US 2006/0222043 A1Published application

Apparatus and method for measuring thermal conductivity

OwnerDavid Cahillinventor

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Abstract

An apparatus and method for measuring and mapping thermal conductivity and thermal diffusivity at micrometer scale resolution. The apparatus and method utilize a mode-locked femtosecond pulsed laser in a pump-probe configuration to analyze time-domain thermoreflectance of a specimen to evaluate its thermal conductivity in micro-scale, so that, if desired, an image of thermal conductivity distribution of micro-scale regions may be obtained therefrom. A multi-layer, complete three-dimensional model that takes into account the entire three-dimensional heat flow in cylindrical coordinates enables micro-scale measurements to be made at an accuracy of about 90% of well-accepted values.

Claims6

Dependent claims

A method for measuring the thermal conductivity on micrometer length scales, the method comprising:

depositing a transducer film onto a specimen, the said transducer film is preferably pure aluminum, and the said transducer film has preferably a thickness about 50 to 200 nanometers;
providing a mode-locked femtosecond pulsed laser, the said laser has a wavelength in the range of about 740 to about 840 nanometers, and the said laser has preferably a wavelength of about 770 nanometer;
providing a beam splitter, the said beam splitter separates the said pulsed laser beam into the pump beam and the probe beam;
providing a modulator to modulate the said pump beam to a frequency in the range of 10 kHz to 20 MHz, preferably to a frequency of about 10 MHz, and the said modulator is preferably an electro-optic modulator;
providing a variable delay mechanism for the said pump beam, the said variable delay may preferably be a retroreflector with a movable corner-cube mirror or prism, the said variable delay mechanism can produce a delay time (t) from −100 to 10000 picoseconds, preferably about −100 to 4000 picoseconds;
focusing the said pump beam onto a spot on the surface of the said transducer film on the said specimen, the said pump beam heats the near surface layer of the said transducer film, the temperature at the surface of the said transducer film decays as the heat is conducted through the transducer film to the specimen;
providing a modulator to modulate the frequency of the aforementioned probe beam to the range of 10 to 1000 Hz, preferably to a frequency of about 200 Hz, and the said modulator is preferably a mechanical beam chopper;
focusing the said probe beam on the same spot on the transducer film as the said pump beam, the said probe beam is reflected from the said transducer film and directed to a photodiode detector;
providing a rf lock-in amplifier to detect the signal from the modulation frequencies of the said pump beam, the said rf lock-in amplifier produces in-phase output voltage Vin(t) and out-of-phase voltage Vout(t) that are dependent on the delay time t;
The output signals of the rf lockin-amplifier appear at the modulation frequency F of the probe beam and are measured using two audio frequency lock-ins incorporated into the computer used for data acquisition.
providing a mathematical thermal model to calculate the heat conduction in the transducer film, the interface between the transducer film and the specimen, and the specimen, the said model takes into account the entire three-dimensional heat flow in cylindrical coordinates and takes into account a minimum of three layers (transducer film, interface, and specimen), and the said model relates the ratio of in-phase output and out-of-phase output, Vin(t)/Vout(t), to the delay time t and the thermal conductivity Λ;
performing experiments with varying delay time t and collecting Vin(t)/Vout(t) data, and fitting the thermal model equations with two free parameters:
thermal conductivity Λ and the interface conductance G between the transducer film and the unknown specimen under test, and obtaining both Λ and G, based on the data, plot a curve of Vin(t)/Vout(t) against thermal conductivity Λ.

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An apparatus for measuring the thermal conductivity in micrometer scale, the apparatus comprising:

a mode-locked pulsed laser, the said laser has a wavelength between about 740 and about 840 nanometer, the said laser preferably has a wavelength of 770 nanometer, and the said laser is preferably a Ti:sapphire laser with femtosecond pulses;
a beam splitter, the said beam splitter separates the said pulsed laser into two beams:
the pump/heat beam and the probe beam;
a modulator to modulate the said pump beam into a frequency in the range of 10 kHz to 20 MHz, preferably to a frequency of about 10 MHz, and the said modulator is preferably an electro-optic modulator;
a variable delay mechanism for the said pump beam, the said variable delay mechanism is preferably a retroreflector with a movable corner-cube mirror or prism, and the said variable delay mechanism can produce a delay time (t) varying from −100 to 10000 picoseconds, preferably about −100 to 4000 picoseconds;
an objective lens to focus the said pump beam onto a spot on the surface of the said transducer film on the said specimen;
a modulator to modulate the frequency of the probe beam to the range of 10 to 1000 Hz, preferably to a frequency of about 200 Hz, the said modulator is preferably a mechanical beam chopper, the said probe beam is focused on the same spot on the transducer thin films as the pump beam;
a rf lock-in amplifier to detect the signal from the modulation frequencies of the said pump beam, the said rf lock-in amplifier produces in-phase output voltage Vin(t) and out-of-phase voltage Vout(t) that are dependent on the delay time t;
The output signals of the rf lockin-amplifier appear at the modulation frequency F of the probe beam and are measured using two audio frequency lock-in amplifiers incorporated into the computer used for data acquisition.
a minimum of one computer, the said computer has an executive software that embodies the aforementioned thermal model that takes into account the entire three-dimensional heat flow in cylindrical coordinates and takes into account a minimum of three layers (the transducer film, the interface between the specimen and the transducer film, and the specimen), the said model relates the ratio of in-phase output and out-of-phase output, Vin(t)/Vout(t), to the delay time t and the thermal conductivity Λ.

7 more elements

Dependencies are inferred from the claim text.

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Abstract

A method for measuring the thermal conductivity on micrometer length scales, the method comprising:

depositing a transducer film onto a specimen, the said transducer film is preferably pure aluminum, and the said transducer film has preferably a thickness about 50 to 200 nanometers;
providing a mode-locked femtosecond pulsed laser, the said laser has a wavelength in the range of about 740 to about 840 nanometers, and the said laser has preferably a wavelength of about 770 nanometer;
providing a beam splitter, the said beam splitter separates the said pulsed laser beam into the pump beam and the probe beam;
providing a modulator to modulate the said pump beam to a frequency in the range of 10 kHz to 20 MHz, preferably to a frequency of about 10 MHz, and the said modulator is preferably an electro-optic modulator;
providing a variable delay mechanism for the said pump beam, the said variable delay may preferably be a retroreflector with a movable corner-cube mirror or prism, the said variable delay mechanism can produce a delay time (t) from −100 to 10000 picoseconds, preferably about −100 to 4000 picoseconds;
focusing the said pump beam onto a spot on the surface of the said transducer film on the said specimen, the said pump beam heats the near surface layer of the said transducer film, the temperature at the surface of the said transducer film decays as the heat is conducted through the transducer film to the specimen;
providing a modulator to modulate the frequency of the aforementioned probe beam to the range of 10 to 1000 Hz, preferably to a frequency of about 200 Hz, and the said modulator is preferably a mechanical beam chopper;
focusing the said probe beam on the same spot on the transducer film as the said pump beam, the said probe beam is reflected from the said transducer film and directed to a photodiode detector;
providing a rf lock-in amplifier to detect the signal from the modulation frequencies of the said pump beam, the said rf lock-in amplifier produces in-phase output voltage Vin(t) and out-of-phase voltage Vout(t) that are dependent on the delay time t;
The output signals of the rf lockin-amplifier appear at the modulation frequency F of the probe beam and are measured using two audio frequency lock-ins incorporated into the computer used for data acquisition.
providing a mathematical thermal model to calculate the heat conduction in the transducer film, the interface between the transducer film and the specimen, and the specimen, the said model takes into account the entire three-dimensional heat flow in cylindrical coordinates and takes into account a minimum of three layers (transducer film, interface, and specimen), and the said model relates the ratio of in-phase output and out-of-phase output, Vin(t)/Vout(t), to the delay time t and the thermal conductivity Λ;
performing experiments with varying delay time t and collecting Vin(t)/Vout(t) data, and fitting the thermal model equations with two free parameters:
thermal conductivity Λ and the interface conductance G between the transducer film and the unknown specimen under test, and obtaining both Λ and G, based on the data, plot a curve of Vin(t)/Vout(t) against thermal conductivity Λ.

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