Method for measuring elasticity modulus of semiconductor material

Abstract

The invention discloses a method for measuring the elasticity modulus of a semiconductor material, which comprises the following steps of: exciting the semiconductor material by using femtosecond laser pulse through an ultrafast laser pumping detection technology, enabling the material to generate thermoelastic pressure, transmitting the thermoelastic pressure into the material, and measuring the elasticity modulus of the semiconductor material by using detection pulses at different moments. And detecting the thermoelastic pressure transmission rate of the material, and finally calculating the elastic modulus of the semiconductor material according to the quantitative relationship between the elastic modulus and the thermoelastic pressure transmission rate. According to the measuring method, the optical area can be as small as micron dimension, so that the elasticity modulus of the micron-dimension semiconductor material can be tested. In addition, mechanical pressure does not need to be applied to the semiconductor material based on optical measurement, measurement of the elastic modulus of the material can be completed in a non-contact mode, and damage to the material is avoided. Therefore, the method has wide development potential.

Description

Technical Field

[0001] The present invention relates to the field of measuring the elastic modulus of materials, and relates to a method for measuring the elastic modulus of semiconductor materials. Background Art

[0002] The elastic modulus is a physical quantity reflecting the elasticity of a material and is one of the key parameters for measuring the mechanical properties of a material. At the macroscopic scale, the elastic modulus is a measure of the ability of a material to respond to elastic deformation; at the microscopic scale, the elastic modulus reflects the bonding strength between atoms, molecules or ions, and the crystal structure, bonding mode, etc. will all affect the elastic modulus of the material. Accurately measuring the elastic modulus of a material is of great significance for material selection, structural design and performance evaluation.

[0003] The measurement of the elastic modulus is mainly based on Hooke's law, that is, within the elastic range, the stress of a material is proportional to the strain, and its value is the proportional coefficient of stress and strain. The traditional measurement method is mainly to apply a mechanical external force to cause elastic deformation of the material, and then measure the corresponding deformation of the stress, so that the elastic modulus can be calculated in combination with the size and force of the material. Because this method requires applying a mechanical external force to the material, in the actual measurement process, traditional elastic modulus measurement tools (such as elastic modulus measuring instruments) have high requirements for the size and shape of the material. For example, the material needs to reach a relatively large size to facilitate the application of external force; if the elastic model is too small, it may also lead to the inability to precisely measure the elastic modulus. In addition, the traditional contact measurement method will also cause irreparable damage to the material, resulting in material loss.

[0004] In recent years, for the measurement of the elastic modulus, the nanoindentation method (using a nanoindenter to apply a small load on the surface of the material and calculating the elastic modulus by measuring the relationship between the indentation depth and the load), the ultrasonic method (a method for determining the elastic modulus by measuring the propagation speed of sound waves in a semiconductor material, using an ultrasonic transmitter and receiver to measure the time difference of sound waves passing through the material, and then calculating the elastic modulus), etc. have also been reported, but these methods have problems such as insufficient accuracy and damage to the sample. Summary of the Invention

[0005] Aiming at the technical problems existing in the background art, the purpose of the present invention is to provide a method for measuring the elastic modulus of semiconductor materials.

[0006] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0007] The first aspect of the present invention provides a method for measuring the elastic modulus of semiconductor materials, including the following steps:

[0008] S1. Use femtosecond laser pulses to irradiate the surface of the semiconductor material to be measured, and excite its vibration through ultrafast laser pump-probe technology;

[0009] S2. Detect the intensity of the probe light reflected by the material, obtain the intensity of the probe light with and without the action of the pump light, thereby obtain the transient reflection dynamics spectrum of the semiconductor material, and simultaneously obtain the oscillation signal of the coherent acoustic phonon action generated by the thermoelastic stress action;

[0010] S3. Analyze the oscillation signal of the coherent acoustic phonon action, obtain the phonon velocity and the mass density of the material, and calculate the elastic modulus of the material according to the phonon velocity and the mass density of the material by using the elastic mechanics formula.

[0011] Preferably, in step S1, irradiating the surface of the semiconductor material to be measured with femtosecond laser pulses and exciting its vibration by the ultrafast laser pump-probe technique includes:

[0012] S11. Use femtosecond pulsed light as the pump light to first excite the surface of the semiconductor material sample and excite it to a high-energy excited state. Subsequently, use the supercontinuum white light generated by the sapphire crystal Sapphire as the probe light to make the probe light and the pump light achieve spatial coincidence and temporal coincidence. Temporal coincidence means controlling the light pulses of the probe light and the pump light with a certain time delay to reach the surface of the semiconductor material sample at the same time point;

[0013] S12. Use an optical chopper Chopper to modulate the repetition frequency of the pump light, while the repetition frequency of the probe light remains the original repetition frequency, and regard 2 ms as a cycle.

[0014] In step S2, obtaining the transient reflection dynamics spectrum of the semiconductor material by detecting the change amplitude of the reflectivity difference of the material over time after being excited by a spectrometer includes:

[0015] S21. Assume that within the first 1 ms of a cycle at time 0, since the probe light and the pump light achieve temporal coincidence, it is equivalent to having both the pump light and the probe light acting on the material surface at the same time. At this time, detect the intensity of the probe light reflected after the pump light modulates the reflectivity of the semiconductor material surface by a spectrometer;

[0016] S22. Within the second 1 ms of the same cycle with the action of the optical chopper Chopper, the original pump light is blocked. At this time, only the probe light acts on the surface of the semiconductor material without the action of the pump light. At this time, detect the intensity of the probe light reflected when the reflectivity of the material surface is not modulated by a spectrometer, and obtain the intensity of the probe light with and without the action of the pump light;

[0017] S23. Substitute the obtained probe light intensity into formula (1-2) to calculate the change amplitude of the transient reflectivity of the material surface at t = 0

[0018]

[0019] Among them, is the light intensity of the reflected light at wavelength λ at time t after pump excitation; represents the light intensity of the reflected light at wavelength λ without pump;

[0020] S24. Use the optical delay line ODL to achieve a time delay relative to the pump light by increasing the optical path of the probe light. Assume that based on time 0, by extending the optical path of the probe light, the probe light pulse arrives at the sample surface 1 ps after the pump light pulse arrives at the material surface. At this time, the transient reflectivity change amplitude after the pump light acts for 1 ps is detected. By analogy, by continuously changing the relative time delay between the probe light and the pump light using the optical delay line, the transient reflection dynamics spectrum of the semiconductor material is measured.

[0021] Preferably, in step S3, the oscillating signal of the action of the coherent acoustic phonons is analyzed to obtain the phonon velocity and the mass density of the material, and based on the phonon velocity and the mass density of the material, the elastic modulus of the material is calculated using the elastic mechanics formula, including:

[0022] Under the action of the coherent acoustic phonons generated by the thermoelastic stress, the transient reflection dynamics of the material and a superimposed oscillating signal are obtained. Subsequently, the carrier background is removed using the adjacent averaging method, and then the oscillating signal attributed to the action of the coherent acoustic phonons is extracted. The frequency f of the oscillating signal is extracted using the sinedamp fitting formula. After consulting the data to obtain the refractive index n of the material at the detection wavelength λ and the mass density ρ of the material, the phonon velocity v of the semiconductor material is calculated through formula (1-4):

[0023]

[0024] Furthermore, the elastic modulus C of the semiconductor material is calculated through formula (1-5):

[0025]

[0026] The present invention has the following beneficial effects:

[0027] (1) The present invention provides a method for measuring the elastic modulus of a semiconductor material. This method uses the ultrafast laser pump-probe technique to excite the semiconductor material with femtosecond laser pulses, causing the material to generate thermoelastic pressure. Subsequently, the thermoelastic pressure is transmitted into the material. By using probe pulses at different times, the transmission rate of the thermoelastic pressure of the material is detected. Furthermore, based on the quantitative relationship between the elastic modulus and the transmission rate of the thermoelastic pressure, the elastic modulus of the semiconductor material along the transmission direction is calculated. The optical measurement area of the measurement method of the present invention can be as small as the micron level, so the elastic modulus of materials at the micron level can be tested.

[0028] (2) The measurement method of the present invention is based on the excitation and detection of femtosecond laser spectral signals, without applying mechanical pressure to the material, and can complete the measurement of the elastic modulus of semiconductor materials in a non-contact manner, avoiding damage to the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0030] Figure 1 It is a schematic structural diagram of a measurement system for the elastic modulus of a semiconductor material;

[0031] Figure 2 It is a TR kinetic diagram of gallium arsenide single crystal minus the carrier background. Among them, the solid line in the figure is the fitting curve based on the formula sine damp fitting formula. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] In the following description, specific details such as specific system structures and technologies are proposed for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the present invention can also be implemented in other embodiments without these specific details.

[0033] Refer to Figure 1 , the present invention provides a measurement system for the elastic modulus of a semiconductor material, and the system includes:

[0034] Femtosecond fiber laser (Fs-laser): It is used to emit ultrashort pulse laser onto the surface of the semiconductor material and excite its vibration;

[0035] Optical system: It is used to focus and guide the ultrashort pulse laser beam and collect the reflected light signal generated by the vibration;

[0036] It includes several convex lenses L, namely the first convex lens L1, the second convex lens L2, the third convex lens L3, and the fourth convex lens L4; several reflectors M, namely the first reflector M1, the second reflector M2, the third reflector M3, the fourth reflector M4, the fifth reflector M5, the sixth reflector M6, the seventh reflector M7, the eighth reflector M8, the ninth reflector M9, the tenth reflector M10, the eleventh reflector M11, the twelfth reflector M12, the thirteenth reflector M13, and the fourteenth reflector M14; two beam splitters S, namely the first beam splitter S1 and the second beam splitter S2; several aperture stops A, namely the first aperture stop A1, the second aperture stop A2, the third aperture stop A3, the fourth aperture stop A4, the fifth aperture stop A5, the sixth aperture stop A6, and the seventh aperture stop A7; three neutral variable attenuators F, namely the first neutral variable attenuator F1, the second neutral variable attenuator F2, and the third neutral variable attenuator F3; two optical filters, namely the first optical filter F4 and the second optical filter F5; two off-axis parabolic mirrors, namely the first off-axis parabolic mirror OAP1 and the second off-axis parabolic mirror OAP2; as well as an optical chopper Chopper, a second harmonic generation crystal BBO, a sapphire crystal Sapphire, and an optical delay line ODL.

[0037] Spectrometer: It is used to detect the light intensity of the probe light with and without the action of the pump light, so as to obtain the transient reflection dynamics spectrum of the semiconductor material, and at the same time, obtain the oscillation signal of the coherent acoustic phonon action generated by the thermoelastic stress action.

[0038] Data processing module: It is used to analyze the oscillation signal of the coherent acoustic phonon action, obtain the phonon velocity, and calculate the elastic modulus of the material according to the phonon velocity and the mass density of the material (which can be obtained by referring to the literature) using the elastic mechanics formula.

[0039] After the sample is excited by the pump light, the reflectivity difference ΔA R (λ,t) changes with time t, and is specifically expressed as shown in the following formula (1-1):

[0040]

[0041] Where, is the light intensity of the reflected light at wavelength λ at time t after pump excitation; represents the light intensity of the reflected light at wavelength λ without pump;

[0042] The transient reflectivity change amplitude of the material surface can be given by the reflectivity difference Specifically, it is expressed as shown in the following formula (1-2):

[0043]

[0044] Based on the above theory, in order to obtain the transient reflection kinetics spectrum of a semiconductor material, the present invention uses femtosecond pulsed light with a photon energy higher than the bandgap of the semiconductor material as the pump light. First, the pump light excites the sample surface. Subsequently, supercontinuum white light generated by a sapphire crystal (Sapphire) is used as the probe light to achieve spatial and temporal coincidence of the probe light and the pump light. Temporal coincidence means controlling the light pulses of the probe light and the pump light to reach the sample surface at the same time point.

[0045] In order to achieve the states of without pump light and with pump light in the above theory, the present invention applies an optical chopper (Chopper) to modulate the repetition frequency of the pump light to 500 Hz, while the repetition frequency of the probe light remains at the original 1 kHz. Then, 2 ms can be regarded as a cycle. Assuming that within the first 1 ms of a cycle at time 0, since the probe light and the pump light achieve temporal coincidence, it is equivalent to having both the pump light and the probe light acting on the material surface simultaneously. At this time, the spectrometer detects the intensity of the probe light reflected after the pump light modulates the reflectivity of the sample surface. Subsequently, within the second 1 ms of the same cycle with the action of the optical chopper (Chopper), the original pump light is blocked. At this time, only the probe light acts on the material surface without the action of the pump light. That is, at this time, the spectrometer detects the intensity of the probe light reflected when the reflectivity of the material surface is not modulated. Thus, the intensities of the probe light with and without the action of the pump light are obtained. Substituting the obtained probe light intensities into formula (1-2), the amplitude of the transient reflectivity change of the material surface at time 0 can be calculated.

[0046] In order to obtain a complete transient reflection kinetics spectrum, it is necessary to change the time difference between the probe light and the pump light reaching the material surface. For this purpose, the present invention uses an optical delay line (ODL) in the probe light path to achieve a relative time delay with respect to the pump light by increasing the optical path of the probe light. Assuming that based on time 0, by extending the optical path of the probe light, the probe light pulse reaches the sample surface 1 ps after the pump light pulse reaches the material surface. At this time, detection is performed to obtain the amplitude of the transient reflectivity change 1 ps after the action of the pump light. And so on. By continuously changing the relative time delay between the probe light and the pump light using the optical delay line, a complete transient reflection kinetics spectrum of the semiconductor material can be measured.

[0047] The working process of the above measurement system is as follows: The femtosecond pulsed light with a repetition frequency of 1 kHz and a wavelength of 800 nm emitted from the femtosecond laser first passes through the first beam splitter S1 and is divided into a probe optical path and a pump optical path. Among them, the pump light is reflected by the first mirror M1 and then passes through the optical chopper Chopper to modulate the repetition frequency of the pump light to 500 Hz, and the pump light is modulated into femtosecond pulsed light with a wavelength of 400 nm by the second harmonic generation crystal BBO. After being reflected by the second mirror M2, the third mirror M3 and focused by the first convex lens L1, the modulated pump light finally converges on the sample Sample;

[0048] The probe light is reflected by the fourth mirror M4 and the fifth mirror M5 and then enters the optical delay line ODL to control the time delay between the pump light and the probe light. After the probe light exits from the optical delay line ODL, it is redirected by the mirror group composed of the sixth mirror M6 and the seventh mirror M7, and finally focused by the second convex lens L2 onto the sapphire crystal Sapphire to generate supercontinuum white light. The second neutral variable attenuator F2 and the third neutral variable attenuator F3 are used to adjust the light intensity entering the sapphire crystal Sapphire. The supercontinuum white light is collimated by the first off-axis parabolic mirror OAP1 and then divided into a reference optical path and a probe optical path by the second beam splitter S2. Among them, the first filter F4 is used to filter out the residual 800 nm light during the generation of the supercontinuum white light.

[0049] The reference light is redirected by the mirror group composed of the eighth mirror M8, the ninth mirror M9 and the tenth mirror M10 and then focused by the third convex lens L3, and then reflected by the eleventh mirror M11 and finally enters the spectrometer; the probe light is focused on the sample by the second off-axis parabolic mirror OAP2 and spatially coincides with the pump light; the probe light carrying the sample information reflected from the sample surface is reflected by the mirror group composed of the twelfth mirror M12, the thirteenth mirror M13 and the fourteenth mirror M14 and finally focused by the fourth convex lens L4 and enters the spectrometer; the second filter F5 is used to filter out the residual pump light signal in the probe light.

[0050] (2) Excitation to generate thermoelastic stress

[0051] Thermoelastic stress refers to the stress generated by the thermal expansion effect caused by energy transfer when a material is excited by external energy (such as light, heat, etc.). Specifically, when the material absorbs the energy of the pump light, if the photon energy exceeds the bandgap of the material, the excess energy will be transferred to the lattice in the form of heat, causing the lattice vibration to intensify and thermal expansion. This thermal expansion will generate stress inside the material, namely thermoelastic stress σ TE , which is expressed by the following formula (1-3):

[0052]

[0053] Among them, B is the bulk modulus; β is the coefficient of thermal expansion; N is the density of excited carriers; hν is the photon energy of the pump light; E g is the material bandgap; C p is the heat capacity. The above formula shows that the thermoelastic pressure is closely related to the physical properties of the material (such as bulk modulus, coefficient of thermal expansion, etc.) and external excitation conditions (such as photon energy, carrier density, etc.).

[0054] (3) The thermoelastic pressure transmits and modulates the reflected detection signal, generating periodic oscillations

[0055] When the material is excited by external energy (such as pump light), the excess energy is transferred to the lattice in the form of heat energy, resulting in thermal expansion and generating thermoelastic pressure σ TE , this pressure will cause thermal expansion and lattice vibration, and then generate periodic stress propagation. This stress propagates through the elastic modulus C and phonon velocity v of the material. Among them, the phonon velocity v can be determined by the Brillouin oscillation frequency f, and is specifically expressed as shown in the following formula (1-4):

[0056]

[0057] Among them, λ is the detection wavelength, and n is the refractive index of the material at the detection wavelength λ.

[0058] The relationship between the phonon velocity v and the elastic modulus C and mass density ρ can be expressed by the following formula (1-5):

[0059]

[0060] When the thermoelastic pressure propagates in the material, it will cause periodic vibration of the lattice. This vibration will modulate the reflection characteristics of the material. When the detection light irradiates the surface of the material, the reflected signal will be affected by this periodic vibration, generating a periodic oscillation signal. By measuring the periodic oscillation of the reflected signal, the dynamic parameters such as the phonon velocity and elastic modulus of the material can be deduced inversely. If the calculated values of these parameters are consistent with the actual values, the transmission and modulation effects of the thermoelastic pressure in the material are verified.

[0061] Example 1

[0062] Taking the example of obtaining the elastic modulus of gallium arsenide single crystal, the present invention discovers that under the action of coherent acoustic phonons generated by thermoelastic stress, an oscillation signal is superimposed on the basis of obtaining the transient reflection dynamics of the material. Subsequently, the carrier background is removed using the adjacent averaging method, and the oscillation signal attributed to the action of coherent acoustic phonons is extracted, as Figure 2 shown. Subsequently, the initial phase t c of the oscillation signal, the period ω, and the amplitude A are extracted using the sinedamp fitting formulaB , the frequency f, the phonon lifetime of coherent acoustic phonons, the refractive index n of the material at the detection wavelength λ, the mass density ρ of the material, etc. are shown in Table 1. After obtaining the frequency f of the oscillation signal, substituting it together with the detection wavelength λ (720 nm) and the refractive index n (3.57) of the material at the detection wavelength into formula (1-4), the phonon velocity of gallium arsenide single crystal can be calculated (which is 4719 m / s).

[0063] Table 1

[0064]

[0065] Subsequently, substituting the phonon velocity v (4719 m / s) and the mass density (5317 kg / m 3 ) of gallium arsenide single crystal into formula (1-5), the elastic modulus of gallium arsenide single crystal is finally calculated to be 118.4 GPa. In the previous Brillouin spectroscopy research based on the recording method of Fabry-Perot interferometer, the phonon velocity of gallium arsenide was about (4719.3 m / s), which is consistent with the value calculated from the experimental data of the present invention. This value is also close to the literature value of the elastic modulus of gallium arsenide (118.41 GPa), thus proving the reliability and effectiveness of the method of the present invention.

[0066] The present invention is not limited to the above specific embodiments. Various transformations made by those of ordinary skill in the art starting from the above concepts without creative labor fall within the protection scope of the present invention.

Claims

1. A method for measuring the elastic modulus of a semiconductor material, characterized in that: The following steps are involved: S1. Use femtosecond laser pulses to illuminate the surface of the semiconductor material to be tested and stimulate its vibration through ultrafast laser pump-probe technology; S2. Detect the intensity of the probe light reflected by the material, obtain the intensity of the probe light with and without the pump light, and then obtain the transient reflection dynamics spectrum of the semiconductor material, and at the same time obtain the oscillation signal of the coherent acoustic phonon effect generated by the thermoelastic stress; S3. Analyze the oscillation signal of the coherent acoustic phonon action to obtain the phonon velocity and the mass density of the material, and calculate the elastic modulus of the material using the elastic mechanics formula based on the phonon velocity and the mass density of the material.

2. The method for measuring the elastic modulus of a semiconductor material according to claim 1, characterized in that: In step S1, the surface of the semiconductor material to be tested is irradiated with a femtosecond laser pulse, and its vibration is excited by ultrafast laser pump detection technology, including: S11. Use femtosecond pulse light as pump light to first excite the surface of the semiconductor material sample to a high-energy excited state, and then use supercontinuum white light generated by sapphire crystal Sapphire as detection light to make the detection light and pump light overlap in space and time. Time overlap means controlling the light pulses of the detection light and pump light that have been delayed for a certain time to arrive at the surface of the semiconductor material sample at the same time point; S12. Use an optical chopper to modulate the repetition rate of the pump light, while keeping the repetition rate of the detection light at the original repetition rate, and regard 2ms as one cycle.

3. The method for measuring the elastic modulus of a semiconductor material according to claim 1, characterized in that: In step S2, the step of detecting the amplitude of the reflectivity difference change over time after the material is excited by a spectrometer to obtain a transient reflection dynamic spectrum of the semiconductor material includes: S21. Assume that in the first 1ms of a cycle at time 0, the detection light and the pump light are time-coincident, which is equivalent to the pump light and the detection light acting on the material surface at the same time. At this time, the spectrometer detects the intensity of the detection light reflected after the pump light modulates the reflectivity of the semiconductor material surface; S22. In the second 1ms of the same cycle, the original pump light is blocked by the optical chopper. At this time, the semiconductor material surface is only affected by the detection light but not the pump light. At this time, the intensity of the detection light reflected when the reflectivity of the material surface is not modulated is detected by the spectrometer, and the intensity of the detection light with and without the pump light is obtained. S23, substituting the obtained detection light intensity into formula (1-2), and calculating the transient reflectivity change amplitude of the material surface at time t=0 in, is the intensity of the reflected light at wavelength λ at time t after pump excitation; It represents the intensity of reflected light at wavelength λ when there is no pump; S24. Use optical delay line (ODL) to increase the optical path length of the detection light to achieve a time delay relative to the pump light. Assume that at time 0, by extending the optical path length of the detection light, the detection light pulse reaches the sample surface 1ps after the pump light pulse reaches the material surface. At this time, the transient reflectivity change amplitude 1ps after the pump light is applied is detected. Similarly, by using an optical delay line to continuously change the relative time delay between the detection light and the pump light, the transient reflection dynamics spectrum of the semiconductor material can be tested.

4. The method for measuring the elastic modulus of a semiconductor material according to claim 3, characterized in that: In step S3, the oscillation signal of the coherent acoustic phonon action is analyzed to obtain the phonon velocity and the mass density of the material, and the elastic modulus of the material is calculated using the elastic mechanics formula according to the phonon velocity and the mass density of the material, including: Under the action of coherent acoustic phonons generated by thermoelastic stress, the transient reflection dynamics of the material and an oscillation signal superimposed are obtained. The carrier background is then removed using the adjacent averaging method. The oscillation signal attributed to the coherent acoustic phonons is then extracted. The frequency f of the oscillation signal is extracted using the sinedamp fitting formula. After consulting the data to obtain the refractive index n of the material at a known detection wavelength λ and the mass density ρ of the material, the phonon velocity v of the semiconductor material is calculated using formula (1-4): Then, the elastic modulus C of the semiconductor material is calculated by formula (1-5):

Images