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REVIEW PAPERS

Thermometry and Thermal Transport in Micro/Nanoscale Solid-State Devices and Structures

[+] Author and Article Information
David G. Cahill

Department of Materials Science and Engineering, and the Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, IL 61801

Kenneth Goodson

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

Arunava Majumdar

Department of Mechanical Engineering, University of California, Berkeley, CA 94720e-mail: majumdar@me.berkeley.edu

J. Heat Transfer 124(2), 223-241 (Dec 07, 2001) (19 pages) doi:10.1115/1.1454111 History: Received July 27, 2001; Revised December 07, 2001
Copyright © 2002 by ASME
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Figures

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Electron micrographs of (left) an array of vertical cavity surface emitting lasers (VCSEL) on a single wafer and (right) the cross of an individual VCSEL. Each laser contains multiple layers of III–V semiconductor materials which are approximately 60–100 nm in the Bragg mirrors of the laser or 1–10 nm in the active quantum well region.
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Electron micrographs of (left) an array of SiGe superlattice thermionic microcoolers on a single wafer and (right) the cross section of a single device showing the SiGe/Si superlattice structure. The superlattice period is approximately 10 nm.
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Schematic diagram of a scanning thermal microscope (SThM). It consists of a sharp temperature sensing tip mounted on a cantilever probe. The sample is scanned in the lateral directions while the canitilever deflections are monitored using a laser beam-deflection technique. Topographical and thermal images can be thermally obtained. The thermal transport at the tip-sample contacts consists of air, liquid and solid-solid conduction pathways. A simple thermal resistance network model of the sample and probe combination shows that when the sample is at temperature Ts, the tip temperature Tt depends on the values of the thermal resistances of the tip-sample contact, Rts, the tip, Rt, and the cantilever probe, Rc.
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Electron micrographs of a two-armed cantilever probe with a pyramid-shaped tip at the free end. The tip contains a Pt-Cr thermocouple junction at its apex which is approximately 500 nm in lateral size.
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Cantilever deflection and temperature response of the probe as a function of sample vertical position. The sample was a 350 nm wide electrically heated metal line. When the sample approaches the tip, the cantilever deflection remains unchanged till a jump to contact. During this time, the tip temperature rises very gradually due to air conduction. Corresponding to jump to contact the tip temperature suddenly rises due to liquid conduction. As the sample is pushed up the cantilever deflects linearly, while the tip temperature increases linearly due to increase in solid-solid contact area to a certain constant value. When the sample is retracted away, the solid-solid conductance decreases, but at a different rate, indicating some hysteresis due to plastic deformation of the tip or the sample. The tip remains in contact for a longer duration due to surface tension forces. When the tip snaps out of contact from the sample, there is a sudden drop in temperature due to loss of liquid film conduction.
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(left) Schematic diagram, (middle) topographical image, and (right) thermal image of the cross-section of a vertical cavity laser. The region imaged is approximately 6 μm on either side of the active quantum well region, which includes the p-doped and n-doped Bragg mirrors consisting of alternating layers of AlAs and AlGaAs. The thermal image was obtained after a current was applied and the device was lasing.
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Topographical and thermal images of electrically heated: (a) multiwall carbon nanotube (MWCN) about 10 nm in diameter with 22.4 μA flowing through it; (b) single wall carbon nanotube (SWCN) 1-2 nm in diameter with 15 μA (top) and 19.3 μA flowing through it. The temperature profile of the MWCN is parabolic in nature indicating a diffusive flow of electrons. At low bias, the SWCN is heated only at the contacts suggesting ballistic flow, while at higher bias the SWCN is heated in the bulk, most likely due to optical phonon emission. All measurements were made at room temperature.
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Picosecond thermoreflectance and acoustics apparatus at the University of Illinois using a single objective and an integrated dark-field microscope. The pump and probe beams are parallel at the back-focal-plane of the objective lens but offset by ≈ 4 mm. The aperture in front of the detector rejects the small fraction of pump beam that leaks through the polarizing beam splitter.
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Picosecond thermoreflectance data (solid circles) for thermal transport through an epitaxial TiN/MgO(001) structure at room temperature. The ratio of the in-phase to out-of-phase signals of the lock-in amplifier at f=9.8 MHz is plotted as function of the thermal diffusion length in TiN; the delay time t is given on the top axis. The TiN layer thickness is 100 nm. We assume that the thermal conductivity of the TiN film is given by the Wiedemann-Franz law, Λ=LT/ρ=58 W m−1 K−1; the thermal conductivity of MgO is 51 W m−1 K−1 . The solid and dashed lines are fits to the data using Eq. 3 with one free parameter, the interface thermal conductance G. The solid line is the best fit, G=0.42 GW m−2 K−1. The upper and lower dashed lines are for G=0.2 and G=1.0 GW m−2 K−1, respectively.
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The sketches indicate the impact of grain and molecular orientation on the anisotropy
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Electron micrograph of the suspended heater structure used for measuring thermal conductivity of nanowires. Also laid across the heater is a multiwall carbon nanotube bundle 150 nm in diameter. The Pt heater coil on one of the suspended islands is heated and its temperature is measured by resistance thermometry. The temperature of the other island increases due to conduction through the nanowire, which is also measured by resistance thermometry. The temperature difference for a known heat flow rate from the heated island can be used to estimate the thermal conductivity of the nanowire.
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Temperature dependence of thermal conductivity of a multiwall carbon nanotube. The dashed line corresponds to a T2 temperature dependence. The thermal conductivity is about 3000 W/m-K at room temperature, which includes the contact resistances at the two islands.
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Electron micrographs of novel electronic films and devices: (a) Diamond passivation film on aluminum. Diamond films are promising for enhanced heat removal from power integrated circuits and for fast thermal sensors. (b) Transmission electron micrograph of a VLSI metal-silicon contact, which has failed during a current pulse of sub-microsecond duration. The temperature rise is strongly influenced by the properties of the surrounding passive material.
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(a) Schematic of the setup for scanning laser-reflectance imaging of interconnects and semiconductor devices; (b) experimental data for the temperature distribution across the corner of an electrically heated metal intercorrect.
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(a) Relationship of the transmittance and spatial resolution of optical imaging technologies, showing the promise of the solid immersion lens for thermal imaging. The curve plots the sixth power dependence of transmittance on diameter for a circular aperature. (b) Scanning electron micrograph of the silicon lens and tip and the pyrex mount. (c) Transmission data collected by an InSb CCD array through a patterned two-bridge structure with and without the SIL.
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(a) Data for bulk silicon compared with data for silicon single-crystal films and polysilicon. (b) Predictions and data for single-crystal silicon films of thickness down to 74 nm at room temperature as a function of film thickness. (c) Contributions to the thermal resistivity, 1/k, as a function of temperature for a doped polysilicon layer.
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Comparison of selected data for interface thermal conductance: (i) individual interfaces measured by picosecond thermoreflectance 52, Al/Al2O3 (open diamonds) and Pb/c-C (filled triangles); (ii) conductance of the a-GeSbTe2.5/ZnS interface (open triangles) from a multilayer sample 129, (iii) series conductance of the top and bottom interfaces of metal-SiO2-silicon structures (MOS, filled circles) 99. The solid line is the calculated diffuse mismatch conductance of Al/Al2O3 using the Debye model; the dashed line is the theoretical prediction for Al/Al2O3 using a lattice-dynamical calculation of a model fcc interface 52. The right axis gives the thickness of a film with Λ=1 W m−1 K−1 that has the thermal conductance corresponding to the left axis.
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Selected data for the through-thickness thermal conductivity of superlattices with bilayer periods of ≈ 5 nm; data for GaAs-AlAs (open circles, 5.67 nm period 54) were measured by picosecond thermoreflectance; data for Si-Ge (open triangles, 5 nm period 142; filled circles, 4.4 nm period 104) and InAs-AlSb (open diamonds, 6.5 nm period 164) were measured using the 3ω method. Data for Si0.85Ge0.15142 and Ga0.4Al0.6As144 alloys are included for comparison.

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