Dielectric function and electronic structure of nondegenerate rocksalt ScN: Spectroscopic ellipsometry and GW calculations

In this work, we determine the dielectric function of ScN in a spectral range from 0.9 to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>6.4</a:mn> <a:mspace width="0.28em"/> <a:mi>eV</a:mi> </a:mrow> </a:math> by spectroscopic ellipsometry from nondegenerate doped, bulk-like samples. Several models are applied to the obtained dielectric functions yielding the main critical-point transition energies. These results are compared with state-of-the-art computations, where the band structure of ScN is calculated using Heyd-Scuseria-Ernzerhof (HSE06) hybrid functionals and quasiparticle corrections in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>G</c:mi> <c:mn>0</c:mn> </c:msub> <c:msub> <c:mi>W</c:mi> <c:mn>0</c:mn> </c:msub> </c:mrow> </c:math> approach. Furthermore, the dielectric function of ScN is derived from the computed band structure by solving the Bethe-Salpeter equation to account for electron-hole-pair interactions. We find exceptional agreement between computed and experimentally determined dielectric functions, where discrete excitons are not observed experimentally. We extrapolate an intrinsic direct band gap of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>(</d:mo> <d:mn>2.182</d:mn> <d:mo>±</d:mo> <d:mn>0.004</d:mn> <d:mo>)</d:mo> <d:mspace width="0.28em"/> <d:mi>eV</d:mi> </d:mrow> </d:math> and an intrinsic indirect band gap of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mo>(</f:mo> <f:mn>1.08</f:mn> <f:mo>±</f:mo> <f:mn>0.02</f:mn> <f:mspace width="0.28em"/> <f:mi>eV</f:mi> </f:mrow> </f:math> ) by taking into account many-body effects, while higher energy critical-point transition energies of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi mathvariant="normal">Γ</h:mi> </h:math> -point transitions are averaged over all samples, yielding <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:msub> <j:mi>E</j:mi> <j:mi mathvariant="normal">Γ</j:mi> </j:msub> <j:mo>=</j:mo> <j:mrow> <j:mo>(</j:mo> <j:mn>3.853</j:mn> <j:mo>±</j:mo> <j:mn>0.006</j:mn> <j:mo>)</j:mo> </j:mrow> <j:mspace width="0.28em"/> <j:mi>eV</j:mi> </j:mrow> </j:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>E</m:mi> <m:msup> <m:mi mathvariant="normal">Γ</m:mi> <m:mo>′</m:mo> </m:msup> </m:msub> <m:mo>=</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mn>5.21</m:mn> <m:mo>±</m:mo> <m:mn>0.02</m:mn> <m:mo>)</m:mo> </m:mrow> <m:mspace width="0.28em"/> <m:mi>eV</m:mi> </m:mrow> </m:math> . Critical-point transitions in the computed band structure, although, deviate from the experimental ones due to the omission of electron-hole-interaction, where the deviation increases with increasing energy. The dielectric limit of the electronic system is determined as <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:msub> <p:mi>ɛ</p:mi> <p:mi>∞</p:mi> </p:msub> <p:mo>=</p:mo> <p:mn>8.38</p:mn> <p:mo>±</p:mo> <p:mn>0.04</p:mn> </p:mrow> </p:math> from experiment, where the computed dielectric function reveals almost the same value ( <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:msub> <q:mi>ɛ</q:mi> <q:mi>∞</q:mi> </q:msub> <q:mo>=</q:mo> <q:mn>8.33</q:mn> </q:mrow> </q:math> ). Along with other previous publications, we conclude that solving the Bethe-Salpeter equation is indispensable for the computation of the dielectric function of semiconductors even in the absence of discrete excitons.