Reststrahlen band and optical bandgaps in semiconducting CrN films

We present a comprehensive optical characterization of 200-nm-thick CrN(111) films grown simultaneously on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>Al</a:mi> <a:mn>2</a:mn> </a:msub> <a:msub> <a:mi mathvariant="normal">O</a:mi> <a:mn>3</a:mn> </a:msub> <a:mrow> <a:mo>(</a:mo> <a:mn>0001</a:mn> <a:mo>)</a:mo> </a:mrow> </a:mrow> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>AlN</c:mi> <c:mtext>/</c:mtext> <c:msub> <c:mi>Al</c:mi> <c:mn>2</c:mn> </c:msub> <c:msub> <c:mi mathvariant="normal">O</c:mi> <c:mn>3</c:mn> </c:msub> <c:mrow> <c:mo>(</c:mo> <c:mn>0001</c:mn> <c:mo>)</c:mo> </c:mrow> </c:mrow> </c:math> using plasma-assisted molecular beam epitaxy. Spectroscopic ellipsometry, spanning the far-infrared to ultraviolet range ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>0.04</e:mn> <e:mo>–</e:mo> <e:mn>5.5</e:mn> <e:mspace width="0.28em"/> <e:mi>eV</e:mi> </e:mrow> </e:math> ), is conducted at room temperature to determine the optical constants <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi>n</g:mi> </g:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>k</h:mi> </h:math> of the films. Spectral fits reveal two interband transitions at approximately 0.35 and 0.60 eV. In the infrared range, the ellipsometry data also reveal a pronounced Reststrahlen band stemming from transversal and longitudinal optical phonons at approximately 403 and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mn>629</i:mn> <i:mspace width="0.28em"/> <i:msup> <i:mrow> <i:mi>cm</i:mi> </i:mrow> <i:mrow> <i:mo>−</i:mo> <i:mn>1</i:mn> </i:mrow> </i:msup> </i:mrow> </i:math> , respectively. The relative static and high-frequency permittivities are estimated to be about 39 and 15, respectively. A Born effective charge of approximately 2.7, extracted from the far-infrared region, indicates that CrN is partially ionic.