentration analysis:

・ Analysis of impurity diffusion layer and stress analysis of MOS field effect transistor (MOSFET) ・ Light emitting diode, semiconductor laser Especially, carrier density distribution and stress distribution evaluation in each layer of double hetero structure ・ Variable capacitance diode, avalanche photodiode, Zener Stress, carrier concentration analysis near PN junctions such as photodiodes, tunnel diodes, backward diodes, photodiodes, PIN photodiodes, Schottky photodiodes, solar cells, impat diodes, barit diodes, Gunn diodes, etc. ・ Thyristors (PN junction devices for power control) )
In particular, stress and carrier concentration analysis in the vicinity of PN junctions such as photothyristors, MOS thyristors, reverse blocking thyristors, reverse conducting thyristors, two-way thyristors, etc. evaluation of the GaN substrate that was.

  EXAMPLES Hereinafter, although an Example demonstrates this invention more concretely, these are only illustrations and the scope of the present invention is not limited to these.

  In this example, the stress in the current blocking layer of the semiconductor red laser was measured.

  Figure 4 shows a schematic cross-sectional view of a semiconductor red laser used in this embodiment. 4 includes a p-contact layer 1, an n-GaAs current blocking layer 2, a p-cladding layer 3, an active layer 4, an n-cladding layer 5, and a substrate 6 in this order from the upper surface side. Has been. The current blocking layer including the portions indicated by A and B in FIG. 4 is composed of two-element n-GaAs. Since n-GaAs is a two-element system, there is almost no composition change due to a difference in film forming environment or the like, and two elements exist stably in a 1: 1 composition.

First, as a standard sample, the carrier concentration is in the range of ^{0~5.66 × 10 18 atom / cm 3} , and the n-GaAs wafers with different carrier concentrations are prepared seven. Each of these was irradiated with 488 nm Ar ion laser light, and the emission spectrum was measured, and the relationship between the peak position and half width of the spectrum and the carrier concentration was determined. The results are shown in FIGS. 5 and 6, respectively. As shown, the peak position and full width at half maximum of the standard sample change depending on the carrier concentration, and the concentration dependency is expressed by Equation 4:
^{_{ν std = (1.05 × 10 -20}} ) c + 1.42
And Formula 5:
^{_{w std = (8.32 × 10 -21}} ) c + 7.04 × 10 -2
Can be approximated.

  Next, the emission spectrum at the test site of the semiconductor red laser was determined. Here, as an example, the 488 nm Ar ion laser light was irradiated to the two parts (point A and point B) in FIG. 4, and the emission spectrum from the sample was measured. The emission spectrum of the points A and B, respectively shown in FIGS. 7A and 7B. The two emission spectra are curve-fitted with a Gaussian function, the emission spectrum peak position at point A is 1.4575 eV and the half-value width of 0.1008 eV, the emission spectrum peak position at point B is 1.4647 eV and the half-value width is 0 .1085 eV was obtained. As a function that can be used for curve fitting, a Lorentz function, a false Voigt function, or the like can be used in addition to the above Gauss function.

Substituting the obtained half-value widths of the emission spectra at point A and point B into w _std in Equation 5, the carrier concentrations at points A and B are 3.6636 × 10 ¹⁸ atoms / cm ³ and 4.5802 ×, respectively. 10 ¹⁸ atoms / cm ³ are obtained. By substituting the obtained carrier concentration into c in Equation 4, n-GaAs in a zero stress state with carrier concentrations of 3.66 × 10 ¹⁸ atoms / cm ³ and 4.58 × 10 ¹⁸ atoms / cm ³ is obtained. peak position of the emission spectrum is respectively calculated as 1.4586eV and 1.4683EV. By subtracting the peak position in the zero-stress state calculated in this way from the peak positions obtained from the emission spectra measured at points A and B under stress, the emission spectra due to stress at points A and B are obtained. shift amount of the peak position of, are respectively determined as -0.0011eV and -0.0036EV.

Here, the stress sensitivity coefficient in n-GaAs at a carrier concentration of 3.66 × 10 ¹⁸ atoms / cm ³ is −0.0365 eV / GPa. By dividing the position shift amount -0.0011 eV, a tensile stress of 30.6 MPa acting on the point A is obtained. Similarly, the stress sensitivity coefficient of n-GaAs at a carrier concentration of 4.58 × 10 ¹⁸ atoms / cm ³ is −0.0338 eV / GPa, and the tensile stress acting on the point B is 106 MPa.

Figure 8 shows a semiconductor infrared laser of a cross-sectional structure used in this example. The semiconductor infrared laser of the cross-section of FIG. 8, in order from the top side, p contact layer 11, and a buried layer 12, the current blocking layer 13, the active layer 14 and n layer 15,. The buried layer 12 including the point A of the test site is composed of p-Al _x Ga _1-x As of the three element system.

  According to the procedure shown in the flow chart of FIG. 1, first, a composition x = 0.55 at a point A as a test site was determined for the test sample by the WDS method.

Next, in the obtained composition x = 0.55, epitaxial growth films of p-Al _0.55 Ga _0.45 As with different stress and zero carrier concentration were prepared by MOCVD, and these were used as standard samples. These standard samples were irradiated with an electron beam, the emission spectrum from the sample was measured, and the carrier concentration dependency of the peak position and the half width was obtained. The results are shown in FIG. 9 and FIG. The graphs shown in FIG. 9 and FIG.
^{_{ν std = (1.18 × 10 -19}} ) c + 1.75
And Equation 7:
^{_{w std = (1.75 × 10 -20}} ) c + 0.145
Can be approximated by

Next, in the test sample, the emission spectrum was measured by irradiating the point A with an electron beam to obtain a peak position of 2.0786 eV and a full width at half maximum of 0.1950 eV. By substituting the half-value width of 0.1950 eV of the emission spectrum at point A into w _std in Equation 7, the carrier concentration at point A is 2.84 × 10 ¹⁸ atoms / cm ³ . By substituting the obtained carrier concentration into c in Equation 6, 2 as the peak position of the emission spectrum of p-Al _0.55 Ga _0.45 As in a zero stress state at a carrier concentration of 2.84 × 10 ¹⁸ atoms / cm ^3. Obtain 0.0829 eV. By subtracting the peak position in the zero stress state from the peak position 2.0786 eV of the emission spectrum measured at point A, −0.0043 eV was obtained as the shift amount of the light emission peak position due to stress at point A.

Here, the stress sensitivity coefficient in p-Al _0.55 Ga _0.45 As at a carrier concentration of 2.84 × 10 ¹⁸ atoms / cm ³ is −0.0311 eV / GPa. By dividing the shift amount of the emission peak position due to the stress at −0.0043 eV, a tensile stress of 136 MPa acting on the point A is obtained.

Figure 11 is a schematic top view of epitaxially grown _{p- (Al x Ga 1-x} ) y In 1-y P thin film on a GaAs wafer used in this embodiment. The carrier concentration at the points A, B, C, and D, which are test sites, and the peak position shift amount due to stress were determined according to the procedure shown in FIG. The results are shown in Table 1.

  Hereinafter, the details of the measurement will be described.

  First, when X-ray fluorescence analysis was performed, it was found that the same composition x = 0.6 and y = 0.5 at all four points (A, B, C, and D) of the test sample.

Next, in the obtained composition x = 0.6, y = 0.5, epitaxial growth films of p- (Al _0.6 Ga _0.4 ) _0.5 In _0.5 P with different stress and zero carrier concentration were prepared by the MOCVD method. It was a standard sample. 12 and 13, by measuring the emission spectrum from the sample is irradiated with X-rays to those of the standard sample, shows the result of obtaining the carrier concentration dependence of the peak position and half-value width. The graphs of FIG. 12 and FIG.
^{_{ν std = (2.64 × 10 -21}} ) c + 2.34
And Formula 9:
_{w std = (- 7.28 × 10} -40) c 2 - (4.44 × 10 -22) c + 0.145
It can be approximated to the following relational expression.

Next, in a test sample, A point, B point, X-ray was irradiated to the point C, and point D, the emission spectrum was measured to determine the respective peak positions and half width. Next, the obtained half-value width was substituted into w _std in Equation 9 to determine carrier concentrations at points A, B, C, and D. By substituting the carrier concentration thus determined for c in Equation 8, the peak wavelength of the emission spectrum of p- (Al _0.6 Ga _0.4 ) _0.5 In _0.5 P in the zero stress state at each carrier concentration can be obtained. By subtracting the peak positions in the zero stress state from the peak positions of the emission spectra measured at points A, B, C, and D, the shift amount of the emission peak wavelength due to stress at each point can be obtained. .

  Since the composition at each point is the same, and the carrier concentration at each point is almost the same value as shown in Table 1, the stress sensitivity coefficient at each point is also considered to be almost the same value. Therefore, the difference in stress acting on each point can be relatively estimated from the difference in the shift amount of the emission peak due to the stress at each point. In general, the peak position of the emission spectrum shifts to the high energy side under compressive stress and to the low energy side under tensile stress. Looking at the peak position movement amount due to the stress of Table 1, it can be seen that working stress of all compressed to each point. In particular, the largest compressive stress works at the point D. In this manner, the relative stress acting on each region of the thin film as the test object can be compared more accurately than before. Also, if desired, the stress sensitivity coefficient of the test sample can be obtained, or if the stress sensitivity coefficient of the test sample is known, the value can be used to calculate the absolute stress at each test site. Is possible.

  In the present invention, the carrier concentration and stress of a semiconductor device can be determined relatively easily and with high accuracy by a spectroscopic method, so that an analysis / evaluation method for high-quality crystal growth, device fabrication, etc. As very useful.

Flow diagram illustrating a procedure according to an embodiment of the method for determining the carrier concentration and the stress of the test samples of the present invention Block diagram illustrating the overall configuration of an embodiment of a device for determining the carrier concentration or stress of the test samples of the present invention Flow diagram that illustrates the processing by the calculation unit 23 performs the device for determining the carrier concentration or stress of the test samples of the present invention Schematic cross-sectional view of a semiconductor red laser having a 2-component n-GaAs current blocking layer used in Example 1 The graph which shows the relationship between the peak position of the emission spectrum measured by irradiating the 488-nm Ar ion laser beam to the standard sample of 2 component type compound semiconductor material n-GaAs, and carrier concentration. The graph which shows the relationship between the half value width of the emission spectrum measured by irradiating the 488-nm Ar ion laser beam to the standard sample of 2 component type compound semiconductor material n-GaAs, and carrier concentration. (A) The emission spectrum at the point A of the n-GaAs current blocking layer of the semiconductor red laser of FIG. 4; (B) The emission spectrum at the point B of the n-GaAs current blocking layer of the semiconductor red laser of FIG. Figure Sectional schematic diagram of a semiconductor infrared laser including a buried layer composed of p-Al _x Ga _1-x As of the three-element system used in Example 2 The figure which shows the relationship between the peak position of the emission spectrum of several standard samples from which carrier concentration used in Example 2 differs, and carrier concentration. The figure which shows the relationship between the half value width of the emission spectrum of several standard samples from which carrier concentration differs in Example 2, and carrier concentration. Used in Example _{3 p- (Al x Ga 1-} x) schematic top view of a _y In _1-y P membrane Diagram showing the relationship between the peak position and the carrier concentration of the emission spectrum of different standard samples having carrier concentrations used in Example 3 Diagram showing the relationship between the half width and the carrier concentration of the emission spectrum of different standard samples having carrier concentrations used in Example 3

Explanation of symbols

2 n-GaAs current blocking layer _{12 p-Al x Ga 1-} x As buried layer 20 apparatus for determining the carrier concentration and the stress of the present invention 21 spectrum measuring section 22 storage section 23 CPU (arithmetic unit)
24 input unit 25 output unit

Claims (15)

An apparatus for determining the stress acting on the test sample,
A spectrum measurement unit for measuring an emission spectrum at a test site of a test sample;
A storage unit;
An arithmetic unit;
Including an output unit,
The storage unit includes data including an algorithm representing a relationship between a half-value width of an emission spectrum and a carrier concentration obtained in advance using a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample. Data including an algorithm representing a relationship between the peak position of the emission spectrum and the carrier concentration for a plurality of standard samples having the same composition ratio as the test site of the test sample and having different carrier concentrations, and the test sample And the stress sensitivity coefficient data of
The computing unit is
From the emission spectrum measured at the test site of the test sample, calculating the half width and peak position of the emission spectrum;
Calculating a carrier concentration at a test site of the test sample from a half value width of the emission spectrum of the test sample based on an algorithm representing a relationship between the half-value width of the emission spectrum of the standard sample and the carrier concentration; ,
Based on an algorithm representing the relationship between the peak position and the carrier concentration of the emission spectrum of the standard sample, and calculating the in carrier concentration of the test sample, the peak positions of the emission spectrum of the standard sample,
By calculating a difference value between the calculated peak position of the emission spectrum of the standard sample and the measured peak position of the emission spectrum of the test sample, the peak position shift amount due to the stress of the emission spectrum of the test sample is calculated. And getting the steps
From the peak position movement amount and the stress sensitivity coefficient of the test sample, the formula:
Δν = Πσ
(Δν: peak position shift amount of emission spectrum of test site of test sample, Π: stress sensitivity coefficient, σ: stress acting on test site of test sample)
Based on, performs arithmetic processing includes a step of calculating the stress acting the said measurement site of the test sample,
The output unit outputs the calculated stress value.   Wherein the output unit further outputs the calculated carrier concentration of the test sample, according to claim 1. An apparatus for determining a carrier concentration at a test site of a test sample,
A spectrum measurement unit for measuring an emission spectrum at a test site of a test sample;
A storage unit;
An arithmetic unit;
Including an output unit,
The storage unit includes data including an algorithm representing a relationship between a half-value width of an emission spectrum and a carrier concentration obtained in advance using a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample. And store
The computing unit is
Wherein the emission spectrum measured at the measurement site of the test sample, and calculating the half value width of the emission spectrum,
Calculating a carrier concentration of the standard sample in a half value width of the emission spectrum of the test sample based on an algorithm representing a relationship between the half value width of the emission spectrum of the standard sample and the carrier concentration. ,
The output unit outputs the carrier concentrations the calculated device.   The apparatus according to claim 1, wherein the test sample is a semiconductor device.   The apparatus according to any one of claims 1 to 3, wherein the emission spectrum is obtained by irradiating a sample with an arbitrary electromagnetic wave in a wavelength range from electron beam, ion, or γ-ray to visible light. A computer program for determining a stress acting on a test sample,
From the emission spectrum measured at the measurement site of the test sample, determining the half width and the peak position of the emission spectrum,
Based on an algorithm representing a relationship between a half-value width of an emission spectrum and a carrier concentration obtained in advance using a plurality of standard samples having different carrier concentrations and having the same composition ratio as the test site of the test sample, from the half-value width of the emission spectrum of the step of calculating a carrier concentration in the measurement site of the test sample,
Based on an algorithm representing the relationship between the peak position of the emission spectrum and the carrier concentration, which is obtained in advance using a plurality of standard samples having different carrier concentrations and having the same composition ratio as the test site of the test sample. Calculating the peak position of the emission spectrum of the standard sample at the carrier concentration of the sample;
By calculating a difference value between the calculated peak position of the emission spectrum of the standard sample and the measured peak position of the emission spectrum of the test sample, the peak position shift amount due to the stress of the emission spectrum of the test sample is calculated. and the obtaining step, and the peak position movement amount, from the stress sensitivity coefficient of the test sample, wherein:
Δν = Πσ
(Δν: peak position shift amount of emission spectrum of test site of test sample, Π: stress sensitivity coefficient, σ: stress acting on test site of test sample)
A program for causing a computer to perform a process including a step of calculating a stress acting on the test site of the test sample based on the above. A computer program for determining the carrier concentration of the test sample,
The step of determining the half-value width of the emission spectrum from the emission spectrum measured at the test site of the test sample, and the emission spectrum obtained for a standard sample having the same composition ratio as the test site of the test sample in advance A program for causing a computer to perform processing including a step of calculating a carrier concentration of a test sample from a half value width of an emission spectrum of the test sample based on an algorithm representing a relationship between a half width and a carrier concentration .   The test sample is a semiconductor device, a program according to claim 6 or 7.   The program according to claim 6 or 7, wherein the emission spectrum is obtained by irradiating a sample with an arbitrary electromagnetic wave in a wavelength range from electron beam, ion, or γ-ray to visible light. A method of determining the stress acting on the test sample,
In the measurement site of the test sample, the emission spectrum was measured, to obtain a half-width and the peak position of the spectrum process,
The light emission of the test sample based on the relationship between the half-value width of the emission spectrum and the carrier concentration determined in advance using a standard sample having a plurality of different carrier concentrations having the same composition ratio as the test site of the test sample. from the half-value width of the spectrum, the step of calculating a carrier concentration in the measurement site of the test sample,
The carrier of the test sample based on the relationship between the peak position of the emission spectrum and the carrier concentration determined in advance using a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample. calculating a peak position of the emission spectrum of the standard sample at a concentration,
By calculating a difference value between the calculated peak position of the emission spectrum of the standard sample and the measured peak position of the emission spectrum of the test sample, the peak position shift amount due to the stress of the emission spectrum of the test sample is calculated. step determining, and includes said peak position movement amount, wherein the stress sensitivity coefficient of the test sample, the step of calculating the stress acting the said measurement site of a test sample, the method.   The relationship between the full width at half maximum of the emission spectrum of the standard sample and the carrier concentration is the emission spectrum of a plurality of standard samples having a plurality of different carrier concentrations with known carrier concentrations having the same composition ratio as the test site of the test sample. The method according to claim 10, which is determined by measuring and deriving a relationship between a half-value width of an emission spectrum of the standard sample and a carrier concentration.   The algorithm representing the relationship between the peak position of the emission spectrum of the standard sample and the carrier concentration is obtained by calculating a plurality of standard samples having a plurality of different carrier concentrations with a known carrier concentration having the same composition ratio as the test site of the test sample The method according to claim 10, wherein the method is obtained by measuring an emission spectrum and deriving a relationship between a peak position of the emission spectrum of the standard sample and a carrier concentration. In the step of calculating the stress, the formula:
Δν = Πσ
(Δν: peak position shift amount of emission spectrum of test site of test sample, Π: stress sensitivity coefficient, σ: stress acting on test site of test sample)
The method according to claim 10, wherein A method for determining a carrier concentration of a test sample,
A step of measuring an emission spectrum at a test site of the test sample to obtain a half width of the emission spectrum, and a plurality of standard samples having different carrier concentrations having the same composition ratio as the test site of the test sample in advance obtained, on the basis of the relationship between the half width and the carrier concentration of an emission spectrum, said from the half width of the emission spectrum of the test sample, the step of calculating the carrier concentration in the measurement site of the test sample,
Including the method.   The relationship between the full width at half maximum of the emission spectrum of the standard sample and the carrier concentration is the emission spectrum of a plurality of standard samples having a plurality of different carrier concentrations with known carrier concentrations having the same composition ratio as the test site of the test sample. The method according to claim 14, which is determined by measuring and deriving a relationship between a half-value width of an emission spectrum of the standard sample and a carrier concentration.

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