Current-voltage characteristics of Al/SiO 2 / p -Si MOS tunnel diodes with a spatially nonuniform oxide thickness
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Current–Voltage Characteristics of Al/SiO2/p-Si MOS Tunnel Diodes with a Spatially Nonuniform Oxide Thickness M. I. Vexler, S. E. Tyaginov, A. F. Shulekin^, and I. V. Grekhov Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia ^e-mail: [email protected] Received December 22, 2005; accepted for publication January 26, 2006
Abstract—The effect of nonuniform distribution of the insulator thickness on the behavior of Al/SiO2/p-Si MOS tunnel structures with a (1–4)-nm-thick insulator is studied. The character and magnitude of the effect depend on the applied bias. In any conditions, the nonuniformity of the SiO2 thickness enhances the total through currents as compared to those flowing across a uniform oxide layer of the same nominal thickness. Further, the potential of the inversion layer changes in the inversion mode. The calculations performed take into account the tunnel transport between the Si conduction band and the metal, that between the Si valence band and the metal (including in the inversion mode, the resonant transport, which is less clearly pronounced because of the thickness nonuniformity), and the band-to-band tunneling in the semiconductor. PACS numbers: 85.30.Mn, 73.40.Qv, 73.40.Gk DOI: 10.1134/S1063782606090223
1. INTRODUCTION Metal–oxide–semiconductor (MOS) structures with SiO2 as the insulator are one of the principal objects of study of modern technical physics of semiconductors. In view of the general tendency toward miniaturization of components in electronics, of primary concern are MOS structures with the average insulator thickness dn ≈ (1–4) nm, which can be used in the gate section of FETs, in spite of the presence of through tunneling current [1–3]. The term “average thickness” is necessary here, because any film has some scatter in the local thickness d, characterized by a standard deviation σd ; for SiO2, this scatter is usually 0.1–0.3 nm [3–5]. In this study, we assume, as was done in [4–6], that the value of d (d > 0) is distributed according to the Gauss law (d – dn) 1 Γ ( d ) = ----------------- exp – -------------------- , 2 2πσ d 2σ d 2
(1)
and analyze the effect of spatial nonuniformity of thickness on the electrical characteristics of Al/SiO2/p-Si MOS tunnel structures. This problem is becoming increasingly topical because of the decrease in dn in modern devices. Further, the discussion of the effect of σd is not without interest in the study of consequences of damage to a tunnel-thin SiO2 layer, because the scatter of its thickness increases upon degradation of the oxide. It seems intuitively obvious that, owing to the strong dependence of tunneling probability on d, current will sharply increase with σd at fixed average value of dn. However, as will be shown below, this effect can
manifest itself in a more complicated manner, with the quantitative and even qualitative behavior varying between different operation modes. 2. LOCAL MODEL OF A TUNNEL MOS DIODE In simulations of the current–voltage (I–V) c
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