Academia.eduAcademia.edu

Figure 49 – uploaded by Indrayush De

See full PDFdownloadDownload figure
Figure 49. Thermo-resistive 4-point probe and its configuration. for the specific heat, the Debye temperature and the phonon velocity. The 4-point probe is very similar to in its functioning and architecture of the 2-point probe but

Figure 49 Thermo-resistive 4-point probe and its configuration. for the specific heat, the Debye temperature and the phonon velocity. The 4-point probe is very similar to in its functioning and architecture of the 2-point probe but

Related Figures (158)

Figure 1. Schematic description of the inverse heat conduction problem in thermal characterization experiment. parameters By and Bm respectively. system/material need to be identified. Indeed, the interactions between the disturbance and the
Figure 1. Schematic description of the inverse heat conduction problem in thermal characterization experiment. parameters By and Bm respectively. system/material need to be identified. Indeed, the interactions between the disturbance and the
Figure 2. (a) 20 micrometer microthermocouple for direct measuring of (b) resin temperature (Kensuke Tsuchiya, Micro machining technology for micro devices [1]).
Figure 2. (a) 20 micrometer microthermocouple for direct measuring of (b) resin temperature (Kensuke Tsuchiya, Micro machining technology for micro devices [1]).
absolute change due to the difficult calibration stage.
absolute change due to the difficult calibration stage.
measure the absolute change of surface temperature. radiation intensity at a specific wavelength and considering the surface emissivity, one can viodern research has seen strides in Infrared (IR) thermography (Figure 4) in tandem with hermoreflectance imagining where the former is generally good for low reflectivity materials aving high emissivity and the latter is better for high reflectivity materials surface [3]. IR hermography uses infrared sensitive camera to obtain thermal image using Planck’s blackbody aw to determine temperature of hot object for minimum wavelengths of 3 um. Obtaining the adiation intensity at a specific wavelength and considering the surface emissivity, one car
measure the absolute change of surface temperature. radiation intensity at a specific wavelength and considering the surface emissivity, one can viodern research has seen strides in Infrared (IR) thermography (Figure 4) in tandem with hermoreflectance imagining where the former is generally good for low reflectivity materials aving high emissivity and the latter is better for high reflectivity materials surface [3]. IR hermography uses infrared sensitive camera to obtain thermal image using Planck’s blackbody aw to determine temperature of hot object for minimum wavelengths of 3 um. Obtaining the adiation intensity at a specific wavelength and considering the surface emissivity, one car
measurements using a photodetector that can resolve thermal transients with sub microsecond
measurements using a photodetector that can resolve thermal transients with sub microsecond
Figure 7. Schematic representation of the aperture of NSOM [6]. Another sort of measurement is achieved using Raman Spectroscopy (Figure 8) that uses short
Figure 7. Schematic representation of the aperture of NSOM [6]. Another sort of measurement is achieved using Raman Spectroscopy (Figure 8) that uses short
Table 1 Comparison of various types of Thermal Measurement Techniques at the microscale.
Table 1 Comparison of various types of Thermal Measurement Techniques at the microscale.
2.3.A short overview of progress in SThM, STP and thermocouple probe
2.3.A short overview of progress in SThM, STP and thermocouple probe
noticeable change in the tip temperature is less than 0.1 millidegree. region. The voltage change at the tip is sensed by the other end of the probe and the minimum
noticeable change in the tip temperature is less than 0.1 millidegree. region. The voltage change at the tip is sensed by the other end of the probe and the minimum
Figure 11. Thin Film Thermocouple Probe devised by A. Majumdar in 1995 [18].
Figure 11. Thin Film Thermocouple Probe devised by A. Majumdar in 1995 [18].
to increase the spatial resolution.
to increase the spatial resolution.
Figure 14. Thermocouple Probe proposed by Y. Suzuki in 1996 [21]. topographical images were a big drawback (Figure 13). This probe led to the spatial resolution of the thermal images to 10 nm. However, anomalies it
Figure 14. Thermocouple Probe proposed by Y. Suzuki in 1996 [21]. topographical images were a big drawback (Figure 13). This probe led to the spatial resolution of the thermal images to 10 nm. However, anomalies it
Figure 15. Thermocouple Probe tip as fabricated by G. Mills et al. in 1998 [22]. but still, sadly, didn’t manage to obtain proper images (Figure 14).
Figure 15. Thermocouple Probe tip as fabricated by G. Mills et al. in 1998 [22]. but still, sadly, didn’t manage to obtain proper images (Figure 14).
Figure 17. Thermocouple probe demonstrated by K. Kim and colleagues [24]. 2.4.The Thermoresistive probes
Figure 17. Thermocouple probe demonstrated by K. Kim and colleagues [24]. 2.4.The Thermoresistive probes
transfer and surface temperature fields. particles. It was also able to detect local heating of active samples so as to investigate heat flux
transfer and surface temperature fields. particles. It was also able to detect local heating of active samples so as to investigate heat flux
Figure 22. Thermoresistive probe produced by Kelvin Nanotechnology containing a Si3N,4 cantilever and a Pd heater [28]. nm topographic and thermal spatial resolution with temperature resolution of 0.1K. [28].
Figure 22. Thermoresistive probe produced by Kelvin Nanotechnology containing a Si3N,4 cantilever and a Pd heater [28]. nm topographic and thermal spatial resolution with temperature resolution of 0.1K. [28].
Figure 23. SEM image of a Thermoresistive probe. The thermoresistive tips used for scanning thermal microscopy are mostly conical in shape with a spherical tip apex for optimal tip thermal conductance and a spring constant of around 0.3 N/m [26]. The tip radius of curvature of modern thermoresistive probes are around 50 nm and they have a very short time response, around few tens of microsecond with the temperature coefficient of the electrical resistance at around 0.0012 /K [27]. The probe tip is around 10 um. This length allows creating separation necessary between the cantilever and the sample, which thereby, notably in case of hot sample in thermometric measurements, reduces the cantilever heating. A SEM image of the tip of a thermoresistive micro-fabricated probe is given in Figure heating. A SEM image of the tip of a thermoresistive micro-fabricated probe is given in Figure
Figure 23. SEM image of a Thermoresistive probe. The thermoresistive tips used for scanning thermal microscopy are mostly conical in shape with a spherical tip apex for optimal tip thermal conductance and a spring constant of around 0.3 N/m [26]. The tip radius of curvature of modern thermoresistive probes are around 50 nm and they have a very short time response, around few tens of microsecond with the temperature coefficient of the electrical resistance at around 0.0012 /K [27]. The probe tip is around 10 um. This length allows creating separation necessary between the cantilever and the sample, which thereby, notably in case of hot sample in thermometric measurements, reduces the cantilever heating. A SEM image of the tip of a thermoresistive micro-fabricated probe is given in Figure heating. A SEM image of the tip of a thermoresistive micro-fabricated probe is given in Figure
Figure 24. The figure compares the thermal map of a CNT modified SP probe and a standard SiO» probe. a) Temperature distribution at the tip of a the CNT modified SP probe providing effective thermal link with the sample, b) Temperature distribution using a standard SiO> probe. Both simulations were performed under vacuum condition; c) variation of tip temperature with change of sample thermal conductivity d) sensitivity of CNT and SiO> probe [29]. the nanotube whereas thicker multiwall tubes of 50nm are good as thermal probes.
Figure 24. The figure compares the thermal map of a CNT modified SP probe and a standard SiO» probe. a) Temperature distribution at the tip of a the CNT modified SP probe providing effective thermal link with the sample, b) Temperature distribution using a standard SiO> probe. Both simulations were performed under vacuum condition; c) variation of tip temperature with change of sample thermal conductivity d) sensitivity of CNT and SiO> probe [29]. the nanotube whereas thicker multiwall tubes of 50nm are good as thermal probes.
‘igure 25. SEM image of SThM cantilever attached with NW [69]. in contact with the sample via. an attached nanowire (Figure 25). cantilever and Pd/NiCr heat resistors as well as thermal sensors and apex zone of the probe was
‘igure 25. SEM image of SThM cantilever attached with NW [69]. in contact with the sample via. an attached nanowire (Figure 25). cantilever and Pd/NiCr heat resistors as well as thermal sensors and apex zone of the probe was
Another form of thermoresistive probe used notably for data storage systems and lithographic
Another form of thermoresistive probe used notably for data storage systems and lithographic
Figure 27. SEM image of the tip of a doped Si probe. The tip is around 1.7m high and has a radius less than 20 nm
Figure 27. SEM image of the tip of a doped Si probe. The tip is around 1.7m high and has a radius less than 20 nm
Figure 28. Micromachined probe with its various parts which is surrounded by metals tracks [63].
Figure 28. Micromachined probe with its various parts which is surrounded by metals tracks [63].
experimental noise can lead to an increase in the temperature and spatial resolution. temperature sensor. The authors concluded by saying that better probe design and a reduction of conduction in air is a dominant factor in such a technique as the whole cantilever acts as the
experimental noise can lead to an increase in the temperature and spatial resolution. temperature sensor. The authors concluded by saying that better probe design and a reduction of conduction in air is a dominant factor in such a technique as the whole cantilever acts as the
get rid of the necessity of sensor nanofabrication and also provide very high spatial resolution (1
get rid of the necessity of sensor nanofabrication and also provide very high spatial resolution (1
Figure 32. Schematic diagram of a cantilever array [67].
Figure 32. Schematic diagram of a cantilever array [67].
the figure denotes the linear least square fit with a slope of 0.153+0.003 cm K. as a function of k; obtained after calibration tests performed by the authors. The solid line seen ir
the figure denotes the linear least square fit with a slope of 0.153+0.003 cm K. as a function of k; obtained after calibration tests performed by the authors. The solid line seen ir
reduces at high conductivities.
reduces at high conductivities.
approximately 30 nm using gold as reference with a deviation of less than 2%.
approximately 30 nm using gold as reference with a deviation of less than 2%.
logarithmic dependence of amplitude. The Figure 36 is linear in the logarithm of frequency and the slopes observed are inversely
logarithmic dependence of amplitude. The Figure 36 is linear in the logarithm of frequency and the slopes observed are inversely
2.6.1. Physical phenomena description Heat transfer between the probe and the sample surface can take place in various forms as seen on Figure 37 [43] [41]. There is the obvious direct heat transfer due to the mechanical contact between the probe tip and the sample but there are other forms of heat transfer around the tip of Heat transfer between the probe and the sample surface can take place in various forms as seen
2.6.1. Physical phenomena description Heat transfer between the probe and the sample surface can take place in various forms as seen on Figure 37 [43] [41]. There is the obvious direct heat transfer due to the mechanical contact between the probe tip and the sample but there are other forms of heat transfer around the tip of Heat transfer between the probe and the sample surface can take place in various forms as seen
Table 3. Effective heat transfer coefficient between the cantilever and surrounding air performed by different researchers During contact measurement, the great impact of this heat transfer can be realized by noticing
Table 3. Effective heat transfer coefficient between the cantilever and surrounding air performed by different researchers During contact measurement, the great impact of this heat transfer can be realized by noticing
Table 4. Demonstration of tip-sample thermal conductance performed using heated cantilever. 2.7.1. Temperature measurement
Table 4. Demonstration of tip-sample thermal conductance performed using heated cantilever. 2.7.1. Temperature measurement
Figure 41. PN thermoelectric couples as used by L.D.P. Lopez and colleagues in 2004 [53]. -oefficient is higher there and the junction is made up of materials of low thermal conductivit The largest heat source is located at the PN junction of the setup due to the fact that the Peltier
Figure 41. PN thermoelectric couples as used by L.D.P. Lopez and colleagues in 2004 [53]. -oefficient is higher there and the junction is made up of materials of low thermal conductivit The largest heat source is located at the PN junction of the setup due to the fact that the Peltier
the circumstances that the material properties of all the involved materials are known (Figure 2.7.2. Thermal properties measurements
the circumstances that the material properties of all the involved materials are known (Figure 2.7.2. Thermal properties measurements
around 100 nm to produce thermal images under vacuum conditions (Figure 43) [59].
around 100 nm to produce thermal images under vacuum conditions (Figure 43) [59].
Figure 44. Schematic diagram of the SThM experimental technique. The two modes are detailed in section 4.1 and 4.2 respectively. The setup is capable working either with the continuous wave (DC) mode or the 3~@ (AC) mode.
Figure 44. Schematic diagram of the SThM experimental technique. The two modes are detailed in section 4.1 and 4.2 respectively. The setup is capable working either with the continuous wave (DC) mode or the 3~@ (AC) mode.
Figure 45. AFM Nanosurf Easyscan 2. AFM head and controller. steps of 1 nm. 3.2.3. Thermal Probes The contact force between the probe and the sample is accurately controlled using a feedback-
Figure 45. AFM Nanosurf Easyscan 2. AFM head and controller. steps of 1 nm. 3.2.3. Thermal Probes The contact force between the probe and the sample is accurately controlled using a feedback-
Figure 46. Schematic diagram of the process of fabrication of grooved SThM probe /2//3/. The Figure 47 below provides a general idea of a modern SThM probe.
Figure 46. Schematic diagram of the process of fabrication of grooved SThM probe /2//3/. The Figure 47 below provides a general idea of a modern SThM probe.
Table 5 Thermal properties of thermal SiOz and amorphous Si3N, (k: thermal conductivity, p: density and C,: specific heat, @, : Debye temperature, vr: phonon transverse velocity, vi: phonon longitudinal velocity) at room temperature.
Table 5 Thermal properties of thermal SiOz and amorphous Si3N, (k: thermal conductivity, p: density and C,: specific heat, @, : Debye temperature, vr: phonon transverse velocity, vi: phonon longitudinal velocity) at room temperature.
Figure 48. (left) A close up view of the 2-point probe with the Pd strip deposited at the tip. (Right) View of the NiCr Current Limiters that bound the current passing the Pd strip at 1 mA
Figure 48. (left) A close up view of the 2-point probe with the Pd strip deposited at the tip. (Right) View of the NiCr Current Limiters that bound the current passing the Pd strip at 1 mA
Table 7. The different dimensions and parameters of the various parts of the 4-point probe (from fe 3.2.4. The function generator
Table 7. The different dimensions and parameters of the various parts of the 4-point probe (from fe 3.2.4. The function generator
system. Figure 50 provides the functional block diagram of the lock-in.
system. Figure 50 provides the functional block diagram of the lock-in.
one variable resistance R, and an unknown one Rprobe. This is achieved by balancing the bridge
one variable resistance R, and an unknown one Rprobe. This is achieved by balancing the bridge
Figure 52. Image showing the process of isolation of the third harmonic using the differential amplifier stage.
Figure 52. Image showing the process of isolation of the third harmonic using the differential amplifier stage.
Although the Operational Amplifiers (AO) have been chosen to work within a large frequency
Although the Operational Amplifiers (AO) have been chosen to work within a large frequency
Figure 55. Active Vibration Control using Accurion's workbench (Principles of Halcyonics Active Vibration Isolation Technology, Accurion). performed on its surface, we have placed the desktop unit above it and on top of the later
Figure 55. Active Vibration Control using Accurion's workbench (Principles of Halcyonics Active Vibration Isolation Technology, Accurion). performed on its surface, we have placed the desktop unit above it and on top of the later
Figure 56. Image showing the experimental setup of SThM in the Laboratory. at the laboratory is given in the Figure 56. remains very limited and cannot be maintained during the scan. The complete experimental setup
Figure 56. Image showing the experimental setup of SThM in the Laboratory. at the laboratory is given in the Figure 56. remains very limited and cannot be maintained during the scan. The complete experimental setup
Figure 57. SEM Images showing the adhesion of dust on the probes after several uses.
Figure 57. SEM Images showing the adhesion of dust on the probes after several uses.
Figure 58. vCD Images showing the state of the tip of the probes after several uses.
Figure 58. vCD Images showing the state of the tip of the probes after several uses.
Figure 59. Possible configurations met when according to the surface roughness. in Figure 59. It is assumed that the contact radius is 7. interfere with the temperature measurement in case we faced the specific configurations reported
Figure 59. Possible configurations met when according to the surface roughness. in Figure 59. It is assumed that the contact radius is 7. interfere with the temperature measurement in case we faced the specific configurations reported
balanced in order to have V=0, and one has:
balanced in order to have V=0, and one has:
Figure 60. Working in the passive mode
Figure 60. Working in the passive mode
during the scan of the surface by the probe.
during the scan of the surface by the probe.
Figure 63. Measured V3w=/(7) when the probe is out-of-contact. different frequencies. This operation is done obviously when the probe is out-of-contact. measuring the third harmonic of the voltage drop as a function of the current for at least two
Figure 63. Measured V3w=/(7) when the probe is out-of-contact. different frequencies. This operation is done obviously when the probe is out-of-contact. measuring the third harmonic of the voltage drop as a function of the current for at least two
temperature to achieve the coefficient of resistance. Figure 65. Experimental setup for measuring probe coefficient of resistance. With the data obtained, a graph can be plotted with the variation of probe resistance due tc
temperature to achieve the coefficient of resistance. Figure 65. Experimental setup for measuring probe coefficient of resistance. With the data obtained, a graph can be plotted with the variation of probe resistance due tc
regression.
regression.
We repeated then the calibration stage in tis new configuration. Figure 68 and Figure 69 give us
We repeated then the calibration stage in tis new configuration. Figure 68 and Figure 69 give us
Table 8. Comparison of Palladium Thermal Coefficient of Resistance found in our work with previously published values. The Table 8 proves that the value of the thermal coefficient resistance (TCR) that we have noted that Kelvin Nanotechnology is the provider of thermal probes for Anasys Instruments and
Table 8. Comparison of Palladium Thermal Coefficient of Resistance found in our work with previously published values. The Table 8 proves that the value of the thermal coefficient resistance (TCR) that we have noted that Kelvin Nanotechnology is the provider of thermal probes for Anasys Instruments and
Figure 70 Measurement of the 4-point probe electrical resistance R(7) as a function of temperature. Extraction of the thermal coefficient ag. Standard deviation is less than 0.5% temperature during the calibration experiment. Figure 70 reports the measured variation of the electrical probe resistance as a function
Figure 70 Measurement of the 4-point probe electrical resistance R(7) as a function of temperature. Extraction of the thermal coefficient ag. Standard deviation is less than 0.5% temperature during the calibration experiment. Figure 70 reports the measured variation of the electrical probe resistance as a function
mcrease as the force increases. However this point will be discussed later in more details <
mcrease as the force increases. However this point will be discussed later in more details <
Figure 72. Schematic diagram of the surface scanning process by the probe. [he acquisition time is dependent on the number of experimental points on the surface of the
Figure 72. Schematic diagram of the surface scanning process by the probe. [he acquisition time is dependent on the number of experimental points on the surface of the
contributions as represented in Figure 75.
contributions as represented in Figure 75.
and a denotes the thermal diffusivity. This equation can be also written as: The mesh is thus very critical regarding the expected value of the phase, notably at the high elements close to the heated surface. The minimal size is then chosen as:
and a denotes the thermal diffusivity. This equation can be also written as: The mesh is thus very critical regarding the expected value of the phase, notably at the high elements close to the heated surface. The minimal size is then chosen as:
Figure 77: 1D heat transfer in a semi-infinite domain using the infinite domain node. owards -45°, with higher frequency values. Using the semi-infinite node, the frequency is equa!
Figure 77: 1D heat transfer in a semi-infinite domain using the infinite domain node. owards -45°, with higher frequency values. Using the semi-infinite node, the frequency is equa!
‘igure 79: 2D axisymmetric heat transfer in a semi-infinite medium using FEA. FEA in that configuration. EA or the exact solutions, fit very well, showing the reliability of the semi-infinite node in the
‘igure 79: 2D axisymmetric heat transfer in a semi-infinite medium using FEA. FEA in that configuration. EA or the exact solutions, fit very well, showing the reliability of the semi-infinite node in the
Figure 80: simulation of the amplitude and phase of the frequency dependent average temperature on the heated disk. Comparison between the FEA simulation and exact solution (4.10). Material is SiO.
Figure 80: simulation of the amplitude and phase of the frequency dependent average temperature on the heated disk. Comparison between the FEA simulation and exact solution (4.10). Material is SiO.
The values are reported in Table 9. resistance of the Au layer can be viewed as the two resistances in series as:
The values are reported in Table 9. resistance of the Au layer can be viewed as the two resistances in series as:
and its approximation with identified values of do, bo and y is reported in Figure 87. In DC, it is found the thermal resistance of the SiN layer as: The constants a, b and c depend on the value or R. Using the Levenberg-Marquardt algorithm we
and its approximation with identified values of do, bo and y is reported in Figure 87. In DC, it is found the thermal resistance of the SiN layer as: The constants a, b and c depend on the value or R. Using the Levenberg-Marquardt algorithm we
occurs that is characterized by the 1/ 4{j@ term. behaves as a thermal capacitance. Between those two typical behaviours, a semi-infinite ot thermal resistance. At high frequency, the asymptotic behaviour is a,/b, j@, meaning the probe
occurs that is characterized by the 1/ 4{j@ term. behaves as a thermal capacitance. Between those two typical behaviours, a semi-infinite ot thermal resistance. At high frequency, the asymptotic behaviour is a,/b, j@, meaning the probe
simultaneously also from frequency dependent measurements. and R. is constant; there is thus no chance to identify separately those two paramete:
simultaneously also from frequency dependent measurements. and R. is constant; there is thus no chance to identify separately those two paramete:
impulse response can be at time ¢; as: Figure 92: Going from fixed to moving reference frame attached to heat source (representation in the xz plane).
impulse response can be at time ¢; as: Figure 92: Going from fixed to moving reference frame attached to heat source (representation in the xz plane).
may now write the temperature rise in the new reference frame: 4.7.2. Appendix B: heat transfer in a semi-infinite medium whose surface is submitted to a motion disk heat flux at constant velocity v. X denotes the coordinate of the source at time ¢ in the reference frame fixed to the source. We The heat flux is applied on the shape of a disk with radius 7p with a Gaussian distribution of the
may now write the temperature rise in the new reference frame: 4.7.2. Appendix B: heat transfer in a semi-infinite medium whose surface is submitted to a motion disk heat flux at constant velocity v. X denotes the coordinate of the source at time ¢ in the reference frame fixed to the source. We The heat flux is applied on the shape of a disk with radius 7p with a Gaussian distribution of the
Considering a periodic heat flux, the average temperature over the disk is obtained using the The impulse response for a motionless disk heat source at the surface of a semi-infinite mediun
Considering a periodic heat flux, the average temperature over the disk is obtained using the The impulse response for a motionless disk heat source at the surface of a semi-infinite mediun
len 1, > Ja/ w, Va, the solution comes to that of the 1D heat transfer solution in a semi
len 1, > Ja/ w, Va, the solution comes to that of the 1D heat transfer solution in a semi
Nith g=./p/a. The boundary condition (4.113) gives B=0. Boundary condition (4.112) leads
Nith g=./p/a. The boundary condition (4.113) gives B=0. Boundary condition (4.112) leads
conductor. Then, the solution in the Laplace domain is:
conductor. Then, the solution in the Laplace domain is:
Table 10 Specification of the thermal SiO. sample for our experiments. The average roughness has been measured using the AFM mode.
Table 10 Specification of the thermal SiO. sample for our experiments. The average roughness has been measured using the AFM mode.
Levenberg-Marquardt algorithm (see appendix at the end of this chapter) and the model we
Levenberg-Marquardt algorithm (see appendix at the end of this chapter) and the model we
Table 11. Contact radius and thermal contact resistance reported in the literature for the used probe.
Table 11. Contact radius and thermal contact resistance reported in the literature for the used probe.
to the identified values of R, reported in Figure 94. Figure 94. Value of the identified R, when varying the contact radius ro. Residuals at the end of the minimization process are also reported. It is observed that a relative change of 40% in r0 leads to a relative change of 28 % in the value
to the identified values of R, reported in Figure 94. Figure 94. Value of the identified R, when varying the contact radius ro. Residuals at the end of the minimization process are also reported. It is observed that a relative change of 40% in r0 leads to a relative change of 28 % in the value
Figure 95. The contact area varies according to the experimental configuration. represented in Figure 95.
Figure 95. The contact area varies according to the experimental configuration. represented in Figure 95.
Table 12 Specifications of First Experiment Performed with Moving Probe also the amplitude and phase for the probe out-of-contact from the surface and the probe in static
Table 12 Specifications of First Experiment Performed with Moving Probe also the amplitude and phase for the probe out-of-contact from the surface and the probe in static
Table 13 Resistance of Contact obtained from different probe speeds under contact condition over a known sample of SiO» not a surprising result since several studies at the macroscopic level have shown that the sliding
Table 13 Resistance of Contact obtained from different probe speeds under contact condition over a known sample of SiO» not a surprising result since several studies at the macroscopic level have shown that the sliding
Figure 96 Measured amplitude vs. frequency for contact and non-contact conditions. standard deviation on the measured voltage by the lock-in that is less that 5%.
Figure 96 Measured amplitude vs. frequency for contact and non-contact conditions. standard deviation on the measured voltage by the lock-in that is less that 5%.
Figure 97 Measured phase vs. frequency for contact and non-contact conditions.
Figure 97 Measured phase vs. frequency for contact and non-contact conditions.
Figure 98. This figure tries to replicate the movement of the probe across one line when the probe scans one line of the surface of the sample. The brown triangles indicate the probe while the blue shapes mark the area of contact. The measured topography and probe temperature are also represented on the right for the image (the shadowed area on the temperature image indicates the temperature increase when the probe approaches the edge of the SiOz step). the image as well as the measures temperature along the line on Figure 99 when f=3000 Hz. cantilever is 5 nN. We reported the temperature measured when the probe scanned one line «
Figure 98. This figure tries to replicate the movement of the probe across one line when the probe scans one line of the surface of the sample. The brown triangles indicate the probe while the blue shapes mark the area of contact. The measured topography and probe temperature are also represented on the right for the image (the shadowed area on the temperature image indicates the temperature increase when the probe approaches the edge of the SiOz step). the image as well as the measures temperature along the line on Figure 99 when f=3000 Hz. cantilever is 5 nN. We reported the temperature measured when the probe scanned one line «
Table 14. Thermal properties of SiO2, GaAs and air used for the finite element simulation.
Table 14. Thermal properties of SiO2, GaAs and air used for the finite element simulation.
Figure 100. Geometry of the studied configuration represented on the left image. The mesh is represented at the right.
Figure 100. Geometry of the studied configuration represented on the left image. The mesh is represented at the right.
vs. the contact radius 7o, the thermal contact resistance R, and the probe thermal impedance Z,
vs. the contact radius 7o, the thermal contact resistance R, and the probe thermal impedance Z,
It must be also noted that, using the identified parameters we retrieved well the temperature
It must be also noted that, using the identified parameters we retrieved well the temperature
Table 15. The table above shows the thermal conductivity (k), density (p), specific heat (C,), Debye temperature (©), sound velocity (v), roughness (Ra), approximate mean free path (A) for Palladium, PMMA, SiO2, ZnO, Ti02, Al2O3, MgO and Si3N, respectively
Table 15. The table above shows the thermal conductivity (k), density (p), specific heat (C,), Debye temperature (©), sound velocity (v), roughness (Ra), approximate mean free path (A) for Palladium, PMMA, SiO2, ZnO, Ti02, Al2O3, MgO and Si3N, respectively
of the probe was not permitted any longer.
of the probe was not permitted any longer.
Figure 107 Measured magnitude of the temperature probe according to the frequency for the out of contact and the contact mode with the different materials.
Figure 107 Measured magnitude of the temperature probe according to the frequency for the out of contact and the contact mode with the different materials.
Figure 108. Normalized measured temperature, with respect to the maximum temperature at each frequency, according to the thermal conductivity at four frequencies (filled circles: measurements, plain line: theory from identified values of R, and ro). performing the experiment on SiO, under atmospheric conditions. that found under atmosphere. This was therefore not a very surprising result. On the other hand,
Figure 108. Normalized measured temperature, with respect to the maximum temperature at each frequency, according to the thermal conductivity at four frequencies (filled circles: measurements, plain line: theory from identified values of R, and ro). performing the experiment on SiO, under atmospheric conditions. that found under atmosphere. This was therefore not a very surprising result. On the other hand,
agreement with those achieved using the minimization process. However, it is clear that the error
agreement with those achieved using the minimization process. However, it is clear that the error
Table 16 Calculation of Ry, from the approximation of the Diffuse Mismatch Model at high temperature.
Table 16 Calculation of Ry, from the approximation of the Diffuse Mismatch Model at high temperature.
Table 17. Atomic density (1), density (p), specific heat (C,), Debye temperature (©), thermal conductivity (k) & phonon longitudinal (vz) and transverse (v7) velocity of bulk In3SbTe2
Table 17. Atomic density (1), density (p), specific heat (C,), Debye temperature (©), thermal conductivity (k) & phonon longitudinal (vz) and transverse (v7) velocity of bulk In3SbTe2
Figure 111 A: Heat transfer model for the out-of-contact operation mode (leading to the identification of Zp). Heat transfer model for the contact mode when B: the probe is in contact with the SiO2/Si substrate, C: the probe is in contact with the NW.
Figure 111 A: Heat transfer model for the out-of-contact operation mode (leading to the identification of Zp). Heat transfer model for the contact mode when B: the probe is in contact with the SiO2/Si substrate, C: the probe is in contact with the NW.
the amplitude and phase (obtained by the SThM san mode) at 523 Hz.
the amplitude and phase (obtained by the SThM san mode) at 523 Hz.
Figure 113 Cross-sectional area measurement of the Nanowire across the A line We therefore obtained the cross-section of the two nanowires as represented in Figure 113.
Figure 113 Cross-sectional area measurement of the Nanowire across the A line We therefore obtained the cross-section of the two nanowires as represented in Figure 113.
Figure 114. Blue square symbol: temperature and Phase in out-of-contact Measurement; red circle symbol: temperature and phase measurement for the probe in contact either with the Si0,/Si substrate (averaged over area A, Figure 112) or the nanowire (averaged over area B, Figure 112); the red line is the calculated temperature and phase identified from R, using the minimization procedure for the 13 nm thickness nanowire. mages and our analytical solution we have the results reported in Figure 114 and Figure 115 From the experimental results averaged over the areas A and B obtained from the experimental
Figure 114. Blue square symbol: temperature and Phase in out-of-contact Measurement; red circle symbol: temperature and phase measurement for the probe in contact either with the Si0,/Si substrate (averaged over area A, Figure 112) or the nanowire (averaged over area B, Figure 112); the red line is the calculated temperature and phase identified from R, using the minimization procedure for the 13 nm thickness nanowire. mages and our analytical solution we have the results reported in Figure 114 and Figure 115 From the experimental results averaged over the areas A and B obtained from the experimental
Table 18 Calculated thermal resistance R; from equation (6.1) (line 2) or the minimization procedure [fit] (line 3) in K.W"', calculated R; in K.m*.W"' using the contact area Anw=2 to Inw (line 4), calculated Rnw from linear regression (line 5) and value of Rnw from the thermal conductivity for bulk In3SbTe2 (see Table 17) (line 6).
Table 18 Calculated thermal resistance R; from equation (6.1) (line 2) or the minimization procedure [fit] (line 3) in K.W"', calculated R; in K.m*.W"' using the contact area Anw=2 to Inw (line 4), calculated Rnw from linear regression (line 5) and value of Rnw from the thermal conductivity for bulk In3SbTe2 (see Table 17) (line 6).
Figure 115. Blue square symbol: temperature and Phase in out-of-contact Measurement; red circle symbol: temperature and phase measurement for the probe in contact either with the SiO2/Si substrate (averaged over area A, Figure 112) or the nanowire (averaged over area B, Figure 112); the red line is the calculated temperature and phase identified from R, using the minimization procedure for the 23 nm thickness nanowire.
Figure 115. Blue square symbol: temperature and Phase in out-of-contact Measurement; red circle symbol: temperature and phase measurement for the probe in contact either with the SiO2/Si substrate (averaged over area A, Figure 112) or the nanowire (averaged over area B, Figure 112); the red line is the calculated temperature and phase identified from R, using the minimization procedure for the 23 nm thickness nanowire.
temperature obtained from previous analysis. The Table 19 lists all the necessary thermal properties of the different parts of the sample at room The Titanium (Ti) layer is thin enough to be considered as pure thermal resistance with the thermal boundary resistance (TBR) between the TiN and AlCu interface being around 5 x 10° Km?.W” obtained from literature. The TBR between the TiN layer and the GST (qa) layer 1: around 5.5 x 10° Km?.W” also obtained from previous studies. Hence, our scanning therma microscopic research will aim to understand the TBR between the vertical interface of GST anc
temperature obtained from previous analysis. The Table 19 lists all the necessary thermal properties of the different parts of the sample at room The Titanium (Ti) layer is thin enough to be considered as pure thermal resistance with the thermal boundary resistance (TBR) between the TiN and AlCu interface being around 5 x 10° Km?.W” obtained from literature. The TBR between the TiN layer and the GST (qa) layer 1: around 5.5 x 10° Km?.W” also obtained from previous studies. Hence, our scanning therma microscopic research will aim to understand the TBR between the vertical interface of GST anc
obtain the variation of amplitude and phase as seen in the figure below.
obtain the variation of amplitude and phase as seen in the figure below.
Table 20 Values of Known Parameters parameters have been reported in the Erreur ! Source du renvoi introuvable.
Table 20 Values of Known Parameters parameters have been reported in the Erreur ! Source du renvoi introuvable.
)bviously we found that the sensitivity on Z, is huge, meaning that making a small error on this parameter will lead to a very high deviation on the calculated temperature of the prot
)bviously we found that the sensitivity on Z, is huge, meaning that making a small error on this parameter will lead to a very high deviation on the calculated temperature of the prot
Figure 120. Fit between the experimental data (dots), when the probe follows the direction represented in the inset, and the simulated probe temperature (red line) using the identified values of the four parameters at the end of the minimization process. The simulated probe temperature is calculated from the thermal conductivity of the GST (green line) in order to demonstrate the sensitivity to this parameter for instance. simulated probe temperature on Figure 120.
Figure 120. Fit between the experimental data (dots), when the probe follows the direction represented in the inset, and the simulated probe temperature (red line) using the identified values of the four parameters at the end of the minimization process. The simulated probe temperature is calculated from the thermal conductivity of the GST (green line) in order to demonstrate the sensitivity to this parameter for instance. simulated probe temperature on Figure 120.
Table 21 Properties of the glass fiber present in the PyC composite sample resistance at the interfaces between the matrix and the fiber. The fiber is made of a single glass
Table 21 Properties of the glass fiber present in the PyC composite sample resistance at the interfaces between the matrix and the fiber. The fiber is made of a single glass
minimization is achieved using the Levenberg-Marquardt algorithm. The standard deviation fot
minimization is achieved using the Levenberg-Marquardt algorithm. The standard deviation fot
Figure 126. Measured temperature (left) and phase (right) against 2m. Plain lines are simulations using the identified Re when the probe is in contact with the silica fiber and the identified kerr of the PyC when the probe is in contact with the PyC. that only the amplitude can be used in order to identify the thermal conductivity of the PyC. and out-of-contact modes. The difference in the phase for each condition is very small, meaning
Figure 126. Measured temperature (left) and phase (right) against 2m. Plain lines are simulations using the identified Re when the probe is in contact with the silica fiber and the identified kerr of the PyC when the probe is in contact with the PyC. that only the amplitude can be used in order to identify the thermal conductivity of the PyC. and out-of-contact modes. The difference in the phase for each condition is very small, meaning
Figure 127. The 50x50 um? images obtained via experiments under atmospheric conditions using Scanning Thermal Microscopy at 1125 Hz showing the topography, amplitude and phase from left to right respectively. topography, amplitude and phase images are represented in Figure 127. To measure the thermal boundary resistance between the matrix and the fiber of the sample, we performed a SThM sweep of the specimen at 1125 Hz with a current of 750 yA under atmospheric condition. The experiments have been performed over an image edge size of 50 micrometers with 256 points of measurement per line at a speed of 0.25 lines per second. The 1 ae 41 41 i? . 7 a Se ——— ~ micrometers with 256 points of measurement per line at a speed of 0.25 lines per second. The
Figure 127. The 50x50 um? images obtained via experiments under atmospheric conditions using Scanning Thermal Microscopy at 1125 Hz showing the topography, amplitude and phase from left to right respectively. topography, amplitude and phase images are represented in Figure 127. To measure the thermal boundary resistance between the matrix and the fiber of the sample, we performed a SThM sweep of the specimen at 1125 Hz with a current of 750 yA under atmospheric condition. The experiments have been performed over an image edge size of 50 micrometers with 256 points of measurement per line at a speed of 0.25 lines per second. The 1 ae 41 41 i? . 7 a Se ——— ~ micrometers with 256 points of measurement per line at a speed of 0.25 lines per second. The
Table 22. Main achievements regarding the validation experiments. of the water meniscus All the main results have been reported in Table 22.
Table 22. Main achievements regarding the validation experiments. of the water meniscus All the main results have been reported in Table 22.
Related topics:
Thermal ResistanceThermal Boundary ResistanceThermal Characterization
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved