Semiconductor electric field characterization method based on absorption spectrum Urbach tail

Abstract

The invention provides a semiconductor electric field characterization method based on an absorption spectrum Urbach tail, and the method comprises the steps: obtaining an actual spectrum of a to-be-detected sample, the actual spectrum being an actual absorption spectrum or an actual surface photovoltage spectrum; an electric field value is set, a fitting spectrum is obtained according to fitting of the electric field value, the fitting spectrum is a fitting absorption spectrum or a fitting surface photovoltage spectrum, and the error between the fitting spectrum and the actual spectrum is calculated; if the error meets a convergence condition, taking the electric field value as a characterization electric field of the to-be-detected sample; and if the error does not meet the convergence condition, resetting the electric field value, fitting according to the reset electric field value to obtain a fitted spectrum, and calculating the error between the fitted spectrum and the actual spectrum until the error meets the convergence condition. According to the method, excessive auxiliary equipment does not need to be adopted, and single-point in-situ independent measurement can be carried out on any position of the sample to be measured.

Description

Technical Field

[0001] This application belongs to the field of optoelectronic device technology, and specifically relates to a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum. Background Technology

[0002] One of the difficulties in characterizing electric fields using traditional methods is that the electric field lies below the surface. In single-crystal systems, the electric field gradually decays to zero with depth, necessitating deconvolution processing for single-crystal testing. In contrast, the electric field of quantum wells lies tens of nanometers below the surface, requiring lateral cleavage for testing. However, lateral cleavage struggles to achieve atomically flat surfaces. Furthermore, electric field testing methods often require the assistance of other techniques or specialized sample preparation. Experimental techniques, such as Kelvin probe microscopy combined with Raman spectroscopy, and Franz-Keldysh oscillation-based spectroscopy combined with modulation and lock-in amplification techniques, all require specific methods for structural fabrication, such as electron holographic microscopy requiring fibrillation-based sample preparation, and capacitance-voltage characteristic analysis necessitating the fabrication of Schottky junctions on the surface.

[0003] So how can we directly reflect electric field information, especially for point-to-point analysis in industrial applications? Optics seems to be a solution. Currently, two optical features related to electric fields are the Franz-Keldysh oscillation and the Urbach tail (also known as the absorption edge), and their typical characteristic structures are as follows: Figure 1 As shown, the yellow and pink parts represent the FK oscillation and the Urbach tail, respectively. Figure 2 As shown, only the absorption spectrum in (a) exhibits Franz-Keldysh oscillations, while all four cases show Urbach tail characteristics. This indicates that the Franz-Keldysh oscillation requires a sufficiently wide uniform electric field, and is not applicable to quantum well cases (where the absorption spectrum becomes a stepped upward line due to quantum confinement) or non-uniform field cases (where the oscillatory characteristics of the absorption spectrum disappear). In comparison, the Urbach tail signal does not require modulation or lock-in amplification techniques, nor does it require special sample preparation, thus making it more promising for simple and direct industrial applications. Summary of the Invention

[0004] The technical problem addressed by this application is: how to provide a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum that can perform in-situ independent testing without relying on too many testing devices.

[0005] This application provides a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum, the semiconductor electric field characterization method comprising:

[0006] Obtain the actual spectrum of the sample to be tested, wherein the actual spectrum is the actual absorption spectrum or the actual surface photovoltage spectrum;

[0007] Set an electric field value, and obtain a fitted spectrum based on the electric field value. The fitted spectrum is either a fitted absorption spectrum or a fitted surface photovoltage spectrum. Calculate the error between the fitted spectrum and the actual spectrum.

[0008] If the error satisfies the convergence condition, the electric field value is used as the characterization electric field of the sample to be tested.

[0009] If the error does not meet the convergence condition, the electric field value is reset, and the fitted spectrum is obtained based on the reset electric field value, and the error between the fitted spectrum and the actual spectrum is calculated, until the error meets the convergence condition.

[0010] Optionally, the method for obtaining the fitted spectrum based on the electric field value includes:

[0011] A band structure model is established based on the electric field values;

[0012] The electron eigenfunction, hole eigenfunction, and eigenenergy are calculated based on the band structure model.

[0013] The transition energy is determined based on the eigenenergy difference between the electron and hole eigenfunctions, the transition intensity is determined based on the overlap between the electron and hole eigenfunctions, and the fitted spectrum is obtained based on the transition energy and the transition intensity.

[0014] Optionally, if the error does not meet the convergence condition, the method for resetting the electric field value includes:

[0015] Calculate the slope of the fitted spectrum and the slope of the actual spectrum respectively;

[0016] If the slope of the fitted spectrum is greater than the slope of the actual spectrum, then the electric field value is reduced;

[0017] If the slope of the fitted spectrum is less than the slope of the actual spectrum, the electric field value is increased.

[0018] Optionally, the method for determining whether the error between the fitted spectrum and the actual spectrum meets the convergence condition is as follows: if the decrease or increase in the electric field value is less than 1 MV / cm, then the convergence condition is met.

[0019] Optionally, the band structure model is a uniform band structure model or a non-uniform band structure model.

[0020] Optionally, the semiconductor electric field characterization method further includes:

[0021] When the band structure model is a uniform band structure model and the error meets the convergence condition, a first electric field value and a first fitted spectrum are obtained; when the band structure model is a non-uniform band structure model and the error meets the convergence condition, a second electric field value and a second fitted spectrum are obtained.

[0022] Calculate the first root mean square error between the first fitted spectrum and the actual spectrum, and calculate the second root mean square error between the second fitted spectrum and the actual spectrum;

[0023] If the first root mean square error is less than the second root mean square error, then the first electric field value is used as the characterization electric field of the sample under test; if the first root mean square error is greater than the second root mean square error, then the second electric field value is used as the characterization electric field of the sample under test.

[0024] This application provides a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum, which has the following technical advantages:

[0025] This method does not require excessive auxiliary equipment and can perform single-point in-situ and independent measurements at any location on the sample to be tested. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of a typical semiconductor absorption spectrum in the prior art.

[0027] Figure 2 This is a schematic diagram of the absorption spectrum under different electric fields.

[0028] Figure 3 This is a schematic diagram showing the variation of the Urbach tail with the electric field under uniform and non-uniform fields.

[0029] Figure 4 This is a schematic diagram of the absorption spectra under different broadening factors and different quantum well widths.

[0030] Figure 5 A schematic diagram comparing the Urbach tails of the absorption spectra when the broadening factor is sufficiently large and the quantum well width is sufficiently large.

[0031] Figure 6 A trend plot of the broadening factor required to fit the absorption spectrum broadening corresponding to different quantum well widths to the case where the quantum well width is large enough.

[0032] Figure 7 This is a flowchart of a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum, according to one or more embodiments.

[0033] Figure 8 This is a schematic diagram of an actual SPV and a fitted SPV according to one or more embodiments.

[0034] Figure 9 This is a schematic diagram of the actual absorption spectrum and the fitted absorption spectrum according to one or more embodiments, and a corresponding error diagram.

[0035] Figure 10 The electric field at different locations is obtained by fitting according to one or more embodiments. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0037] Before describing the various embodiments of this application in detail, the technical concept of this application is first briefly described: Current semiconductor electric field characterization methods typically require a large number of auxiliary devices and are difficult to perform in-situ independent tests. Therefore, this application provides a semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum. The key step is to use different electric field values ​​to fit and obtain a fitted spectrum, making the fitted spectrum gradually approximate the actual spectrum of the sample under test, thereby finding the most suitable electric field value to characterize the electric field of the sample under test. The actual spectrum and the fitted spectrum are absorption spectra or surface photovoltage spectra. This method does not require excessive auxiliary equipment and can perform single-point in-situ and independent measurements at any location on the sample under test. The specific principle of the semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum of this application will be described below with reference to more embodiments.

[0038] Before describing the specific steps, the relevant principles of the Urbach tail characterizing the electric field in the absorption spectrum will be discussed.

[0039] Currently, the Urbach tail is known to be an exponential function related to the incident light energy E, and it can be categorized into two cases: one with and without exciton influence. The electric field strength F is included in the Urbach eigenenergy, and the Urbach energy determines the decay rate of the exponent. Furthermore, previous researchers used the parameter ab to measure the decay rate of the exponent. Based on the decay rate of the exponent, the Urbach characteristic energy can be obtained, thus deriving the electric field value F. However, these analyses are only applicable to uniform fields and not to non-uniform fields; that is, existing methods cannot characterize all types of electric fields using the Urbach tail.

[0040] like Figure 3 As shown, (a) represents the variation of the Urbach tail with the electric field under a uniform field, and (b) represents the variation of the Urbach tail with the electric field under a non-uniform field. In (b), the electric field value is F. maxThe absorption spectrum is normalized using values ​​at 3.5 eV. As the electric field increases, the slope of the Urbach tail gradually increases; therefore, electric field modeling can be used to obtain a better fit to the absorption spectrum. Figure 3 As can be seen, the larger the electric field, the slower the Urbach tail rises.

[0041] The core of Urbach-based optical analysis is to simplify multi-parameter fitting into single-parameter F-fitting. This simplification is based on the equivalence of the broadening factor γ and the quantum well width L, including the following three points:

[0042] 1. Increasing both γ and L will make the Urbach absorption spectrum smoother. Figure 4 (a) represents the absorption spectrum with increased broadening factor γ. Figure 4 (b) Increase the absorption spectrum of the quantum well width L, where the electric field value F = 0.3 MV / cm.

[0043] 2. The Urbach tails of the absorption spectra for γ→∞ and L→∞ are consistent. For example... Figure 5 As shown, comparing the Urbach tails of the absorption spectra when γ is sufficiently large (here γ = 12 meV, L = 10 nm) and when L is sufficiently large (here γ = 0 meV, L = 60 nm), it can be seen that the difference between the two is small. Here, the electric field value F = 0.3 MV / cm.

[0044] 3. As L increases, the amount of γ required to broaden the Urbach tail of a certain segment of the absorption spectrum to the L→∞ limit decreases. For example... Figure 6 The diagram shows the trend of γ required to broaden the absorption spectrum corresponding to different values ​​of L to fit the case where L is sufficiently large. As L increases, the required broadening factor γ gradually decreases. Since the temperature broadening factor at room temperature is approximately 26 meV, γ is sufficiently large. Based on the equivalence explained in the above three points, we can assume that L is sufficiently large, thus simplifying the multi-parameter fitting to a single-parameter fitting of F. Therefore, the fitted absorption spectrum or the fitted surface photovoltage spectrum can be obtained based on the single parameter of the electric field value, without needing to utilize the broadening factor γ and the quantum well width L.

[0045] Specifically, such as Figure 7 As shown, the semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum in this embodiment includes the following steps:

[0046] Step S10: Obtain the actual spectrum of the sample to be tested, wherein the actual spectrum is the actual absorption spectrum or the actual surface photovoltage spectrum;

[0047] Step S20: Set the electric field value, and obtain a fitted spectrum based on the electric field value. The fitted spectrum is either a fitted absorption spectrum or a fitted surface photovoltage spectrum. Calculate the error between the fitted spectrum and the actual spectrum.

[0048] Step S30: If the error meets the convergence condition, the electric field value is used as the characterization electric field of the sample to be tested.

[0049] Step S40: If the error does not meet the convergence condition, reset the electric field value, and fit the fitted spectrum based on the reset electric field value and calculate the error between the fitted spectrum and the actual spectrum until the error meets the convergence condition.

[0050] Since the surface photovoltage spectrum (SPV) is proportional to the absorption spectrum, the surface photovoltage spectrum can be used instead of the absorption spectrum. That is, in steps S10 and S20, the actual absorption spectrum, the fitted absorption spectrum, or the actual surface photovoltage spectrum and the fitted surface photovoltage spectrum can be used.

[0051] In one or more embodiments, a method for fitting electric field values ​​to obtain a fitted spectrum includes:

[0052] Establish a band structure model based on the electric field values;

[0053] The electron eigenfunction, hole eigenfunction, and eigenenergy were calculated based on the band structure model.

[0054] The transition energy is determined based on the eigenenergy difference between the electron and hole eigenfunctions, the transition intensity is determined based on the overlap between the electron and hole eigenfunctions, and the fitted spectrum is obtained based on the transition energy and the transition intensity.

[0055] For example, the band structure model can be either a uniform band structure model or a non-uniform band structure model. To obtain more accurate electric field values, this embodiment uses both band structure models for fitting simultaneously, and selects the fitting result with smaller error by comparing the errors of the two models.

[0056] In one or more embodiments, the semiconductor electric field characterization method further includes:

[0057] First, when the band structure model is a uniform band structure model and the error meets the convergence condition, a first electric field value and a first fitted spectrum are obtained. When the band structure model is a non-uniform band structure model and the error meets the convergence condition, a second electric field value and a second fitted spectrum are obtained. The first fitted spectrum can be either a fitted absorption spectrum or a fitted surface photovoltage spectrum, and the second fitted spectrum can also be either a fitted absorption spectrum or a fitted surface photovoltage spectrum.

[0058] Next, the first root mean square error between the first fitted spectrum and the actual spectrum is calculated, and the second root mean square error between the second fitted spectrum and the actual spectrum is calculated.

[0059] Finally, if the first root mean square error is less than the second root mean square error, the first electric field value is used as the characterization electric field of the sample under test; if the first root mean square error is greater than the second root mean square error, the second electric field value is used as the characterization electric field of the sample under test.

[0060] For example, in step S40, if the error does not meet the convergence condition, the method for resetting the electric field value includes: calculating the slope of the fitted spectrum and the slope of the actual spectrum respectively; if the slope of the fitted spectrum is greater than the slope of the actual spectrum, then the electric field value is reduced; if the slope of the fitted spectrum is less than the slope of the actual spectrum, then the electric field value is increased. The method for judging whether the error between the fitted spectrum and the actual spectrum meets the convergence condition is: if the decrease or increase in the electric field value is less than 1 MV / cm, then the convergence condition is met. In the above repetition process, the electric field value is continuously adjusted and gradually approaches the actual electric field. When the adjustment amount (decrease or increase) of the electric field value is less than 1 MV / cm, it indicates that the fitted electric field value is very close to the actual electric field, the loop can be stopped, and the fitted electric field value at this time is used as the characterization electric field of the sample.

[0061] like Figure 8 As shown, the black line is the SPV spectrum at a certain point in the GaN single crystal, and the red line is the fitted SPV. The electric field used for fitting was obtained by the least squares method, and the value is 0.8 MV / cm.

[0062] like Figure 9 As shown, Figure 9 (A), (B), and (C) represent the absorption spectra at different doping concentrations, where the black dashed line represents the experimentally measured absorption spectrum, the blue solid line represents the absorption spectrum obtained by the traditional method (using an ellipsometer), and the red solid line represents the absorption spectrum obtained by the method in this embodiment. Figure 9 (D), (E), and (F) represent the root mean square error between the fitted absorption spectrum and the experimentally measured absorption spectrum, respectively. Figure 9 The results show that the absorption spectrum obtained in this embodiment is closer to the experimental data, and therefore the corresponding electric field is closer to the actual electric field.

[0063] like Figure 10 As shown, five points were selected in the figure for fitting, and the electric fields from point 1 to point 5 were 0.8MV / cm, 0.96MV / cm, 1.06MV / cm, 1.02MV / cm and 0.8MV / cm, respectively.

[0064] The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum provided in this embodiment allows for in-situ and independent testing. On the one hand, it enables in-situ non-destructive testing; on the other hand, it requires no other techniques or the fabrication of special structures. Furthermore, compared to the traditional Franz-Keldysh optical method, it does not require auxiliary phase-locked loop technology and is theoretically applicable to non-uniform or narrow electric fields, unlike the Franz-Keldysh method which is only applicable to sufficiently wide uniform fields. Thus, the optical information itself sufficiently reflects the electric field information. Due to the equivalence of the SPV and the absorption spectrum, nanoscale electric field characterization can be performed, combining morphology and electric field information. It can also be further combined with an in-situ external field (optical, electrical, magnetic, and mechanical) coupling characterization system to achieve dynamic response analysis of the electric field under the synergistic effect of multiple physics fields.

[0065] The specific embodiments of this application have been described in detail above. Although some embodiments have been shown and described, those skilled in the art should understand that modifications and improvements can be made to these embodiments without departing from the principles and spirit of this application as defined by the claims and their equivalents, and such modifications and improvements should also be within the protection scope of this application.

Claims

1. A semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum, characterized in that, The semiconductor electric field characterization method includes: Obtain the actual spectrum of the sample to be tested, wherein the actual spectrum is the actual absorption spectrum or the actual surface photovoltage spectrum; Set an electric field value, and obtain a fitted spectrum based on the electric field value. The fitted spectrum is either a fitted absorption spectrum or a fitted surface photovoltage spectrum. Calculate the error between the fitted spectrum and the actual spectrum. If the error satisfies the convergence condition, the electric field value is used as the characterization electric field of the sample to be tested. If the error does not meet the convergence condition, the electric field value is reset, and the fitted spectrum is obtained based on the reset electric field value, and the error between the fitted spectrum and the actual spectrum is calculated, until the error meets the convergence condition.

2. The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum according to claim 1, characterized in that, Methods for obtaining a fitted spectrum based on the electric field value include: A band structure model is established based on the electric field values; The electron eigenfunction, hole eigenfunction, and eigenenergy were calculated based on the band structure model. The transition energy is determined based on the eigenenergy difference between the electron and hole eigenfunctions, the transition intensity is determined based on the overlap between the electron and hole eigenfunctions, and the fitted spectrum is obtained based on the transition energy and the transition intensity.

3. The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum according to claim 1, characterized in that, If the error does not meet the convergence condition, the method for resetting the electric field value includes: Calculate the slope of the fitted spectrum and the slope of the actual spectrum respectively; If the slope of the fitted spectrum is greater than the slope of the actual spectrum, then the electric field value is reduced; If the slope of the fitted spectrum is less than the slope of the actual spectrum, the electric field value is increased.

4. The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum according to claim 1, characterized in that, The method for determining whether the error between the fitted spectrum and the actual spectrum meets the convergence condition is as follows: if the decrease or increase in the electric field value is less than 1 MV / cm, then the convergence condition is met.

5. The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum according to claim 2, characterized in that, The band structure model can be either a uniform band structure model or a non-uniform band structure model.

6. The semiconductor electric field characterization method based on the Urbach tail of the absorption spectrum according to claim 5, characterized in that, The semiconductor electric field characterization method further includes: When the band structure model is a uniform band structure model and the error meets the convergence condition, a first electric field value and a first fitted spectrum are obtained; when the band structure model is a non-uniform band structure model and the error meets the convergence condition, a second electric field value and a second fitted spectrum are obtained. Calculate the first root mean square error between the first fitted spectrum and the actual spectrum, and calculate the second root mean square error between the second fitted spectrum and the actual spectrum; If the first root mean square error is less than the second root mean square error, then the first electric field value is used as the characterization electric field of the sample under test; if the first root mean square error is greater than the second root mean square error, then the second electric field value is used as the characterization electric field of the sample under test.

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