NONLINEAR EFFECTS IN SPLIT RING RESONATORS LOADED WITH HETEROSTRUCTURE BARRIER VARACTORS Jorge Carbonell, 1 Vicente E. Boria, 1 and Didier Lippens 2 1 Instituto de Telecomunicaciones y Aplicaciones Multimedia (ITEAM), Universidad Polite ´ cnica de Valencia, Camino de Vera s/n, E-46022 Valencia, Spain; Corresponding author: jorcarol@dcom.upv.es 2 IEMN, Universite ´ des Sciences et Technologies de Lille, Avenue H. Poincare ´ , BP 60069, 59652 Villeneuve d’Ascq Cedex, France Received 3 July 2007 ABSTRACT: The advantages afforded by the symmetrical C(V) charac- teristics of Heterostructure Barrier Varactor (HBV) diodes for the fabri- cation of nonlinear metamaterials are investigated numerically. The studies are conducted by means of full-wave numerical modelling along with circuit analysis. It is believed that the HBV technologies can re- place the conventional Schottky diode not only in up and down fre- quency conversion left-handed devices, but also by bringing new func- tionality in terms of space filtering for unbiased devices. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 474 – 479, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23122 Key words: nonlinear metamaterials; heterostructure barrier varactor (HBV); tuneability; split-ring resonators (SRRs); planar structures 1. INTRODUCTION Nonlinear metamaterials are now attracting much attention with the prospect to tune their dispersion characteristics [1]. The tune- ability under DC bias of double negative and double positive media were in particular demonstrated using varactor diodes and ferroelectric films [2, 3]. Harmonic generation and parametric amplification were also investigated at microwave frequencies [4]. With respect to the use of varactor diodes, a Schottky diode technology was preferentially used, as in [5]. This device has to be reverse-biased and moreover, it requires hard pumping. For unbi- ased devices, a weak influence of the electromagnetic signal was studied resulting mostly of the so called self-biasing effect. The originality of the present work stems from the use of a nonlinear device, the so-called heterostructure barrier varactor (HBV), which exhibits a symmetric C(V) characteristic. It is shown that such symmetry property permits one to use an unbiased device and to strengthen the control of the dispersion characteristic under a moderate dynamic signal. 2. NONLINEARITY VIA HETEROSTRUCTURE BARRIER VARACTOR DIODES The basic underlying ideas concerning the design of nonlinear varactors can be understood from Figure 1, which illustrates the variations of the capacitance C(V) of (a) a conventional varactor Schottky and (b) a Heterostructure Barrier Varactor (HBV). For the former, it is well known that the capacitance of the junction is due to the depleted zone formed at the metal/semiconductor inter- face under zero bias conditions. This depletion effect results in a built-in potential (V bi ). Under forward bias, the depleted zone is shrinking so that the capacitance is further increasing until the voltage threshold for conduction reaches V bi . Under reverse con- ditions the depleted zone edge increases with a concomitant de- crease of the capacitance. This decrease is achieved until punch through conditions are met, which means that the depletion effect saturates when the depleted zone boundary reaches the N+ con- tacting layer. For highly doped varactors, the value of this satura- tion capacity can also be limited by breakdown effect. In conclu- sion, the best way to use a Schottky varactor is to reverse bias the diode with hard pumping. Instead of using a metal/semiconductor interface (Schottky heterojunction with a triangular shaped internal field), the HBV takes advantage of the conduction (valence band) offset of semi- conductor heterojunctions. By this means of alternating low gap and wide gap semiconductors, it is possible to create a rectangular- shaped barrier instead than a triangular one (see Fig. 2). Basically, the barrier profile is symmetric around the middle of the barrier and this symmetry is preserved if the heterostructure barrier is clad between two moderate doped semiconductor regions where the depleted region modulation takes place. As a conse- Figure 1 C(V) (dashed line) and I(V) (solid line) characteristics for (a) a Schottky varactor (b) an HBV 474 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 50, No. 2, February 2008 DOI 10.1002/mop