Methods for establishing a carrier concentration database, methods for measuring carrier concentration, and testing systems.

Abstract

This invention provides a method for establishing a carrier concentration database, a method for testing carrier concentration, and a testing system. The method for establishing the carrier concentration database includes: establishing theoretical models of a finite dipole model and a Drood model; adjusting the effective probe length and the ratio of effective induced charge to total induced charge in the theoretical models to calculate the carrier concentration of a standard sample, obtaining several first spectral information; detecting the second spectral information of the standard sample using a terahertz near-field detection device; fitting the first spectral information and the second spectral information to obtain the best-fit model corresponding to the current carrier concentration; repeating the above steps to establish the carrier concentration database. This invention not only better represents near-field scattering signals and the interaction between the probe and the sample, but also effectively overcomes the error problems existing in calculations using only formulas, which is beneficial to further improving the accuracy of semiconductor carrier concentration calculation.

Description

Technical Field

[0001] This invention relates to the field of terahertz application technology, and in particular to a method for establishing a carrier concentration database, a method for testing carrier concentration, and a testing system. Background Technology

[0002] In the semiconductor industry, the carrier concentration of semiconductors is a core parameter of the electrical properties of semiconductor materials. It directly determines the conductivity of the material and is the basis for constructing the functions of devices such as PN junctions, MOSFETs, and BJTs. Key performance parameters such as built-in potential, threshold voltage, switching speed, and power consumption are all strictly constrained by it. How to achieve effective and non-destructive semiconductor testing has been a long-standing problem in the semiconductor industry.

[0003] Traditional semiconductor detection methods primarily rely on the Hall effect and spectral analysis. This involves fabricating electrodes and analyzing the Hall voltage, or determining carrier concentration and mobility by analyzing the absorption and reflection spectra of semiconductor materials at a specific wavelength. However, Hall effect-based methods require electrode fabrication, which is highly damaging to the sample and prevents observation of material details, making high-resolution imaging difficult. Spectroscopic methods often employ infrared spectroscopy and Raman spectroscopy in conjunction with the material, but these methods are insensitive to low carrier concentrations, limiting their ability to detect subtle concentration differences and defect distributions within semiconductor devices.

[0004] Semiconductors exhibit excellent response to electromagnetic waves in the terahertz band, effectively improving detection performance. However, terahertz far-field detection suffers from low spatial resolution, struggling to achieve nanometer-level resolution. Patent CN114563372A discloses a method for measuring carrier concentration in terahertz materials. After obtaining sample spectral information, it derives the complex permittivity of the sample based on the theoretical relationship between material optical parameters and sample signals. Then, it calculates the complex conductivity of the material based on the complex permittivity, and finally calculates the carrier concentration based on the dependence of complex conductivity on carrier concentration. This method utilizes terahertz near-field technology to detect semiconductor carrier concentration, enabling non-destructive measurement of carrier concentration in materials at the nanoscale. However, this method, by calculating carrier concentration solely through formulas after acquiring near-field spectral information, ignores errors introduced by the formula's assumptions, application scenarios, and limitations. Furthermore, the calculation process fails to reflect the interaction between the probe and the sample, thus requiring further improvement in the accuracy of the results. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a method for establishing a carrier concentration database, a method for testing carrier concentration, and a testing system. This database is constructed based on a finite dipole model, which more accurately reflects the interaction between the probe and the sample. Furthermore, by combining the theoretical model with experimental data, the optimal fitting model for different concentrations is determined, effectively overcoming the errors inherent in calculations using only formulas. This is beneficial for further improving the accuracy of semiconductor carrier concentration calculations.

[0006] On one hand, the present invention provides a method for establishing a carrier concentration database, the method comprising the following steps:

[0007] A theoretical model including a finite dipole model and a Drood model is established. The effective probe length and the ratio of effective induced charge to total induced charge in the theoretical model are adjusted to calculate the first spectral information of a standard sample with known carrier concentration.

[0008] The second spectral information of the standard sample was detected using a terahertz near-field detection device.

[0009] By fitting several pieces of the first spectral information and the second spectral information, the best fitting model corresponding to the current carrier concentration is obtained;

[0010] Repeat the above steps to store different carrier concentrations and their corresponding spectral information, the effective probe length of the best-fit model, and the ratio of effective induced charge to total induced charge into the carrier concentration database, thus establishing the carrier concentration database.

[0011] In this technical solution, the parameters stored in the carrier concentration database include several carrier concentrations, the spectral information corresponding to each carrier concentration, and the effective probe length and the ratio of effective induced charge to total induced charge of the best-fit model corresponding to each carrier concentration. The process of acquiring these parameters is the process of establishing the carrier concentration database.

[0012] In this technical solution, when establishing the carrier concentration database, a theoretical model is first established, including a finite dipole model and a Drood model. The finite dipole model better represents the near-field scattering signal and reflects the interaction between the probe and the sample. According to the theoretical model, given the known carrier concentration, two parameters—the effective probe length and the ratio of effective induced charge to total induced charge—are variables, and both parameters change with the carrier concentration. Actual measurements are needed to determine the effective probe length and charge ratio at a given carrier concentration. The total induced charge refers to the total charge generated when the probe approaches the sample, while the effective induced charge refers to the charge that makes the main contribution to the scattered field.

[0013] Therefore, in this technical solution, the first spectral information calculated by the theoretical model and the second spectral information detected by the terahertz near-field detection device are combined to jointly determine the best fitting model corresponding to each carrier concentration, thereby determining the spectral information, effective probe length, and ratio of effective induced charge to total induced charge corresponding to each carrier concentration.

[0014] Specifically, for a standard sample with a known carrier concentration, different probe effective lengths and the ratio of effective induced charge to total induced charge are used as input parameters to a theoretical model to obtain several different theoretical models, thereby outputting several different first spectral information. However, theoretical calculations alone cannot confirm the true spectral information corresponding to the current carrier concentration. Therefore, a terahertz near-field detection device is used to detect the standard sample, obtain the near-field spectrum of the standard sample, and obtain second spectral information based on the near-field spectrum. The order in which the first and second spectral information are obtained can be adjusted.

[0015] Next, after obtaining several pieces of first and second spectral information, the first and second spectral information are fitted together. The first and second spectral information can be fitted using any existing fitting method. When the difference between a certain first and second spectral information is less than or equal to a threshold, the theoretical model corresponding to that first spectral information is determined as the best-fit model for the current carrier concentration. This best-fit model can be considered to characterize the scattered field formed by the interaction between the probe and the sample. The two parameters input to the best-fit model—the effective probe length and the ratio of effective induced charge to total induced charge—also correspond to the current carrier concentration. Finally, the carrier concentration, spectral information, effective probe length, and the ratio of effective induced charge to total induced charge are used as stored data in the carrier database. The spectral information stored in the carrier database can be either the first or second spectral information corresponding to the best-fit model.

[0016] Finally, repeat the above steps to obtain different carrier concentrations and their corresponding spectral information, effective probe length, and the ratio of effective induced charge to total induced charge, thus completing the establishment of the carrier concentration database. The number of carrier concentrations in the database can be set according to actual needs.

[0017] In this technical solution, a theoretical model is constructed based on the finite dipole model. Then, through theoretical calculations and experimental data, the optimal fitting model for different concentrations is determined, specifying the effective probe length, the ratio of effective induced charge to total induced charge, and the optimal model values. This not only better represents the near-field scattering signal and the interaction between the probe and the sample but also effectively overcomes the errors inherent in calculations using only formulas, thus improving the accuracy of semiconductor carrier concentration calculations. Furthermore, in the theoretical model, the effective probe length and the ratio of effective induced charge to total induced charge are primarily related to the testing environment and are less affected by other factors. Therefore, even with limited carrier concentration data stored in the carrier concentration database, relatively high accuracy can still be achieved.

[0018] The theoretical model specifically includes the following formulas:

[0019] First, the scattered field formed by the interaction between the probe and the sample is expressed as:

[0020]

[0021] Where r is the first reflection coefficient, E i E is the amplitude of the incident electric field. s Let α be the amplitude of the scattered field. eff The effective polarization of the probe.

[0022] Furthermore, the effective polarizability α of the probe eff Represented as:

[0023]

[0024] In the formula, C is an intermediate quantity. and These are also intermediate values, representing the probe-sample distance and the probe's own contribution to the effective polarizability. Let be the second reflection coefficient, where . and Further expressed as:

[0025]

[0026]

[0027] In the formula, k is the ratio of effective induced charge to total induced charge, L is the effective length of the probe, H is the distance from the probe to the sample, W0 is the initial effective range of the probe, and R... t W is the radius of curvature of the probe tip. i This represents the near-field interaction range after the probe-sample interaction. H can be expressed by the formula... The calculation is complete. The other parameters in the above formula are further calculated using the following formula:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Where Q0 is the total amount of polarization charge induced at the tip in the absence of a sample, and E0 is the incident electric field intensity. Let be the dielectric constant of the sample. Using the above formula, the effective polarizability α of the probe is... eff This can be expressed as time t and the sample dielectric constant. The function.

[0034] Furthermore, according to the semiconductor Drud model, the sample dielectric constant Represented as:

[0035]

[0036] In the formula, It is the high-frequency dielectric constant. For the frequency used in the experiment, The plasma resonant frequency, is the damping coefficient.

[0037] Furthermore, and Calculated using the following formula:

[0038]

[0039]

[0040] In the formula, Let be the vacuum dielectric constant, n be the carrier concentration, e be the electron charge, m* be the effective mass of holes or electrons, and c0 be the speed of light in vacuum. As a baseline parameter describing the intrinsic mobility characteristics of charge carriers, pc is a scattering parameter. Cr is a constant related to the maximum mobility, used to describe the upper limit characteristic of carrier mobility; Cr is a constant related to the mobility-concentration relationship; and Cs is a constant related to another type of mobility-concentration relationship. As constants reflecting the contribution of the scattering process to mobility, α is a constant describing the relationship between mobility and doping concentration, and β is a constant describing the relationship between mobility and doping concentration during scattering.

[0041] Therefore, the dielectric constant of the sample Only The function of α, when substituted into the formula, gives the effective polarizability α of the probe. eff It is a function of time and carrier concentration only.

[0042] The effective polarization α of the probe eff Fourier series expansion yields:

[0043]

[0044] Where j is an imaginary number, Ω is the frequency of probe vibration in nΩ, and n corresponds to n in the spectral information Fn, which is the order of the signal, and Fn is the amplitude of the nth order. The phase difference is denoted as n. Therefore, the amplitude and phase difference of the nth order in this formula are only related to the sample carrier concentration, thus reflecting the dielectric information of the sample. At least one of the amplitudes of the nth order, such as the 1st to 4th order amplitudes, or the phase difference, can be used as spectral information stored in the carrier concentration database.

[0045] Based on the above theoretical model, when establishing the database, for the same known carrier concentration, by changing the ratio of effective induced charge to total induced charge and the effective probe length, multiple different theoretical models can be obtained, outputting several different first spectral information. Based on the measured second spectral information, the best-fit model for a certain known carrier concentration and its corresponding ratio of effective induced charge to total induced charge and effective probe length can be determined.

[0046] Furthermore, the first spectral information and the second spectral information are fitted using the least squares method. When the sum of the squared residuals between the first spectral information and the second spectral information is minimized, the optimal fitting model is obtained. The effective probe length and the ratio of effective induced charge to total induced charge corresponding to the optimal fitting model are used as the effective probe length and the ratio of effective induced charge to total induced charge for the corresponding carrier concentration, and are stored in the carrier concentration database.

[0047] In this technical solution, multiple different theoretical models are obtained by adjusting two parameters: the effective probe length and the ratio of effective induced charge to total induced charge. After incorporating a known carrier concentration, different theoretical models generate different first spectral information. Subsequently, the least squares method is used to fit each first spectral information with the second spectral information, and the theoretical model with the smallest sum of squared residuals is taken as the best fitting model for the current carrier concentration.

[0048] In adjusting the effective probe length and the ratio of effective induced charge to total induced charge, the effective probe length is adjusted from 80μm to 200μm, while the ratio of effective induced charge to total induced charge is adjusted from 0.4 to 1.0, thereby achieving a more efficient establishment of the theoretical model and the best fitting model.

[0049] On the other hand, the present invention provides a carrier concentration testing system, specifically, the carrier concentration testing system includes:

[0050] A terahertz near-field detection device is used to acquire the near-field spectrum of a sample to be tested and to obtain the spectral information of the sample to be tested from the near-field spectrum.

[0051] The carrier concentration database is established by the above-mentioned carrier concentration database establishment method. The carrier concentration database stores different carrier concentrations and their corresponding spectral information, the effective probe length of the best fitting model, and the ratio of effective induced charge to total induced charge.

[0052] The analysis unit is used to fit the spectral information of the sample to be tested with the spectral information in the carrier concentration database to obtain the carrier concentration of the sample to be tested.

[0053] In this technical solution, the terahertz near-field detection device can be any existing terahertz near-field detection device. Preferably, the terahertz near-field detection device includes a vector network analyzer, an S-parameter testing module, an optical path system, an atomic force microscope (AFM) system, and a lock-in amplifier. The vector network analyzer and the S-parameter testing module can generate electromagnetic waves in the range of 0.50 THz to 0.75 THz. The designed optical path system enables signal transmission from the S-parameter testing module. Combined with the lock-in amplifier and high-order demodulation technology, terahertz near-field optical characterization of standard samples or samples under test is achieved. Simultaneously, to ensure beam quality and a sufficiently small focused spot diameter at the AFM probe tip, lenses, short-focal-length parabolic mirrors, etc., are required for spot collimation and convergence.

[0054] Furthermore, the analysis unit is used to fit the spectral information of the sample to be tested with the spectral information in the carrier concentration database, thereby deducing the carrier concentration of the sample to be tested.

[0055] Further, the analysis unit fits the spectral information of the sample to be tested with the spectral information in the carrier concentration database, including the following steps:

[0056] S1: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value;

[0057] S2: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested;

[0058] S3: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested.

[0059] S4: Repeat step S3 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

[0060] In this technical solution, in step S1, the analysis unit first acquires the spectral information of the sample to be tested, and compares this spectral information with the spectral information in the carrier concentration database. The carrier concentration with the closest spectral information in the database is determined as the initial concentration value. Preferably, the spectral information is a second-order or third-order amplitude. The spectral information can also be a first-order amplitude, a fourth-order amplitude, or a phase difference.

[0061] In this technical solution, in step S2, after determining the initial concentration value, the spectral information corresponding to the initial concentration value is obtained, and the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested is calculated. The difference in spectral information varies depending on the amount of data stored in the database.

[0062] In step S3, the concentration estimate is determined based on the difference in spectral information. This concentration estimate does not exist in the carrier database and is only generated to approximate the true concentration of the sample to be tested. Therefore, the effective probe length and the ratio of effective induced charge to total induced charge in this concentration estimate are unknown.

[0063] To determine the values ​​of the probe effective length and the ratio of effective induced charge to total induced charge for concentration estimation, a fitting process is performed based on all or part of the carrier concentration data in the carrier concentration database. This yields the probe effective length and the ratio of effective induced charge to total induced charge under the current concentration estimation, and the spectral information corresponding to the current concentration estimation is then calculated. Next, the difference between the spectral information corresponding to the current concentration estimation and the spectral information of the sample to be tested is calculated. If this difference is greater than a threshold, the above steps are repeated. Based on this difference, a new concentration estimation is determined, and the values ​​of the probe effective length and the ratio of effective induced charge to total induced charge for the new concentration estimation are inferred. The spectral information of the new concentration estimation is then calculated, and the difference between the new spectral information and the spectral information of the sample to be tested is calculated. This process is repeated until the spectral information gradually approximates the spectral information of the sample to be tested. Finally, when the difference in spectral information is less than or equal to the threshold, the concentration estimation corresponding to this spectral information can be used as the carrier concentration of the sample to be tested.

[0064] In this technical solution, the data processing method of the analysis unit allows the carrier concentration database to avoid storing too much carrier concentration and related data. By utilizing the characteristics that the effective probe length and the ratio of effective induced charge to total induced charge are relatively unaffected by changes, the two parameters for concentration estimation can be more accurately inferred based on the fitting of the two parameters with the carrier concentration. Then, the spectral information is calculated, and finally the carrier concentration of the sample to be tested is approximated, which greatly reduces the amount of data storage and the cost of establishing the database. At the same time, this method also avoids the problem of inaccurate fitting when directly using carrier concentration and spectral information, as well as the problem of large storage requirements for near-field spectrum.

[0065] Another object of the present invention is to provide a carrier concentration testing method based on any of the aforementioned carrier concentration databases, the method comprising the following steps:

[0066] The near-field spectrum of the sample to be tested is acquired, and the spectral information of the sample to be tested is obtained from the near-field spectrum;

[0067] The carrier concentration of the sample is obtained by fitting the spectral information of the sample to be tested with the spectral information in the carrier concentration database.

[0068] Further, the process of fitting the spectral information of the sample to be tested with the spectral information in the carrier concentration database includes the following steps:

[0069] S1: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value;

[0070] S2: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested;

[0071] S3: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested.

[0072] S4: Repeat step S3 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

[0073] Compared with the prior art, the present invention has the following advantages and beneficial technical effects:

[0074] This invention constructs a theoretical model based on the finite dipole model, and then determines the effective probe length, effective induced charge to total induced charge ratio of the best fitting model under different concentrations through theoretical calculations and experimental data. This not only better represents the near-field scattering signal and the interaction between the probe and the sample, but also effectively overcomes the error problem that exists in the calculation by formula alone, which is conducive to further improving the calculation accuracy of semiconductor carrier concentration.

[0075] In this invention, the effective probe length and the ratio of effective induced charge to total induced charge are mainly related to the test environment and are less affected by other factors. Therefore, even if the carrier concentration database stores relatively little carrier concentration data, relatively high accuracy can still be obtained.

[0076] The data processing method in this invention allows the carrier concentration database to avoid storing excessive amounts of carrier concentration and related data. By leveraging the relatively small changes in two parameters—the effective probe length and the ratio of effective induced charge to total induced charge—the two parameters for concentration estimation can be more accurately inferred based on the fitting of these two parameters with the carrier concentration. This allows for the calculation of spectral information, ultimately approximating the carrier concentration of the sample under test, significantly reducing data storage and database establishment costs. Furthermore, this method avoids the problems of inaccurate fitting when directly using carrier concentration and spectral information, as well as the large storage requirements for near-field spectra.

[0077] This invention enables more efficient establishment of theoretical models and higher fitting efficiency of the best-fit model by setting the adjustment range of the effective probe length and the ratio of effective induced charge to total induced charge. Attached Figure Description

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0079] Figure 1 This is a flowchart illustrating a method for establishing a carrier concentration database according to an embodiment of the present invention;

[0080] Figure 2 This is a schematic block diagram of the testing process for a standard sample with known carrier concentration provided in an embodiment of the present invention;

[0081] Figure 3 This is a structural block diagram of the terahertz near-field detection device provided in an embodiment of the present invention;

[0082] Figure 4 This is a schematic flowchart of a carrier concentration testing method provided in an embodiment of the present invention.

[0083] Figure labeling: 1-Atomic force laser, 2-Four-quadrant receiver, 3-AFM probe, 4-Sample to be tested, 5-Scanning head, 6-TPX lens, 7-Reflector, 8-Off-axis parabolic mirror, 9-Vector network analyzer, 10-S-parameter testing module, 11-RF amplifier, 12-Mixer, 13-Voltage amplifier, 14-Lock-in amplifier, 15-Atomic force microscope control system. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] In the description of this invention, it should be understood that the terms "front", "rear", "left", "right", "up", "down", "vertical", "horizontal", "high", "low", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting the scope of protection of this invention.

[0086] Example 1:

[0087] Provide a method for establishing a carrier concentration database, such as Figure 1 As shown, the method for establishing this carrier concentration database includes the following steps:

[0088] A theoretical model including a finite dipole model and a Drood model is established. The effective probe length and the ratio of effective induced charge to total induced charge in the theoretical model are adjusted to calculate the first spectral information of a standard sample with known carrier concentration.

[0089] The second spectral information of the standard sample was detected using a terahertz near-field detection device.

[0090] By fitting several pieces of the first spectral information and the second spectral information, the best fitting model corresponding to the current carrier concentration is obtained;

[0091] Repeat the above steps to store different carrier concentrations and their corresponding spectral information, the effective probe length of the best-fit model, and the ratio of effective induced charge to total induced charge into the carrier concentration database, thus establishing the carrier concentration database.

[0092] In some preferred embodiments, the first spectral information and the second spectral information are fitted using the least squares method. When the sum of the squared residuals between the first spectral information and the second spectral information is minimized, the best fitting model is obtained. The effective probe length and the ratio of effective induced charge to total induced charge corresponding to the best fitting model are used as the effective probe length and the ratio of effective induced charge to total induced charge for the corresponding carrier concentration and are stored in the carrier concentration database.

[0093] In some embodiments, the effective length of the probe is adjusted from 80 μm to 200 μm, and the ratio of the effective induced charge to the total induced charge is adjusted from 0.4 to 1.0.

[0094] In some embodiments, the spectral information includes amplitude and / or phase difference. In some preferred embodiments, the first and second spectral information are second-order or third-order amplitudes. This is because the background noise of higher-order signals is smaller, but their values ​​are also smaller. Therefore, in a more preferred embodiment, a compromise is made to use second-order or third-order amplitudes as the spectral information.

[0095] like Figure 2As shown, taking a standard sample with a known carrier concentration n0 as an example, by setting different effective probe lengths and the ratio of effective induced charge to total induced charge, and substituting these values ​​into the theoretical model, several theoretical models with parameter combinations 1, 2, 3, ..., n can be obtained. Then, by inputting the known carrier concentration n0 into each model, several first spectral information (spectrum 1, spectrum 2, ..., spectrum n) can be output. Using a terahertz near-field detection device, the actual spectrum of the standard sample with a known carrier concentration n0 can be detected, i.e., the second spectral information. Finally, by fitting, the best-fit model with the known carrier concentration n0 can be obtained. The concentration n0, the effective probe length of the corresponding best-fit model, the ratio of effective induced charge to total induced charge, and the spectral information are then stored in a carrier concentration database.

[0096] Example 2:

[0097] Based on Example 1, as a preferred embodiment of the theoretical model, the theoretical model includes the following formula:

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] In the formula, r is the first reflection coefficient, and E i E is the amplitude of the incident electric field. s Let α be the amplitude of the scattered field. eff For the effective polarizability of the probe, C, , As an intermediate quantity, Here, k is the ratio of effective induced charge to total induced charge, H is the distance from the probe to the sample, W0 is the initial effective range of the probe, and R is the second reflection coefficient. t Where is the radius of curvature of the probe tip, L is the effective length of the probe, and W is the effective length of the probe tip. i The near-field range after probe-sample interaction is given, Q0 is the total amount of polarization charge induced by the probe tip in the absence of a sample, and E0 is the incident electric field intensity. The dielectric constant of the sample is . It is the high-frequency dielectric constant. The dielectric constant in vacuum is . For the frequency used in the experiment, The plasma resonant frequency, is the damping coefficient, n is the carrier concentration, e is the electron charge, m* is the effective mass of holes or electrons, c0 is the speed of light in vacuum, and is the reference parameter describing the intrinsic migration characteristics of carriers. pc Cr, Cs α and β are all constants.

[0111] Based on the above model, the effective polarization rate α of the probe is... eff Fourier series expansion yields:

[0112]

[0113] Where Fn is the magnitude of the nth order, Ω represents the phase difference, j is the imaginary sign, and Ω is the frequency of the probe vibration.

[0114] In some preferred embodiments, The value is 11.9.

[0115] In some preferred embodiments, pc = 9.26 × 10 16 Cr = 2.33 × 10 17 Cs = 6.1 × 10 20 , =44.9, =470.5, =7, α=0.779, β=2.

[0116] Based on the above theoretical model, when establishing the database, for the same known carrier concentration, by changing the ratio of effective induced charge to total induced charge and the effective probe length, multiple different theoretical models can be obtained, outputting several different first spectral information. Based on the measured second spectral information, the best-fit model for a certain known carrier concentration and its corresponding ratio of effective induced charge to total induced charge and effective probe length can be determined.

[0117] Example 3:

[0118] Based on the above embodiments, a carrier concentration testing system is provided, the system comprising:

[0119] A terahertz near-field detection device is used to acquire the near-field spectrum of a sample to be tested and to obtain the spectral information of the sample to be tested from the near-field spectrum.

[0120] The carrier concentration database is the carrier concentration database established in any of the foregoing embodiments. The carrier concentration database stores different carrier concentrations and their corresponding spectral information, the effective probe length of the best fitting model, and the ratio of effective induced charge to total induced charge.

[0121] The analysis unit is used to fit the spectral information of the sample to be tested with the spectral information in the carrier concentration database to obtain the carrier concentration of the sample to be tested.

[0122] In this embodiment, the analysis unit is used to fit the spectral information of the sample to be tested with the spectral information in the carrier concentration database, thereby deducing the carrier concentration of the sample to be tested.

[0123] In one or more embodiments, the spectral information in the database is compared with the spectral information of the sample to be tested, and the carrier concentration corresponding to the spectral information with the smallest difference is the carrier concentration of the sample to be tested.

[0124] Example 4:

[0125] Based on the above embodiments, such as Figure 3 As shown, the terahertz near-field detection device mainly consists of four parts. The first part, the atomic force microscope, includes an atomic force laser 1, a four-quadrant receiver 2, an AFM probe 3, a sample to be tested 4, and a scanning head 5. The second part, the optical path system, includes a TPX lens 6, a reflector 7, and an off-axis parabolic mirror 8. The third part, the laser generation and detection unit, includes a vector network analyzer 9, an S-parameter testing module 10, an RF amplifier 11, a mixer 12, and a voltage amplifier 13. The fourth part includes a lock-in amplifier 14 and an atomic force microscope control system 15.

[0126] In each part, the atomic force laser 1 is incident on the probe cantilever and reflected, then received by the four-quadrant receiver 2. Simultaneously, the AFM probe 3 vibrates at a certain frequency, and the sample to be tested 4 is placed on the scanning head 5, which can be displaced in the x, y, and z directions. The terahertz laser generated by the S-parameter testing module 10 is collimated by the TPX converging lens, reflected by the reflector 7, and finally converged onto the tip of the AFM probe 3 by the off-axis parabolic mirror 8. The resulting scattered field is transmitted back to the S-parameter testing module 10 through the opposite optical path and is received. The vector network analyzer 9, combined with the S-parameter testing module 10, generates a terahertz wave within a certain frequency range. The received signal passes sequentially through the RF amplifier 11, mixer 12, voltage amplifier 13, and lock-in amplifier 14. The lock-in amplifier 14 receives the test signal and the probe vibration signal provided by the atomic force microscope control system 15, demodulates and amplifies the signal, and outputs the demodulated higher-order signal to the atomic force microscope control system 15, realizing signal amplification and demodulation at the probe vibration frequency and its higher-order frequencies.

[0127] In this embodiment, by combining the vector network analyzer 9 with the atomic force microscope, it not only has the advantages of being sensitive to carrier concentration and being able to perform frequency sweep to obtain the optimal frequency point, but also can use atomic force microscopy technology to improve imaging resolution, reduce damage to the sample, and realize quantitative detection of semiconductor carrier concentration.

[0128] During testing, the vector network analyzer 9, in conjunction with the S-parameter test module 10, generates a laser with a frequency of 0.5THz to 0.75THz. One channel and three channels of the vector network analyzer 9 are respectively connected to the RF input channel and the local oscillator input channel of the S-parameter test module 10. The S-parameter test module 10 multiplies the RF signal by 48 times to generate a terahertz signal of 0.623THz. This signal is output through a horn antenna, which uses a WR1.5 antenna with a gain of 25dB. The terahertz laser is collimated by the TPX lens 6, and its direction is adjusted by the reflector 7. Finally, the off-axis parabolic mirror 8 focuses the terahertz laser onto the tip of the AFM probe 3. The focal length of the TPX lens 6 is 10 mm, and the focal length of the off-axis parabolic mirror 8 is 24 mm. The AFM probe 3 vibrates under the control of piezoelectric ceramics at a frequency of 10 kHzΩ-100 kHzΩ. The AFM probe 3 is a 200 μm cantilever with an 80 μm tip, and the tip curvature radius is approximately 20 nm (RMN, 25PtIr-200H). After the terahertz laser interacts with the probe and the sample, the scattered field is modulated by the vibration frequency of the probe. Its far-field signal passes through the same optical path as the incident wave and is received by the S-parameter test module 10. Subsequently, the S-parameter testing module 10 mixes the frequency-doubled 0.623THz signal and the signal modulated by the sample and AFM probe 3 with the local oscillator signal to obtain a 7.5MHz reference intermediate frequency signal and a 7.5MHz+NΩ test intermediate frequency signal, respectively. These signals are then output through the reference intermediate frequency signal output port and the test intermediate frequency signal output port of the S-parameter testing module 10. Next, the two output signals are amplified by the RF amplifier 11 with a gain of 20dB. The amplified reference intermediate frequency signal and the test intermediate frequency signal are then connected to the local oscillator signal (LO) port and the RF signal port of the mixer 12, respectively, to obtain an NΩ signal. This signal is amplified by the voltage amplifier with a gain of 40dB and finally connected to the lock-in amplifier 14. The lock-in amplifier 14 performs phase-locked demodulation and amplification at the probe vibration frequency Ω based on the probe vibration signal provided by the atomic force microscope, obtaining signals of orders 1-4. The four demodulated signals are then output to the atomic force microscope control system 15 to achieve imaging of higher-order signals. Subsequently, the carrier concentration of the sample under test can be obtained by analyzing the amplitude and / or phase.

[0129] Example 5:

[0130] Based on the above embodiments, the analysis unit fits the spectral information of the sample to be tested with the spectral information in the carrier concentration database, including the following steps:

[0131] S1: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value;

[0132] S2: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested;

[0133] S3: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested.

[0134] S4: Repeat step S3 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

[0135] Specifically, taking the spectral information as a second-order amplitude as an example, the spectral information F2 of the sample to be tested is obtained. 测 Then, it was compared with the spectral information in the database. The comparison results showed that the closest spectral information was F20. Therefore, the carrier concentration n0 corresponding to the spectral information F20 was taken as the initial concentration value.

[0136] The concentration estimate n is set based on the initial concentration value. 估1 Among them, the concentration estimate n 估1 The selection can be based on the known carrier concentrations and their corresponding spectral information in the database. For example, if the database already contains carrier concentrations n0 and n1, and the spectral information of the sample to be tested is closer to that of concentration n0, then after determining concentration n0 as the initial concentration, the concentration estimate n... 估1 This is closer to concentration n0 than concentration n1. Subsequently, based on all or part of the carrier concentration, probe effective length, and the ratio of effective induced charge to total induced charge data from the carrier database, a concentration estimate n is obtained. 估1 The corresponding effective probe length L 估1 and the ratio k of effective induced charge to total induced charge 估1 . n 估1 L 估1 k 估1 After inputting the theoretical model, the concentration n is calculated. 估1 Corresponding spectral information F2 估1 .

[0137] Next, calculate the spectral information F2. 估1 With spectral information F2 测 The difference between ΔF2 估1 If ΔF2 估1 If the difference is greater than the threshold, then the difference is calculated based on the spectral information ΔF2. 估1 To adjust the concentration estimate to n 估2 Concentration n 估2It can get closer to the concentration estimate n 估1 Or, the initial concentration value is n0, and the concentration n is determined. 估2 The corresponding L 估2 and k 估2 Substitute into the theoretical model to calculate F2 估2 Then calculate the spectral information difference ΔF2 估2 Repeat this step until, for example, the difference ΔF2 is reached. 估5 If ΔF2 is less than or equal to the threshold, then 估5 Corresponding concentration estimate concentration n 估5 This is then taken as the carrier concentration of the sample to be tested.

[0138] In this embodiment, the data processing method of the analysis unit allows the carrier concentration database to avoid storing too much carrier concentration and related data. By taking advantage of the fact that the effective probe length and the ratio of effective induced charge to total induced charge are relatively unaffected by changes, the two parameters for concentration estimation can be more accurately inferred based on the fitting of the two parameters with the carrier concentration. Then, the spectral information is calculated, and finally the carrier concentration of the sample to be tested is approximated, which greatly reduces the amount of data storage and the cost of establishing the database. At the same time, this method also avoids the problem of inaccurate fitting when directly using carrier concentration and spectral information, as well as the problem of large storage requirements for near-field spectrum.

[0139] Example 6:

[0140] Based on the above embodiments, a method is provided as follows: Figure 4 The carrier concentration testing method shown includes the following steps:

[0141] S1: Collect the near-field spectrum of the sample to be tested, and obtain the spectral information of the sample to be tested from the near-field spectrum;

[0142] S2: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value;

[0143] S3: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested;

[0144] S4: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested.

[0145] S5: Repeat step S4 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

[0146] In this embodiment, the theoretical model used to calculate the spectral information is the same as the theoretical model used to establish the carrier concentration database.

[0147] The terms "first," "second," etc., used in this invention (e.g., first spectral information, second spectral information, etc.) are merely for clarity of description and are not intended to limit any order or emphasize importance. Furthermore, the term "connection" used in this invention, unless otherwise specified, can refer to a direct connection or an indirect connection via other components.

[0148] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a carrier concentration database, characterized in that, The method includes the following steps: A theoretical model including a finite dipole model and a Drud model is established. The effective probe length and the ratio of effective induced charge to total induced charge in the theoretical model are adjusted to calculate the first spectral information of a standard sample with known carrier concentration. The second spectral information of the standard sample was detected using a terahertz near-field detection device. By fitting several pieces of the first spectral information and the second spectral information, the best fitting model corresponding to the current carrier concentration is obtained; Repeat the above steps to store different carrier concentrations and their corresponding spectral information, the effective probe length of the best-fit model, and the ratio of effective induced charge to total induced charge into the carrier concentration database, thus establishing the carrier concentration database. The theoretical model is as follows: Where r is the first reflection coefficient, E i E is the amplitude of the incident electric field. s Let α be the amplitude of the scattered field. eff For the effective polarizability of the probe, C, , As an intermediate quantity, Here, k is the ratio of effective induced charge to total induced charge, H is the distance from the probe to the sample, W0 is the initial effective range of the probe, and R is the second reflection coefficient. t Where is the radius of curvature of the probe tip, L is the effective length of the probe, and W is the effective length of the probe tip. i The near-field range after probe-sample interaction is given, Q0 is the total amount of polarization charge induced by the probe tip in the absence of a sample, and E0 is the incident electric field intensity. The dielectric constant of the sample is... It is the high-frequency dielectric constant. The dielectric constant in vacuum is . For the frequency used in the experiment, The plasma resonant frequency, Where is the damping coefficient, n is the carrier concentration, e is the electron charge, m* is the effective mass of holes or electrons, and c0 is the speed of light in vacuum. As a baseline parameter describing the intrinsic mobility characteristics of charge carriers, pc is a scattering parameter. Cr, Cs α and β are all constants; Based on the above model, the effective polarization rate α of the probe is... eff Fourier series expansion yields: Where Fn is the magnitude of the nth order, Ω represents the phase difference, j is the imaginary sign, and Ω is the frequency of the probe vibration.

2. The method for establishing a carrier concentration database according to claim 1, characterized in that, The first spectral information and the second spectral information are fitted using the least squares method. When the sum of the squared residuals between the first spectral information and the second spectral information is minimized, the best fitting model is obtained. The effective probe length corresponding to the best fitting model is used as the effective probe length for the corresponding carrier concentration. The ratio of the effective induced charge to the total induced charge corresponding to the best fitting model is used as the ratio of the effective induced charge to the total induced charge for the corresponding carrier concentration, and is stored in the carrier concentration database.

3. The method for establishing a carrier concentration database according to any one of claims 1 to 2, characterized in that, The effective length of the probe can be adjusted from 80μm to 200μm, and the ratio of the effective induced charge to the total induced charge can be adjusted from 0.4 to 1.

0.

4. The method for establishing a carrier concentration database according to any one of claims 1 to 2, characterized in that, Spectral information includes amplitude and / or phase difference.

5. A method for measuring carrier concentration, characterized in that, The method includes the following steps: The near-field spectrum of the sample to be tested is acquired, and the spectral information of the sample to be tested is obtained from the near-field spectrum; The carrier concentration of the sample to be tested is obtained by fitting the spectral information of the sample to be tested with the spectral information in the carrier concentration database. Wherein, the carrier concentration database adopts the carrier concentration database as described in any one of claims 1 to 4; The process of fitting the spectral information of the sample to be tested with the spectral information in the carrier concentration database includes the following steps: Step S1: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value; Step S2: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested; Step S3: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested. Step S4: Repeat step S3 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

6. A carrier concentration testing system, characterized in that, The system includes: A terahertz near-field detection device is used to acquire the near-field spectrum of a sample to be tested and to obtain the spectral information of the sample to be tested from the near-field spectrum. The carrier concentration database is adopted as described in any one of claims 1 to 4. The carrier concentration database stores different carrier concentrations and their corresponding spectral information, the effective probe length of the best fitting model, and the ratio of effective induced charge to total induced charge. An analysis unit is used to fit the spectral information of the sample to be tested with the spectral information in the carrier concentration database to obtain the carrier concentration of the sample to be tested. The analysis unit fits the spectral information of the sample to be tested with the spectral information in the carrier concentration database, including the following steps: Step S1: Obtain the spectral information of the sample to be tested, compare the spectral information of the sample to be tested with the spectral information in the carrier concentration database, and determine the initial concentration value; Step S2: Calculate the difference between the spectral information corresponding to the initial concentration value and the spectral information of the sample to be tested; Step S3: Determine the concentration estimate based on the spectral information difference. According to the carrier concentration, probe effective length, and ratio of effective induced charge to total induced charge in the carrier concentration database, determine the spectral information corresponding to the current concentration estimate, and calculate the spectral information difference between the spectral information corresponding to the current concentration estimate and the spectral information of the sample to be tested. Step S4: Repeat step S3 until the difference in the spectral information is less than or equal to the threshold, and use the concentration estimate corresponding to the spectral information as the carrier concentration of the sample to be tested.

7. The carrier concentration testing system according to claim 6, characterized in that, The terahertz near-field detection device includes a vector network analyzer, an S-parameter testing module, an optical path system, an atomic force microscope system, and a lock-in amplifier.

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