Modeling of a biosensor using Tamm resonance excited by graphene
Zaky A. Zaky, Arafa H. Aly
Abstract
In this paper, nanoscale pores in silicon layers are exploited to model and optimize a one-dimensional hybrid graphene-porous silicon photonic crystal biosensor. The physical nature of the proposed sensor is based on Tamm resonance. The transfer matrix method is applied to detect the change of the index of refraction in an aqueous solution. The proposed model is ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">P</mml:mi> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">P</mml:mi> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">G</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">b</mml:mi> <mml:mi mathvariant="normal">s</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:math> , in which <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">P</mml:mi> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">P</mml:mi> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> are porous silicon layers with different porosities, N is the number of periods, and G is the number of graphene layers. The numerical simulations show that the proposed sensor has good performance. The variation of the number of periods, number of graphene layers, porosities, thicknesses of silicon layers, incident angles, and the sample layer thickness affect the performance of the sensor. By varying these parameters, the sensitivity and figure of merit of the sensor can be controlled. The study shows that the sensitivity and figure of merit of the proposed sensor reach 4.75 THz/RIU and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>475</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">R</mml:mi> <mml:mi mathvariant="normal">I</mml:mi> <mml:mi mathvariant="normal">U</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , respectively. The proposed sensor has a good capability in biological detection within terahertz. It is the first time, to our knowledge, that graphene has been used to excite the Tamm resonance using the photonic crystal of porous silicon and using it in biosensing applications.