A method for measuring carrier concentration of terahertz band materials

Abstract

The present invention relates to a method for measuring the carrier concentration of materials in the terahertz band, and belongs to the field of terahertz application technology. The method comprises: S1: using a terahertz spectroscopy system to measure a terahertz reference signal when there is no sample and a terahertz sample signal when there is a material sample, and using Fourier transform to obtain a reference signal and a sample signal in the frequency domain; S2: using the ratio of the reference signal and the sample signal in the frequency domain to obtain an amplitude ratio and a phase difference; S3: according to the theoretical relationship between the optical parameters of the material and the sample signal, inverting the complex dielectric constant of the sample, and then calculating the complex conductivity of the material; S4: according to the dependence of the complex conductivity on the carrier concentration, calculating the material carrier concentration of the material at different wavelengths. The present invention is applicable to different terahertz systems, and can realize non-destructive measurement of material carriers in the range of millimeters to micrometers and then to nanometers.

Description

Technical Field

[0001] The invention belongs to the technical field of terahertz application, and relates to a method for measuring carrier concentration of terahertz band materials. Background Art

[0002] Terahertz (THz) nondestructive testing is one of the important application directions of THz technology. THz waves are between millimeter waves and infrared light. THz waves can penetrate many materials that infrared cannot penetrate, such as paper, plastic, ceramics and semiconductors. Compared with X-ray detection, THz waves have lower energy (1THz~4meV), which can make up for the obvious disadvantage that X-rays can easily cause radiation damage to the human body.

[0003] The optical parameters of materials are an important basis for studying the physical and chemical properties of materials. The concentration and motion state of carriers play a key role in the conductive properties and luminescent properties of semiconductors. The carrier concentration of materials is usually measured by the Hall effect, but there is a large error in its detection accuracy, and it is impossible to directly detect the carrier concentration in the terahertz band; secondly, the sample size of the Hall effect measurement is limited, and it cannot measure samples in the entire size range from millimeters, microns to nanometers. Therefore, it is necessary to develop an effective method for detecting the carrier concentration of terahertz wave materials. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a method for measuring carrier concentration of materials in the terahertz band, so as to solve the problems of large detection error, inability to directly detect and limited sample size in the prior art.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for measuring carrier concentration of terahertz band material, the method comprising the following steps:

[0007] S1: Using the terahertz spectroscopy system to measure the terahertz reference signal E without a sample r (t) and the terahertz sample signal E when there is a material sample s (t), and use Fourier transform to obtain the reference signal E in the frequency domain r (ω) and the sample signal E s (ω);

[0008] S2: Using the reference signal E in the frequency domain r (ω) and sample signal E s (ω) ratio A(ω) to obtain the amplitude ratio T(ω) and phase difference

[0009] S3: Based on the theoretical relationship between the material optical parameters and the sample signal, the complex dielectric constant of the sample is inverted Then the complex conductivity of the material is calculated

[0010] S4: Calculate the carrier concentration of the material at different wavelengths based on the dependence of complex conductivity on carrier concentration.

[0011] Further, in step S1, the terahertz spectroscopy system includes: a terahertz time-domain spectroscopy system, a terahertz Fourier spectrometer, a terahertz detection system based on a photoconductive micro-antenna probe, and a terahertz scattering scanning near-field optical detection system.

[0012] Furthermore, in step S3, the theoretical relationship between the material optical parameters and the sample signal includes: far-field and near-field inversion relationships.

[0013] Further, in step S3, when applied to a near-field measurement system, mainly for a terahertz scattering scanning near-field optical microscopy imaging system, a near-field inversion relationship is used, and the reference signal E in the frequency domain is r (ω) and sample signal E s The ratio of (ω) to A(ω) is:

[0014]

[0015] in, represents the n-th order Fourier coefficient; α eff,r With α eff,s denote the effective polarizability of the reference and sample probes, α eff,r / s The expression is:

[0016]

[0017] Where a represents the probe curvature radius, d represents the distance between the probe and the sample; α represents the probe polarizability, β r / s Denotes the dielectric response function of the reference or sample, α and β r / s The expressions are:

[0018]

[0019]

[0020] in, represents the complex dielectric function of the probe, represents the complex dielectric function of the reference or sample; then, according to the known complex dielectric function of the reference The complex dielectric function of the sample is obtained by inversion And calculate the sample complex conductivity

[0021] Further, in step S3, when applied to the measurement of millimeter and micrometer size samples, the far-field inversion relationship is adopted, and the real refractive index n(ω) and extinction coefficient k(ω) of the sample are respectively:

[0022]

[0023]

[0024] Among them, T(ω) and are the amplitude ratio and phase difference obtained using the reference and sample terahertz spectra, n0 is the refractive index of air, c is the speed of light, ω is the terahertz wavelength, and l is the sample thickness;

[0025] Then, the complex dielectric constant of the sample is calculated using the obtained real refractive index n(ω) and extinction coefficient k(ω) And the complex conductivity

[0026]

[0027] Further, in step S4, the dependence of the complex conductivity on the carrier concentration includes: Drude model, Lorentz model, Drude-Lorentz model and Drude-Smith model.

[0028] The beneficial effects of the present invention are:

[0029] 1) The measurement method of the present invention can realize direct measurement of carrier concentration of materials in the terahertz band and has the capability of non-destructive testing.

[0030] 2) The carrier measurement method adopted by the present invention is applicable to different terahertz systems and can realize the carrier measurement of materials ranging from millimeter to micrometer and then to nanometer scale.

[0031] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0033] Figure 1 This is a flow chart of the method for measuring carrier concentration of terahertz band materials of the present invention. DETAILED DESCRIPTION

[0034] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0035] See also Figure 1 This embodiment provides a method for measuring carrier concentration of terahertz band materials, which specifically includes the following steps:

[0036] 1) Using the terahertz spectroscopy system, measure the terahertz reference signal E when there is no sample and when there is a sample (reflection or transmission mode) r (t) and the terahertz sample signal E when there is a material sample s (t), and use Fourier transform to obtain the reference signal E in the frequency domain r (ω) and the sample signal E s (ω).

[0037] Among them, the terahertz spectroscopy system includes: terahertz time-domain spectroscopy system, terahertz Fourier spectrometer, terahertz detection system based on photoconductive micro-antenna probe and terahertz scattering scanning near-field optical detection system.

[0038] 2) Using E r (ω) and E s (ω) ratio A(ω) to obtain the amplitude ratio T(ω) and phase difference

[0039] 3) Calculate the complex refractive index of the sample using the inversion relationship between the material's optoelectronic parameters and the terahertz signal (including the far-field and near-field inversion relationships). Complex conductivity And the complex dielectric constant

[0040] ① When used for millimeter and micron size sample measurement, the far-field inversion relationship is used, and the sample real refractive index n(w) and extinction coefficient k(w) are respectively:

[0041]

[0042]

[0043] Among them, T(ω) and are the amplitude ratio and phase difference obtained using the reference and sample terahertz spectra, n0 is the refractive index of air, c is the speed of light, ω is the terahertz wavelength, and l is the sample thickness. Subsequently, the complex refractive index of the sample can be calculated using the obtained real refractive index n(ω) and extinction coefficient k(w): Complex conductivity And the complex dielectric constant

[0044] ②When used in near-field measurement systems, mainly for terahertz scattering scanning near-field optical microscopy imaging systems, the near-field inversion relationship is used, and the ratio of the reference and sample terahertz spectra is:

[0045]

[0046] in, represents the n-th order Fourier coefficient, α eff,s With α eff,r represent the effective polarizability of the sample and reference probes, α eff,r / s It can be expressed as:

[0047]

[0048] Where α represents the probe polarizability, β r / s represents the dielectric response function of the reference or sample, a represents the probe curvature radius, d represents the distance between the probe and the sample, α and β r / s Can be expressed as:

[0049]

[0050]

[0051] in, represents the complex dielectric function of the probe, represents the complex dielectric function of the reference or sample. Finally, the experimentally obtained A(w) and the known reference complex dielectric function are used to The complex dielectric function of the sample is obtained by inversion And further calculate the sample complex conductivity

[0052] 4) Calculate the material carrier concentration N using the dependence of complex conductivity on carrier concentration c .

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A method for measuring carrier concentration of terahertz band materials, characterized in that: The method comprises the following steps: S1: Using the terahertz spectroscopy system to measure the terahertz reference signal E without a sample r (t) and the terahertz sample signal E when there is a material sample s (t), and use Fourier transform to obtain the reference signal E in the frequency domain r (ω) and the sample signal E s (ω); S2: Using the reference signal E in the frequency domain r (ω) and sample signal E s (ω) ratio A(ω) to obtain the amplitude ratio T(ω) and phase difference S3: Based on the theoretical relationship between the material optical parameters and the sample signal, the complex dielectric constant of the sample is inverted Then the complex conductivity of the material is calculated The theoretical relationship between material optical parameters and sample signals includes far-field and near-field inversion relationships; ① When used for millimeter and micron size sample measurement, the far-field inversion relationship is used, and the sample real refractive index n(ω) and extinction coefficient k(ω) are respectively: Where n0 is the refractive index of air, c is the speed of light, w is the terahertz wavelength, and l is the sample thickness; Then, the complex dielectric constant of the sample is calculated using the obtained real refractive index n(ω) and extinction coefficient k(ω) And the complex conductivity ② When used in a near-field measurement system, the near-field inversion relationship is used, and the reference signal E in the frequency domain is r (ω) and sample signal E s The ratio of (ω) to A(ω) is: in, represents the n-th order Fourier coefficient; α eff，r With α eff，s denote the effective polarizability of the reference and sample probes, α eff，r / s The expression is: Where a represents the probe curvature radius, d represents the distance between the probe and the sample; α represents the probe polarizability, β r / s Denotes the dielectric response function of the reference or sample, α and β r / s The expressions are: in, represents the complex dielectric function of the probe, represents the complex dielectric function of the reference or sample; then, according to the known complex dielectric function of the reference The complex dielectric function of the sample is obtained by inversion And calculate the sample complex conductivity S4: Calculate the carrier concentration of the material at different wavelengths based on the dependence of complex conductivity on carrier concentration.

2. The method for measuring carrier concentration of terahertz band materials according to claim 1, characterized in that: In step S1, the terahertz spectroscopy system includes: a terahertz time-domain spectroscopy system, a terahertz Fourier spectrometer, a terahertz detection system based on a photoconductive micro-antenna probe, and a terahertz scattering scanning near-field optical detection system.

3. The method for measuring carrier concentration of terahertz band materials according to claim 1, characterized in that: In step S4, the dependence of the complex conductivity on the carrier concentration includes: Drude model, Lorentz model, Drude-Lorentz model and Drude-Smith model.

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