Tunable plasmonics on epsilon-near-zero materials: the case for a quantum carrier model

Abstract

The carrier density profile in metal-oxide-semiconductor (MOS) capacitors is computed under gating using two classical models - conventional drift-diffusion (CDD) and density-gradient (DG) - and a self-consistent Schrödinger-Poisson (SP) quantum model. Once calibrated the DG model approximates well the SP model while being computationally more efficient. The carrier profiles are used in optical mode computations to determine the gated optical response of surface plasmons supported by waveguides incorporating MOS structures. Indium tin oxide (ITO) is used as the semiconductor in the MOS structures, as the real part of its optical permittivity can be driven through zero to become negative under accumulation, enabling epsilon-near-zero (ENZ) effects. Under accumulation the predictions made by the CDD and SP models differ considerably, in that the former predicts one ENZ point but the latter predicts two. Consequently, the CDD model significantly underestimates perturbations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>e</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> of surface plasmons (by ∼4×) and yields incorrect details in surface plasmon fields near ENZ points. The discrepancy is large enough to invalidate the CDD model in MOS structures on ENZ materials under accumulation, strongly motivating a quantum carrier model in this regime.