A method for measuring dynamic thermal expansion properties of nanofilms

Abstract

The present application discloses a method for measuring the dynamic thermal expansion properties of a nanofilm, which relates to the field of measurement technology. The method is applied to an ellipsometer provided with a temperature-controlled hot stage. The method comprises: controlling the temperature of a thin film sample on the hot stage according to a resonant temperature modulation program, and obtaining a thickness-time curve of the thin film using the ellipsometer; based on the obtained thickness-time curve, determining the amplitude and phase of the resonant dynamic change of the film thickness in response to the temperature modulation program using a digital signal processing method, and obtaining an amplitude-time curve and a phase-time curve; and then determining the apparent thermal expansion coefficient, reversible thermal expansion coefficient, and irreversible thermal expansion coefficient of the thin film sample; the present application measures the thermal expansion behavior of the thin film sample by setting a temperature modulation program, thereby accurately determining the reversible thermal expansion coefficient and its real and imaginary parts, as well as the irreversible thermal expansion coefficient of the thin film sample, thereby accurately reflecting the molecular motion and thermal relaxation behavior of the nanofilm.

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 nanofilm. Background Art

[0002] In recent years, the rapid development of thin film sample preparation technology has made the use of optical thin film samples a convenient way 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, weaponry, aerospace, and new energy. They play a vital role in the production and manufacturing of integrated circuits, laser devices, biochips, and liquid crystal displays. Measuring thin film sample properties (such as film thickness, refractive index, extinction coefficient, and other optical parameters) is an indispensable step in thin film sample design and manufacturing.

[0003] Spectroscopic ellipsometry (ellipsometer) offers advantages such as fast measurement speed, high data throughput, automated analysis, non-contact operation, high sensitivity, and non-destructiveness. As a thin film sample measurement technique, it is widely used in industrial fields such as semiconductor manufacturing. Spectroscopic ellipsometry (ellipsometry), employed by ellipsometry, is a conventional method for measuring the properties of thin film samples. Its basic principle is to measure the relative changes in amplitude and phase difference between two orthogonal polarization components of a light beam after reflection or transmission through a thin film sample, broadly represented by the symbols Ψ and Δ. These relative changes in amplitude and phase difference are the result of the coherent superposition of multiple reflections (or refractions) of the light beam within the thin film sample system and carry information about the optical constants of the film sample. Using optical models (such as the Cauchy dispersion equation), properties such as the thickness (with subnanometer resolution) and refractive index of the film sample can be fitted. However, this traditional spectroscopic ellipsometry has certain limitations: it cannot distinguish between the contributions of reversible changes (such as thermal expansion or glass transition) and irreversible changes (such as crystallization, chemical reactions, or degradation) in the properties of the film sample. Therefore, classical ellipsometry has difficulty in accurately distinguishing various complex transformations, and thus has difficulty in understanding and explaining the apparent changes in the properties of thin film samples at the level of their microstructure and molecular motion state. 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 of the film sample as well as its real and imaginary parts, thereby accurately reflecting the microstructure and molecular motion state of the nanofilm sample, 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, the method being applied to an ellipsometer equipped with a temperature-controlled hot stage; the temperature-controlled hot stage being used to carry a thin film sample; the temperature-controlled hot stage being further used to control the temperature of the thin film sample according to a temperature modulation program; the temperature modulation program comprising a superimposed linear temperature variation program and a resonant temperature modulation program;

[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 thin film sample, the apparent thickness-time curve of the thin film sample is determined using a numerical integration averaging 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 using 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 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 process; 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; 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 a temperature modulation program to obtain a thickness-time curve of the thin film sample, including:

[0020] Preparation of film samples;

[0021] Place the film sample on a temperature-controlled hot stage, and after aligning the optical path, control the temperature of the film sample according to the temperature modulation program;

[0022] Obtaining an ellipsometry spectrum of the thin 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 ellipsometry spectrometer to obtain a thickness-time curve of the thin film sample.

[0024] Optionally, the integral averaging 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] Where, α app (t) is the apparent thermal expansion coefficient of the film sample.

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

[0031] 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;

[0032] 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.

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

[0034] Where, 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] Where 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] Where, 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 nanofilms. By superimposing a resonant temperature modulation program, the film sample is induced to produce a resonant dynamic thickness change in response to the temperature modulation change; the phase lag between the dynamic thickness change of the sample and the temperature modulation program is compared, and then the reversible thermal expansion coefficient and irreversible thermal expansion coefficient caused by the thermal expansion process of the film sample, as well as the real part and imaginary part of the reversible thermal expansion coefficient, are distinguished; the present application is essentially a temperature modulation ellipsometry method, which provides a more reliable method for characterizing materials, decomposes complex transformations into easily analyzable components, separates mutually overlapping transformations, improves sensitivity, and detects weak transformations; and provides 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 following briefly introduces the drawings required for use in the embodiments. 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 creative work.

[0045] Figure 1 This is a flow chart of the thermal expansion properties of a thin 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 Schematic diagram of a variable temperature resonant temperature modulation process in an embodiment of the present application, wherein T=130-50°C;

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

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

[0050] Figure 6 Schematic diagram of 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 Schematic diagram of 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 Graph showing the amplitude and phase of the dynamic change in film thickness of a polystyrene film sample as a function of average temperature in one embodiment of the present application;

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

[0054] Figure 10 is a graph showing the change of the real and imaginary parts 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] Figure 11 Schematic diagram of a variable temperature resonant temperature modulation process in an embodiment of the present application, wherein T=45-145°C;

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

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

[0058] Figure 14 FIG1 is a graph showing the variation of the amplitude of the dynamic change of the film thickness of a polyethylene terephthalate film sample as a function of the average temperature in an embodiment of the present application;

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

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

[0061] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to 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. The method is applied to an ellipsometer equipped with a temperature-controlled hot stage. The temperature-controlled hot stage is used to carry a thin film sample. The temperature-controlled hot stage is also used to control the temperature of the thin film sample according to a temperature modulation program. The temperature modulation program includes a superimposed linear temperature variation program and a resonant temperature modulation program. 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 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. 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: Control the temperature of the thin film sample on the temperature-controlled hot plate according to a temperature modulation program to obtain a thickness-time curve for the thin film sample. Prepare the thin film sample. Place the thin film sample on the temperature-controlled hot plate, align the optical path, and then control the temperature of the thin film sample according to the temperature modulation program. Obtain the ellipsometry spectrum of the thin film sample during the temperature control process. The ellipsometry spectrum includes an amplitude ratio spectrum Ψ(λ, t) and a phase difference spectrum Δ(λ, t). Use a spectroscopic ellipsometry to fit the ellipsometry spectrum to obtain a thickness-time curve for the optical thin film sample.

[0069] Specifically, a thin film sample loaded on the surface of a silicon wafer is prepared. The thin film sample is placed on a temperature-controlled hot stage of an ellipsometer and the necessary optical path alignment is performed. The temperature of the thin film sample is programmed to be controlled by the temperature-controlled hot stage 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 over 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 thin 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 thickness of the thin film sample 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 provided by the ellipsometry spectrometer, the time-dependent change in 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 (abbreviated 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 thin film sample, the apparent thickness-time curve of the thin 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, a digital signal processing method is used to determine an amplitude-time curve and a phase-time curve of the thin film sample. Both the amplitude-time curve and the phase-time curve are used to describe the resonant dynamic change in the thickness of the thin film sample in response to the resonant temperature modulation. Digital signal processing methods include function fitting, discrete Fourier transform, fast Fourier transform, or digital lock-in amplification.

[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 with 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 derivative formula. The numerical derivative formula is:

[0080] Where, 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] Where, 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. 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. is the initial phase of the resonant temperature modulation program. is the phase-time curve of the thin film sample.

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

[0087] Where 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 thin film sample, the irreversible thermal expansion coefficient of the thin 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] Where, 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 and irreversible thermal expansion of thin film samples caused by glass transitions, phase changes, chemical changes, and other processes during temperature fluctuations. Reversible thermal expansion reflects the thermal relaxation behavior of the thin film sample. Its real part corresponds to the energy stored in the sample under temperature control, while its imaginary part corresponds to energy dissipation. Irreversible thermal expansion reflects the thickness change caused by phase transitions, chemical reactions, degradation, and other processes.

[0092] In another exemplary embodiment, a method for measuring the glass transition of a thin film sample by temperature modulation 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 the 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 of 0.51 °C / min; the modulation amplitude of the temperature modulation part 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 as follows Figure 4 and Figure 5 As shown; taking the spectra at t=5 and 19 minutes 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 5. 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, as shown in Figure 7 .

[0099] (7) Yes Figure 6 The dynamic changes of h(t) are digitally processed (in this case, a digital phase-locked amplification algorithm is used) to extract its amplitude (Ah) and phase angle at a frequency of ω = 2.09 rad / min. 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 this film sample with the average temperature, as well as the change of the reversible thermal expansion coefficient and irreversible thermal expansion coefficient with the average temperature at a frequency of ω = 1.67 rad / min, see Figure 9 It can be seen that at high and low temperatures, the apparent thermal expansion coefficient is consistent with the reversible thermal expansion coefficient, while 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. This 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 on 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 Figure 10 It can be seen that when the temperature is lowered to about 110°C, α' begins to decrease in a step-like manner, from 0.00065°C-1 to 0.00021°C-1, corresponding to the glass transition of the PS film sample and the resulting change in the expansion coefficient. At the same time, α" shows a peak at 100-110°C, corresponding to the internal friction dissipation caused by the glass transition of the film sample.

[0102] In another exemplary embodiment, a method for measuring the cold crystallization behavior of a thin film sample by temperature modulation under a temperature ramp 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 spectrometer (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 AT of the temperature modulation part is 1.5°C, the frequency ω = 2.7 rad / min, that is, the period tp ≈ 2.3 min, see Figure 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 the following example: Figure 12 .

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

[0107] (5) Yes Figure 12 The dynamic changes of h(t) in the waveform are digitally processed (in this case, a digital phase-locked amplification algorithm is used), and the change of its amplitude (Ah) with time or average temperature at a frequency of ω = 2.7 rad / min can be extracted (the change with time can be converted into the change with average temperature based on Tav(t). See Figure 14 .

[0108] (6) Calculate the change of the apparent thermal expansion coefficient of this film sample with the average temperature, as well as the change of the reversible thermal expansion coefficient and irreversible thermal expansion coefficient with the average temperature at a frequency of ω = 2.7 rad / min, see Figure 15. It can be seen that when the temperature is raised 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 is raised 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 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 Figure 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) 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 nanofilm is implemented.

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

[0111] In an exemplary embodiment, a computer program product is provided, including a computer program. 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 skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented 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 memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may 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 may 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 databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0115] The technical features of the above embodiments can 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 document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may 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 nanofilms, characterized in that: The method for measuring the dynamic thermal expansion properties of a nanofilm is applied to an ellipsometer equipped with a temperature-controlled hot stage; the temperature-controlled hot stage is used to carry a thin film sample; the temperature-controlled hot stage is also used to control the temperature of the thin film sample according to a temperature modulation program; the temperature modulation program includes a superimposed linear temperature variation program and a resonant temperature modulation program; 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 thin film sample, the apparent thickness-time curve of the thin film sample is determined using a numerical integration averaging 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 using 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 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 process; 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; 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; Place the film sample on a temperature-controlled hot stage, and after aligning the optical path, control the temperature of the film sample according to the temperature modulation program; Obtaining an ellipsometry spectrum of the thin 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 ellipsometry spectrometer to obtain a thickness-time curve of the thin film sample.

4. The method for measuring the dynamic thermal expansion properties of nanofilm according to claim 2, characterized in that: The integral averaging 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: Where, 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 thin film sample, the reversible thermal expansion coefficient of the thin 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 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.

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: Where, 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); Where 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), Where, α nr (t) is the irreversible thermal expansion coefficient of the film sample.

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