Method for measuring dynamic thermal expansion property of nano-film

Abstract

The invention discloses a method for measuring the dynamic thermal expansion property of a nano-film, and relates to the technical field of measurement, and the method is applied to an ellipsometer provided with a temperature control heat table. The method comprises the following steps: controlling the temperature of a film sample on a heating stage according to a resonant temperature modulation program, and acquiring a thickness-time curve of the film by using an ellipsometer; based on the obtained thickness-time curve, a digital signal processing method is used for determining the amplitude and phase of resonant dynamic change generated by the film thickness responding to a temperature modulation program, and an amplitude-time curve and a phase-time curve are obtained; further determining the apparent thermal expansion coefficient, the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient of the film sample; by setting the temperature modulation program and measuring the thermal expansion behavior of the film sample, the reversible thermal expansion coefficient, the real part, the imaginary part and the irreversible thermal expansion coefficient of the film sample can be accurately measured, so that the molecular movement and the thermal relaxation behavior of the nano film can be accurately reflected.

Description

Technical Field

[0001] The present application relates to the field of measurement technology, and in particular to a method for measuring the dynamic thermal expansion properties of a nano film. Background Art

[0002] In recent years, the rapid development of thin film sample preparation technology has made it a convenient way to use optical thin film samples to improve device performance. Due to their unique properties, optical thin film samples have been widely used in high-tech fields such as information detection, weapons and equipment, aerospace, and new energy, and play an important role in the production and manufacturing of integrated circuits, laser devices, biochips, and liquid crystal displays. The measurement of thin film sample properties (such as film thickness, refractive index, or extinction coefficient and other optical parameters) is an indispensable part of thin film sample design and manufacturing process.

[0003] Ellipsometers (ellipsometry) have the advantages of fast measurement speed, large data collection throughput, automated analysis, non-contact, high sensitivity and non-destructiveness. As a thin film sample measurement technology, they are widely used in industrial fields such as semiconductor preparation. Ellipsometry (ellipsometry) applied by ellipsometry is a conventional method for measuring the properties of thin film samples. Its basic principle is to measure the relative change in amplitude and relative change in phase difference of two orthogonal polarization components after the light beam is reflected or transmitted by the thin film sample, which are generally represented by the symbols Ψ and Δ; the relative change in amplitude and relative change in phase difference are the results of coherent superposition of multiple reflections (or refractions) of the light beam in the thin film sample system, and carry the optical constant information of the thin film sample. Using optical models (such as the Cauchy dispersion formula), the properties of the thin film sample such as thickness (resolution can reach sub-nanometer level) and refractive index can be fitted. However, this traditional ellipsometry has certain limitations: it cannot distinguish the contribution of reversible changes (such as thermal expansion or glass transition) and irreversible changes (such as crystallization, chemical reaction or degradation) in the process of changing the properties of the thin film sample. Therefore, it is difficult for classical ellipsometry to accurately distinguish various complex transformations, and thus it is difficult to understand and explain the apparent changes in the properties of thin film samples at the level of the microstructure and molecular motion state of thin film samples. Summary of the invention

[0004] The purpose of this application is to provide a method for measuring the dynamic thermal expansion properties of nanofilms, which can measure the thermal expansion behavior of film samples by setting a temperature modulation program, thereby accurately determining the irreversible thermal expansion coefficient and reversible thermal expansion coefficient and its real and imaginary parts of the film samples, thereby accurately reflecting the microstructure and molecular motion state of the nanofilm samples, as well as the thermal relaxation behavior.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] The present application provides a method for measuring the dynamic thermal expansion properties of a nanofilm, which is applied to an ellipsometer provided with a temperature-controlled hot stage; the temperature-controlled hot stage is used to carry a film sample; the temperature-controlled hot stage is also used to control the temperature of the film sample according to a temperature modulation program; the temperature modulation program includes a linear temperature change program and a resonant temperature modulation program that are superimposed;

[0007] The method for measuring the dynamic thermal expansion properties of the nanofilm includes:

[0008] According to the temperature modulation program, the temperature of the film sample on the temperature-controlled hot stage is controlled to obtain the thickness-time curve of the film sample;

[0009] Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the film sample, the apparent thickness-time curve of the film sample is determined by a numerical integration average method;

[0010] Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the thin film sample, an amplitude-time curve and a phase-time curve of the thin film sample are determined by a digital signal processing method; the amplitude-time curve and the phase-time curve are both used to describe the resonant dynamic change of the thickness of the thin film sample in response to the resonant temperature modulation;

[0011] Based on the average temperature and frequency of the temperature modulation program and the apparent thickness-time curve of the film sample, the apparent thermal expansion coefficient of the film sample under the temperature modulation program is determined by using a numerical derivative formula;

[0012] Based on the average temperature, frequency, amplitude and phase of the temperature modulation program, as well as the amplitude-time curve and phase-time curve of the film sample, the reversible thermal expansion coefficient of the film sample under the temperature modulation program, as well as the real part and imaginary part of the reversible thermal expansion coefficient are determined using the reversible thermal expansion formula;

[0013] Based on the apparent thermal expansion coefficient and reversible thermal expansion coefficient of the film sample, the irreversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the difference formula.

[0014] Optionally, the temperature modulation procedure is:

[0015] T(t)=T av (t)+T dyn (t);

[0016] T av (t) = T0 + qt;

[0017]

[0018] Where, T(t) is the temperature modulation program; Tav (t) is the average temperature, i.e., the linear temperature program; T dyn (t) is the resonant temperature modulation program; T0 is the starting temperature of the linear temperature change program; q is the temperature change rate of the linear temperature change program; t is the time; A T is the amplitude of the resonant temperature modulation program; ω is the frequency of the resonant temperature modulation program, ω=2π / t p , t p is the period of the resonant temperature modulation program amplitude; It is the initial phase of the resonant temperature modulation program.

[0019] Optionally, the temperature of the thin film sample on the temperature-controlled hot stage is controlled according to the temperature modulation program to obtain a thickness-time curve of the thin film sample, including:

[0020] Preparation of film samples;

[0021] The film sample is placed on a temperature-controlled hot stage, and the temperature of the film sample is controlled according to the temperature modulation program after the optical path is aligned;

[0022] Obtaining the ellipsometry spectrum of the film sample during the temperature control process; the ellipsometry spectrum includes: an amplitude ratio spectrum and a phase difference spectrum;

[0023] The ellipsometry spectrum is fitted using an ellipsometer to obtain a thickness-time curve of the film sample.

[0024] Optionally, the integral average formula is:

[0025]

[0026] Where h(t) is the thickness-time curve; h app (t) is the apparent thickness-time curve; t' is the integral variable.

[0027] Optionally, the digital signal processing method includes a function fitting method, a discrete Fourier transform method, a fast Fourier transform method or a digital phase-locked amplification method.

[0028] Optionally, the numerical derivation formula is:

[0029] In the formula, α app (t) is the apparent thermal expansion coefficient of the film sample.

[0030] Optionally, based on the average temperature, frequency, amplitude and phase of the temperature modulation program, and the amplitude-time curve and phase-time curve of the film sample, determining the reversible thermal expansion coefficient of the film sample under the temperature modulation program, and the real part and the imaginary part of the reversible thermal expansion coefficient, including: based on the average temperature, frequency and amplitude of the temperature modulation program, and the amplitude-time curve of the film sample, using the reversible thermal expansion formula, determining the reversible thermal expansion coefficient of the film sample under the temperature modulation program;

[0031] Based on the reversible thermal expansion coefficient and phase-time curve of the film sample, the real part of the reversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the real part formula;

[0032] Based on the reversible thermal expansion coefficient and phase-time curve of the film sample, the imaginary part of the reversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the imaginary part formula.

[0033] Optionally, the reversible thermal expansion formula is:

[0034] In the formula, α r (t) is the reversible thermal expansion coefficient of the film sample; A h (t) is the amplitude-time curve of the film sample; A T is the amplitude of the temperature modulation program.

[0035] Optionally, the real part formula is: α'(t)=α r (t)·cosδ(t);

[0036] in,

[0037] Where α'(t) is the real part of the reversible thermal expansion coefficient; δ(t) is the intermediate parameter; is the initial phase of the resonant temperature modulation program; is the phase-time curve of the thin film sample;

[0038] The imaginary part formula is: α"(t)=α r (t)·sinδ(t);

[0039] Wherein, α"(t) is the imaginary part of the reversible thermal expansion coefficient.

[0040] Optionally, the difference formula is: α nr (t) = α app (t)-α r (t),

[0041] In the formula, α nr (t) is the irreversible thermal expansion coefficient of the film sample.

[0042] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0043] The present application provides a method for measuring the dynamic thermal expansion properties of a nanofilm. By superimposing a resonant temperature modulation program, a film sample is induced to produce a resonant dynamic thickness change in response to the change in temperature modulation; the phase lag between the dynamic thickness change of the sample and the temperature modulation program is compared, thereby distinguishing the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient caused by the thermal expansion of the film sample, as well as the real part and the imaginary part of the reversible thermal expansion coefficient; the present application is essentially a temperature modulation ellipsometry, which provides a more reliable method for characterizing materials, decomposing complex transformations into easily analyzable components, separating mutually overlapping transformations, improving sensitivity, and detecting weak transformations; and providing more sufficient information for understanding the microscopic nature of the properties of film samples and their thermal responses. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 This is a flow chart of the thermal expansion properties of a film sample in one embodiment of the present application;

[0046] Figure 2 This is a temperature modulation process-thin film sample curve diagram in an embodiment of the present application;

[0047] Figure 3 This is a schematic diagram of a variable temperature resonant temperature modulation process of T = 130 ~ 50 ° C in an embodiment of the present application;

[0048] Figure 4 This is an elliptical polarization spectrum diagram of a polymer film sample in an embodiment of the present application in response to wavelength at t=5min;

[0049] Figure 5 This is an elliptical polarization spectrum diagram of a polymer film sample in an embodiment of the present application at t=19min in response to wavelength;

[0050] Figure 6 Schematic diagram of the film thickness data of a polystyrene film sample measured under a variable temperature resonant temperature modulation program of T=130-50°C in one embodiment of the present application;

[0051] Figure 7 This is a schematic diagram of the apparent film thickness data of a polystyrene film sample calculated under a variable temperature resonant temperature modulation program of T=130-50°C in one embodiment of the present application;

[0052] Figure 8 A graph showing the variation of the amplitude and phase of the dynamic variation of the film thickness of a polystyrene film sample in one embodiment of the present application with the average temperature;

[0053] Fig. 9 A graph showing changes in the apparent thermal expansion coefficient, the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient of a polystyrene film sample as a function of average temperature in one embodiment of the present application;

[0054] Fig.10 is a graph showing the variation of the real part and the imaginary part of the reversible thermal expansion coefficient of a polystyrene film sample as a function of the average temperature in an embodiment of the present application;

[0055] Fig.11 This is a schematic diagram of a variable temperature resonant temperature modulation procedure of T=45-145°C in an embodiment of the present application;

[0056] Fig.12 Schematic diagram of the film thickness data of a polyethylene terephthalate film sample measured under a variable temperature resonant temperature modulation program of T=45-145°C in one embodiment of the present application;

[0057] Fig.13 Schematic diagram of apparent film thickness data of a polyethylene terephthalate film sample calculated under a variable temperature resonant temperature modulation program of T=45-145°C in one embodiment of the present application;

[0058] Fig.14 A graph showing the variation of the amplitude of the dynamic variation of the film thickness of a polyethylene terephthalate film sample with the average temperature in an embodiment of the present application;

[0059] Fig.15 This is a graph showing the variation of the apparent thermal expansion coefficient, the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient of a polyethylene terephthalate film sample with the average temperature in one embodiment of the present application. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0061] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0062] In an exemplary embodiment, a method for measuring the dynamic thermal expansion properties of a nanofilm is provided, and the method for measuring the dynamic thermal expansion properties of a nanofilm is applied to an ellipsometer provided with a temperature-controlled hot stage. The temperature-controlled hot stage is used to carry a film sample. The temperature-controlled hot stage is also used to control the temperature of the film sample according to a temperature modulation program. The temperature modulation program includes a linear temperature variation program and a resonant temperature modulation with a superimposed setting. The temperature modulation program is:

[0063] T(t)=T av (t)+T dyn (t).

[0064] T av (t) = T0 + qt.

[0065]

[0066] Where T(t) is the temperature modulation process. av (t) is the average temperature, i.e., a linear temperature variation program. dyn (t) is the resonant temperature modulation program. T0 is the starting temperature of the linear temperature change program. q is the temperature change rate of the linear temperature change program. t is the time. A T is the amplitude of the resonant temperature modulation program. ω is the frequency of the resonant temperature modulation program, ω=2π / t p , t p is the period of the resonant temperature modulation program amplitude. It is the initial phase of the resonant temperature modulation program.

[0067] like Figure 1 , the measurement methods of dynamic thermal expansion properties of nanofilms include:

[0068] Step 101: According to the temperature modulation program, the temperature of the thin film sample on the temperature-controlled hot stage is controlled to obtain the thickness-time curve of the thin film sample. Prepare the thin film sample. Place the thin film sample on the temperature-controlled hot stage, and after the optical path is aligned, control the temperature of the thin film sample according to the temperature modulation program. Obtain the elliptical polarization spectrum of the thin film sample during the temperature control process. The elliptical polarization spectrum includes: an amplitude ratio spectrum Ψ(λ, t) and a phase difference spectrum Δ(λ, t). Use an elliptical polarization spectrometer to fit the elliptical polarization spectrum to obtain the thickness-time curve of the optical thin film sample.

[0069] Specifically, prepare a thin film sample loaded on the surface of a silicon wafer. Place the thin film sample on a temperature-controlled hot stage of an ellipsometer and perform necessary optical path alignment. Use the temperature-controlled hot stage to program the temperature of the thin film sample according to the temperature modulation program (see Figure 2 ), and at the same time, an ellipsometer is used to collect the continuously changing ellipsometric spectrum of the thin film sample in real time to obtain the change of the thickness of the thin film sample with time in real time. Figure 2In the figure, the solid line on the left represents the temperature curve; the dotted line on the left represents the thickness change of the film sample; the solid line on the right represents the temperature modulation Tdyn(t) curve; the dotted line on the left represents the resonant dynamic change hdyn(t) of the film sample thickness in response to the temperature modulation program, which is the difference between the thickness and the apparent thickness (i.e., hdyn=h-happ).

[0070] Among them, A T is the amplitude of the resonant temperature modulation program. ω is the frequency of the resonant temperature modulation program, ω=2π / t p , t p is the period of the resonant temperature modulation program amplitude. is the initial phase of the resonant temperature modulation program. The dynamic response of the film sample thickness (h) is also in the form of a sine wave with a frequency of ω, and Ah is the dynamic response amplitude of the thickness. is the initial thickness phase. The phase difference between hdyn(t) and Tdyn(t)

[0071] By fitting the amplitude ratio spectrum Ψ(λ, t) and the phase difference spectrum Δ(λ, t) using the analysis software of the ellipsometry spectrometer, the time-dependent change of the thickness h(t) of the thin film sample in response to the temperature modulation program can be obtained (e.g. Figure 2 These changes include two contributions: one is the response to the linear temperature change program in the program; the other is the dynamic response to the resonant temperature modulation program (referred to as dynamic response), which also shows resonant fluctuations (see Figure 2 ).

[0072] Step 102: Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the film sample, the apparent thickness-time curve of the film sample is determined using a numerical integral averaging method. The integral averaging formula is:

[0073]

[0074] Where h(t) is the thickness-time curve. app (t) is the apparent thickness-time curve. t' is the integral variable.

[0075] Step 103: Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the thin film sample, the amplitude-time curve and the phase-time curve of the thin film sample are determined by a digital signal processing method. The amplitude-time curve and the phase-time curve are both used to describe the resonant dynamic change of the thickness of the thin film sample in response to the resonant temperature modulation. The digital signal processing method includes a function fitting method, a discrete Fourier transform method, a fast Fourier transform method or a digital lock-in amplification method.

[0076] Furthermore, the following parameters are extracted by digital signal processing methods:

[0077] 1. The dynamic change of thickness corresponds to the amplitude of the frequency ω and the change of the amplitude with time Ah(t).

[0078] 2. The dynamic change of thickness corresponds to the phase of frequency ω and the change of phase over time

[0079] Step 104: Based on the average temperature and frequency of the temperature modulation program and the apparent thickness-time curve of the film sample, the apparent thermal expansion coefficient of the film sample under the temperature modulation program is determined using a numerical derivation formula. The numerical derivation formula is:

[0080] In the formula, α app (t) is the apparent thermal expansion coefficient of the film sample.

[0081] Step 105: Based on the average temperature, frequency, amplitude and phase of the temperature modulation program, as well as the amplitude-time curve and phase-time curve of the thin film sample, the reversible thermal expansion coefficient of the thin film sample under the temperature modulation program, as well as the real part and imaginary part of the reversible thermal expansion coefficient are determined using the reversible thermal expansion formula. Based on the average temperature, frequency and amplitude of the temperature modulation program, as well as the amplitude-time curve of the thin film sample, the reversible thermal expansion coefficient of the thin film sample under the temperature modulation program is determined using the reversible thermal expansion formula. Based on the reversible thermal expansion coefficient and phase-time curve of the thin film sample, the real part of the reversible thermal expansion coefficient of the thin film sample under the temperature modulation program is determined using the real part formula. Based on the reversible thermal expansion coefficient and phase-time curve of the thin film sample, the imaginary part of the reversible thermal expansion coefficient of the thin film sample under the temperature modulation program is determined using the imaginary part formula. The reversible thermal expansion formula is:

[0082] In the formula, α r (t) is the reversible thermal expansion coefficient of the film sample. h (t) is the amplitude-time curve of the film sample. T is the amplitude of the temperature modulation program.

[0083] The real part formula is: α'(t) = α r (t)·cosδ(t).

[0084] in,

[0085] Where α'(t) is the real part of the reversible thermal expansion coefficient and δ(t) is the intermediate parameter. It is the initial phase of the resonant temperature modulation program. Phase-time curve of the thin film sample.

[0086] The formula for the imaginary part is: α”(t)=α r (t)·sinδ(t).

[0087] Wherein, α"(t) is the imaginary part of the reversible thermal expansion coefficient.

[0088] Step 106: Based on the apparent thermal expansion coefficient and the reversible thermal expansion coefficient of the film sample, the irreversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using a difference formula.

[0089] The difference formula is: α nr (t) = α app (t)-α r (t).

[0090] In the formula, α nr (t) is the irreversible thermal expansion coefficient of the film sample.

[0091] Combined with Tav(t), α app (t), α r (t), α'(t), α”(t), α nr (t) can analyze the reversible thermal expansion and irreversible thermal expansion caused by the glass transition, phase change, chemical change, etc. of the thin film sample during the temperature change process. Among them, the reversible thermal expansion reflects the thermal relaxation behavior of the thin film sample. Its real part corresponds to the energy storage of the sample under the temperature control program, while the imaginary part corresponds to the energy dissipation. The irreversible thermal expansion reflects the thickness change caused by the phase change, chemical reaction, degradation, etc. of the thin film sample.

[0092] In another exemplary embodiment, a temperature modulation method for measuring the glass transition of a thin film sample under a cooling program is provided.

[0093] (1) Polystyrene (PS) with a molecular weight of 270 kDa and a polymer dispersibility index (PDI) of 1.03 was selected, and a thin film sample with a thickness of 100 nm was prepared on a 12 mm × 12 mm silicon wafer by spin coating.

[0094] (2) The sample was placed on a temperature-controlled sample stage (model: Linkam HFSEL600, USA) of a calibrated spectroscopic ellipsometer (model: JA Woollam RC2, USA) and the optical path was aligned.

[0095] (3) Temperature control is performed according to the temperature control program, using the linear cooling condition Tav(t) = T0-qt, the starting temperature T0 = 130 °C, and the linear cooling rate is 0.51 °C / min; the modulation amplitude of the temperature modulation part is AT = 1.5 °C, the frequency ω = 2.1 rad / min, that is, the period tp = 3.00 min, see Figure 3 .

[0096] (4) The collected time-resolved ellipsometry spectra Ψ(λ, t) and Δ(λ, t) are shown in Figure 4 and Figure 5 As shown; taking the spectra at t=5 and 19min as examples, the wavelength range of the collected spectra is 300-1500nm.

[0097] (5) By fitting the time-resolved ellipsometry spectra Ψ(λ, t) and Δ(λ, t), the thickness (h) of the polymer film sample and its time-varying curve are obtained, as shown in Figure 6 .

[0098] (6) Yes Figure 6 The apparent thickness-time curve happ(t) is obtained by integrating and averaging h(t) in the equation: Figure 7 .

[0099] (7) Yes Figure 6 The dynamic changes of h(t) in the waveform are processed by digital signal processing (in this case, the digital phase-locked amplification algorithm is used), and its amplitude (Ah) and phase angle at the frequency ω = 2.09 rad / min can be extracted. Changes with time or average temperature (changes with time can be converted to changes with average temperature using Tav(t)), see Figure 8 .

[0100] (8) Calculate the change of the apparent thermal expansion coefficient of the film sample with the average temperature, as well as the change of the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient with the average temperature at a frequency of ω = 1.67 rad / min, see Fig. 9 It can be seen that at high and low temperatures, the apparent thermal expansion coefficient is consistent with the reversible thermal expansion coefficient, and the irreversible thermal expansion coefficient is close to 0. At the glass transition, the temperature at which the apparent thermal expansion coefficient changes is lower than the reversible thermal expansion coefficient, which reflects that the apparent thermal expansion coefficient is a static response corresponding to linear temperature increase and is sensitive to factors such as thermal history; while the reversible thermal expansion coefficient reflects the thermal relaxation behavior of the sample at the time scale of tp.

[0101] (9) Calculate the change of the real and imaginary parts of the reversible expansion coefficient of the film sample with the average temperature, see Fig.10 It can be seen that when the temperature drops to about 110℃, α' begins to decrease in a step-like manner, from 0.00065℃-1 to 0.00021℃-1, which corresponds to the glass transition of the PS film sample and the change in expansion coefficient caused by it; at the same time, at 100-110℃, α" shows a peak, which corresponds to the internal friction dissipation caused by the glass transition of the film sample.

[0102] In another exemplary embodiment, a temperature modulation measurement of cold crystallization behavior of a thin film sample under a temperature ramp program is provided.

[0103] (1) Polyethylene terephthalate (PET) with a weight average molecular weight of 30 kDa and a PDI of 1.87 was selected as the sample to be tested, and a uniform thin film sample with a thickness of 330 nm was prepared on a 12 mm × 12 mm silicon wafer by spin coating.

[0104] (2) The equipment also uses an ellipsometer (RC2) with a Linkam temperature-controlled hot stage. The temperature is controlled according to the temperature program shown in formula 1. In this example, the linear heating condition Tav(t) = T0 + qt is used, the starting temperature T0 = 45°C, and the linear heating rate is 0.68°C / min; the modulation amplitude of the temperature modulation part is AT = 1.5°C, the frequency ω = 2.7 rad / min, that is, the period tp ≈ 2.3min, see Fig.11 .

[0105] (3) By fitting the collected time-resolved ellipsometry spectra Ψ(λ, t) and Δ(λ, t), we can obtain the time-varying curve of the film sample thickness h(t), as shown in Fig.12 .

[0106] (4) Yes Fig.12 The apparent thickness-time curve happ(t) is obtained by integrating and averaging h(t) in the equation: Fig.13 .

[0107] (5) Yes Fig.12 The dynamic change of h(t) in the above example is processed by digital signal (in this example, the digital phase-locked amplification algorithm is used), and its amplitude (Ah) change with time or average temperature at frequency ω = 2.7rad / min can be extracted (the change with time can be converted into the change with average temperature according to Tav(t)). Fig.14 .

[0108] (6) Calculate the change of the apparent thermal expansion coefficient of the film sample with the average temperature, as well as the change of the reversible thermal expansion coefficient and the irreversible thermal expansion coefficient with the average temperature at a frequency of ω = 2.7 rad / min, see Fig.15. It can be seen that when the temperature rises to about 70°C, the reversible thermal expansion coefficient rises in a step-like manner, from 0.00024°C-1 to 0.00064°C-1, which corresponds to the glass transition of the PET film sample and the resulting change in thermal expansion behavior; at the same time, at 70-80°C, the irreversible thermal expansion coefficient shows a peak, which corresponds to the effect brought about by the thermal history of the film sample. In addition, when the temperature rises to above 90°C, the reversible thermal expansion coefficient decreases again, from 0.00064°C-1 to 0.00056°C-1, which corresponds to the decrease in the thermal expansion coefficient caused by the cold crystallization of the PET film sample; in addition, the irreversible thermal expansion coefficient shows another peak, which corresponds to the irreversible volume shrinkage of the film sample due to the cold crystallization process (see Fig.13 ).

[0109] In an exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, a memory, an input / output interface (I / O for short) and a communication interface. The processor, the memory and the input / output interface are connected via a system bus, and the communication interface is connected to the system bus via the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a method for measuring the dynamic thermal expansion properties of a nano film is implemented.

[0110] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0111] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0112] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0113] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0114] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0115] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for measuring the dynamic thermal expansion properties of a nanofilm, characterized in that: The method for measuring the dynamic thermal expansion properties of the nanofilm is applied to an ellipsometer provided with a temperature-controlled hot stage; the temperature-controlled hot stage is used to carry the film sample; the temperature-controlled hot stage is also used to control the temperature of the film sample according to a temperature modulation program; the temperature modulation program includes a linear temperature change program and a resonant temperature modulation program that are superimposed; The method for measuring the dynamic thermal expansion properties of the nanofilm includes: According to the temperature modulation program, the temperature of the film sample on the temperature-controlled hot stage is controlled to obtain the thickness-time curve of the film sample; Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the film sample, the apparent thickness-time curve of the film sample is determined by a numerical integration average method; Based on the average temperature and frequency of the temperature modulation program and the thickness-time curve of the thin film sample, an amplitude-time curve and a phase-time curve of the thin film sample are determined by a digital signal processing method; the amplitude-time curve and the phase-time curve are both used to describe the resonant dynamic change of the thickness of the thin film sample in response to the resonant temperature modulation; Based on the average temperature and frequency of the temperature modulation program and the apparent thickness-time curve of the film sample, the apparent thermal expansion coefficient of the film sample under the temperature modulation program is determined by using a numerical derivative formula; Based on the average temperature, frequency, amplitude and phase of the temperature modulation program, as well as the amplitude-time curve and phase-time curve of the film sample, the reversible thermal expansion coefficient of the film sample under the temperature modulation program, as well as the real part and imaginary part of the reversible thermal expansion coefficient are determined using the reversible thermal expansion formula; Based on the apparent thermal expansion coefficient and reversible thermal expansion coefficient of the film sample, the irreversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the difference formula.

2. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 1, characterized in that: The temperature modulation procedure is: T(t)=T av (t)+T dyn (t); T av (t)=T0+qt; Where, T(t) is the temperature modulation program; T av (t) is the average temperature; T dyn (t) is the resonant temperature modulation program; T0 is the starting temperature of the linear temperature change program; q is the temperature change rate of the linear temperature change program; t is the time; A T is the amplitude of the resonant temperature modulation program; ω is the frequency of the resonant temperature modulation program, ω=2π / t p , t p is the period of the resonant temperature modulation program amplitude; It is the initial phase of the resonant temperature modulation program.

3. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 1, characterized in that: According to the temperature modulation program, the temperature of the film sample on the temperature-controlled hot stage is controlled to obtain the thickness-time curve of the film sample, including: Preparation of film samples; The film sample is placed on a temperature-controlled hot stage, and the temperature of the film sample is controlled according to the temperature modulation program after the optical path is aligned; Obtaining the ellipsometry spectrum of the film sample during the temperature control process; the ellipsometry spectrum includes: an amplitude ratio spectrum and a phase difference spectrum; The ellipsometry spectrum is fitted using an ellipsometer to obtain a thickness-time curve of the film sample.

4. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 2, characterized in that: The integral average formula is: Where h(t) is the thickness-time curve; h app (t) is the apparent thickness-time curve; t' is the integral variable.

5. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 1, characterized in that: The digital signal processing method includes a function fitting method, a discrete Fourier transform method, a fast Fourier transform method or a digital phase-locked amplification method.

6. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 4, characterized in that: The numerical derivation formula is: In the formula, α app (t) is the apparent thermal expansion coefficient of the film sample.

7. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 6, characterized in that: Based on the average temperature, frequency, amplitude and phase of the temperature modulation program, as well as the amplitude-time curve and phase-time curve of the film sample, the reversible thermal expansion coefficient of the film sample under the temperature modulation program, as well as the real and imaginary parts of the reversible thermal expansion coefficient are determined, including: Based on the average temperature, frequency and amplitude of the temperature modulation program and the amplitude-time curve of the film sample, the reversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the reversible thermal expansion formula; Based on the reversible thermal expansion coefficient and phase-time curve of the film sample, the real part of the reversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the real part formula; Based on the reversible thermal expansion coefficient and phase-time curve of the film sample, the imaginary part of the reversible thermal expansion coefficient of the film sample under the temperature modulation program is determined using the imaginary part formula.

8. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 7, characterized in that: The reversible thermal expansion formula is: In the formula, α r (t) is the reversible thermal expansion coefficient of the film sample; A h (t) is the amplitude-time curve of the film sample; A T is the amplitude of the temperature modulation program.

9. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 8, characterized in that: The real part formula is: α'(t) = α r (t)·cosδ(t); in, Where α'(t) is the real part of the reversible thermal expansion coefficient; δ(t) is the intermediate parameter; is the initial phase of the resonant temperature modulation program; is the phase-time curve of the thin film sample; The imaginary part formula is: α"(t)=α r (t)·sinδ(t); Wherein, α"(t) is the imaginary part of the reversible thermal expansion coefficient.

10. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 9, characterized in that: The difference formula is: α nr (t) = α app (t)-α r (t), In the formula, α nr (t) is the irreversible thermal expansion coefficient of the film sample.

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