CN116879347A - Heterojunction thermophysical property measuring method and device - Google Patents

Heterojunction thermophysical property measuring method and device Download PDF

Info

Publication number
CN116879347A
CN116879347A CN202310706629.7A CN202310706629A CN116879347A CN 116879347 A CN116879347 A CN 116879347A CN 202310706629 A CN202310706629 A CN 202310706629A CN 116879347 A CN116879347 A CN 116879347A
Authority
CN
China
Prior art keywords
heating
heterojunction
sample
measured
temperature rise
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202310706629.7A
Other languages
Chinese (zh)
Inventor
曹炳阳
刘朝阳
杨光
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tsinghua University
Original Assignee
Tsinghua University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tsinghua University filed Critical Tsinghua University
Priority to CN202310706629.7A priority Critical patent/CN116879347A/en
Publication of CN116879347A publication Critical patent/CN116879347A/en
Pending legal-status Critical Current

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00Investigating or analyzing materials by the use of thermal means
    • G01N25/20Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08Thermal analysis or thermal optimisation

Abstract

The invention provides a method and a device for measuring thermal physical properties of a heterojunction, comprising the following steps: heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured. According to the invention, thermal excitation is carried out on the surface of the heterojunction sample to be measured, the temperature rise changes of the sample surface at different moments are measured, so that the temperature change discrete points are obtained, the thermophysical properties of the heterojunction sample to be measured are measured in situ at one time according to the temperature change discrete points, and the measurement of the thermophysical properties of the heterojunction with higher precision and higher efficiency is realized.

Description

Heterojunction thermophysical property measuring method and device
Technical Field
The invention relates to the technical field of semiconductors, in particular to a method and a device for measuring thermal physical properties of a heterojunction.
Background
A heterojunction is an interface region formed by two different solid-state materials in contact, and the combination of multiple heterojunctions within one device becomes a heterostructure. According to the basic structure of a semiconductor device, heterostructures can be divided into metal-semiconductor heterojunction, PN junction, semiconductor-semiconductor heterojunction, MOS structure and the like, and are widely applied to various advanced technical fields such as power electronics, radio frequency communication, photovoltaic photoelectricity, thermoelectric and the like.
In decades into the microelectronic age, the feature size of integrated circuits has continuously decreased according to moore's law, i.e., the number of transistors on a chip doubles every 18-24 months. With the improvement of integration level and working power, the self-heating effect of the transistor is also enhanced, and the electric performance and reliability of the chip are affected, so that effective thermal management is needed. The thermal property characterization is the basis of advanced chip thermal management, and has important research and application significance in the fields of analysis and prediction of the electrothermal performance of devices, guidance and optimization of the thermal design of the devices and the like. However, there is still a lack of high-precision, high-efficiency thermophysical property testing methods applicable to various heterostructures in the field.
The current experimental methods for heterojunction thermophysical property measurement mainly comprise a time domain thermal reflection method, a Raman spectrum method and a 3 omega electrical method.
The time domain thermal reflection method is a measuring method of an unbalanced thermal process, heating light and detecting light are generated by an ultrashort pulse laser light source, and temperature variation of a position is extracted from reflectivity seeds measured through experiments by establishing a double-temperature model, so that parameters such as normal thermal conductivity of a film, interface thermal resistance and the like are obtained. Because the frequency of heating light is 0.2-20 MHz, the corresponding heat penetration depth is only hundred nanometers, so that the interface thermal resistance of the measuring signal to the micron-scale film heterostructure and the sensitivity of the substrate thermal conductivity are lower. The Raman spectroscopy utilizes the shift of the characteristic peak frequency to determine the temperature at the laser spot, and derives the thermophysical property of the heterostructure from the temperature distribution inside the sample. But measurement uncertainties at room temperature can be as high as 40%, temperature uncertainties of about 5K, spatial temperature resolution in the vertical direction typically greater than 1 μm, which limits the accuracy of the test. In addition, raman spectroscopy is generally only capable of measuring the thermophysical properties of the heterostructure of optically transparent thin films. The 3 omega electric method is to prepare a metal film with a certain shape on a sample to be detected through a photoetching technology and an evaporation or sputtering technology, to introduce 1 omega alternating current on a heating electrode, to measure a 3 omega voltage signal on a detection electrode, and to derive related thermophysical properties through theoretical approximation and reasoning. However, this method requires a series of reference samples with different film thicknesses and is insensitive to the volumetric heat capacity of the material at lower frequencies.
In summary, the heterojunction thermophysical property measurement method in the prior art has the defect of low measurement accuracy and low measurement efficiency.
Disclosure of Invention
The invention provides a method and a device for measuring thermal physical properties of a heterojunction, which are used for solving the defects of lower measurement precision and lower measurement efficiency in the prior art and realizing the measurement of the thermal physical properties of the heterojunction with higher precision and higher efficiency.
The invention provides a heterojunction thermophysical property measuring method, which comprises the following steps:
heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power;
determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value;
and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
According to the method for measuring the thermal physical properties of the heterojunction, provided by the invention, the heterojunction sample to be measured is heated within the test duration to obtain the heating temperature rise value and the heating power, and the method specifically comprises the following steps:
arranging a heating electrode on at least part of the surface of the heterojunction sample to be tested; wherein the heating electrode has a preset width and shape;
Switching on a pulse square wave heating voltage with a first preset parameter to the heating electrode; wherein the pulse width of the pulse square wave is deltat 1 Duty cycle d 1 The method comprises the steps of carrying out a first treatment on the surface of the The voltage of the pulse square wave is U;
according to the voltage of the pulse square wave and the current passing through the heating electrode, heating power is calculated;
and measuring the average temperature rise of the surface of the heating electrode by using a heat reflection method to obtain a heating temperature rise value.
According to the method for measuring the thermal physical properties of the heterojunction, provided by the invention, the heterojunction sample to be measured is heated within the test duration to obtain the heating temperature rise value and the heating power, and the method specifically comprises the following steps:
a layer of metal sensor is arranged on the surface of the film of the heterojunction sample to be detected;
irradiating the surface of the metal sensor with a pulse square wave modulated heating laser with a second preset parameter; wherein the power of the heating laser is P, and the spot area of the heating laser is A 0 The method comprises the steps of carrying out a first treatment on the surface of the The pulse width of the pulse square wave is delta t 2 Duty cycle d 2
Measuring the temperature rise of the center of the heterojunction sample to be measured by using a thermal reflection method so as to obtain a heating temperature rise value;
and taking the power of the heating laser as heating power.
According to the method for measuring the thermal physical properties of the heterojunction sample, provided by the invention, the thermal physical properties of the heterojunction sample to be measured are calculated according to the variation discrete points, the heating power, the effective heat conduction area and the layer thicknesses of the heterojunction sample to be measured, and the method specifically comprises the following steps:
obtaining a thermal resistance-heat capacity structural function according to the variation discrete points and the heating power;
identifying an interface of the heterojunction sample to be detected by utilizing the thermal resistance-heat capacity structure function, and reading accumulated thermal resistance and accumulated heat capacity of a node-heat conduction interface;
and separating the geometric parameters and thermophysical properties of the accumulated thermal resistance and the accumulated heat capacity by utilizing the thicknesses of all layers of the heterojunction sample to be detected and the effective heat conduction area so as to obtain the thermophysical properties of the heterojunction sample to be detected.
According to the method for measuring the thermal physical properties of the heterojunction, which is provided by the invention, a thermal resistance-thermal capacity structural function is obtained according to the variation discrete points and the heating power, and the method specifically comprises the following steps:
obtaining a junction temperature transient response curve according to the change discrete point and the heating power;
sequentially performing differentiation, deconvolution, discrete processing and sectional integration on the junction temperature transient response curve to obtain a Foster network;
Transforming the Foster network to obtain a Cauer network;
and obtaining a heat resistance-heat capacity structural function according to the Cauer network.
According to the method for measuring the thermal physical properties of the heterojunction, provided by the invention, the effective heat conduction area is determined based on the heating temperature rise value, and the method specifically comprises the following steps:
and calculating the effective heat conduction area based on the initial section of the heating temperature rise value according to the semi-infinite transient heat conduction theory.
The invention also provides a heterojunction thermophysical property measuring device, which comprises:
the testing unit is used for heating the heterojunction sample to be tested within the testing time length to obtain a heating temperature rise value and heating power;
a discrete unit for determining a variation discrete point and an effective heat conduction area of the heating Wen Shengzhi over time within the test period based on the heating temperature rise value;
and the calculating unit is used for calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method for measuring the thermal physical properties of the heterojunction as described above when executing the program.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method of measuring a thermal physical property of a heterojunction as described in any of the above.
The invention also provides a computer program product comprising a computer program which when executed by a processor implements a method of measuring a thermophysical property of a heterojunction as described in any one of the above.
According to the method and the device for measuring the thermal physical properties of the heterojunction, the heterojunction sample to be measured is heated within the test duration, and the heating temperature rise value and the heating power are obtained; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured. According to the invention, thermal excitation is carried out on the surface of the heterojunction sample to be measured, the temperature rise changes of the sample surface at different moments are measured, so that the temperature change discrete points are obtained, the thermophysical properties of the heterojunction sample to be measured are measured in situ at one time according to the temperature change discrete points, and the measurement of the thermophysical properties of the heterojunction with higher precision and higher efficiency is realized.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for measuring the thermophysical properties of a heterojunction provided by the invention;
FIG. 2 is a schematic diagram of a cross section of a heterojunction sample structure to be tested according to one embodiment of the method for measuring thermal physical properties of a heterojunction provided by the present invention;
FIG. 3 is a top view of a sample structure and test area of a heterojunction to be tested according to one embodiment of the method for measuring thermal physical properties of a heterojunction provided by the present invention;
FIG. 4 is a schematic diagram of a cross section of a sample structure of a heterojunction to be tested according to yet another embodiment of the method for measuring thermal physical properties of a heterojunction provided by the present invention;
FIG. 5 is a schematic waveform diagram of a pulse square wave of one embodiment of a method for measuring thermal physical properties of a heterojunction provided by the present invention;
FIG. 6 is a schematic diagram of a structure of a device for measuring thermal physical properties of a heterojunction according to the present invention;
Fig. 7 is a schematic structural diagram of an electronic device provided by the present invention.
Reference numerals:
201: a film; 202: an interface; 203: a substrate; 204: heating the electrode; 205: an insulating layer; 206: a metal sensor;
610: a test unit; 620: a discrete unit; 630: a calculation unit;
710: a processor; 720: a communication interface; 730: a memory; 740: a communication bus.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the field of semiconductor devices, there is a high-efficiency and nondestructive thermal characterization method, called a structural function method, and the basic flow is to measure junction temperature transient response curves corresponding to the on/off states of the devices by using a temperature-sensitive electrical parameter method, then establish an equivalent thermal resistance-capacitance network, and extract the structural function curve reflecting the heat conduction paths and the characteristics of the devices by numerical algorithms such as deconvolution, discrete time constant spectrum, impedance conservation network transformation and the like. However, since the time resolution of the electrical test method is 1 μs at most, the test result is difficult to characterize the heat transport condition in the near junction region heterostructure. In addition, the structural function curve is a comprehensive expression of the structural thermophysical parameters and geometric parameters, and the thermophysical properties of the material cannot be quantitatively analyzed.
Based on the defects of lower measurement precision and lower measurement efficiency in the heterojunction thermophysical property measurement method in the prior art, and the problem that the time resolution of a structural function method is limited and the thermophysical property of a near-junction heterostructure is difficult to characterize, the invention provides a heterojunction thermophysical property measurement method and device.
The method for measuring the thermophysical properties of the heterojunction of the present invention is described below with reference to fig. 1 to 5. Fig. 1 is a schematic flow chart of a method for measuring thermal physical properties of a heterojunction, as shown in fig. 1, the method comprises the following steps:
step 110: and heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power.
As shown in fig. 2, the structure of the heterojunction sample to be tested includes a thin film 201, an interface 202, and a substrate 203. In some embodiments of the present invention, the material of the film 201 includes at least one of a gallium nitride film, a gallium arsenide film, a silicon film, a germanium film, a molybdenum disulfide film, a silicon carbide film, a gallium arsenide film, an indium arsenide film, an aluminum gallium arsenide film, an aluminum arsenide film, a gallium phosphide film, an indium phosphide film, a zinc oxide film, a zinc telluride film, a titanium dioxide film, and the like. The thickness of the thin film 201 is not particularly limited, and for example, the thickness of the thin film 201 may be 1 μm to 100 μm.
In addition, the material of the substrate 203 is not particularly limited, and any hard solid material can be tested by the above method. In some embodiments, the material of the substrate 203 comprises at least one of a non-radioactive inorganic non-metallic solid material, a non-radioactive inorganic metal solid material, a non-radioactive organic non-metallic solid material, and a non-radioactive organic metal solid material, in other embodiments, the substrate 203 may be selected from at least one of gallium nitride, aluminum nitride, tantalum nitride, gallium oxide, aluminum oxide, sapphire, silicon, germanium, silicon germanium alloy, silicon dioxide, quartz, silicon carbide, silicon nitride, diamond, graphite, highly oriented pyrolytic graphite, boron arsenide, gallium arsenide, indium arsenide, aluminum gallium arsenide, aluminum arsenide, gallium phosphide, indium phosphide, zinc oxide, hafnium dioxide, titanium nitride, magnesium oxide, lithium niobate, strontium titanate, strontium ruthenate, and mica, in which case the substrate 203 also comprises a composite thereof. The thickness of the substrate 203 is not particularly limited, and for example, the thickness of the substrate 203 may be 10 μm to 1cm. Thereby, the thickness of the substrate 203 is prevented from being too thin and from being broken during the test.
In the actual operation process, when the heterojunction sample to be detected is heated, the heating method comprises two methods, and electric heating or laser heating is used. The electric heating needs to switch on pulse square wave heating voltage to the heterojunction sample to be detected, and the laser heating needs to irradiate pulse square wave modulated heating laser to the surface of the heterojunction sample to be detected. The waveforms of the pulse square waves of the two methods are shown in FIG. 5, and the pulse width of the pulse square wave of the electric heating is recorded as deltat 1 Duty cycle d 1 The pulse width of the laser heated pulse square wave is denoted at 2 Duty cycle d 2
And after heating is started, obtaining a heating temperature rise value and heating power in the test duration. It should be noted that the test duration is in the range of 0 to Δt (or Δt to 2Δt) after the start of the pulse square wave, that is, in the heating mode of electric heating, the test duration is in the range of 0 to Δt after the start of the pulse square wave 1 (or Deltat) 1 ~2Δt 1 ) Time frame. For the heating mode of laser heating, the test duration is 0-deltat after the beginning of the pulse square wave 2 (or Deltat) 2 ~2Δt 2 ) Time frame. The heating temperature rise value is obtained by a thermal reflection method. For the heating mode of electric heating, the heating power is the power of electric heating. For the heating system of laser heating, the heating power is the power of laser heating.
Step 120: based on the heating temperature rise value, a variation discrete point and an effective heat conduction area of the heating Wen Shengzhi that varies with time during the test period are determined. That is, in the test duration, discrete points of change of the heating temperature rise value with time are formed according to the heating temperature rise values of different time nodes. The effective heat transfer area is calculated from the initial section of heating Wen Shengzhi according to the semi-infinite transient heat transfer theory. It is noted that in some embodiments, determining the effective heat transfer area based on the heating temperature rise value may be considered part of a post-processing algorithm based on the theory of a thermal resistance-heat capacity network. In some embodiments, the initial segment may be selected to be 50ns to 1 μs.
Step 130: and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured. Specifically, by utilizing a post-processing algorithm based on a thermal resistance and heat capacity network theory, discrete points of change are fed, and meanwhile, heating power, an effective heat conducting area and thicknesses of layers of a heterojunction sample to be measured are fed, so that thermophysical properties of the heterojunction sample to be measured are obtained at one time. The thermal physical property of the heterojunction sample to be tested at least comprises one of film heat conductivity, film volume heat capacity, substrate heat conductivity, substrate volume heat capacity and interface thermal resistance.
Based on the above embodiment, in the method, in a test period, a heterojunction sample to be tested is heated by using an electric heating mode, and a heating temperature rise value and heating power are obtained, which specifically includes:
step 210: when the heterojunction sample to be tested is heated by using an electric heating mode, a heating electrode 204 is arranged on at least part of the surface of the heterojunction sample 201 to be tested.
Specifically, a heating electrode 204 is disposed on at least a portion of the surface of the thin film 201 of the heterojunction sample to be tested, which is far from the substrate 203, the heating electrode 204 has a predetermined width and shape, and the arrangement of the heterojunction sample to be tested and the heating electrode is described with reference to fig. 2 and 3. Further, as shown in FIG. 3, in some embodiments, the heating electrode 204 has a serpentine structure with an electrode width of 50 μm, an electrode spacing of 5 μm, a single electrode length of 0.1mm to 5mm, and a number of 10 to 40 electrodes.
In actual operation, if the material forming the thin film 201 has good conductivity, the insulating layer 205 may be disposed on the surface of the thin film 201 to prevent electrode crosstalk and leakage, and then the heating electrode 204 is disposed on at least a portion of the surface of the insulating layer 205, as shown in fig. 2.
Further, the material of the heating electrode 204 is not particularly limited and is selected from electrode materials commonly used in the art, for example, in some embodiments, the heating electrode 204 in the present invention may be each independently selected from at least one of Au, pt, pd, ag, cr, ni, ti, cu and Al.
Further, as shown in fig. 2, the material of the insulating layer 205 is not particularly limited, and in particular, in some embodiments, the insulating layer 205 may be at least one selected from silicon dioxide, hafnium dioxide, zirconium dioxide, aluminum oxide, gallium oxide and silicon nitride, and one skilled in the art may select the thermal conductivity and the volumetric heat capacity of the insulating layer 205 of the heterojunction sample to be tested according to actual needs.
Step 220: the heating electrode 204 is connected with a pulse square wave heating voltage with a first preset parameter, the amplitude of the pulse square wave heating voltage is U, and the pulse width of the pulse square wave heating voltage is deltat 1 With a duty cycle d 1 The pulse waveform is referred to in fig. 5. Further, for the electrical heating type test method, in some embodiments, the amplitude U of the pulse square wave heating voltage is 5V-20V, the pulse width Deltat 1 Is 0.1 ms-100 ms, duty ratio d 1 10 to 50 percent.
Step 230: the current through the heater electrode 204 is measured and has an amplitude I. Heating power p=ui is calculated using the voltage and the current.
Step 240: by using a heat reflection method, an LED light source with the wavelength lambda is selected, the average temperature rise delta T of the surface of the heating electrode 204 is measured as a heating temperature rise value, and further a variation discrete point of delta T along with time is obtained. In some embodiments, the average temperature rise of the surface of the heater electrode 204 is measured using a reflectance thermal imaging system. Further, for the electrical heating type test method, in some embodiments, the LED light source wavelength λ may be 340nm to 780nm, specifically, at least one of 340nm,365nm,405nm,455nm, 505nm,530nm, 245 nm, 650 nm,780nm, etc., and the actual selection may be based on the reflectance temperature coefficient (C th ) Select the corresponding higher C th The wavelength of the absolute value, the specific value can be finished by consulting literature or actual calibration.
Based on the above embodiment, in the method, a heterojunction sample to be tested is heated by using a laser heating mode in a test duration, and a heating temperature rise value and heating power are obtained, which specifically includes:
step 310: when the heterojunction sample to be measured is heated by using the laser heating method, a metal sensor 206 is disposed on the surface of the thin film 201 of the heterojunction sample to be measured.
Specifically, a layer of metal sensor 206 is processed on the surface of the thin film 201 of the heterojunction sample to be measured far from the substrate 203, and the arrangement of the heterojunction sample to be measured and the metal sensor 206 is shown in fig. 4.
Further, the material of the metal sensing layer is not particularly limited, and materials commonly used in the art may be selected, for example, in some embodiments, at least one of Au, pt, al, and Ni may be selected.
Step 320: irradiating the surface of the metal sensing layer 206 with a pulse square wave modulated heating laser with a second preset parameter; wherein the power of the heating laser is P, and the spot area of the heating laser is A 0 The method comprises the steps of carrying out a first treatment on the surface of the Pulse width of pulse square wave is delta t 2 The method comprises the steps of carrying out a first treatment on the surface of the The duty cycle of the pulse square wave is d 2 The pulse waveform is referred to in fig. 5. In some embodiments, the heating laser is generated by a laser source, spot diameter d 0 1 μm to 100 μm, the spot areaThe power amplitude P of the pulse square wave is 1W-20W, and the pulse width delta t 2 Is 0.1 ms-10 ms, duty ratio d 2 10 to 50 percent.
Step 330: and measuring the central temperature rise delta T of the heterojunction sample to be measured by using a thermal reflection method and using detection light as a heating temperature rise value, and further obtaining a variation discrete point of delta T along with time. The probe light may be selected from a laser light source, for example, another laser light split in a laser light source that emits a heating laser, and in some embodiments, a steady state thermal reflection system is used to measure the temperature rise of the center of the heterojunction sample under test.
Step 340: the power P of the heating laser was used as the heating power.
Based on the above embodiment, in the method, the thermal physical properties of the heterojunction sample to be measured are calculated according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured, and specifically include:
obtaining a thermal resistance-heat capacity structural function according to the variation discrete points and the heating power;
identifying an interface of the heterojunction sample to be detected by utilizing the thermal resistance-heat capacity structure function, and reading accumulated thermal resistance and accumulated heat capacity of a node-heat conduction interface;
And separating the geometric parameters and thermophysical properties of the accumulated thermal resistance and the accumulated heat capacity by utilizing the thicknesses of all layers of the heterojunction sample to be detected and the effective heat conduction area so as to obtain the thermophysical properties of the heterojunction sample to be detected.
Specifically, in some embodiments, the post-processing algorithms based on the theory of the heat resistance and heat capacity network include post-processing algorithm 1, post-processing algorithm 2, and post-processing algorithm 3.
And obtaining a thermal resistance-heat capacity structural function according to the variation discrete points and the heating power by using the post-processing algorithm 1. The post-processing algorithm 2 is an algorithm for determining the effective heat conduction area according to the heating temperature rise value. And obtaining the thermophysical property of the heterojunction sample to be detected according to the thermal resistance-heat capacity structural function, the thicknesses of all layers of the heterojunction sample to be detected and the effective heat conduction area by utilizing a post-processing algorithm 3.
Specifically, firstly, a thermal resistance-heat capacity structural function is obtained by utilizing a post-processing algorithm 1 through changing discrete points and heating power, and then, the thermal physical property of the heterojunction sample to be measured is obtained by utilizing a post-processing algorithm 3 through calculation of the thermal resistance-heat capacity structural function, the thicknesses of all layers of the heterojunction sample to be measured and the effective heat conduction area. It should be noted that the order of execution of the post-processing algorithms 1 and 2 precedes the post-processing algorithm 3, but the order of the post-processing algorithms 1 and 2 is not fixed. In one embodiment, post-processing algorithm 1, post-processing algorithm 2, post-processing algorithm 3 are performed sequentially. In another embodiment, post-processing algorithm 2 is performed first, then post-processing algorithm 1 is performed, and finally post-processing algorithm 3 is performed.
Further, the post-processing algorithm 1 includes: obtaining a junction temperature transient response curve according to the change discrete points and the heating power, sequentially carrying out numerical differentiation, smooth denoising, interpolation encryption, extrapolation of an initial segment, fourier deconvolution or Bayesian deconvolution, discrete time constant spectrum, constructing a Foster network by sectional integration, transforming an impedance conservation network into a Caser network, accumulating to obtain an integral thermal resistance-thermal capacitance structural function, and differentiating to obtain a differential thermal resistance-thermal capacitance structural function.
The post-processing algorithm 2 includes: according to the semi-infinite transient heat conduction theory, the effective heat conduction area is calculated according to the initial section of heating Wen Shengzhi.
The post-processing algorithm 3 includes: and identifying the interface of the heterostructure by utilizing the mathematical characteristic of the thermal resistance-heat capacity structure function on the interface of the heat conduction structure, and reading the accumulated thermal resistance and accumulated heat capacity of the node-heat conduction interface. And separating geometric parameters and thermophysical properties from the structural function by utilizing the heat conduction characteristic, and extracting the thermophysical properties of the heterojunction sample to be detected. The heat conduction characteristic comprises the thickness of each layer of the heterojunction sample to be tested and the effective heat conduction area. The thermal physical property of the heterojunction sample to be tested at least comprises one of film heat conductivity, film volume heat capacity, substrate heat conductivity, substrate volume heat capacity and interface thermal resistance.
It should be understood that, before the post-processing algorithm 3, the measurement of the thickness of each layer of the heterojunction sample to be measured occurs, and in the actual operation process, a typical wafer manufacturer directly gives the measurement of the thickness of each layer of the heterojunction sample to be measured, without secondary characterization.
According to the method for measuring the thermal physical properties of the heterojunction, firstly, the thermal excitation is carried out on the surface of a sample through current or laser, then, the temperature rise change of the surface of the sample at different moments is measured through a transient photo-thermal test method, and finally, the volume heat capacity, the heat conductivity and the interface heat resistance of the thin film and the substrate are extracted from a temperature response curve at one time through a set of post-processing algorithm based on a thermal resistance heat capacity network theory. The heterojunction thermophysical property measuring method provided by the invention has at least the following advantages:
the test precision is high. Obtaining a junction temperature response curve with high time resolution by using a transient photo-thermal test method, and extracting thermophysical properties by using a high numerical precision algorithm;
high efficiency and rapidness. The in-situ measurement of five thermophysical properties of the volume heat capacity and the heat conductivity of the heterostructure film and the substrate and the interface thermal resistance can be realized only by one test without a reference sample;
the applicability is wide. The set of flow is suitable for different transient photo-thermal testing methods and is suitable for heterostructures of different types and sizes.
Based on the above embodiments, the present invention provides an illustration of performing one measurement using the heterojunction thermophysical property measurement method described above.
Sequentially depositing a silicon dioxide oxygen burying layer with the thickness of 2 mu m and a silicon film with the thickness of 50 mu m on a silicon substrate with the thickness of 400 mu m to obtain a silicon heterostructure sample on an insulator, arranging an insulating layer on one side of a silicon device layer far away from the silicon substrate, wherein the insulating layer is made of silicon dioxide and has the thickness of 25nm, arranging a heating electrode on the surface of the insulating layer far away from the silicon device layer, and measuring the volume heat capacity, the heat conductivity and the interface heat resistance of the film and the substrate of the heterostructure sample by adopting a finite element simulation electric heating technology, wherein the specific process is as follows:
(1) Heating electrodes H are arranged on at least part of the surface of the film far away from the substrate, the electrode width is 50 mu m, the electrode spacing is 5 mu m, the length of a single electrode is 1.4mm, and the number of the electrodes is 27.
(2) And a pulse square wave heating voltage is connected to the heating electrode, the amplitude of the pulse square wave heating voltage is 20V, the pulse width of the pulse square wave heating voltage is 10ms, and the duty ratio of the pulse square wave heating voltage is 50%. The current through the heated electrode was measured and had a magnitude of 0.328A. And using finite element simulation to measure the average temperature rise delta T of the surface of the heating electrode, and obtaining a discrete point of delta T changing along with time.
(3) The heating power was calculated as 6.5533W using the voltage and current.
(4) The average temperature rise delta T discrete point within the time range of 10ms to 20ms after the pulse starts is fed into the post-processing algorithm 1, and meanwhile, the heating power 6.5533W is fed, and the thermal resistance-heat capacity structural function C is calculated (R )。
(5) The initial section of the average temperature rise delta T of the surface of the heating electrode is fed into the post-treatment algorithm 2 to obtain the effectiveHeat conduction area is 2.824mm 2
(6) By thermal resistance-heat capacity structural function C (R ) Effective heat conduction area 2.824mm 2 And heterostructure layers with thickness of 400 μm/50 μm are fed into the post-processing algorithm 3 to obtain the film thermal conductivity k at one time f Is 113.09 W.m -1 ·K -1 Volumetric heat capacity of filmIs 1.52E6J m -3 ·K -1 Substrate thermal conductivity t sub Is 117.75 W.m -1 ·K -1 Substrate volume heat capacity->1.64E6J.m -3 ·K -1 Interface thermal resistance R I 2238.1m 2 K·GW -1
It should be specifically noted here that finite element simulation means: and constructing a model with the same structure as the actual sample in a computer, setting the same electrothermal boundary conditions, and simulating the actual condition of the measured sample, thereby obtaining the corresponding thermophysical parameters by calculation.
The final test results are shown in Table 1.
Table 1 test results
In summary, through the experimental results shown in table 1, it can be seen that the method for measuring the thermal physical properties of the heterojunction provided by the invention can realize accurate measurement of the volumetric heat capacity and the thermal conductivity of the heterostructure film and the substrate and the thermal interface resistance, and the relative error between the measurement result and the theoretical value is within 20%, thus proving the practicability and the reliability of the method for measuring the thermal physical properties of the heterojunction provided by the invention.
According to the method for measuring the thermal physical properties of the heterojunction, the heterojunction sample to be measured is heated within the test duration, and the heating temperature rise value and the heating power are obtained; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured. According to the invention, thermal excitation is carried out on the surface of the heterojunction sample to be measured, the temperature rise changes of the sample surface at different moments are measured, so that the temperature change discrete points are obtained, the thermophysical properties of the heterojunction sample to be measured are measured in situ at one time according to the temperature change discrete points, and the measurement of the thermophysical properties of the heterojunction with higher precision and higher efficiency is realized.
The heterojunction thermophysical property measuring device provided by the invention is described below, and the heterojunction thermophysical property measuring device described below and the heterojunction thermophysical property measuring method described above can be referred to correspondingly. Fig. 6 is a schematic structural diagram of a device for measuring thermal physical properties of a heterojunction according to the present invention, as shown in fig. 6, including a testing unit 610, a discrete unit 620, and a calculating unit 630, wherein,
The testing unit 610 is configured to heat the heterojunction sample to be tested within a testing duration, and obtain a heating temperature rise value and heating power;
a discrete unit 620 for determining a variation discrete point and an effective heat conduction area of the heating Wen Shengzhi over time within the test period based on the heating temperature rise value;
the calculating unit 630 is configured to calculate the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conducting area and the thickness of each layer of the heterojunction sample to be measured.
Based on the above embodiment, in the device, heating is performed on a heterojunction sample to be tested in a test duration to obtain a heating temperature rise value and heating power, and the device specifically includes:
arranging a heating electrode on at least part of the surface of the heterojunction sample to be tested; wherein the heating electrode has a preset width and shape;
switching on a pulse square wave with a first preset parameter to the heating electrodeA heating voltage; wherein the pulse width of the pulse square wave is deltat 1 Duty cycle d 1 The method comprises the steps of carrying out a first treatment on the surface of the The voltage of the pulse square wave is U;
according to the voltage of the pulse square wave and the current passing through the heating electrode, heating power is calculated;
And measuring the average temperature rise of the surface of the heating electrode by using a heat reflection method to obtain a heating temperature rise value.
Based on the above embodiment, in the device, heating is performed on a heterojunction sample to be tested in a test duration to obtain a heating temperature rise value and heating power, and the device specifically includes:
a layer of metal sensor is arranged on the surface of the film of the heterojunction sample to be detected;
irradiating the surface of the metal sensor with a pulse square wave modulated heating laser with a second preset parameter; wherein the power of the heating laser is P, and the spot area of the heating laser is A 0 The method comprises the steps of carrying out a first treatment on the surface of the The pulse width of the pulse square wave is delta t 2 Duty cycle d 2
Measuring the temperature rise of the center of the heterojunction sample to be measured by using a thermal reflection method so as to obtain a heating temperature rise value;
and taking the power of the heating laser as heating power.
Based on the above embodiment, in the apparatus, the thermal physical properties of the heterojunction sample to be measured are calculated according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured, and specifically include:
obtaining a thermal resistance-heat capacity structural function according to the variation discrete points and the heating power;
Identifying an interface of the heterojunction sample to be detected by utilizing the thermal resistance-heat capacity structure function, and reading accumulated thermal resistance and accumulated heat capacity of a node-heat conduction interface;
and separating the geometric parameters and thermophysical properties of the accumulated thermal resistance and the accumulated heat capacity by utilizing the thicknesses of all layers of the heterojunction sample to be detected and the effective heat conduction area so as to obtain the thermophysical properties of the heterojunction sample to be detected.
Based on the above embodiment, in the device, the thermal resistance-heat capacity structural function is obtained according to the variation discrete points and the heating power, and specifically includes:
obtaining a junction temperature transient response curve according to the change discrete point and the heating power; sequentially performing differentiation, deconvolution, discrete processing and sectional integration on the junction temperature transient response curve to obtain a Foster network;
transforming the Foster network to obtain a Cauer network;
and obtaining a heat resistance-heat capacity structural function according to the Cauer network.
Based on the above embodiment, in the apparatus, determining the effective heat conduction area based on the heating temperature rise value specifically includes:
and calculating the effective heat conduction area based on the initial section of the heating temperature rise value according to the semi-infinite transient heat conduction theory.
According to the method and the device for measuring the thermal physical properties of the heterojunction, the heterojunction sample to be measured is heated within the test duration, and the heating temperature rise value and the heating power are obtained; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured. According to the invention, thermal excitation is carried out on the surface of the heterojunction sample to be measured, the temperature rise changes of the sample surface at different moments are measured, so that the temperature change discrete points are obtained, the thermophysical properties of the heterojunction sample to be measured are measured in situ at one time according to the temperature change discrete points, and the measurement of the thermophysical properties of the heterojunction with higher precision and higher efficiency is realized.
Fig. 7 illustrates a physical schematic diagram of an electronic device, as shown in fig. 7, which may include: processor 710, communication interface (Communications Interface) 720, memory 730, and communication bus 740, wherein processor 710, communication interface 720, memory 730 communicate with each other via communication bus 740. The processor 710 may invoke logic instructions in the memory 730 to perform a heterojunction thermophysical property measurement method comprising: heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
Further, the logic instructions in the memory 730 described above may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product comprising a computer program, the computer program being storable on a non-transitory computer readable storage medium, the computer program, when executed by a processor, being capable of performing the method of measuring a thermal physical property of a heterojunction provided by the methods described above, the method comprising: heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the method of measuring a thermal physical property of a heterojunction provided by the above methods, the method comprising: heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power; determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value; and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for measuring a thermal physical property of a heterojunction, comprising:
heating the heterojunction sample to be tested within the test duration to obtain a heating temperature rise value and heating power;
determining a discrete point of change and an effective heat transfer area of the heating Wen Shengzhi over time over the test period based on the heating temperature rise value;
and calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
2. The method for measuring the thermal physical properties of the heterojunction according to claim 1, wherein the heating of the heterojunction sample to be measured is performed within a test duration to obtain a heating temperature rise value and a heating power, and the method specifically comprises the following steps:
Arranging a heating electrode on at least part of the surface of the heterojunction sample to be tested; wherein the heating electrode has a preset width and shape;
switching on a pulse square wave heating voltage with a first preset parameter to the heating electrode; wherein the pulse width of the pulse square wave is deltat 1 Duty cycle d 1 The method comprises the steps of carrying out a first treatment on the surface of the The voltage of the pulse square wave is U;
according to the voltage of the pulse square wave and the current passing through the heating electrode, heating power is calculated;
and measuring the average temperature rise of the surface of the heating electrode by using a heat reflection method to obtain a heating temperature rise value.
3. The method for measuring the thermal physical properties of the heterojunction according to claim 1, wherein the heating of the heterojunction sample to be measured is performed within a test duration to obtain a heating temperature rise value and a heating power, and the method specifically comprises the following steps:
a layer of metal sensor is arranged on the surface of the film of the heterojunction sample to be detected;
irradiating the surface of the metal sensor with a pulse square wave modulated heating laser with a second preset parameter; wherein the power of the heating laser is P, and the spot area of the heating laser is A 0 The method comprises the steps of carrying out a first treatment on the surface of the The pulse width of the pulse square wave is delta t 2 Duty cycle d 2
Measuring the temperature rise of the center of the heterojunction sample to be measured by using a thermal reflection method so as to obtain a heating temperature rise value;
and taking the power of the heating laser as heating power.
4. The method according to claim 1, wherein the calculation of the thermophysical properties of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the respective layer thicknesses of the heterojunction sample to be measured specifically comprises:
obtaining a thermal resistance-heat capacity structural function according to the variation discrete points and the heating power;
identifying an interface of the heterojunction sample to be detected by utilizing the thermal resistance-heat capacity structure function, and reading accumulated thermal resistance and accumulated heat capacity of a node-heat conduction interface;
and separating the geometric parameters and thermophysical properties of the accumulated thermal resistance and the accumulated heat capacity by utilizing the thicknesses of all layers of the heterojunction sample to be detected and the effective heat conduction area so as to obtain the thermophysical properties of the heterojunction sample to be detected.
5. The method of claim 4, wherein obtaining a thermal resistance-thermal capacitance structural function from the varying discrete points and the heating power, comprises:
Obtaining a junction temperature transient response curve according to the change discrete point and the heating power; sequentially performing differentiation, deconvolution, discrete processing and sectional integration on the junction temperature transient response curve to obtain a Foster network;
transforming the Foster network to obtain a Cauer network;
and obtaining a heat resistance-heat capacity structural function according to the Cauer network.
6. The method according to claim 1, wherein determining an effective heat conduction area based on the heating temperature rise value specifically comprises:
and calculating the effective heat conduction area based on the initial section of the heating temperature rise value according to the semi-infinite transient heat conduction theory.
7. A heterojunction thermophysical property measuring device, comprising:
the testing unit is used for heating the heterojunction sample to be tested within the testing time length to obtain a heating temperature rise value and heating power;
a discrete unit for determining a variation discrete point and an effective heat conduction area of the heating Wen Shengzhi over time within the test period based on the heating temperature rise value;
and the calculating unit is used for calculating the thermophysical property of the heterojunction sample to be measured according to the variation discrete point, the heating power, the effective heat conduction area and the thickness of each layer of the heterojunction sample to be measured.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method of measuring the thermophysical properties of the heterojunction according to any one of claims 1 to 6 when executing the program.
9. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the heterojunction thermophysical property measurement method of any one of claims 1 to 6.
10. A computer program product comprising a computer program, characterized in that the computer program, when executed by a processor, implements the method of measuring a thermophysical property of a heterojunction according to any one of claims 1 to 6.
CN202310706629.7A 2023-06-14 2023-06-14 Heterojunction thermophysical property measuring method and device Pending CN116879347A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310706629.7A CN116879347A (en) 2023-06-14 2023-06-14 Heterojunction thermophysical property measuring method and device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310706629.7A CN116879347A (en) 2023-06-14 2023-06-14 Heterojunction thermophysical property measuring method and device

Publications (1)

Publication Number Publication Date
CN116879347A true CN116879347A (en) 2023-10-13

Family

ID=88268816

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310706629.7A Pending CN116879347A (en) 2023-06-14 2023-06-14 Heterojunction thermophysical property measuring method and device

Country Status (1)

Country Link
CN (1) CN116879347A (en)

Similar Documents

Publication Publication Date Title
Lim et al. Elucidating the long-range charge carrier mobility in metal halide perovskite thin films
Cho et al. Near-junction thermal management: Thermal conduction in gallium nitride composite substrates
Hopkins et al. Criteria for cross-plane dominated thermal transport in multilayer thin film systems during modulated laser heating
CN108169279B (en) Based on VO2Thin film thermal conductivity measuring device and method for thin film
CN108614005B (en) Method and system for testing thermophysical property parameters based on multilayer composite material
TWI650552B (en) Method and apparatus for x-ray fluorescence analysis
EP2840385A1 (en) Lock-in thermography method and system for determining material layer parameters of a sample
Augarten et al. Calculation of quantitative shunt values using photoluminescence imaging
CN107843616A (en) The apparatus and method of the thermal conductivity of quick measurement thin-film material
Yuan et al. Nanosecond transient thermoreflectance method for characterizing anisotropic thermal conductivity
Segovia et al. High Accuracy Ultrafast Spatiotemporal Pump–Probe Measurement of Electrical Thermal Transport in Thin Film Gold
JP7477500B2 (en) Steady-state thermoreflectance method and system for measuring thermal conductivity - Patents.com
Rausch et al. Thin-film thermal-conductivity measurement on semi-conducting polymer material using the 3ω technique
CN116879347A (en) Heterojunction thermophysical property measuring method and device
CN110174185B (en) Spatial scanning dual-wavelength Raman flashing method and device for representing substrate nanowire
WO2004055498A1 (en) Method and apparatus for measuring thickness of thin films via transient thermoreflectance
Burzo et al. Influence of the metallic absorption layer on the quality of thermal conductivity measurements by the transient thermo-reflectance method
CN113567824B (en) Picosecond laser-based thermal resistance measuring device and method for nucleation layer of gallium nitride device
Wang et al. A square pulse thermoreflectance technique for the measurement of thermal properties
EP3339828B1 (en) Device and method for evaluating at least one operating condition of a heat exchanger
Komarov et al. Performance analysis of the transient thermo-reflectance method for measuring the thermal conductivity of single layer materials
Székely Evaluation of short pulse and short time thermal transient measurements
Burzo et al. A study of the effect of surface metalization on thermal conductivity measurements by the transient thermo-reflectance method
Chassain et al. Bayesian estimation of thermal properties using periodically pulsed photothermal radiometry: A focus on interfacial thermal resistances between layers
Jeong et al. In-plane thermal conductivity measurement with nanosecond grating imaging technique

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination