Chapter 2

CMOS Metamaterial

Devices

2.1 Introduction

Metamaterial was ﬁrst demonstrated by [54] with the use of split ring res-

onator (SRR) and metallic wire, among which SRR and metallic wire show

the properties of negative permeability (µ) and negative permittivity (ε) at

the resonance frequency, respectively. Metamaterial is not a traditionally de-

ﬁned materia l. It comprises many periodic or non-periodic unit cells. By giving

diﬀerent structure and property to these unit cells, the whole array of unit

cells, which is the metamaterial, would show some prope rties that do not nat-

urally exist. A more clear deﬁnition can be found in Figure 2.1 [55], where

both x and y axes correspond to the material relative permittivity (ε

r

) and

permeability (µ

r

), respectively. Most natural materials lie on the horizontal

line in the 1s t quadrant (ε

r

> 0, µ

r

> 0) with a relative permittivity larger

than 1 and a nearly unity relative permeability. But with metamaterial, by

giving diﬀerent design for unit cells, theoretically we can construc t a material

located in any of the regions of Figure 2.1 that enables many interesting appli-

cations. According to the transmission and reﬂection pr operty, metama terial

can be categorized into two types: non-resonant-type and resonant-type.

Metamaterial in the 1st and 3rd quadrants are transmission-types, where

EM wave is able to propagates inside. The EM wave that propagates in the

1st quadrant (ε

r

> 0 , µ

r

> 0 ) has a positive phase velo city, which is a linear

function of frequency. But when metamaterial appears in the 3rd quadra nt

(ε

r

< 0, µ

r

< 0), it is called left-handed material. Left-handed material has a

non-linear negative phase velocity, which means when the energy propagates

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