Thickness Dependence of the Effective Masses in a Strained Thin Silicon Film Viktor Sverdlov 1 , Oskar Baumgartner 1 , Thomas Windbacher 1 , Franz Schanovsky 2 , and Siegfried Selberherr 1 1 Institute for Microelectronics 2 Christian Doppler Laboratory for TCAD at the Institute for Microelectronics TU Wien Gußhausstraße 27-29/E360 A-1040 Wien, Austria {sverdlov|baumgartner|windbacher|schanovsky|selberherr}@iue.tuwien.ac.at Abstract— By comparing results obtained with the density- functional method, empirical pseudo-potential method, and empirical tight-binding method it is demonstrated that the conduction band structure is accurately described by the two- band k·p model. The later model is used to investigate the subband structure in ultra-thin (001) silicon films. It is demonstrated for the first time that the unprimed subbands with the same quantum number are not equivalent in ultra-thin films and develop different effective masses along [110] and [-110] directions. Using the two-band k·p model the dependence of the subband effective masses on strain and thickness is calculated. It is shown that the mass along tensile stress in [110] direction decreases with strain guaranteeing current enhancement in thin films. Shear strain also introduces large splitting between the unprimed subbands with the same n. Finally, the dependence of the effective masses in primed subbands is calculated and found to agree well with recent pseudopotential calculations. Keywords - two-band k·p model, shear strain, subband splitting, strain and thickness dependent effective masses I. INTRODUCTION The rapid increase in computational power and speed of integrated circuits is supported by the continuing size reduction of semiconductor devices’ feature size [1]. With scaling apparently approaching its fundamental limits, the semiconductor industry is facing critical challenges and new engineering solutions are required to improve CMOS device performance. Strain-induced current enhancement is one of the most attractive solutions to increase the device speed and will maintain its key position among possible technology innovations. In addition, a multi-gate MOSFET architecture is expected to be introduced for the 22nm technology node. Combined with a high-k dielectric/metal gate technology and strain engineering, a multi-gate MOSFET appears to be the ultimate device for high-speed operation with excellent channel control, reduced leakage currents, and low power budget. Uniaxial [110] strain modifies the transversal effective masses of the two (001) valleys [2]. The mass change is accurately described by the two-band kp model of the conduction band [3]. The two-band kp model [2-4] provides a general framework to compute the subband structure, in particular the dependence of the subband effective masses on shear strain. In case of a square potential well with infinite walls, which is a good approximation for the confining potential in ultra-thin Si films, the dispersion equations were obtained [5], however, an accurate analysis of the electron subband structure is still missing. Here we describe the subband structure and the dependence of the subband effective masses on strain and thickness t by solving the two-band kp model in a thin (001) film under [110] tensile strain numerically. This allows an analysis of subband energies and effective masses for both primed and unprimed subbands in (001) silicon films. II. THE TWO-BAND KP MODEL The two-band kp model was suggested first in [2] to explain experimentally observed strain dependence of the cyclotron effective mass on the orientation of the external magnetic field. It can be written as Figure 1. Comparison of the conduction band of silicon computed with DFT, EPM, sp 3 d 5 s * , and the k p method. The k p model is accurate up to an energy of 0.5eV. 978-1-4244-3947-8/09/$25.00 ©2009 IEEE 51