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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" dtd-version="3.0">
  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">JSSS</journal-id>
<journal-title-group>
<journal-title>Journal of Sensors and Sensor Systems</journal-title>
<abbrev-journal-title abbrev-type="publisher">JSSS</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">J. Sens. Sens. Syst.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2194-878X</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/jsss-4-313-2015</article-id><title-group><article-title>Efficient thermal infrared emitter with high radiant power</article-title>
      </title-group><?xmltex \runningtitle{Efficient thermal infrared emitter with high radiant power}?><?xmltex \runningauthor{T.~Ott et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Ott</surname><given-names>T.</given-names></name>
          <email>tobias.ott@tu-dresden.de</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Schossig</surname><given-names>M.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Norkus</surname><given-names>V.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Gerlach</surname><given-names>G.</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>Institute for Solid-State Electronics, Technische Universität Dresden,  01062 Dresden, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">T. Ott (tobias.ott@tu-dresden.de)</corresp></author-notes><pub-date><day>13</day><month>November</month><year>2015</year></pub-date>
      
      <volume>4</volume>
      <issue>2</issue>
      <fpage>313</fpage><lpage>319</lpage>
      <history>
        <date date-type="received"><day>17</day><month>September</month><year>2015</year></date>
           <date date-type="accepted"><day>12</day><month>October</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015.html">This article is available from https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015.html</self-uri>
<self-uri xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015.pdf">The full text article is available as a PDF file from https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015.pdf</self-uri>


      <abstract>
    <p>Sensitive and selective gas measurements are crucial for a large variety of
applications, e.g., explosion protection. Optical gas detection is usually
based on the gas' absorption of infrared radiation (IR). It is the leading
technique in terms of accuracy, reliability, and economic efficiency. Since
most gas measurements are made in the two wavelength ranges of
<inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">…</mml:mi><mml:mn> 5</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">…</mml:mi><mml:mn> 14</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m, a broadband IR
source is necessary. In this paper, we report on a novel thermal IR emitter
with high radiant power and a near-blackbody emission characteristic that can
be modulated electrically. The layout of the IR source had been optimized by
use of finite element analyses (FEA)  in order to get an adequate electrical resistance as well
as a homogeneous temperature distribution and a minimum deflection of the
radiating element. Due to its excellent thermal isolation from the heat sink,
the electrical power consumption is very low. Operating temperatures of up to
1400 K are possible, so that the fabricated IR source features a very high
radiant power. Its application in gas analysis will improve the performance
and efficiency of gas measurement systems.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Explosion hazards mostly arise from flammable gases and vapors.
Instead of avoiding their ignition by explosion protection measurements, it
may be preferable to detect them before they become ignitable. Depending on
the application, different measuring principles for the detection of gases
and vapors can be used, e.g., electrochemical sensors <xref ref-type="bibr" rid="bib1.bibx3" id="paren.1"/>,
semiconductor sensors <xref ref-type="bibr" rid="bib1.bibx4" id="paren.2"/>, and point or open-path infrared gas
detectors <xref ref-type="bibr" rid="bib1.bibx5" id="paren.3"/>. Optical gas detection by use of infrared radiation
(IR) is the leading technique in terms of accuracy, reliability, and economic
efficiency. Since most gas measurements are made in the two wavelength ranges
of <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">…</mml:mi><mml:mn> 5</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">…</mml:mi><mml:mn> 14</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m, a
broadband IR source with a near-blackbody emission characteristic is
necessary. For reliable measurements, the generation of a stable spectrum of
infrared radiation is crucial. Very low detection limits can be realized by a
long optical path, where more gas molecules are involved in the IR
absorption, but this requires a very powerful IR source. According to
Planck's law of thermal radiation, the spectrum of a thermal emitter with a
blackbody characteristic depends only on its temperature <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx6" id="paren.4"/>. The totally emitted radiant power <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given
by the Stefan–Boltzmann law<?xmltex \hack{\newpage}?><?xmltex \hack{\noindent}?>
          <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow></mml:math></disp-formula>
        with emissivity <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>, Stefan–Boltzmann constant <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>, and the
radiating area <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Consequently, a high radiation power is
mainly realized by a high operating temperature of the thermal emitter, but
also by a high and wavelength-independent emissivity of infrared radiation.
Especially portable gas sensing devices require a low energy consumption of
the IR source. For this reason, the radiating element has to be optimized
regarding an excellent thermal isolation.</p>
</sec>
<sec id="Ch1.S2">
  <title>Design and technology</title>
      <p>In <xref ref-type="bibr" rid="bib1.bibx9" id="text.5"/> and <xref ref-type="bibr" rid="bib1.bibx8" id="text.6"/>, we reported on a novel IR
absorber based on a nanostructured NiCr alloy that features a very high and
spectrally homogeneous absorptivity. From Kirchhoff's law <xref ref-type="bibr" rid="bib1.bibx6" id="paren.7"/>,
          <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mi mathvariant="italic">ε</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        it is known that for the maintenance of thermal equilibrium, the absorptivity
<inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> at wavelength <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula> and temperature <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> must be equal to the
emissivity <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula>. Therefore, good absorbers are also good emitters.
Since NiCr is one of the most used materials in heating elements, for
instance in toasters and hairdryers, we studied the application of the
nanostructured NiCr absorber (Fig. <xref ref-type="fig" rid="Ch1.F1"/>) in thermal infrared
emitters to increase their emittance. By depositing the nanostructured NiCr
layer on a thin NiCr foil, the high-temperature stability of the
nanostructures could be verified with a first prototype of a thermal IR
emitter in a TO-39 package (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). Thereby, operation
in air causes an oxidation of the surface. The speed of oxidation and the
thickness of the oxide are increased with increasing temperature. As a
consequence, the spectral emissivity of the nanostructured surface is
affected. In contrast, an operation in an inert gas atmosphere does not
change its optical properties even at very high temperatures. The layout of
the first prototype had some disadvantages. First, it had a very low
electrical resistance of about 1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>, which is not practicable to
use. In addition, the temperature distribution was not homogeneous, as can be
seen from Fig. <xref ref-type="fig" rid="Ch1.F2"/>. Finally, it had a relatively high
power consumption of about 5 W due to the poor thermal isolation of the
radiating element.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>SEM (scanning electron microscopy) picture of a nanostructured NiCr
absorber.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f01.jpg"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p>First prototype of a thermal infrared emitter with a nanostructured
high-emissivity layer operating at about 1170 K.</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f02.jpg"/>

      </fig>

</sec>
<sec id="Ch1.S3">
  <title>Layout of an ideal heating conductor</title>
      <p>As already mentioned, an ideal thermal emitter should feature a high
electrical resistance and a low heat capacity (also referred to as thermal
mass) in order to be modulated electrically. Furthermore, most of the
electrical input power should be transformed into radiant power. This can be
achieved by a good thermal isolation, a high emissivity near
100 % and a high average temperature of the emitting
area. The emissivity and the average temperature, however, do not have any
effect on the shape of the heating conductor. So the focus is on improving
thermal isolation and electrical resistance. A simplified current-carrying
heating conductor is shown in Fig. <xref ref-type="fig" rid="Ch1.F3"/>. In
order to improve its geometric shape, the theoretical dependencies need to be
considered.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Physical dimensions and boundary conditions of a simplified heating
conductor. </p></caption>
        <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f03.pdf"/>

      </fig>

      <p>The electrical resistance <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> of a rectangular conductor is
          <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϱ</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>l</mml:mi><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>Q</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϱ</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>l</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>d</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϱ</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the specific electrical resistance of the
conductor material and <inline-formula><mml:math display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula> is the conductor length. The cross section <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>Q</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
is the product of conductor thickness <inline-formula><mml:math display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> and its width <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>. As given by
Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>), the radiant power is proportional to the
emitting area <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>; thus,
          <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>b</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>l</mml:mi></mml:mrow></mml:math></disp-formula>
        should be maximized. The conductor material is NiCr. To achieve a high
resistance and maximize the emitting area corresponding to Eqs. (<xref ref-type="disp-formula" rid="Ch1.E3"/>)
and (<xref ref-type="disp-formula" rid="Ch1.E4"/>), the conductor layout can be optimized as follows.
<list list-type="order"><list-item><p>Choose conductor length <inline-formula><mml:math display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula> as large as possible.</p></list-item><list-item><p>Minimize cross section <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>Q</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by reducing conductor thickness <inline-formula><mml:math display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula>, because a smaller conductor width <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> cuts down on the emitting area.</p></list-item></list><?xmltex \hack{\newpage}?><?xmltex \hack{\noindent}?>Further requirements for thermal emitters are a high modulation depth
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">m</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (see Sect. <xref ref-type="sec" rid="Ch1.S5"/> for further explanation)
and low thermal losses, which can be described with thermal conductance. The
thermal conductance <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is proportional to the conductor's cross
section <xref ref-type="bibr" rid="bib1.bibx2" id="paren.8"><named-content content-type="post">p. 6</named-content></xref>:
          <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="italic">λ</mml:mi></mml:msub><mml:mo>∝</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>Q</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        The modulation depth is defined here by the ratio of the achievable
temperature difference under electrical modulation with frequency <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
vs. the maximum temperature difference without modulation at approximately
direct current
          <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">m</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        Due to its thermal inertia, the heating conductor requires a certain amount
of time to reach the equilibrium temperature after it is turned on. If the
modulation frequency is too high, the emitter is not able to reach its
equilibrium temperature any more. Thus, the temperature difference <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and therefore modulation depth <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">m</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> decrease.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p>Input power and dissipated heat fluxes of the emitter in  the TO-39 housing. For simplification, convection is
neglected.
</p></caption>
        <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f04.pdf"/>

      </fig>

      <p>The thermal model by <xref ref-type="bibr" rid="bib1.bibx10" id="text.9"/> is used to understand the dynamic
heating and cooling of the emitter under cyclic excitation. The model
describes these thermodynamic processes analytically.
Figure <xref ref-type="fig" rid="Ch1.F4"/> shows the heating conductor in
the TO-39 housing. The input power <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is transformed completely
into Joule heat. This heat is dissipated into the environment through
<list list-type="bullet"><list-item><p>radiation <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,</p></list-item><list-item><p>solid-state heat conduction within the heating conductor (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Solid</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>)
and the header pins (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Pin</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), as well as</p></list-item><list-item><p>heat conduction (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">Gas</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> through the filling gas.</p></list-item></list>
These dissipated heat fluxes will be collectively referred to as
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">diss</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> subsequently. To describe the thermodynamic behavior of the
arrangement, the heat capacity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> needs to be considered additionally.
For the system, the first law of thermodynamics <xref ref-type="bibr" rid="bib1.bibx2" id="normal.10"><named-content content-type="post">p. 108</named-content></xref> applies:
          <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">diss</mml:mi></mml:msub><mml:mtext>.</mml:mtext></mml:mrow></mml:math></disp-formula>
        The change in the internal energy <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>U</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula> can be
described with the heat capacity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as follows <xref ref-type="bibr" rid="bib1.bibx2" id="normal.11"><named-content content-type="post">p.
109</named-content></xref>:
          <disp-formula id="Ch1.E8" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mtext>,</mml:mtext></mml:mrow></mml:math></disp-formula>
        where
          <disp-formula id="Ch1.E9" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi>U</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        By inserting Eq. <xref ref-type="disp-formula" rid="Ch1.E8"/> into Eq. <xref ref-type="disp-formula" rid="Ch1.E7"/>,
the rewritten balance equation results:
          <disp-formula id="Ch1.E10" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mover accent="true"><mml:mi>Q</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">diss</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mtext>.</mml:mtext></mml:mrow></mml:math></disp-formula></p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p>Temperature distribution of <bold>(a)</bold> meander-shaped and
<bold>(b)</bold> spiral-shaped emitters.
</p></caption>
        <?xmltex \igopts{width=412.564961pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f05.jpg"/>

      </fig>

      <p>If the dissipated heat flux and the input power are not modified, the heating
and cooling speed is faster the lower the heat capacity of the conductor is.
In consequence, the reduction of the heat capacity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increases
the modulation depth:
          <disp-formula id="Ch1.E11" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub><mml:mo>↓</mml:mo><mml:mo>⇒</mml:mo><mml:msub><mml:mi mathvariant="normal">m</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>↑</mml:mo><mml:mtext>.</mml:mtext></mml:mrow></mml:math></disp-formula>
        The conductor's heat capacity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given by
          <disp-formula id="Ch1.E12" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">th</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>l</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>b</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>d</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>c</mml:mi><mml:mi>v</mml:mi></mml:msub><mml:mtext>,</mml:mtext></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>c</mml:mi><mml:mi>v</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the volume-specific heat capacity.</p>
      <p>Considering the given objective on modulation depth and thermal losses, the
following conclusions result.
<list list-type="bullet"><list-item><p>To ensure a low thermal conductance for a given conductor's width  <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>, the element thickness <inline-formula><mml:math display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> should be as small as possible.</p></list-item><list-item><p>A small element thickness beneficially leads to a low thermal mass.</p></list-item></list>
In conclusion, a low element thickness yields to high electrical resistance,
high modulation depth and low thermal losses. The emitting area is maximized
by increasing the conductor's length and width. Regarding the layout, an
ideal heating conductor is as thin, as long and as wide as possible. In
consequence we choose a thin and long spiral to come as close as possible to
an ideal conductor shape.</p>
</sec>
<sec id="Ch1.S4">
  <title>Finite element analysis of heating conductors</title>
      <p>To evaluate the quality of a thermal emitter, further criteria must be
analyzed. Thermal emitters are optical devices, so the heating conductor
needs to stay in focus while under thermal load, meaning a low deflection is
required. Furthermore, the mean element temperature directly affects the
emitted radiant power. So temperature should be evenly distributed, leading
to a high mean temperature. To assess these characteristics, finite element
analyses (FEA) have been carried out. The goal is to compare meander-shaped
(Fig. <xref ref-type="fig" rid="Ch1.F5"/>a) and spiral-shaped conductors
(Fig. <xref ref-type="fig" rid="Ch1.F5"/>b) with respect to electrical resistance,
temperature distribution and out-of-plane deflection (called displacement in
FEA).</p>
      <p>The boundary conditions for the FEA are the following.
<list list-type="bullet"><list-item><p>Thermal: heat sink with <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>U</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at the pins of the TO39
header;</p></list-item><list-item><p>electrical: voltage <inline-formula><mml:math display="inline"><mml:mi>U</mml:mi></mml:math></inline-formula> at the pins;</p></list-item><list-item><p>optical: emissivity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">top</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.9</mml:mn></mml:mrow></mml:math></inline-formula> of the top
surface (with  NiCr nanostructures) and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">bottom</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></inline-formula> of the bottom surface (blank
metal); and</p></list-item><list-item><p>mechanical: fixed support at TO39 pins.</p></list-item></list>
NiCr is used as material. As already mentioned, it can be assumed that all of
the electrical input power is transformed into Joule heat.</p>
      <p>Table <xref ref-type="table" rid="Ch1.T1"/> shows the results of the analyses. The
temperature distribution of the meander-shaped emitter
(Fig. <xref ref-type="fig" rid="Ch1.F5"/>a) reproduces the visual appearance shown
in Fig. <xref ref-type="fig" rid="Ch1.F2"/>, where hotter areas are brighter. Compared to
the meander shape, the spiral-shaped element has far more electrical
resistance as well as a uniform temperature distribution
(Fig. <xref ref-type="fig" rid="Ch1.F5"/>b). This leads to a higher mean
temperature of the spiral, although the maximum element temperatures of both
layouts are equal. Due to the higher mean temperature, the spiral-shaped
conductor is twice as efficient as the meander-shaped conductor regarding
emitted radiant power. The fixed support of the conductor ends forces the
elements to buckle under thermal load. Fig. <xref ref-type="fig" rid="Ch1.F6"/>
shows the meander displacement as a result of buckling. After a longer period
in operation, we discovered malfunction of the emitter caused by buckling
(Fig. <xref ref-type="fig" rid="Ch1.F7"/>), which is not tolerable. The magnitude
of the spiral displacement is much lower (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>u</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn>0.3</mml:mn></mml:mrow></mml:math></inline-formula> mm), and
tolerable.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Comparison of meander-shaped and spiral-shaped heating conductors
(results of FEA).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Meander</oasis:entry>  
         <oasis:entry colname="col3">Spiral</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Resistance <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">1<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">30<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Emitting area <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">ca. 16 mm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">2.8 mm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Maximum temparature <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of emitting area</oasis:entry>  
         <oasis:entry colname="col2">750 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>  
         <oasis:entry colname="col3">750 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Mean temperature <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">630 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>  
         <oasis:entry colname="col3">720 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Electrical input power <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">3 W</oasis:entry>  
         <oasis:entry colname="col3">0.4 W (see Fig. <xref ref-type="fig" rid="Ch1.F11"/>)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Radiant power <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">724 mW</oasis:entry>  
         <oasis:entry colname="col3">185 mW</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Efficiency <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">el</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">24 %</oasis:entry>  
         <oasis:entry colname="col3">46 %</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Displacement <inline-formula><mml:math display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> at <inline-formula><mml:math display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">&gt; 1 mm (malfunction)</oasis:entry>  
         <oasis:entry colname="col3">&lt; 0.3 mm</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Calculated with volume-weighted element temperatures.<?xmltex \hack{\\}?><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> Calculated with <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">top</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">bottom</mml:mi></mml:msub></mml:mfenced><mml:mi mathvariant="italic">σ</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">emit</mml:mi></mml:msub><mml:msup><mml:mi>T</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>
where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">top</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.9</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ε</mml:mi><mml:mi mathvariant="normal">bottom</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn></mml:mrow></mml:math></inline-formula>.</p></table-wrap-foot></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><caption><p>Displacement (deflection) of the meander in <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">mm</mml:mi></mml:math></inline-formula>.
</p></caption>
        <?xmltex \igopts{width=193.47874pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f06.jpg"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><caption><p>Malfunction of the meander-shaped emitter caused by buckling.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f07.png"/>

      </fig>

<?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S5">
  <title>Experimental results</title>
      <p>New prototypes were fabricated that have the spiral shape. By reducing the
thickness of the radiating element to about 10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m, a direct
electrical modulation of the emitted radiation becomes possible. This is an
important feature for its application in gas sensing devices because the most
commonly used pyroelectric IR detectors are only sensitive to AC signals.
Accordingly, it eliminates the use of a mechanical chopper for radiation
modulation and, therefore, enables miniaturization and allows for more
compact gas sensing devices. The spiral radiating elements were fabricated by
ion beam etching of a thin NiCr foil and have a radiating area of about
2.8 mm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>. Both sides are coated with a 2 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>m thick nanostructured
layer of high emissivity (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). The
radiating elements are hermetically sealed into common TO-39 housings with a
krypton atmosphere (Fig. <xref ref-type="fig" rid="Ch1.F9"/>). In order to use the
backside-emitted radiation, a reflector is integrated into the TO-39 housing.
In this way, a 70 % higher signal was achieved.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><caption><p>Measured spectral emissivity of the novel thermal  infrared emitters with spiral
filament.
</p></caption>
        <?xmltex \igopts{width=156.490157pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f08.pdf"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><caption><p>Prototype of a thermal infrared emitter with the near-blackbody
emission characteristic in TO-39 housing.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f09.jpg"/>

      </fig>

      <p>The electrical and optical properties of the new prototypes were studied. We
found an adequate electrical cold resistance of about <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>31</mml:mn><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow></mml:math></inline-formula> and a slightly higher hot resistance of about <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>33</mml:mn><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F10"/>). Accordingly, the
emitters can be operated at 3.3 V, a common voltage used in portable
devices. In this case, the mean electrical power consumption is <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>330</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">mW</mml:mi><mml:mo>±</mml:mo><mml:mn>20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">mW</mml:mi></mml:mrow></mml:math></inline-formula>, with an operating temperature
of 970 K (Fig. <xref ref-type="fig" rid="Ch1.F11"/>). For temperature
measurement the spectral radiance has been measured with a monochromator as
can be seen in Fig. <xref ref-type="fig" rid="Ch1.F13"/>. Then the maximum of the
spectral radiance has been determined and converted into a temperature with
Wien's displacement law. The temperature error is estimated at <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>30 K.
Comparable thin-film emitters reach only a maximum temperature of about
800 K at the same electrical input power <xref ref-type="bibr" rid="bib1.bibx7" id="paren.12"><named-content content-type="post">p. 5</named-content></xref>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><caption><p>Measured current-voltage characteristic of the IR emitter from
Fig. <xref ref-type="fig" rid="Ch1.F9"/>.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f10.pdf"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><caption><p>Measured operating temperature in dependence on the electrical power for the IR emitter from
Fig. <xref ref-type="fig" rid="Ch1.F9"/>.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f11.pdf"/>

      </fig>

      <p>The thin and low-mass radiating element allows the IR source to be modulated
electrically. By applying a square-wave voltage, the emitter is switched on
and off. Because a non-contact and fast measurement of the temperature of the
electrically modulated source is not possible at the moment, the emitted
radiant flux <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Φ</mml:mi></mml:math></inline-formula> is measured with a broadband and fast IR detector.
Another advantage of this approach is the possibility to compare the emitter
with commercial IR sources, e.g., from <xref ref-type="bibr" rid="bib1.bibx7" id="normal.13"/> and
<xref ref-type="bibr" rid="bib1.bibx1" id="normal.14"/>. The frequency response measured with the radiant
flux is called normalized optical emission (NOE):
          <disp-formula id="Ch1.E13" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mtext>NOE</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="normal">Φ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mtext>.</mml:mtext></mml:mrow></mml:math></disp-formula>
        With increasing frequency, NOE decreases due to the thermal inertia of the
emitter. Consequently, the frequency response has a low-pass characteristic
(Fig. <xref ref-type="fig" rid="Ch1.F12"/>). The measurement results show a maximum
modulation frequency of about 3 Hz for 50 % NOE. This is sufficient for
most applications. However, the NOE and the modulation depth can be simply
increased by a further reduction of the thermal mass.</p>
      <p>Finally, the measurement results of the spectral radiance validate the
near-blackbody emission characteristic of this thermal infrared source
(Fig. <xref ref-type="fig" rid="Ch1.F13"/>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12"><caption><p>Measured frequency response of the emitter for a constant voltage square-wave
drive.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f12.pdf"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13"><caption><p>Comparison of the measured spectral radiance of the novel IR source
and a blackbody radiator of the same temperature.
</p></caption>
        <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://jsss.copernicus.org/articles/4/313/2015/jsss-4-313-2015-f13.pdf"/>

      </fig>

</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <title>Conclusion and outlook</title>
      <p>In this paper, we presented a novel
thermal IR emitter for application in optical gas detection. It features a
very high radiant power, near-blackbody emission characteristic and can be
modulated electrically. Due the excellent thermal isolation from the heat
sink, the electrical power consumption is very low. This enables an
application in portable gas sensing devices. Since the used NiCr alloy allows
a permanent operation at temperatures of up to 1400 K, the fabricated IR
source should feature a long-term stable performance and a long lifetime.
Finally, its application in gas analysis will improve the performance and
efficiency of gas measurement systems. Further improvements will target the
reduction of the thermal mass of the radiating element in order to increase
its modulation depth.</p>
</sec>

      
      </body>
    <back><ack><title>Acknowledgements</title><p>The authors would like to thank the German Research Foundation (DFG) for
supporting this work under grant number GE 779/32.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?> Edited by: W. A. Minkina<?xmltex \hack{\newline}?> Reviewed by: two
anonymous referees</p></ack><?xmltex \hack{\newpage}?><?xmltex \hack{\newpage}?><ref-list>
    <title>References</title>

      <ref id="bib1.bibx1"><label>Axetris AG()</label><mixed-citation>Axetris AG: Infrared Source EMIRS50, available at:
<uri>https://static.axetris.com/-/media/downloads/400 axag/infrared sources/fl - infrared source emirs50_en.pdf</uri>  (last
access: 31 August 2015), 2014.</mixed-citation></ref>
      <ref id="bib1.bibx2"><label>Baehr and Stephan(2011)</label><mixed-citation>Baehr, H. and Stephan, K.: Heat and Mass Transfer, Springer Berlin
Heidelberg, 737 pp.,
<ext-link xlink:href="http://dx.doi.org/10.1007/978-3-642-20021-2" ext-link-type="DOI">10.1007/978-3-642-20021-2</ext-link>, 2011.</mixed-citation></ref>
      <ref id="bib1.bibx3"><label>Bakker(2004)</label><mixed-citation>Bakker, E.: Electrochemical Sensors, Anal. Chem., 76, 3285–3298,
<ext-link xlink:href="http://dx.doi.org/10.1021/ac049580z" ext-link-type="DOI">10.1021/ac049580z</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx4"><label>Capone et al.(2004)Capone, Forleo, Francioso, Rella, Siciliano,
Spadavecchia, Presicce, and Taurino</label><mixed-citation>Capone, S., Forleo, A., Francioso, L., Rella, R., Siciliano, P.,
Spadavecchia,
J., Presicce, D. S., and Taurino, A. M.: Solid State Gas Sensors: State of
the Art and Future Activities, ChemInform, 35, 1335–1348,
<ext-link xlink:href="http://dx.doi.org/10.1002/chin.200429283" ext-link-type="DOI">10.1002/chin.200429283</ext-link>, 2004.</mixed-citation></ref>
      <ref id="bib1.bibx5"><label>Goode et al.(1999)Goode, Yokelson, Susott, and Ward</label><mixed-citation>Goode, J. G., Yokelson, R. J., Susott, R. A., and Ward, D. E.: Trace gas
emissions from laboratory biomass fires measured by open-path Fourier
transform infrared spectroscopy: Fires in grass and surface fuels, J.
Geophys. Res.-Atmos., 104, 21237–21245,
<ext-link xlink:href="http://dx.doi.org/10.1029/1999JD900360" ext-link-type="DOI">10.1029/1999JD900360</ext-link>, 1999.</mixed-citation></ref>
      <ref id="bib1.bibx6"><label>Howell et al.(2010)Howell, Siegel, and Menguc</label><mixed-citation>Howell, J. R., Siegel, R., and Menguc, M. P.: Thermal Radiation Heat
Transfer,
CRC press Taylor &amp; Francis, 5th edn., Boca Raton, p. 61, <ext-link xlink:href="http://dx.doi.org/10.1002/zamm.201290025" ext-link-type="DOI">10.1002/zamm.201290025</ext-link>,
2010.
</mixed-citation></ref><?xmltex \hack{\newpage}?>
      <ref id="bib1.bibx7"><label>Micro-Hybrid Electronic GmbH()</label><mixed-citation>Micro-Hybrid Electronic GmbH: INFRARED COMPONENTS &amp; SYSTEMS –
Micro-Hybrid
Product Catalog 2014/2015, available at:
<uri>http://finder.micro-hybrid.de/fileadmin/user/IR-systems-documents/Micro-Hybrid_IR_Katalog_s.pdf</uri>  (last access: 27 August
2015), 2014.</mixed-citation></ref>
      <ref id="bib1.bibx8"><label>Schossig(2012)</label><mixed-citation>Schossig, M.: Optical Absorption Layers for Infrared Radiation, in: Bio and
Nano Packaging Techniques for Electron Devices: Advances in Electronic Device
Packaging, edited by: Gerlach, G. and Wolter, K., chap. 18,   355–381,
Springer Berlin Heidelberg, <ext-link xlink:href="http://dx.doi.org/10.1007/978-3-642-28522-6" ext-link-type="DOI">10.1007/978-3-642-28522-6</ext-link>, 2012.</mixed-citation></ref>
      <ref id="bib1.bibx9"><label>Schossig et al.(2010)Schossig, Norkus, and Gerlach</label><mixed-citation>Schossig, M., Norkus, V., and Gerlach, G.: Infrared Responsivity of
Pyroelectric Detectors With Nanostructured NiCr Thin-Film Absorber, Sensors Journal, IEEE, 10, 1564–1565, <ext-link xlink:href="http://dx.doi.org/10.1109/JSEN.2010.2046162" ext-link-type="DOI">10.1109/JSEN.2010.2046162</ext-link>, 2010.</mixed-citation></ref>
      <ref id="bib1.bibx10"><label>Schulz et al.(2005)Schulz, Müller, Lloyd, and
Ferber</label><mixed-citation>Schulz, O., Müller, G., Lloyd, M., and Ferber, A.: Impact of
environmental
parameters on the emission intensity of micromachined infrared sources,
Sensor. Actuat. A-Phys., 121, 172–180,
<ext-link xlink:href="http://dx.doi.org/10.1016/j.sna.2004.12.010" ext-link-type="DOI">10.1016/j.sna.2004.12.010</ext-link>, 2005.</mixed-citation></ref>

  </ref-list><app-group content-type="float"><app><title/>

    </app></app-group></back>
    </article>
