Navigation aids in the search for future high-k dielectrics: Physical and electrical trends O. Engstro ¨m a, * , B. Raeissi a , S. Hall b , O. Buiu b , M.C. Lemme c , H.D.B. Gottlob c , P.K. Hurley d , K. Cherkaoui d a Chalmers University of Technology, Department of Microtechnology and Nanoscience, SE-412 96 Go ¨ teborg, Sweden b University of Liverpool, Brownlow Hill, Liverpool L69 3GJ, UK c AMO GmbH, Otto Blumenthal-Str. 25, 52074 Aachen, Germany d Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland The review of this paper was arranged by Simon Deleonibus Abstract From experimental literature data on metal oxides combined with theoretical estimates, we present empirical relations for k-values and energy band offset values, that can be used in the search for gate dielectric materials fulfilling the needs of future CMOS generations. Only a few materials investigated so far have properties meeting the demands for k and energy band offset values in the development of CMOS down to 22 nm. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: High-k dielectrics; Dielectric constant; CMOS; Rare earth oxides 1. Introduction Finding an alternative gate material with high dielectric constants for coming CMOS generations is one of the most challenging problems in the continuous development of electronics [1]. The requirements for these materials are rig- orous. Beside the absolute need for higher k-values, the energy band offsets to silicon, interface and bulk charges and thermal stability, are among the properties that need to satisfy the demands set by MOS production processes. Even if a metal oxide seems to be the most probable candi- date [2], the search can hardly be performed without clues based on physical regularities, empirical or theoretical, among oxides based on different metals in the periodic system. Two of the most elementary quantities that need to be considered are the dielectric constant, k, and the energy band-offset values, DE c and DE v , between the conduction and the valence bands of the oxide and the silicon crystal, respectively. In this paper, we present data trends for metal oxides, which can be used in the search of materials fulfill- ing these basic properties. 2. Physical properties of dielectrics From a microscopic point of view, the dielectric con- stant, k, is determined by the polarizability, a. The relation between the two quantities is given by the Clausius–Mos- otti expression [3]: k ¼ ½1 þ 2 3 4p a V m  ½1  1 3 4p a V m  ; ð1Þ where V m is the volume per molecule in the dielectric. In the present form, the polarizability is expressed in the unit of volume. When expressing the polarization, P, in MKS- units [4] as P = a c F/V m , where F is the applied electric field, 0038-1101/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2007.02.021 * Corresponding author. Tel.: +46 31 772 1861; fax: +46 31 772 3622. E-mail address: olof.engstrom@mc2.chalmers.se (O. Engstro ¨m). www.elsevier.com/locate/sse Solid-State Electronics 51 (2007) 622–626