Thanks also to Nick Doh, Peishi Cheng, Chengyun Hua, Zoila Jurado, and Andrew Robbins, who were wonderful officemates; and Junlong Kou for your helpful discussions. Thanks also to Alex Wertheim, Bert Mendoza, Guy DeRose, Carol Garland, Nathan Lee, and other staff at the Kavli Nanoscience Institute.
INTRODUCTION
- Radiation in the Far Field
- Radiation in the Near Field
- Graphene: Tunable Plasmonic Material
- Overview
But only recently in 2017 modulation of heat flux in the near field has been experimentally demonstrated with VO2 [63]. In this thesis, we use the tunability of graphene plasmons by electrostatic bias to experimentally modulate the radiative heat flux in the near field.
SEMICONDUCTOR-DIELECTRIC SELECTIVE SOLAR ABSORBER
- Introduction
- Model Thin Film Optical Properties
- Optimization for Spectral Selectivity
- Fabrication of Device
- Characterization of Optical Properties
- Conclusion
Using the simulated absorption of the structure at all incidence angles, shown in Figure 2.3b, we calculate the average solar absorption to be 86.4% and the average thermal emittance to be 4.4%. We measured the spectral reflectance of the sample at room temperature using UV-Vis spectroscopy and Fourier-Transform Infrared Spectroscopy (FTIR), as shown in Figure 2.9a.
RADIATIVE HEAT FLUX MODULATION IN THE THERMAL NEAR FIELD
- Introduction
- Graphene Based Radiation Modulation
- NFHT: Graphene Membranes
- Proposed Experiment: Silica Optical Flat & Thermal Oxide on Silicon In this section, the theoretical results from the previous section are weighed againstIn this section, the theoretical results from the previous section are weighed against
- Conclusion
However, further optimization of the heat flux can be extended to cases where the Fermi levels of the upper and lower membranes are allowed to differ. We optimizeηas function of four Fermi levels (µ1on, µon2, µ1o f f, µo f f2) using a derived free search algorithm and the nonlinear optimization package NLopt [124, 125]. The corresponding optimal Fermi levels for the on and off states are shown in Figure 3.6b.
In Figure 3.12a, where the dielectric is 300 nm thick, in a vacuum space greater than 1µm, the shift ratio is close enough to that that the optimization fails and the Fermi levels are meaningless. The spectral thermal conductivity schemes are largely similar to those shown in the previous section, although in this case the Fermi levels are not necessarily optimized.
APPARATUS AND SAMPLE PREPARATION FOR HEAT TRANSFER MEASUREMENT
Introduction
Instrument Layout
The multi meter, muV meter, voltage source and switch box are all controlled by a custom computer interface. The three resistance and voltage signals are labeled Resistance 1, Resistance 2, and Voltage, but all three circuit paths go to the same HI and LO leads of the multimeter. To measure the applied heating power, both the current and voltage switches are opened as shown in Figure 4.4, where the arrows indicate the current path.
The heating power applied to a resistance heater is simply the product of current and voltage.
Heat Flux Sensor Calibration
In the first step, temperatures were kept within 100◦C of room temperature to determine the basic functionality of the sensor. In the second step, the temperatures were lowered to close to 90 K to determine the thermal leakage out of the heater. In the final step, after leakage paths were determined to be insignificant, the sensor was calibrated across all temperatures from room temperature to 90 K.
Prelimary Functionality
The results of the fit are shown in Figure 4.7 with a= 0.6 and T =294 K, indicating that the cryostat is emitting heat to the heat flux sensor. After the heat flux sensor signal is equilibrated, data is recorded within a defined interval (grey). Linear fits to the mean of each interval are used to determine the sensor calibration factor as shown in Figure 4.6.
The background heat flux is mainly radiative, with the cryostat radiating to the sensor. In the radiative model for the radiation shield heat flux experiments, the fit to the ambient temperature is nearly 307 K, which is over 10◦C higher than the recorded laboratory ambient temperature, which is about 294 K.
Determine Thermal Leakage out of the Heater Support
Because modeling all sources of thermal leakage is unreliable, in this section we introduce a simple thermal resistance model to determine the ratio between the heating power sent to the heat flux sensor and the heating power derived from it. By comparing the temperature decay rates of the heater at each step, we relate the ratio of heat lost to heat sent to the sensor. 4.3, the temperature of the heater is limited from below by the background temperature in the limit c → 0.
Since the measured heating temperature is lower than that of the background, the adjustment algorithm approaches the condition c = 0. Therefore, we find that the ratio between the thermal leakage resistance and the thermal resistance of the heat flux sensor is 164 ± 5 .
Characterization at Relevant Liquid Nitrogen Temperatures
Background Heat Flux
The heat that flows through the heater and into the sensor eventually also flows through the sample itself and should not be subtracted from the heat flow signal. The heat flowing directly into the sensor, however, does not flow through the sample and must be subtracted. The background heat flux flowing into the sensor at these temperatures is 20 Wm−2area normalized to the heat flux sensor.
The uncertainty is due to the signal drift of the heat flux sensor, previously mentioned in section 4.3. As the temperature of the heat flux sensor asymptotically approaches its equilibrium value, so does the signal from the heat flux sensor.
Sample Fabrication
The breakdown strength of SiO2 improves as temperature decreases, so all subsequent heat flux measurements where the graphene is biased are performed at low temperature, with the cryostat's cold finger held at 77 K and the heat flux sensor between 86 K and 91 K. The background heat flux flowing into the sensor at these temperatures is 20 Wm−2area, normalized for the heat flux sensor. Each data point in Figure 4.15 is collected after the sensor signal has been smoothed, but the signal is still found to drift by almost 5 µV. The heat flowing through the heater ultimately flows through the sample, meaning that the heat flow should not be subtracted from the final heat flow signal.
Shown in Figure 4.17, for all three wafers, the leakage current through the wafer is measured in time when a voltage is applied across the oxide. A cross-sectional profile of one of the rings, shown in Figure 4.21, indicates clear ridges that can extend over 3 µm high, while the beads are only 100 nm in diameter.
Conclusion
And subtracting fabrication techniques to create SiO2 pillars that require etching the oxide poses a potential risk to graphene and the underlying gate dielectric. As a result, the SiO2 pillars here are grown additively by standard electron beam lithography followed by electron beam deposition.
REALIZATION OF ELECTROSTATIC MODULATION OF HEAT TRANSFER
- Introduction
- Heat Flux Modulation in Time
- Heat Flux Modulation vs Temperature
- Conclusion
For each sample, we observe a reversible change in the measured heat flux as the bias goes up and down. A similar magnitude of change in heat flux is observed for the positive bias as the negative bias. From this data we calculate the heat flux versus the electrostatic bias, shown in Fig.
The temperatures of the heat flux sensor and heater are measured in the experiment. As the dielectric breaks down, current flows and Joule heating occurs, potentially contributing to the measured heat flux.
CONCLUSION AND OUTLOOK
Because the upper and lower substrates are suspended independently, subsequent fabrication of silica would not be necessary. Since the top and bottom substrates would also be driven independently, the graphene-graphene contact resistance could provide a benchmark to determine sample contact, ensuring zero parasitic. However, to use a silicon wafer as a substrate, a back electrode and a gate dielectric would have to be deposited.
Since the mobility of graphene decreases when transferred to a rough surface, it will be necessary to constantly care about the roughness of the surface. Additional attention should be paid to the design of the sample holder, as the spring resistive heater used in this task is likely to be too bulky for smaller, more fragile heterostructures.
TRANSFER MATRIX METHOD
TM Polarized Light - Single Interface
Apply the second equation in Eq.A.3 (Ampère's law) and take the curl of the B. Given the harmonic nature of the E field, the other side of Eq. Exxxxˆˆˆ+Ezzzzˆˆˆ)eikzz + Ex0xxxˆˆˆ+Ez0zzzˆˆˆ e−ikzz. The boundary conditions are that the component of the EEE field parallel to the incident surface is continuous at the surface, and the discontinuity in the parallel component of the BBB field is related to the surface current. Since the BBB field is completely parallel to the interface, the first term in the second half of Eq.
We now define the remaining fields in terms of reflection and transmission coefficients, also referred to as Fresnel coefficients. Because light is TM polarized, such reflection and transmission coefficients are best defined in terms of the magnetic field amplitude: H0(1)y = r Hy(1) and Hy(2) = tHy(1).
TE Polarized Light - Single Interface
In this system with a single interface, there can be no back-propagating field in medium 2 because there is no interface from which the field can reflect. Again, the B-field is harmonic in time, so the right-hand side of the Maxwell-Faraday law becomes The boundary conditions are the same for TE light as for TM light, but the components parallel and normal to the interface are different.
At a general interface at position z, the field amplitudes for TM light are related by Eq. To calculate the Fresnel coefficients, as before, we relate the field amplitudes in the substrate (medium 4) to the incident field amplitudes (in medium 1):. A.68) As a final result, the Fresnel coefficients in terms of matrix elements M[i, j] for TM and TE lights respectively are as follows:.
Harmonic Equations for General Uniaxial Anisotropic Media
Divided into vector components, xxxˆˆˆ :−. A.85) The determinant of the matrix must be zero, otherwise the fields are not zero. Because the matrix is upper triangular, the determinant is simply the product of the diagonal components.
DERIVATION OF ANALYTIC EXPRESSION FOR NEAR FIELD HEAT TRANSFER FOR PLANAR MEDIA
Due to symmetry of the indices, the other half of the Poynting vector is hEyH∗xi=n∗2ω3Θ(ω,T). All that remains is to add the Cartesian components k. Here it is advantageous to assume, without loss of generality, that the wave vector is in the plane parallel to the x-axis, such that ˆk|| = x. B.16). Therefore, the z-component of the Poynting vector evaluated at the interface of the second half-space is z =d.
To obtain the net heat flux, we must also subtract the power transmitted from half-space 2 back to half-space 1. This expression is also valid for multilayer media, where the Fresnel coefficients can be calculated using the transfer matrix method as described in Appendix A [89].
BIBLIOGRAPHY
Near-field radiative heat transfer between parallel Si-doped plates separated by a gap of up to 200 nm. Submicron parallel-plate gap formed by low-density micromachined pillars for near-field radiative heat transfer. Near-field thermal radiation between two closely spaced glass plates exceeding Planck's law of blackbody radiation.
Near-field radiative heat transfer between arrays of doped silicon nanowires. Applied Physics Letters February 2013. Frequency-selective near-field radiative heat transfer between photonic crystal wafers: A computational approach for arbitrary geometries and materials1 Sep20. .
![Figure 1.3: Adapted from Costra et al. [50]. (a) Graphene honeycomb crystal structure and (b) reciprocal lattice](https://thumb-ap.123doks.com/thumbv2/123dok/10416170.0/17.918.168.758.96.361/figure-adapted-costra-graphene-honeycomb-crystal-structure-reciprocal.webp)
![Figure 1.4: Adapted from Costra et al. [50]. Graphene band structure, calculated via a tightbinding method, and a zoomed-in image at one of the Dirac points, showing the linear dispersion](https://thumb-ap.123doks.com/thumbv2/123dok/10416170.0/18.918.194.741.147.442/figure-adapted-costra-graphene-structure-calculated-tightbinding-dispersion.webp)
