Optical measurement method and application of quantum well width

Abstract

The present invention discloses an optical measurement method for quantum well width and its application. The method includes the following steps: obtaining a first reflection signal of incident polarized light from a target under test when there is no laser irradiation; obtaining a second reflection signal of the incident polarized light from the target under test when there is laser irradiation, wherein the energy of the laser is greater than the band gap of the target under test; determining the average energy spacing between absorption peaks of the target under test within the absorption tail region of the band gap based on the first and second reflection signals; and calculating the quantum well width of the target under test based on the average energy spacing. This method can reduce the measurement time period and improve the accuracy of the measurement results without sample preparation.

Description

Technical Field

[0001] The present invention relates to the field of semiconductors, and in particular to an optical measurement method for quantum well width and its application. Background Art

[0002] In the prior art, common methods for measuring quantum well width include Secondary Ion Mass Spectroscopy (SIMS), Kelvin Probe Force Microscope (KPFM), and Transmission Electron Microscope (TEM).

[0003] SIMS can measure the concentration distribution curve of all elements in the sample in the longitudinal direction. Since the inside and outside of the quantum well are composed of different materials, the longitudinal distribution of element concentration can reflect the width of the quantum well. The defect of this measurement method is that the spatial resolution of SIMS is limited and it can only analyze thicker quantum well structures, which is not universal. KPFM can measure the longitudinal distribution of the surface potential of the measured sample after lateral cleavage of the sample. Since there are potential barriers inside and outside the quantum well, the width of the quantum well can be reflected by the distribution of potential. TEM can measure the longitudinal structural composition. Since different elements will show different contrasts in TEM, the brightness and darkness changes of the contrast can reflect the width of the quantum well. The defect of the KPFM and TEM measurement methods is that the measured sample needs to be cleaved, which not only increases the measurement time period, but the exposed surface of the measured sample after treatment will affect the surface potential due to the adsorption of gas molecules, resulting in the measurement result not being a true built-in electric field.

[0004] The information disclosed in this background technology section is only intended to enhance understanding of the overall background of the invention and should not be regarded as an admission or any form of suggestion that the information constitutes the prior art already known to a person skilled in the art. Summary of the Invention

[0005] The object of the present invention is to provide an optical measurement method for quantum well width and its application, which can reduce the time period of the measurement process and improve the accuracy of the measurement results without preparing the measurement sample.

[0006] To achieve the above objectives, an embodiment of the present invention provides an optical measurement method for quantum well width.

[0007] In one or more embodiments of the present invention, the method comprises:

[0008] Acquire a first reflection signal of the target to be measured to the incident polarized light when there is no laser irradiation; acquire a second reflection signal of the target to be measured to the incident polarized light when there is laser irradiation, wherein the energy of the laser is greater than the band gap of the target to be measured; determine the average energy spacing of each absorption peak of the target to be measured in the absorption tail region of the band gap based on the first reflection signal and the second reflection signal; and calculate the quantum well width of the target to be measured based on the average energy spacing.

[0009] In one or more embodiments of the present invention, determining the average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap based on the first reflection signal and the second reflection signal specifically includes:

[0010] Based on the signal difference between the first reflected signal and the second reflected signal, the energy range of the absorption tail region of the target band gap to be measured and the total number of absorption peaks in the absorption tail region are determined; based on the energy range of the absorption tail region, the total number of absorption peaks, and the effective mass of the target holes to be measured, the average energy spacing of the absorption peaks is determined, wherein the effective mass of the target holes to be measured includes the effective mass of heavy holes and the effective mass of light holes.

[0011] In one or more embodiments of the present invention, the method specifically includes:

[0012] Based on the effective mass of the heavy holes and the effective mass of the light holes of the target to be measured, the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks is determined; based on the energy range of the absorption tail region, the total number of absorption peaks, and the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks, the average energy spacing of the absorption peaks is determined.

[0013] In one or more embodiments of the present invention, the calculation formula of the quantum well width of the target to be measured specifically includes:

[0014] The average energy spacing of the absorption peaks is is the ratio of the absorption peak generated by the target heavy hole to be measured, m hh is the effective mass of the heavy hole, m lh is the effective mass of the light hole, m e is the effective mass of the electron, N 峰 is the total number of absorption peaks, h is the reduced Planck constant, and E is the energy range of the absorption tail region; or,

[0015] The average energy spacing of the absorption peaks is is the ratio of the absorption peak generated by the light hole of the target to be measured, m hh is the effective mass of the heavy hole, m lh is the effective mass of the light hole, m e is the effective mass of the electron, N 峰 is the total number of absorption peaks, is the reduced Planck constant, and E is the energy range of the absorption tail region.

[0016] In one or more embodiments of the present invention, the method specifically includes:

[0017] The WKB approximation method is used to calculate the energy distribution of the absorption peak in the absorption tail region, wherein the energy distribution of the absorption peak includes the energy levels of the valence band sub-band and the energy levels of the conduction band sub-band; the intersection of the energy level of each column of the valence band sub-band and the line segment where the band gap is located in the three-dimensional absorption spectrum of the target to be measured is determined; based on the sum of the intersection points and the energy range of the absorption tail region, the average energy spacing of the absorption peaks of the target to be measured in the absorption tail region of the band gap is determined.

[0018] In one or more embodiments of the present invention, the energy level of each valence band sub-band is related to the band gap E g The intersection point j1 of the line segment satisfies The sum of the intersection points j1, i.e. the total number of the absorption peaks, satisfies

[0019] Based on the sum of the intersection points and the energy range of the absorption tail region, determining the average energy spacing of the absorption peaks of the target to be measured in the absorption tail region of the band gap, specifically comprising: performing an integration operation on the sum of the intersection points, and calculating based on the integration operation result and the energy range of the absorption tail region, Reverse deduction The energy range of the absorption tail region is approximately qFL, q is the Lorentz force, F is the electric field strength of the additional electric field of the target to be measured, C k is the coefficient, E 0,e 、E 0,h is the characteristic energy, N e is the number of electronic states in the absorption tail region, m h is the effective mass of the target hole to be measured.

[0020] In one or more embodiments of the present invention, the incident polarized light includes at least two incident angles.

[0021] In another aspect of the present invention, an optical measurement device for quantum well width is provided, which includes a first signal acquisition module, a second signal acquisition module, a first calculation module, and a second calculation module.

[0022] The first signal acquisition module is used to acquire a first reflection signal of the target to be measured to the incident polarized light when there is no laser irradiation.

[0023] The second signal acquisition module is used to acquire a second reflection signal of the target to be measured to the incident polarized light when the target is irradiated with laser light, wherein the energy of the laser light is greater than the band gap of the target to be measured.

[0024] The first calculation module is configured to determine an average energy spacing between absorption peaks of the target to be measured in an absorption tail region of the band gap based on the first reflection signal and the second reflection signal.

[0025] The second calculation module is used to calculate the quantum well width of the target to be measured based on the average energy spacing.

[0026] In one or more embodiments of the present invention, the first calculation module is further used to: determine the energy range of the absorption tail region of the target band gap to be measured and the total number of absorption peaks in the absorption tail region based on the signal difference between the first reflection signal and the second reflection signal; determine the average energy spacing of the absorption peaks based on the energy range of the absorption tail region, the total number of absorption peaks, and the effective mass of the target holes to be measured, wherein the effective mass of the target holes to be measured includes the effective mass of heavy holes and the effective mass of light holes.

[0027] In one or more embodiments of the present invention, the first calculation module is further used to: determine the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks based on the effective mass of the heavy holes and the effective mass of the light holes of the target to be measured; determine the average energy spacing of the absorption peaks based on the energy range of the absorption tail region, the total number of absorption peaks, and the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks.

[0028] In one or more embodiments of the present invention, the first calculation module is further used to: calculate the energy distribution of the absorption peak in the absorption tail region using the WKB approximation method, wherein the energy distribution of the absorption peak includes the energy levels of the valence band sub-band and the energy levels of the conduction band sub-band; determine the intersection of the energy level of each column of the valence band sub-band and the line segment where the band gap is located in the three-dimensional absorption spectrum of the target to be measured; and determine the average energy spacing of the absorption peaks of the target to be measured in the absorption tail region of the band gap based on the sum of the intersection points and the energy range of the absorption tail region.

[0029] In another aspect of the present invention, an electronic device is provided, comprising: at least one processor; and a memory storing instructions, which, when executed by the at least one processor, enable the at least one processor to perform the optical measurement method of quantum well width as described above.

[0030] In another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the optical measurement method of quantum well width as described above are implemented.

[0031] Compared with the prior art, the optical measurement method and application of quantum well width according to the embodiment of the present invention can solve the problems of lengthened time period and reduced accuracy of the test process caused by the sample preparation process in the prior art. By measuring the energy spacing of the absorption peaks in the absorption tail range below the band gap in the sample absorption spectrum, the spatial scale of the electric field in the quantum well, that is, the quantum well width, is deduced, which effectively reduces the time period of the measurement process, improves the energy resolution and measurement accuracy, and has wide adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of a method for optically measuring quantum well width according to one embodiment of the present invention;

[0033] Figure 2 is a two-dimensional function diagram of a semiconductor absorption spectrum according to an optical measurement method of quantum well width according to one embodiment of the present invention ( Figure 2 -(a)) and three-dimensional absorption spectra ( Figure 2 -(b));

[0034] Figure 3 is a diagram showing the change of the energy band structure and wave function distribution of the optical measurement method of the quantum well width according to one embodiment of the present invention, including a semiconductor energy band structure diagram without an electric field ( Figure 3 -(a)) and the semiconductor band structure diagram with electric field ( Figure 3 -(b));

[0035] Figure 4 1 is a schematic diagram of an instrument for an optical measurement method of quantum well width according to an embodiment of the present invention;

[0036] Figure 5 is a structural diagram of an optical measurement device for quantum well width according to one embodiment of the present invention;

[0037] Figure 6 FIG. 4 is a hardware structure diagram of an optical measurement and calculation device for quantum well width according to an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific embodiments.

[0039] Unless expressly stated otherwise, throughout the specification and claims, the term "comprise" or variations such as "include" or "comprising", etc., will be understood to include the stated elements or components but not to exclude other elements or other components.

[0040] A quantum well is a potential well with discrete energy values. Its fundamental characteristic is that, due to the limited width of the quantum well, the carrier wave function is localized in one dimension. As a result, the well walls in the quantum well have a strong confinement effect, limiting the carriers to two-dimensional freedom within the plane parallel to the well walls, and splitting the conduction and valence bands into multiple sub-bands in the perpendicular direction. Many quantum well applications require a high degree of measurement of the quantum well width.

[0041] A triangular potential well is a model of a potential well. One boundary is the infinite vacuum energy level, known as the hard boundary, while the other is a sloping boundary where real space and energy scales extend infinitely. Because the quantum well energy value at each point on the sloping boundary depends on its location, the closer to the hard boundary, the lower the energy value, known as the soft boundary.

[0042] The quantum confined Stark effect (QCSE) refers to the situation where when the width of the quantum well containing the electric field is less than a certain size, the absorption spectrum appears as discrete absorption peaks. As the electric field strength increases, the overall energy level of the electron and hole wave functions decreases, resulting in a red shift of the absorption peak in the absorption spectrum.

[0043] The Franz-Keldysh effect refers to the phenomenon that when a semiconductor surface containing an electric field or a thick semiconductor film is exposed to an electric field, the overall energy level of the electron and hole wave functions decreases, and an absorption tail region appears below the band gap in the absorption spectrum.

[0044] The band gap, also known as the energy gap, refers to the energy difference between the bottom of the valence band and the top of the valence band, also known as the bandgap. The bandgap of a semiconductor is a key characteristic parameter, its magnitude primarily determined by the semiconductor's band structure, specifically its crystal structure and atomic bonding properties. The bandgap reflects the strength of valence electron confinement, representing the minimum energy required to generate intrinsic excitation. The bandgap can be measured using conductivity and spectroscopy. The bandgap value measured using spectroscopy is also known as the optical bandgap.

[0045] The quantum confined Franz-Keldysh (QCFK) effect refers to the situation in which, when the width of a quantum well model containing an electric field approaches infinity, the absorption spectrum exhibits the Franz-Keldysh effect of a semiconductor material with an additional electric field. When the well width is smaller, the absorption spectrum exhibits the quantum confined Stark effect.

[0046] From the above, it can be seen that when the quantum well width is small, the quantum well manifests as a quantum confined Stark effect (QCSE). At this time, the exciton effect is strong, making it possible to identify the absorption peak in the absorption spectrum under a certain electric field. Based on the above principles, the present application hopes to provide an optical measurement method that can obtain the quantum well width by combining measurement and calculation of the triangular potential well model and the absorption peak in the absorption tail region of the absorption spectrum.

[0047] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0048] Example 1

[0049] like Figures 1 to 3 As shown, an optical measurement method for quantum well width in an embodiment of the present invention is introduced, and the method includes the following steps.

[0050] In step S101 , a first reflection signal of the target to be measured to the incident polarized light is obtained when there is no laser irradiation.

[0051] In this embodiment, when no laser is used for measurement, the first reflection signal of the target to be measured under the incident polarized light is scanned.

[0052] Specifically, the incident polarized light may be at a single incident angle or include at least two incident angles. It is understood that measuring polarized light at multiple incident angles can reduce noise signals and improve measurement accuracy, which is not limited in this application.

[0053] In step S102, a second reflection signal of the target to be measured to the incident polarized light is obtained when the target is irradiated with laser light.

[0054] In this embodiment, a laser is added for measurement. After the laser output stabilizes, a second reflection signal of the target is obtained by scanning with incident polarized light at the same angle as the incident polarized light in the absence of the laser. The laser energy should be set to be greater than the bandgap of the target. During the measurement process, the laser energy can be controlled by selecting a laser with an appropriate wavelength based on the energy-wavelength conversion formula. Furthermore, the laser and the incident polarized light should illuminate the same area of ​​the target, or the illumination areas of the laser and the incident polarized light on the target should at least partially overlap.

[0055] In step S103 , based on the first reflection signal and the second reflection signal, an average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap is determined.

[0056] Specifically, computer software can be used to process the first and second reflected signals of the two measurements, fit the absorption coefficients of the two signals, and calculate the difference Δα between the two, that is,

[0057] Δα=α(without laser)-α(with laser).

[0058] Furthermore, the structure of the absorption peak in the absorption tail region of the absorption spectrum of the sample to be measured can be determined by calculating the difference Δα obtained by the two sample reflection signals.

[0059] like Figure 2 As shown, Figure 2 (a) shows a two-dimensional representation of the imaginary part of the dielectric constant ε² as a function of a typical semiconductor. ε² is proportional to the absorption coefficient α, so within a certain energy range, ε² tends to follow α. ε²(ω,0) represents the absence of an electric field, decreasing to zero below the band gap. ε²(ω,0) represents the presence of an electric field, with an absorption tail below the band gap.

[0060] In order to realize the subsequent mathematical calculation, the present invention proposes a new method of displaying semiconductor absorption spectrum data, namely three-dimensional absorption spectrum. Figure 2 -(b), the x coordinate of each point in the figure is the energy E of the final state of the inter-band absorption transition, that is, the conduction band sub-band e , the y coordinate is the energy E of the initial state of the inter-band absorption transition, that is, the valence band sub-band h , the z coordinate is from E h to E e The absorption intensity of the interband transition. Because holes and electrons carry opposite charges, the sum of the intrinsic energies of the conduction band and valence band sub-bands is the incident light energy required for the corresponding transition. Thus, each point on the horizontal axis of the two-dimensional absorption spectrum corresponds to a straight line with a slope of -1 in the three-dimensional absorption spectrum used in the present invention. In the figure, a dashed line segment with a slope of -1 passing through the band gap corresponds to the band gap in the two-dimensional absorption spectrum, and the absorption tail region with weaker absorption below the band gap is represented by a darker point, and the absorption region with stronger absorption above the band gap is represented by a lighter point. The intersection of the kth column of lattices and the line segment where the band gap is located is recorded as point j1.

[0061] like Figure 3 As shown in , the quantum size effect causes the conduction band and valence band in the quantum well to appear as multiple discrete sub-bands, and the energy difference between the sub-bands is related to the width of the quantum well. Figure 3 As shown in -(a), for a quantum well without a built-in electric field, the energy band structure of the valence band and the conduction band in real space is two parallel square potential wells, and the energy difference between the conduction band and the valence band sub-band gradually increases with the increase of the intrinsic energy. Figure 3As shown in Figure 2(b), when the quantum well is charged with an electric field, the valence and conduction bands in real space have a parallel triangular potential well structure of finite width. Furthermore, the energy difference between the conduction and valence subbands decreases with increasing intrinsic energy. Because photon absorption means that the photon energy is exactly the energy difference between a subband of the valence band and a subband of the conduction band, the spacing between the valence and conduction band energy levels can be reflected in the energy spacing between the absorption peaks in the absorption spectrum.

[0062] Based on the above inference, the calculation formula of the quantum well width of the target to be measured is derived.

[0063] First, the WKB approximation method is used to calculate the energy distribution of the absorption peak in the absorption tail region, wherein the energy distribution of the absorption peak includes the energy levels of the valence band sub-band and the energy levels of the conduction band sub-band.

[0064] The WKB (Wentzel–Kramers–Brillouin) approximation refers to a semiclassical approximation method for solving the time-independent Schrödinger equation. The WKB approximation approximates the wave function as an exponential function, where the amplitude or phase of the wave function is assumed to change slowly within the de Broglie wavelength. The approximate form of the wave function is then substituted into the Schrödinger equation and the exponential function form is expanded in series. By applying the WKB approximation to the triangular potential well, the following conclusion can be obtained: the kth energy level satisfies E k =C k E0, where the coefficient Characteristic energy Because C k The increasing trend slows down with the increase of k, so the energy difference between discrete energy levels in the triangular potential well gradually decreases with the increase of intrinsic energy.

[0065] Secondly, the intersection of the energy level of each column of the valence band sub-band and the line segment where the band gap is located in the three-dimensional absorption spectrum of the target to be measured is determined.

[0066] Thirdly, based on the sum of the intersection points and the energy range of the absorption tail region, the average energy spacing of the absorption peaks of the target to be measured in the absorption tail region of the band gap is determined.

[0067] Specifically, the relevant calculation and derivation steps are described as follows.

[0068] S1: Calculate the band gap E g The energy range of the absorption tail region is as follows.

[0069] Depend on Figure 3 As shown, the energy range of the absorption tail region is approximately qFL,

[0070] Wherein, q is the Lorentz force, and F is the electric field strength of the additional electric field of the target to be measured.

[0071] Specifically, the lowest energy levels of the conduction band and the valence band are close to the bottom of the conduction band and the valence band, respectively. Therefore, in the target film to be measured with an additional electric field having an electric field strength of F and a width of L, the incident light energy required for the minimum energy inter-band transition is from E g Reduced to E g -qFL.

[0072] S2: Calculate the energy distribution of the absorption peak in the absorption tail region using the WKB approximation.

[0073] Specifically, when the triangular potential well depth is deep enough, that is, when qFL>>1, the WKB approximation of the Airy function can be used, and the kth valence band subband energy level satisfies E k,h =C k E 0,h , the kth conduction band subband energy level satisfies E k,e =C k E 0,e ,

[0074] Among them, the coefficient Characteristic energy m h is the effective mass of the target hole to be measured, m e is the effective mass of the electron, and h is the reduced Planck constant.

[0075] S3: When qFL>>1, the WKB approximation is again used to calculate the energy distribution of the absorption peak in the absorption tail region.

[0076] like Figure 2 As shown, each discrete absorption peak corresponds to the energy level of a conduction band sub-band and the energy level of a valence band sub-band. From low energy to high energy on the y-axis, the lattice gradually becomes denser. When the depth of the triangular potential well is deep enough, that is, qFL>>1, the energy level of each column of the valence band sub-band is consistent with the band gap E g The intersection point of the line segments is recorded as point j1.

[0077] According to the WKB approximation formula, j1 satisfies Substitution

[0078] get

[0079] S4: Sum the intersection point j1.

[0080] Substitute into formula (1) and have to

[0081] The sum of the intersection points j1, that is, the total number of absorption peaks, satisfies

[0082] where N e is the number of electronic states in the absorption tail region.

[0083] S5: Convert formula (2) into an integral, and we get

[0084]

[0085] Ignoring the first term, we get

[0086] S6: Substituting formula (3) into the energy range qFL in S1, we get

[0087] The average energy spacing of the absorption peaks in the absorption tail region

[0088] In step S104 , the quantum well width of the target to be measured is calculated based on the average energy spacing.

[0089] Specifically, the calculation formula for the average energy spacing of each absorption peak in the absorption tail region is deduced from Inversely, we get

[0090] Furthermore, the holes in actual semiconductor materials include light holes and heavy holes. The effective mass of light holes is m lh Much smaller than the effective mass m of the heavy hole hh From formula (3), we can see that in the absorption tail region below the band gap, the ratio of the number of absorption peaks generated by heavy holes to the number of absorption peaks generated by light holes is

[0091] It can be obtained that the calculation formulas for the quantum well width of the target to be measured specifically include the following two:

[0092] 1) The average energy spacing of the absorption peaks is is the ratio of the absorption peak generated by the target heavy hole to be measured, m hh is the effective mass of the heavy hole, m lh is the effective mass of the light cavity;

[0093] 2) The average energy spacing of the absorption peaks is is the ratio of the absorption peak generated by the light hole of the target to be measured, m hh is the effective mass of the heavy hole, m lh is the effective mass of the light hole.

[0094] Example 2

[0095] like Figures 1 to 4 As shown, an optical measurement method for quantum well width in an embodiment of the present invention is introduced, and the method includes the following steps.

[0096] In this embodiment, an optically biased ellipsometer and semiconductor material GaN are used as examples to measure the absorption spectrum of the target to be measured.

[0097] The incident light of the ellipsometer is a beam of linearly polarized light. When reflected by the measurement sample, the polarization state of the reflected light changes to elliptically polarized light. The optical constants of the sample can be obtained by changing the polarization state amplitude and phase of the light. The optically biased ellipsometer used in this embodiment adds a laser beam to the ellipsometer to detect weak signals from the sample. The principle is that under the laser with energy greater than the band gap, the photogenerated carriers will flow to the surface or body of the semiconductor, causing the surface potential of the semiconductor to change, thereby causing a change in the effective electric field on the semiconductor surface. The weak signal can be reflected by measuring the reflected signals of the sample without laser irradiation and with laser irradiation and taking the difference.

[0098] The semiconductor material GaN is a group III nitride and a direct bandgap semiconductor with the characteristics of fast acoustic wave transmission speed, good chemical and thermal stability, high thermal conductivity, low thermal expansion coefficient, and high breakdown dielectric strength.

[0099] In step S101 , a first reflection signal of the target to be measured to the incident polarized light is obtained when there is no laser irradiation.

[0100] like Figure 4 As shown in the figure, a light-biased ellipsometer is constructed based on an ellipsometer. The specific structure includes a computer, a monochromator, a light detector, a laser, and a sample to be measured. During the measurement process, the incident polarized light of the ellipsometer passes through the light monochromator, enters the sample to be measured, and enters the light detector. The added laser is irradiated perpendicularly to the surface of the sample to be measured.

[0101] In this embodiment, the band gap of the GaN sample to be measured is 3.4 eV. Since the energy of the laser needs to be greater than the band gap of the sample to be measured, when selecting the laser for irradiation, a laser with a wavelength lower than 364.6 nm should be selected.

[0102] Specifically, the ellipsometer is started and the laser is turned off, and the reflected signal of the sample is scanned at multiple measurement angles. The measurement angle refers to the incident polarized light, which can be a single incident angle or at least two incident angles. Specifically, for the sample to be measured in this embodiment and the actual measurement situation, the multiple measurement angles can be 60°, 65°, and 70°.

[0103] It is understandable that performing measurements at multiple measurement angles using an ellipsometer can reduce noise signals and improve measurement accuracy.

[0104] In step S102, a second reflection signal of the target to be measured to the incident polarized light is obtained when the target is irradiated with laser light.

[0105] Specifically, after measuring the sample reflection signal without laser irradiation, the ellipsometer is kept started and the laser is turned on. After the laser output stabilizes, the sample reflection signal at the same angles as the multiple angles measured without laser irradiation is scanned again.

[0106] In step S103 , based on the first reflection signal and the second reflection signal, an average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap is determined.

[0107] Specifically, the computer software corresponding to the ellipsometry is used to process the signals of the two measurements, fit the absorption coefficient without laser irradiation and the absorption coefficient with laser irradiation, and calculate the difference Δα between the two, that is,

[0108] Δα=α(without laser)-α(with laser).

[0109] Furthermore, the structure of the absorption peak in the absorption tail region of the absorption spectrum of the sample to be measured can be determined by calculating the difference Δα obtained by the two sample reflection signals.

[0110] Based on the structure of the absorption peaks in the absorption tail region of the absorption spectrum of the sample to be tested, the total number N of all discrete absorption peaks is read out, and the difference E between the leftmost absorption peak and the band gap is read out.

[0111] In this embodiment, based on the effective mass m of the GaN heavy hole in the sample to be tested, hh =1.25m0, effective mass of light hole m lh =0.20m0, the number of heavy holes is The average energy spacing of the absorption peaks can be calculated based on the heavy holes of the sample to be tested. The average energy spacing of the absorption peaks can be calculated based on the light holes of the sample to be tested.

[0112] In step S104 , the quantum well width of the target to be measured is calculated based on the average energy spacing.

[0113] The average energy spacing of the absorption peaks Substitute the calculation formula of the quantum well width of heavy holes into Inversely calculate the quantum well width L; or the average energy spacing of the absorption peak Substitute the calculation formula of the quantum well width of light holes into The quantum well width L is obtained by reverse deduction.

[0114] Specifically, the quantum well width of the target to be measured is measured by the heavy holes or light holes of the sample to be measured. The difference is that the measurement result of the heavy holes of the sample to be measured is closer to the actual data. Both measurement methods are feasible.

[0115] It should be noted that the measuring instrument, sample to be measured and measuring angle etc. illustrated in this embodiment should not be regarded as limiting the features or scope included in the method of this application, but are only for more clearly describing the technical solution of this application.

[0116] In order to describe this embodiment in more detail, a specific experiment is conducted by taking the semiconductor material GaN as an example, and the measuring instrument is a light-biased ellipsometer.

[0117] Specifically, when the semiconductor material GaN is used as a sample to be measured in an optically biased ellipsometer, the GaN sample is a thin film with a width of L and is in an electric field with an electric field strength of F.

[0118] As shown in Table 1, several possible sets of spatial scales L and electric field intensities F were theoretically simulated. By measuring the signal of the optically biased ellipsometer, the signal data were fitted and calculated accordingly to obtain the spatial scale L1 of the electric field. The difference between this and the actual spatial scale L of the electric field is ΔL = L1 - L.

[0119] Among them, E tot is the energy value of the absorption peak farthest from the band gap in the actual measurement, which is used as the total absorption tail region in the measurement. The calculation formula for the average energy spacing ΔE of the absorption peaks within the absorption tail region is:

[0120]

[0121]

[0122] Table 1

[0123] Table 1 shows that, for the same actual electric field spatial scale L, the larger the electric field strength F, the smaller the error ΔL; and for the same electric field strength F, the larger the actual electric field spatial scale L, the smaller the error. This leads to the conclusion that the error in the quantum well width of the sample under test is inversely proportional to the electric field strength of the additional electric field and the actual width of the quantum well. These experimental data and conclusions can help improve the selection of measurement conditions in practical applications, resulting in more accurate measurement results.

[0124] The optical measurement method and application of quantum well width according to the embodiment of the present invention can solve the problems of lengthened time period and reduced accuracy of the test process caused by the sample preparation process in the prior art. By measuring the energy spacing of absorption peaks in the absorption tail range below the band gap in the sample absorption spectrum, the spatial scale of the electric field in the quantum well, that is, the quantum well width, is deduced, which effectively reduces the time period of the measurement process, improves the energy resolution and measurement accuracy, and has wide adaptability.

[0125] like Figure 5 As shown in FIG. 1 , an optical measurement device for quantum well width according to a specific embodiment of the present invention is introduced.

[0126] In an embodiment of the present invention, the optical measurement device for quantum well width includes a first signal acquisition module 501 , a second signal acquisition module 502 , a first calculation module 503 and a second calculation module 504 .

[0127] The first signal acquisition module 501 is used to acquire a first reflection signal of the target to be measured to the incident polarized light when there is no laser irradiation.

[0128] The second signal acquisition module 502 is configured to acquire a second reflection signal of the target to be measured to the incident polarized light when irradiated with laser light, wherein the energy of the laser light is greater than the band gap of the target to be measured.

[0129] The first calculation module 503 is configured to determine an average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap based on the first reflection signal and the second reflection signal.

[0130] The second calculation module 504 is configured to calculate the quantum well width of the target to be measured based on the average energy spacing.

[0131] The first calculation module 503 is also used to: determine the energy range of the absorption tail region of the target band gap to be measured and the total number of absorption peaks in the absorption tail region based on the signal difference between the first reflected signal and the second reflected signal; determine the average energy spacing of the absorption peaks based on the energy range of the absorption tail region, the total number of absorption peaks, and the effective mass of the target holes to be measured, wherein the effective mass of the target holes to be measured includes the effective mass of the heavy holes and the effective mass of the light holes.

[0132] The first calculation module 503 is also used to: determine the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks based on the effective mass of the heavy holes and the effective mass of the light holes of the target to be measured; determine the average energy spacing of the absorption peaks based on the energy range of the absorption tail region, the total number of absorption peaks, and the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks.

[0133] The first calculation module 503 is also used to: use the WKB approximation method to calculate the energy distribution of the absorption peak in the absorption tail region, wherein the energy distribution of the absorption peak includes the energy levels of the valence band sub-band and the energy levels of the conduction band sub-band; determine the intersection of the energy level of each column of the valence band sub-band and the line segment where the band gap is located in the three-dimensional absorption spectrum of the target to be measured; based on the sum of the intersection points and the energy range of the absorption tail region, determine the average energy spacing of the absorption peaks of the target to be measured in the absorption tail region of the band gap.

[0134] Figure 6 FIG. 6 shows a hardware structure diagram of a computing device 60 for optical measurement of quantum well width according to an embodiment of the present specification. Figure 6 As shown, the computing device 60 may include at least one processor 601, a memory 602 (e.g., a non-volatile memory), a storage 603, and a communication interface 604, and the at least one processor 601, the memory 602, the storage 603, and the communication interface 604 are connected together via a bus 605. The at least one processor 601 executes at least one computer-readable instruction stored or encoded in the storage 602.

[0135] It should be understood that the computer executable instructions stored in the memory 602, when executed, cause the at least one processor 601 to perform the above combined operations in the various embodiments of this specification. Figure 1-5 Describes the various operations and functions.

[0136] In the embodiments of the present specification, the computing device 60 may include, but is not limited to, a personal computer, a server computer, a workstation, a desktop computer, a laptop computer, a notebook computer, a mobile computing device, a smart phone, a tablet computer, a cellular phone, a personal digital assistant (PDA), a handheld device, a messaging device, a wearable computing device, a consumer electronic device, and the like.

[0137] According to one embodiment, a program product such as a machine-readable medium is provided. The machine-readable medium may have instructions (i.e., the above-mentioned elements implemented in software form), which, when executed by a machine, causes the machine to perform the above-mentioned combined embodiments of the present specification. Figure 1-6 Specifically, a system or device equipped with a readable storage medium can be provided, on which software program codes for implementing the functions of any of the above-mentioned embodiments are stored, and a computer or processor of the system or device can be enabled to read and execute the instructions stored in the readable storage medium.

[0138] The optical measurement method and application of quantum well width according to the embodiment of the present invention can solve the problems of lengthened time period and reduced accuracy of the test process caused by the sample preparation process in the prior art. By measuring the energy spacing of absorption peaks in the absorption tail range below the band gap in the sample absorption spectrum, the spatial scale of the electric field in the quantum well, that is, the quantum well width, is deduced, which effectively reduces the time period of the measurement process, improves the energy resolution and measurement accuracy, and has wide adaptability.

[0139] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0140] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0141] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0142] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The steps for the function specified in one or more boxes.

[0143] The foregoing descriptions of specific exemplary embodiments of the present invention are for purposes of illustration and description. These descriptions are not intended to limit the invention to the precise forms disclosed, and it is apparent that many variations and modifications are possible in light of the foregoing teachings. The exemplary embodiments have been selected and described for the purpose of explaining the specific principles of the invention and their practical application, thereby enabling those skilled in the art to realize and utilize a variety of exemplary embodiments of the invention and various options and modifications. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. An optical measurement method for quantum well width, characterized in that: The optical measurement method comprises: Acquire a first reflection signal of the target to be measured to the incident polarized light when there is no laser irradiation; Acquiring a second reflection signal of the target to be measured to the incident polarized light when the target is irradiated with laser light, wherein the energy of the laser light is greater than the band gap of the target to be measured; Determining an average energy spacing between absorption peaks of the target to be measured in an absorption tail region of the band gap based on the first reflection signal and the second reflection signal; and Calculating the quantum well width of the target to be measured based on the average energy spacing; Based on the first reflection signal and the second reflection signal, the average energy spacing of the absorption peaks in the absorption tail region of the band gap of the target to be measured is determined, specifically including: determining the energy range of the absorption tail region of the band gap of the target to be measured and the total number of absorption peaks in the absorption tail region based on the signal difference between the first reflection signal and the second reflection signal; based on the energy range of the absorption tail region, the total number of absorption peaks, and the effective mass of the holes in the target to be measured, determining the average energy spacing of the absorption peaks, wherein the effective mass of the holes in the target to be measured includes the effective mass of the heavy holes and the effective mass of the light holes.

2. The optical measurement method of quantum well width according to claim 1, wherein: Based on the energy range of the absorption tail region, the total number of absorption peaks, and the effective mass of the target hole to be measured, the average energy spacing of the absorption peaks is determined, specifically including: Determining the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks based on the effective mass of the heavy holes and the effective mass of the light holes of the target to be measured; The average energy spacing of the absorption peaks is determined based on the energy range of the absorption tail region, the total number of absorption peaks, and the proportion of absorption peaks generated by heavy holes or the proportion of absorption peaks generated by light holes in the total number of absorption peaks.

3. The optical measurement method of quantum well width according to claim 2, wherein: The calculation formula of the quantum well width of the target to be measured specifically includes: , wherein the average energy spacing of the absorption peaks is , is the ratio of the absorption peaks generated by the heavy holes of the target to be measured, is the effective mass of the heavy hole, is the effective mass of the light hole, is the effective mass of the electron, is the total number of absorption peaks, is the reduced Planck constant, is the energy range of the absorption tail region; or , wherein the average energy spacing of the absorption peaks is , is the ratio of the absorption peaks generated by the light holes of the target to be measured, is the effective mass of the heavy hole, is the effective mass of the light hole, is the effective mass of the electron, is the total number of absorption peaks, is the reduced Planck constant, is the energy range of the absorption tail region, is the quantum well width of the target to be measured.

4. The optical measurement method of quantum well width according to claim 3, wherein: The specific calculation method of the average energy spacing of the absorption peaks includes: The energy distribution of the absorption peak in the absorption tail region is calculated using the WKB approximation method, wherein the energy distribution of the absorption peak includes energy levels of a valence band sub-band and energy levels of a conduction band sub-band; Determining the intersection of the energy level of each column of the valence band sub-band and the line segment where the band gap is located in the three-dimensional absorption spectrum of the target to be measured; and Based on the sum of the intersection points and the energy range of the absorption tail region, the average energy spacing between the absorption peaks of the target to be measured in the absorption tail region of the band gap is determined.

5. The optical measurement method of quantum well width according to claim 4, characterized in that: The energy level and band gap of each valence band sub-band Intersection of the line segments satisfy ; The intersection and satisfying ; Determining an average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap based on the sum of the intersection points and the energy range of the absorption tail region specifically includes: Perform an integral operation on the sum of the intersection points, and calculate based on the integral operation result and the energy range of the absorption tail region , inversely deduced , Among them, the energy range of the absorption tail region is approximately , is the Lorentz force, is the electric field strength of the additional electric field of the target to be measured, is the coefficient, 、 is the characteristic energy, is the number of electronic states in the absorption tail region, is the effective mass of the target hole to be measured, is the sequence number of the energy level, also known as the principal quantum number.

6. The optical measurement method of quantum well width according to claim 1, wherein: The incident polarized light includes at least two incident angles.

7. An optical measurement device for quantum well width, applied to the optical measurement method for quantum well width according to any one of claims 1 to 6, characterized in that: The optical measuring device comprises: A first signal acquisition module is used to acquire a first reflection signal of the target to be measured to the incident polarized light when there is no laser irradiation; A second signal acquisition module is used to acquire a second reflection signal of the target to be measured to the incident polarized light when the target is irradiated with laser light, wherein the energy of the laser light is greater than the band gap of the target to be measured; A first calculation module is configured to determine an average energy spacing between absorption peaks of the target to be measured in the absorption tail region of the band gap based on the first reflection signal and the second reflection signal; The second calculation module is used to calculate the quantum well width of the target to be measured based on the average energy spacing.

8. An electronic device, characterized in that: include: at least one processor; as well as A memory storing instructions, which, when executed by the at least one processor, causes the at least one processor to perform the optical measurement method for the quantum well width according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the optical measurement method for the quantum well width according to any one of claims 1 to 6 is implemented.

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