Second harmonic signal acquisition method of non-uniform ion implantation doping concentration and application

Abstract

The invention belongs to the related technical field of semiconductor doping, and discloses a method for acquiring a second harmonic signal of non-uniform ion implantation doping concentration and an application of the second harmonic signal of the non-uniform ion implantation doping concentration. Determining refractive indexes and absorption coefficients of different depth positions of the ion implantation doping sample under a specific laser wavelength based on an optical property distribution model in the ion implantation doping sample; s2, calculating fundamental frequency light electric field distribution in the doped sample based on the obtained refractive index and absorption coefficient; s3, calculating the polarization intensity and effective second-order polarizability of the non-uniform doped ion implantation sample based on the simplified bond hyperpolarizability model and the fundamental frequency photoelectric field distribution; and S4, calculating far-field second harmonics of the corresponding layers at a predetermined observation angle based on the obtained polarization intensity or effective second-order polarizability of each layer, and carrying out integration on the far-field second harmonics corresponding to all layers to obtain the total intensity of the second harmonics of junction depth far-field radiation. According to the invention, the problem that the measurement sensitivity and repeatability are reduced is solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of semiconductor doping, and more particularly relates to a method for obtaining a second harmonic signal of a non-uniform ion implantation doping concentration and an application thereof. BACKGROUND

[0002] Ion implantation is one of the key processes in IC manufacturing. The monitoring of the ion implantation process and the measurement of the doped P / N structure are essential measurement procedures, the purpose of which is to optimize the ion implantation process, improve the yield, and achieve the expected indicators of the doped structure design. With the continuous reduction of IC feature size, the ion implantation P / N junction depth is also continuously reduced, and a junction depth of less than 20 nm is referred to as a super shallow junction. In order to meet the performance of IC design, the ion implantation dose is also continuously improved, and for example, the plasma implantation process has achieved high-dose doping of more than 1014cm-2. The high-dose doping process also puts higher requirements on the monitoring of the ion implantation process. The current commonly used doping measurement methods include destructive measurement methods such as four-probe method and secondary ion mass spectrometry, and non-destructive techniques such as optical modulation optical reflection technology.

[0003] The optical modulation optical reflection technology is mainly used for monitoring low-dose ion implantation processes. When the optical modulation optical reflection technology is used to monitor high-dose doping required by a super shallow junction, a higher intensity of excitation light is required to improve the measurement sensitivity. When high-intensity light excitation is used to excite a high-doped nanostructure, other physical phenomena are induced, such as strong electric field effect, sample surface charge polarization, and local stress caused by photo-thermal effect. These excitation physical processes will lead to more obvious enhanced nonlinear effects.

[0004] Second harmonic is a nonlinear optical phenomenon. When a strong light beam (laser) is irradiated onto a non-centrosymmetric material, the optical electric field interacts with the electrons inside the material, inducing polarization. In a nonlinear medium, this polarization is not only proportional to the electric field, but also proportional to the square of the electric field. Therefore, if the frequency of the original light wave is , then the generated polarization wave will contain a frequency of The second harmonic is a component of the second harmonic, that is, the second harmonic. Since the second harmonic is a manifestation of the interaction between light and matter, the second harmonic can be used to study the structure of the material, and is applied in the fields of material characterization, biomedicine, optoelectronics, etc. The design of the second harmonic optical system is very mature. A second harmonic generation (SHG) optical inspection system is disclosed in Chinese invention patent CN113167741A for detecting the surface of a sample to form an SHG image. A second harmonic characterization method, a characterization optical system based thereon, and a detection device are disclosed in Chinese invention patent CNA114577726A for obtaining the defect type of a scanned sample, the defect energy level of different defect types, and the fundamental frequency light wavelength corresponding to different defect types. Although these methods have made certain progress in the measurement of semiconductor surface states, they still have some limitations. For example, when facing ion implantation samples with different dopant doses, there is no model to quantitatively describe the relationship between the second harmonic signal and the dopant dose. In addition, the distribution of the fundamental frequency electric field at different depths of the measured point and the change of the second-order nonlinear coefficient with the non-uniform doping concentration will affect the second harmonic signal response.

[0005] In summary, in the process of non-destructive monitoring of ion implantation, due to the limitation of the physical properties of the sample to be measured, the light modulation light reflection technology has certain limitations, resulting in reduced measurement sensitivity and repeatability. At the same time, the existing second harmonic material characterization technology lacks a targeted method for measuring ion implantation samples, and cannot decouple the characterization of the doping concentration distribution. SUMMARY

[0006] In view of the above defects or improvement needs of the prior art, the present application provides a second harmonic signal acquisition method for non-uniform ion implantation doping concentration and application, which aims to solve the problem of low measurement sensitivity and repeatability of the existing non-destructive monitoring method for ion implantation when facing high-dose doped samples.

[0007] To achieve the above-mentioned purpose, according to one aspect of the present application, a second harmonic signal acquisition method for non-uniform ion implantation doping concentration is provided, and the steps are as follows: S1, determining the refractive index and absorption coefficient of the ion implantation doped sample at different depth positions under a specific laser wavelength based on the optical property distribution model of the ion implantation doped sample; S2, calculating the fundamental frequency light electric field distribution in the doped sample based on the obtained refractive index and absorption coefficient; S3, calculating the polarization intensity and effective second-order polarizability of the non-uniformly doped ion implantation sample based on the simplified bond hyperpolarizability model and the fundamental frequency light electric field distribution; S4, calculating the far-field second harmonic of the corresponding layer under the predetermined observation angle based on the polarization intensity or effective second-order polarizability of each layer, and integrating the far-field second harmonics corresponding to all layers to obtain the total intensity of the second harmonic of the junction depth far-field radiation.

[0008] Further, under the laser and doping, the free electron distribution, free hole distribution and temperature distribution in the ion-implanted sample affect the refractive index change in the sample, and the corresponding formula is:

[0009] wherein, is the total refractive index, is the initial refractive index of crystalline silicon at room temperature under the base frequency light, , , are the refractive index changes caused by free electrons, free holes and temperature respectively; , , are the spatial point coordinates of the silicon wafer, is the time.

[0010] Further, for the Drude effect, under the laser irradiation, the free electron, free hole and temperature distribution in the ion-implanted and doped sample are solved by using the two-temperature model and the carrier dynamics model:

[0011] wherein, is the non-equilibrium carrier generated in the doped sample under the light source irradiation, is the bipolar diffusion rate, is the single-photon absorption coefficient, is the two-photon absorption coefficient, is the light intensity distribution on the surface of the sample, is the Planck constant, is the single-photon frequency of the laser, is the carrier recombination rate, is the electron-lattice temperature coupling coefficient, and are the electron heat capacity and lattice heat capacity respectively, and are the electron temperature and lattice temperature respectively, and are the electron thermal conductivity and lattice thermal conductivity respectively, is the silicon band gap energy, is the Boltzmann constant.

[0012] Further, the Drude effect in the doped semiconductor is specifically: wherein is the vacuum permittivity, is the dielectric constant of the doped semiconductor, which is the ratio of the electric displacement vector to the electric field intensity, , is the electric displacement vector, is the electric field intensity, is the dielectric constant of the intrinsic semiconductor, is the carrier concentration, is the charge of an electron, is the conductivity effective mass of an electron, is the damping rate, is the incident light angular frequency.

[0013] Further, the junction depth is of the ion-implanted sample, and the single layer thickness is , and then the light source incident angle is determined, and the refraction angle of the z-th layer is calculated according to Snell's law and the different interlayer refractive indexes obtained in step S1; the refraction angle of the z-1-th layer is the incident angle of the z-th layer, and the relationship between the refractive index and the refraction angle of the z-1-th layer and the z-th layer is , wherein , are the refractive indexes of the z-1-th layer and the z-th layer, respectively, , are the incident angles of the z-1-th layer and the z-th layer, respectively.

[0014] Further, the light intensity at the z-th layer from the sample surface is:

[0015] wherein is the absorption coefficient of the z-th layer from the sample surface; The electric field amplitude of the z-th layer is:

[0016] wherein is the speed of light in vacuum, is the vacuum dielectric constant, is the refractive index of the doped layer.

[0017] Further, the base element and the doped element are determined, and the doped element concentration distribution function is obtained according to the actual doping situation; in the volume , is the laser spot area, the number of doped atoms , and the total number of atoms is ; In the simplified bond hyperpolarizability model, the surface and interface dipole moment and the bulk body quadrupole moment in the bulk are respectively: ,

[0018] wherein is the volume, is the total number of bonds in the considered volume, is the unit vector of the bond, is the second-order bond polarizability corresponding to the bond unit vector, is the volume quadrupole polarizability of the second harmonic generation, , are obtained by first-principle calculation or coupon experiment measurement, is the incident wave electric field at the current position, determined by step S2; is the electric field gradient term, , is a fitting parameter related to the gradient size, is the base frequency light incident propagation direction.

[0019] Further, the second-order polarization intensity generated by the base element atoms is: , the second-order polarization intensity generated by the doped element atoms is: , according to the doping concentration, the second-order dipole moment induced at the z-th layer doped medium interface is:

[0020] The effective second-order polarization rate at the interface is: .

[0021] Further, the volume quadrupole intensity generated by the base element atoms is: , the volume quadrupole intensity generated by the doped element atoms is: , according to the doping concentration, the quadrupole moment induced at the z-th layer doped medium volume is:

[0022] The z-th layer volume quadrupole polarizability is: .

[0023] The application also provides a method for obtaining a non-uniform ion implantation doping concentration, which uses the above-mentioned second harmonic signal acquisition method of non-uniform ion implantation doping concentration to acquire the second harmonic total intensity of the ion implantation doped sample, and then acquires the doping concentration of the ion implantation doped sample based on the mapping relationship between the second harmonic total intensity and the doping concentration.

[0024] Overall, compared with the prior art, the second harmonic signal acquisition method of non-uniform ion implantation doping concentration and application conceived by the present application mainly have the following beneficial effects: 1. The use of second harmonic signal for ion implantation process parameter measurement and characterization solves the problem of the need for high excitation light intensity when using the light modulation reflectance technique (the current mature ion implantation non-destructive testing technique) to face high dose doping, which enhances the non-linear effect, resulting in reduced measurement sensitivity and repeatability.

[0025] 2. The construction of the second-order nonlinear polarization intensity distribution of each doped layer from the physical property change of the ion implantation sample under light injection to the far-field second harmonic intensity can be used for far-field second harmonic signal prediction under different incident light conditions (laser frequency, light intensity, incident angle, etc.) and different doping type ion implantation samples (doping dose, energy, angle, doping element type).

[0026] 3. A complete second harmonic signal acquisition method is provided, which can provide second harmonic measurement technology development and algorithm support for ion implantation doping process in semiconductor production, and can also be used to guide the device selection of the ion implantation second harmonic measurement machine, reducing the research and development cost. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a schematic diagram of a second harmonic signal acquisition method for non-uniform ion implantation doping concentration provided by an embodiment of the present application; Figure 2 is a flowchart of a second harmonic signal acquisition method for non-uniform ion implantation doping concentration provided by an embodiment of the present application; Figure 3 is a concentration distribution graph of phosphorus element in a silicon substrate implanted by phosphorus ions in the depth direction provided by an embodiment of the present application; Figure 4 is a crystal structure graph of phosphorus-doped silicon after complete annealing provided by an embodiment of the present application; Figure 5a 、 Figure 5b and Figure 5c are different types of second harmonic intensity graphs obtained by an embodiment of the present application. DETAILED DESCRIPTION

[0028] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0029] The present application provides a second harmonic signal acquisition method for non-uniform ion implantation doping concentration, which mainly includes the following steps: S1, determining the refractive index and absorption coefficient of the ion-implanted doped sample at different depths under a specific laser wavelength based on the model of the distribution of optical properties in the ion-implanted doped sample.

[0030] According to the model of the distribution of optical properties in the ion-implanted doped sample, the refractive index and absorption coefficient at different depths are obtained by the following method: Under the action of the laser and the doping, the free electron distribution, the free hole distribution, and the temperature distribution in the ion-implanted sample affect the refractive index change in the sample:

[0031] wherein, is the total refractive index, is the initial refractive index of the crystal silicon at the base frequency light at room temperature, , , are the refractive index changes caused by the free electrons, the free holes, and the temperature, respectively; , , are the coordinates of the spatial point of the silicon wafer, is the time. The free electrons and the free holes affect the refractive index through the Drude effect, and the temperature change affects the refractive index through the thermal effect.

[0032] For the Drude effect, under the irradiation of the laser, the free electron, the free hole, and the temperature distribution in the ion-implanted doped sample are solved by using the two-temperature model and the carrier kinetics model:

[0033] wherein, is the non-equilibrium carrier (also known as the excess carrier) generated by the doped sample under the irradiation of the light source, is the bipolar diffusion rate, is the single-photon absorption coefficient, is the two-photon absorption coefficient, is the light intensity distribution on the surface of the sample, is the Planck constant, is the single-photon frequency of the laser, is the carrier recombination rate, is the electron-lattice temperature coupling coefficient, and are the electronic heat capacity and the lattice heat capacity, respectively, and are the electron temperature and the lattice temperature, respectively, and are the electronic thermal conductivity and the lattice thermal conductivity, respectively, is the silicon band gap energy, is the Boltzmann constant.

[0034] The Drude effect in doped semiconductors is specifically as follows: ,in The vacuum permittivity, is the dielectric constant of the doped semiconductor, which is the ratio of the electric displacement vector to the electric field strength. , It is the electric displacement vector. For electric field strength, The dielectric constant of an intrinsic semiconductor (undoped) is... Carrier concentration, The charge carried by an electron. For the effective mass of electron conductance, Damping rate (mean free time of two electron scatterings) (the reciprocal of) ω is the incident light angular frequency.

[0035] Furthermore, based on different doping types (P-type semiconductor or n-type semiconductor), the formula is obtained: middle and item.

[0036] In doped semiconductors, the thermal effect specifically refers to how changes in sample temperature affect the lattice dielectric constant. The formula was fitted using experimental data: ,

[0037] in and These are the normalized temperature coefficients of refractive index and extinction coefficient, respectively. The initial temperature is used as a superscript. At that time, the parameter value is represented at the initial temperature. Further, we can obtain... item.

[0038] Finally, in step S1, the optical property distribution model in the ion-implanted doped sample can be obtained: This optical property distribution model can be used for both fundamental frequency light and second harmonic light.

[0039] S2, calculate the fundamental frequency photoelectric field distribution in the doped sample based on the obtained refractive index and absorption coefficient.

[0040] For ion-implanted samples with continuously varying doping concentrations, they can be considered as multilayered, continuously varying interfaces. The junction depth is... The ion-implanted sample has a single-layer thickness of Then determine the incident angle of the light source. According to Snell's law and the different refractive indexes between layers in S1, the refraction angle of the z-th layer is calculated. The refraction angle of the z-1-th layer is the incident angle of the z-th layer, and the relationship between the refractive index and the refraction angle of the z-1-th layer and the z-th layer is , wherein , are the refractive indexes of the z-1-th layer and the z-th layer, respectively, , are the incident angles of the z-1-th layer and the z-th layer, respectively.

[0041] Further, the reflectivity of each layer is calculated by Fresnel formula, and the Fresnel formula is as follows:

[0042] Further, the light intensity at the z-th layer away from the sample surface is:

[0043] wherein is the absorption coefficient of the z-th layer away from the sample surface.

[0044] Further, the electric field amplitude of the z-th layer is:

[0045] wherein is the speed of light in vacuum, is the vacuum permittivity, is the refractive index of the doped layer. Thus, the fundamental optical electric field distribution in the doped sample can be obtained.

[0046] S3, the polarization intensity and the effective second-order polarizability of the non-uniformly doped ion-implanted sample are calculated based on the simplified bond-hyperpolarizability model (SBHM) and the fundamental optical electric field distribution.

[0047] When the fundamental light irradiates the sample, the dipole moment generated by the surface and interface and the bulk quadrupole moment in the bulk in the polarization intensity model of the non-uniformly doped ion-implanted sample can radiate the frequency-doubled light.

[0048] The polarization intensity of the non-uniformly doped ion-implanted sample is obtained by the following steps: The base element and the doped element are determined, and the doped element concentration distribution function is obtained according to the actual doping situation ; in the volume , is the laser spot area, the number of doped atoms , and the total number of atoms is .

[0049] In the simplified key hyperpolarizability model, the surface and interface dipole moment and the bulk body quadrupole moment in the block are respectively: ,

[0050] wherein is the volume, is the total number of bonds in the considered volume, is the unit vector of the bond, is the second-order bond polarizability corresponding to the bond unit vector, is the second-harmonic generation body quadrupole moment polarizability, are obtained by first-principle calculation or wafer experimental measurement, is the incident wave electric field at the current position, determined by step S2. is a fitting parameter related to the gradient size, which can be obtained by wafer experimental measurement, is the base frequency light incident propagation direction.

[0051] In the z-th layer of the doped sample, the surface and interface dipole moment is calculated as follows: The second-order polarization intensity generated by the base element atoms is: The second-order polarization intensity generated by the doped element atoms is: According to the doping concentration, the second-order dipole moment induced at the doped medium interface in the z-th layer is: Therefore, the effective second-order polarization of the interface is: .

[0052] In the z-th layer of the doped sample, the interlayer body quadrupole moment is calculated as follows: The bulk quadrupole intensity generated by the base element atoms is: The bulk quadrupole intensity generated by the doped element atoms is: According to the doping concentration, the quadrupole moment induced in the doped medium body in the z-th layer is: Therefore, the z-th layer body quadrupole moment polarizability is: .

[0053] Thus, the polarization intensity and effective second-order polarization coefficient of the non-uniformly doped ion implantation sample can be obtained.

[0054] ​​​S4, calculating the far field second harmonic of the layer at a predetermined observation angle based on the obtained polarization intensity or effective second order polarizability of each layer, and integrating the corresponding far field second harmonics of all layers to obtain the total intensity of the second harmonic of the deep junction far field radiation.

[0055] The electric field of the fundamental light inside the ion-implanted sample can be expressed as wherein is the amplitude of the fundamental light electric field of the zth layer, which is obtained from step S2, is the wave number of the fundamental light, , is the refractive index of the fundamental light in the doped sample, which varies with z but the variation is generally small, The average value of the refractive index of the doped sample can be taken, i.e. wherein is the total number of layers, is the refractive index of the fundamental light in the zth layer of the doped sample; is the wavelength of the fundamental light in vacuum. is the propagation distance of the fundamental light in the doped sample, and since the refractive index varies little, the first layer, i.e. the surface refractive angle , . is generally less than 1 nm, and thus the second harmonic light radiated by the bulk quadrupole moment and the interface second dipole moment in the single layer doping can be considered to have the same phase at the sample exit surface. The unit vector of the observation direction is then determined as wherein is the observation angle, i.e. the angle between the exit light and the normal of the interface. At the zth layer from the sample surface, the thickness is The second harmonic electric field of the induced polarization intensity in the crystal at the exit of the sample surface is:

[0056] wherein, is the wave number of the second harmonic, , and are defined and are defined and calculated in the same way, wherein , , is the absorption coefficient of the second harmonic light in the doped sample.

[0057] Thus the intensity of the second harmonic light in the observation direction is: .

[0058] The present application combines a two-temperature model, carrier kinetics, a Drude model, thermal effects, a simplified bond hyperpolarizability model and a second harmonic radiation model, considers the interaction of laser light and matter of ion implantation doped samples, and establishes a method for obtaining a second harmonic signal in a non-uniformly doped sample under a laser light source, from a fundamental light field distribution, a polarization intensity distribution to a far-field second harmonic intensity, aiming to provide a method for predicting the second harmonic response of a non-uniformly doped sample, to provide second harmonic measurement technology development and algorithm support for high-dose ion implantation doping processes in semiconductor production, and to guide the selection of devices for ion implantation second harmonic measurement machines, thereby reducing research and development costs. Although the ion implantation second harmonic measurement is still in its infancy, some parameters used for calculation are not fixed values, but the model proposed in the present application shows good prediction effect for ion implantation samples with different doping concentrations and doping depths.

[0059] The present application also provides a method for obtaining a non-uniform ion implantation doping concentration, which uses the second harmonic signal acquisition method for non-uniform ion implantation doping concentration described above to obtain the total intensity of the second harmonic of the ion implantation doped sample, and then obtains the doping concentration of the ion implantation doped sample based on the mapping relationship between the total intensity of the second harmonic and the doping concentration.

[0060] The present application will be further described in detail below with specific examples.

[0061] Please refer to Figure 1 The present application provides a method for simulating the second harmonic response generated by an ion implantation sample under probe light and pump light, which is based on optical modulation technology and a simplified bond hyperpolarizability model to solve the fundamental light field distribution and second-order polarization of each doped layer, and thereby obtain a far-field second harmonic signal. The scheme provided by the present application simulates the second harmonic signal of the non-contact and non-destructive second harmonic measurement technology, and can be used to guide the practical application of the second harmonic measurement technology in doped samples, thereby better monitoring the manufacturing quality of semiconductors.

[0062] Figure 2 The flowchart of the method for obtaining a reflected second harmonic signal according to the ion implantation concentration characteristics of the present application is as follows: first, construct an optical property distribution model of an ion implantation doped sample, and then determine the refractive index and absorption coefficient at different positions under a specific laser wavelength; then solve the fundamental light field distribution in the doped sample according to the obtained refractive index and absorption coefficient; at the same time, construct a simplified bond hyperpolarizability model of the sample according to the base element, doped element and doping concentration distribution, and solve the second-order polarization intensity of each doped layer; finally, calculate the far-field second harmonic radiated by the polarization intensity of each layer, integrate all layers, and obtain the total intensity of the far-field radiated second harmonic.

[0063] The doped sample selected in the embodiment is phosphorus ion implanted silicon (001) substrate, the junction depth is , the doped layer is a Gaussian distribution profile in the depth direction, and the specific concentration distribution can be referred to Figure 3 , the single layer thickness in Figure 1 is determined by Figure 3 ; the excitation light is a continuous wave of 405 nm emitted by a laser, the power is 0.1 W, the spot radius on the sample surface is ; the probe light is a p-polarized light of 920 nm emitted by a pulse laser, the pulse width is 100 fs, the repetition frequency is 80 MHz, the average power is 0.1 W, and the angle with the excitation light is 45°, the spot radius on the sample surface is , and . The excitation light is used to generate non-equilibrium carriers and non-equilibrium heat in the doped semiconductor, thereby changing the optical property distribution in the doped semiconductor; the probe light is used to induce the generation of second harmonic in the doped semiconductor.

[0064] First, the relevant parameters are determined to solve the two-temperature model and the carrier dynamics recombination model. In actual second harmonic measurement, the measurement time of a single point is usually seconds, and the frequency of the second harmonic detector is megahertz. However, the relaxation time of the electron temperature and the lattice temperature in the two-temperature model is usually completed in picoseconds, which is much smaller than the response time of the second harmonic detector and the measurement time of a single point. Therefore, when solving the two-temperature model and the carrier dynamics recombination model, it can be considered that the electron temperature and the lattice temperature have reached an equilibrium state; on this basis, the pulse laser can be simplified as a continuous laser to solve the above-mentioned recombination model. After the non-equilibrium carrier distribution and the heat distribution of the doped sample under the probe light and the pump light are solved, the optical property distribution, i.e. the complex refractive index distribution, of different positions of the sample is obtained according to the Drude effect and the thermal effect of the doped semiconductor. For the phosphorus implanted silicon sample, the complex refractive index distribution is calculated as follows: The complex refractive index of the Drude effect is:

[0065] For , is the real part of the dielectric constant, is the imaginary part of the dielectric constant, and the relationship between the dielectric constant and the refractive index is , . The extinction coefficient of silicon at 920 nm (probe light of fundamental frequency) and 460 nm (second harmonic generated by light of fundamental frequency) is much smaller than the refractive index (small by two to three orders of magnitude), so , . For in the above complex refractive index formula, in the semiconductor at room temperatureabout 10 -13 s. Therefore, in the visible and near-infrared wavelength band .

[0066] The complex refractive index of thermal effect is: ,

[0067] According to the above formula, the complex refractive index model with temperature change is: ,

[0068] Finally, the complex refractive index distribution model in the phosphorus implanted silicon sample is obtained: The real part of the refractive index , extinction coefficient

[0069] Subsequently, the fundamental optical field distribution in the doped sample is solved according to the complex refractive index distribution model. According to the laser parameters provided in the example, the surface light intensity of the doped sample probe light is According to the Fresnel formula, the reflectivity of each layer of the probe light is calculated The probe light intensity at a depth of z from the surface of the doped sample , and the electric field distribution at this position can be calculated.

[0070] A simplified bond hyperpolarizability model of phosphorus-doped silicon is constructed. In the silicon (001) substrate, phosphorus is doped into silicon by ion implantation process. After complete annealing, the phosphorus element is uniformly distributed and does not form phosphorus-phosphorus bond. The crystal structure is shown in Figure 4 In the SBHM model, different elements have different polarizabilities considering different bond directions, and adjacent atoms will form Si-Si, Si-P, and P-Si (Si-P structure is Si above P, and P-Si structure is Si below P). Figure 4 In the crystal structure shown in , , ,

[0071] Meanwhile, it satisfies , , , .

[0072] For the z-th layer medium from the surface of the doped sample, the interface dipole moment contribution and the bulk quadrupole moment contribution of the layer need to be considered. For the interface contribution, the second harmonic polarization generated by the Si-Si structure is:

[0073] The second harmonic polarization produced by Si-P structure is:

[0074] The second harmonic polarization produced by P-Si structure is:

[0075] In the above three formulas, , are the bond polarizability of silicon atom pointing to -z direction and z direction, respectively, , are the bond polarizability of phosphorus atom pointing to -z direction and z direction, respectively. By Figure 3 , the phosphorus element doping concentration of the layer is , so the number of phosphorus atoms in unit volume is , and the total number of atoms in unit volume is .

[0076] The proportion of Si-P structure and P-Si structure is , and the proportion of Si-Si structure is , then the interface second harmonic polarization intensity at the depth z from the sample surface is:

[0077] where, , the effective second-order polarizability of the layer is .

[0078] For bulk contribution, the bulk polarizability can be represented by the average of the bond polarizability, that is . For Si-Si structure, Si-P structure and P-Si structure, there are , and respectively. The bulk fourth-order polarization intensity produced by the three structures is:

[0079]

[0080]

[0081] The bulk fourth-order second harmonic polarization intensity at the depth z from the sample surface is:

[0082] where, .

[0083] Finally, the far field second harmonic of the polarization intensity of each layer is calculated. The unit vector of the observation direction is determined as In this example, the observation angle is selected as The thickness of the z-th layer is then The electric field of the interface dipole moment and the bulk quadrupole moment induced by the doped layer at the exit surface is

[0084] The total electric field of the second harmonic at the exit is the superposition of the second harmonic generated by each doped layer propagating to the sample surface. The total intensity of the second harmonic is related to the total electric field:

[0085] Figure 5a , Figure 5b and Figure 5c The second harmonic reflectivity of a phosphorous doped silicon sample with a Gaussian doping profile is shown in the examples of the present application. The anisotropic reflectivity of the second harmonic for different polarization states, the interface contribution and bulk contribution for P polarization, and the time dependence of the second harmonic intensity at a certain angle are shown.

[0086] Those skilled in the art can understand that the above description is only preferred embodiments of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for obtaining a second harmonic signal of non-uniform ion implantation doping concentration, characterized in that, The steps are: S1, determining the refractive index and absorption coefficient of the ion-implanted and doped sample at different depths under a specific laser wavelength based on a model of optical property distribution in the ion-implanted and doped sample; S2, calculating the fundamental optical field distribution in the doped sample based on the obtained refractive index and absorption coefficient; S3, calculating the polarization strength and effective second-order polarization rate of the non-uniformly doped ion-implanted sample based on a simplified bond hyperpolarizability model and the fundamental optical field distribution; S4, calculating the far-field second harmonic of the corresponding layer under a predetermined observation angle based on the obtained polarization strength or effective second-order polarization rate of each layer, and integrating the far-field second harmonics of all layers to obtain the total second-harmonic intensity of the junction depth far-field radiation.

2. The method of claim 1, wherein: Under the action of the laser and the doping, the free electron distribution, the free hole distribution and the temperature distribution in the ion-implanted sample affect the refractive index change in the sample, and the corresponding formula is: wherein, is the total refractive index, is the initial refractive index of the crystalline silicon at room temperature under the fundamental light, , , are the refractive index change amounts caused by free electrons, free holes and temperature, respectively; , , are the spatial point coordinates of the silicon wafer, is the time.

3. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 2, characterized in that: For the Drude effect, under the action of the laser, the free electron, free hole and temperature distributions in the ion-implanted and doped sample are solved by using a two-temperature model and a carrier dynamics model: wherein is the non-equilibrium carrier generated by the doped sample under illumination of the light source, is the ambipolar diffusion rate, is the single-photon absorption coefficient, is the two-photon absorption coefficient, is the light intensity distribution at the surface of the sample, is the Planck constant, is the single-photon frequency of the laser, is the carrier recombination rate, is the electron-lattice temperature coupling coefficient, and are the electron heat capacity and the lattice heat capacity, respectively, and are the electron temperature and the lattice temperature, respectively, and are the electron thermal conductivity and the lattice thermal conductivity, respectively, is the silicon band gap energy, is the Boltzmann constant.

4. The method of claim 1, wherein: The Drude effect in the doped semiconductor is specifically: wherein is the vacuum permittivity, is the doped semiconductor permittivity, is the ratio of the electric displacement vector and the electric field intensity, , is the electric displacement vector, is the electric field intensity, is the intrinsic semiconductor permittivity, is the carrier concentration, is the electronic charge amount, is the electronic conductivity effective mass, is the damping rate, is the incident light angular frequency.

5. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 3, characterized in that: The depth of junction is of ion implantation sample, single layer thickness is , then the incident angle of light source is determined , according to Snell's law and the different interlayer refractive index obtained in step S1, the refractive angle of the z layer is calculated; the z-1 layer refractive angle is the z layer incident angle, and the relationship between the refractive index and the refractive angle of the z-1 layer and the z layer is , wherein 、 respectively, the z-1 layer and the z layer refractive index, 、 respectively, the z-1 layer and the z layer incident angle.

6. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 5, characterized in that: The light intensity at the z-th layer from the surface of the sample is: wherein is the absorption coefficient of the z-th layer from the sample surface; The electric field amplitude of the z-th layer is: wherein is the speed of light in vacuum, is the vacuum permittivity, is the refractive index of the doped layer.

7. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 6, characterized in that: Determine the base element and the doping element, and obtain the doping element concentration distribution function according to the actual doping condition ; in the volume , is the laser spot area, the number of doped atoms , the total number of atoms is ; In the simplified key hyperpolarizability model, the surface and interface dipole moments and the bulk quadrupole moment in the bulk are given by: , wherein is the volume, is the total number of bonds within the volume considered, is the unit vector of a bond, is the second order bond polarizability corresponding to the bond unit vector, is the volume quadrupole polarizability of second harmonic generation, , are all calculated by first principle or measured by standard sample experiment, is the incident wave electric field at the current position, determined by step S2; is the electric field gradient term, , is the fitting parameter related to the gradient size, is the base frequency light incident propagation direction.

8. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 7, characterized in that: The second-order polarization strength generated by the base element atoms is: The second order polarization strength generated by the dopant element atoms is: According to the doping concentration, the secondary dipole moment induced at the interface of the zth layer of doped medium is The effective second-order polarization rate at the interface is: 。 9. The method for obtaining second harmonic signals with non-uniform ion implantation doping concentration as described in claim 8, characterized in that: The bulk quadrupole strength generated by the base element atoms is: The bulk quadrupole strength produced by the dopant element atoms is: According to the doping concentration, the quadrupole moment induced by the zth layer of doped dielectric body is: The z-th layer bulk quadrupole moment polarization rate is: 。 10. A method of obtaining a non-uniform ion implantation doping concentration, characterized by: The method for obtaining the total second-harmonic intensity of the ion-implanted and doped sample is obtained by using the method for obtaining the second-harmonic signal of the non-uniform ion-implanted and doped concentration according to any one of claims 1-9, and then the doping concentration of the ion-implanted and doped sample is obtained based on the mapping relationship between the total second-harmonic intensity and the doping concentration.

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