Thermal analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Ga</mml:mi> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:math> -based photonic membranes for optoelectronics

Semiconductor membranes are widely used in research fields that target medical, biological, environmental, and optical applications. Often such membranes derive their functionality from a nanopatterning, which challenges the determination of their optical, electronic, mechanical, and thermal properties. In this work, we demonstrate the noninvasive, all-optical thermal characterization of approximately-800-nm-thick and approximately-150- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mtext fontfamily="times">μ</a:mtext> <a:mi mathvariant="normal">m</a:mi> </a:math> -wide membranes that consist mainly of wurtzite <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi>Ga</e:mi> <e:mi mathvariant="normal">N</e:mi> </e:mrow> </e:math> and a stack of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>In</h:mi> <h:mrow> <h:mn>0.15</h:mn> </h:mrow> </h:msub> <h:msub> <h:mi>Ga</h:mi> <h:mrow> <h:mn>0.85</h:mn> </h:mrow> </h:msub> <h:mrow> <h:mi mathvariant="normal">N</h:mi> </h:mrow> </h:math> quantum wells as a built-in light source. Because of their application in photonics, e.g., for vertical-cavity surface-emitting lasers, such photonic membranes are bright light emitters, which challenges their thermal characterization by optical means. We combine top-view two-laser Raman thermometry (2LRT) with time-resolved photoluminescence spectroscopy to extract the in-plane thermal conductivity <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>κ</k:mi> <k:mtext>in~plane</k:mtext> </k:msub> </k:math> of these membranes, which represents a notable difference from previous studies on epitaxial <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mi>Ga</m:mi> <m:mi mathvariant="normal">N</m:mi> </m:mrow> </m:math> films. Thus, we can disentangle the entire laser-induced power balance. Thermal imaging by Raman spectroscopy yields <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>κ</p:mi> <p:mtext>in plane</p:mtext> </p:msub> <p:mo>=</p:mo> <p:msubsup> <p:mn>165</p:mn> <p:mrow> <p:mo>−</p:mo> <p:mn>14</p:mn> </p:mrow> <p:mrow> <p:mo>+</p:mo> <p:mn>16</p:mn> </p:mrow> </p:msubsup> <p:mspace width="0.2em"/> <p:mrow> <p:mi mathvariant="normal">W</p:mi> </p:mrow> <p:mspace width="0.1em"/> <p:msup> <p:mrow> <p:mi mathvariant="normal">m</p:mi> </p:mrow> <p:mrow> <p:mo>−</p:mo> <p:mn>1</p:mn> </p:mrow> </p:msup> <p:mspace width="0.1em"/> <p:msup> <p:mi mathvariant="normal">K</p:mi> <p:mrow> <p:mo>−</p:mo> <p:mn>1</p:mn> </p:mrow> </p:msup> </p:math> for the best membrane. This result compares well with <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>κ</x:mi> <x:mtext>in plane</x:mtext> </x:msub> <x:mo>=</x:mo> <x:mn>177</x:mn> <x:mspace width="0.2em"/> <x:mrow> <x:mi mathvariant="normal">W</x:mi> </x:mrow> <x:mspace width="0.1em"/> <x:msup> <x:mrow> <x:mi mathvariant="normal">m</x:mi> </x:mrow> <x:mrow> <x:mo>−</x:mo> <x:mn>1</x:mn> </x:mrow> </x:msup> <x:mspace width="0.1em"/> <x:msup> <x:mi mathvariant="normal">K</x:mi> <x:mrow> <x:mo>−</x:mo> <x:mn>1</x:mn> </x:mrow> </x:msup> </x:math> obtained by simulations based on a solution of the linearized phonon Boltzmann transport equation, including three- and four-phonon scattering, as well as phonon-isotope and phonon-boundary scattering. Furthermore, we study how <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>κ</fb:mi> <fb:mtext>in plane</fb:mtext> </fb:msub> </fb:math> is affected by a roughening of the membrane’s back side and additional semiconductor layers. For the membrane with the roughest back side, we observe a reduction of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>κ</hb:mi> <hb:mtext>in plane</hb:mtext> </hb:msub> </hb:math> by almost 40%, which is accompanied by an anisotropy of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:msub> <jb:mi>κ</jb:mi> <jb:mtext>in plane</jb:mtext> </jb:msub> </jb:math> due to etch channel formation. Thanks to the 2LRT approach, such variations and anisotropies of <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:msub> <lb:mi>κ</lb:mi> <lb:mtext>in plane</lb:mtext> </lb:msub> </lb:math> become accessible to the experimentalist via highly spatially resolved temperature maps.