Tunnel charge transport within silicon in reversely-biased MOS tunnel structures M.I. Vexler a, * , A. El Hdiy b , D. Grgec c , S.E. Tyaginov a , R. Khlil b , B. Meinerzhagen c , A.F. Shulekin a , I.V. Grekhov a a A.F. Ioffe Institute, 26 Polytechnicheskaya, 194021 St Petersburg, Russia b LMEN(EA), UFR Sciences, BP 1039, 51687 Reims cedex 2, France c Institut fu ¨r Netzwerktheorie und Schaltungstechnik, TU-Braunschweig, Pf. 3329, 38023 Braunschweig, Germany Received 25 November 2004; received in revised form 5 April 2005; accepted 12 April 2005 Available online 13 June 2005 Abstract The features of the electrical behaviour of a MOS tunnel structure, which arise from the tunnel carrier transport in semiconductor, are considered. For the explicitely given band diagram, the total current increases due to the contribution of electrons in energy range where the only-oxide tunneling is impossible. The resonance transport via the discrete levels in the quantum well may introduce steps in the reverse current–voltage characteristic. The band-to-band tunneling, which is to be treated as semiconductor tunneling, perturbates the balance of minority carriers in the inversion layer, modifying the charge state of a MOS structure. The stationary non-equilibrium support of a large surface carrier concentration becomes therefore possible, and the voltage partitioning in the MOS structure is distorted. q 2005 Elsevier Ltd. All rights reserved. 1. Problem formulation In thin MOS structures, the tunnel transport through the oxide is usually considered [1] to concern the carriers with energies over the Si near-interface conduction band edge E c0 (current component j cm ) and below the valence band edge E v0 (component j v0m ), Fig. 1. However, if the substrate is heavily doped, additional tunnel transport within the semiconductor should come into effect [2,3]. Considering the Al/SiO 2 /p-Si structure, this mechan- ism—in combination with oxide tunneling—will augment the valence-band to metal current j vm (j vm Oj v0m ) via extra- contribution of electrons with the total energies up to E vN . If the band bending q4 s exceeds E g , the electrons with energies from 0 to q4 s KE g will traverse the conduction band of Si or destine in it. The (artificial) difference between ‘destine’ and ‘traverse’ is that the former option relies only on the semiconductor tunnel permeability T s giving rise to the band-to-band tunneling (BBT) current j bb , while the latter suggests the metal and v-band to be also ‘linked by a tunnel process’. The WKB tunnel probability for the latter option is T ox $T s , which is discussed further. Such a division is, of course, a model simplification; the most fair way would be to consider the whole tunnel region fully quantum-mechanically. Taking in mind that the doping of wafers used in modern MOSFETs is increasing (already approaching 10 18 cm K3 ) [4], semiconductor tunneling becomes important from the industrial point of view, and one should pay attention to this effect while studying the MOS structures. Our previous works [5,6] have already been devoted to similar problems. In this paper we aim to present all the important details of modelling, as well as new experimental and simulation results. 2. Semiconductor transmission probability While calculating the probability of semiconductor tunneling T s , the Franz-type dispersion relation is used for the forbidden gap, similarly to what has been done in a previous publication [7] (see also [2]). T s is assumed to Microelectronics Journal 37 (2006) 114–120 www.elsevier.com/locate/mejo 0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.04.048 * Corresponding author. Tel.: C7(812)2479123; fax: C7(812)2479123. E-mail address: shulekin@pop.ioffe.rssi.ru (M.I. Vexler).