{"id":26342,"date":"2024-07-25T19:26:28","date_gmt":"2024-07-25T17:26:28","guid":{"rendered":"https:\/\/www.linseis.com\/methods-of-thermal-analysis\/3-omega-method\/"},"modified":"2024-12-11T14:07:01","modified_gmt":"2024-12-11T13:07:01","slug":"3-omega-method","status":"publish","type":"page","link":"https:\/\/www.linseis.com\/en\/methods\/3-omega-method\/","title":{"rendered":"3 Omega method"},"content":{"rendered":"\t\t
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3\u03c9 Omega method<\/b><\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Linseis<\/span><\/a><\/span><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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3\u03c9 measurement technique – an approach to measuring thermal conductivity<\/h2>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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A widely implemented approach for measuring the thermal conductivity is the 3\u03c9 method. Although initially developed for measuring the thermal conductivity of bulk materials, the method was later extended to the thermal characterization of thin films<\/strong> down to few nm thick.<\/p>

Moreover, the 3\u03c9 technique was then adapted for measurement of the in-plane and cross-plane thermal conductivity of anisotropic films and freestanding membranes. This technique is currently one of the most popular methods for thin-film thermal conductivity characterization<\/strong><\/a>.<\/p>

\u00a0<\/p>

\"Experimenteller Experimental setup (incl. metal line for heating\/sensing) for the 3 Omega technique<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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In the 3\u03c9 method a thin metallic strip, which is in thermal contact with the sample, acts as both a heater and a temperature sensor. For the measurement an AC current,
\"ac<\/p>

with angular modulation frequency \u00a0and amplitude \u00a0passing through the strip, generates a heating source with power<\/p>

\"heating<\/p>

where Rh<\/sub>\u00a0is the resistance of the strip under the experimental conditions, and causes a rise in temperature in the form of<\/p>

\"temperature<\/p>

and consequentially an oscillation in the resistance of the stripe<\/p>

\"Rh\"<\/p>

at the angular frequency 2\u03c9, \u00a0with \u00a0is the temperature coefficient of resistance of the metal strip.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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With regard to the frequency, the phase shift depends on both, the geometry of the heater and the underlying materials.<\/p>\n

By measuring the voltage drop across the heater, according to Ohm\u2019s law, one gets an amplitude modulated signal which has a small component at the third harmonic 3\u03c9, which can be extracted with a lock-in amplifier.<\/p>\n

For the calculation of the sample\u2019s thermal conductivity<\/strong> as well as specific heat capacity<\/strong>, the corresponding heat diffusion equation needs to be solved, which depends on the experimental setup.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Differential 3 Omega approach with two measurements<\/h2>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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A typical cross-plane thermal conductivity approach with a thin film on a bulk substrate is the differential approach with two measurements:<\/p>\n

The first one on the blank substrate only, and the second one includes the layer of interest.<\/p>\n

The layer acts as a thermal resistor connected in series between the heater and the substrate and ensures an increase in the temperature oscillations, in comparison to the measurement without the thin film.<\/p>\n

From this increase, the thermal conductivity of the can be determined using Fourier\u2019s law:<\/p>\n

\"Fouriers<\/p>\n

with w and l are the with and length of the heater.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Differential 3 Omega approach for cross plane thin film thermal conductivity measurements<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Thermal conductivity in the plane using 3w measurement technology<\/h2>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Another experimental setup to determine the in-plane thermal conductivity as well as specific heat capacity, is a heater aligned to the middle of a membrane or suspended substrate, respectively. In this case, the thermal behavior of the suspended part can be evaluated using the following correlation:<\/p>\n

\"correlation-thermal-behaviour-three-omega\"<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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With G=2\u03bbdlb^(-1), is the thermal time constant, b the width and l the length of the membrane and D is the thermal diffusivity.<\/p>\n

\"Integrierter Integrated measurement Chip for in-plane thermal conductivity measurements on thin films using the 3 Omega method<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Which properties will be determined?<\/h2>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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The 3\u03c9 measurement technique is an electrothermal measurement technique for determining the thermal conductivity<\/strong><\/a>, thermal diffusivity<\/strong><\/a> and specific heat capacity<\/strong><\/a> of bulk material (i.e. solid or liquid) and thin layers using an alternating current driven metal strip as heater.<\/p>

The metal heater applied to the sample is heated periodically. The temperature oscillations thus produced are then measured. The thermal conductivity and thermal diffusivity of the sample can be determined from their frequency dependence.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

3\u03c9 Omega method 3\u03c9 measurement technique – an approach to measuring thermal conductivity A widely implemented approach for measuring the thermal conductivity is the 3\u03c9 method. Although initially developed for measuring the thermal conductivity of bulk materials, the method was later extended to the thermal characterization of thin films down to few nm thick. Moreover, […]<\/p>\n","protected":false},"author":5,"featured_media":0,"parent":26322,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-26342","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/pages\/26342","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/comments?post=26342"}],"version-history":[{"count":0,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/pages\/26342\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/pages\/26322"}],"wp:attachment":[{"href":"https:\/\/www.linseis.com\/en\/wp-json\/wp\/v2\/media?parent=26342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}