Discrepancies of the Flat-Band Voltage Models Revealed by Simulations in Sub-50nm SOI Films

C. Ravariu, A. Rusu, F. Babarada, and F. Ravariu (Romania)


Modeling, simulation, SOI structures, interface charges


where NA [cm-3 ] is the doping concentration in substrate, Qox [e/cm2 ] is the surface electric charge density, ΦMS [V] is the metal-semiconductor work function, Cox=εox/xox [F/cm2 ] is the specific oxide capacitance, εSi/ ox is the dielectric permittivity of Silicon, respectively oxide, xox is the BOX (Buried Oxide) thickness and q=1,6x10-19 C is the elementary electric charge. Firstly, in the analytical model ΦMS =0V will be assumed. The flat-band voltage is a key parameter in the electrical characterization of the SOI wafers. The usual models for the flat-band voltage were established for SOI structures with 2µm…0.2 µm Si-film thickness and 40…20nm front oxide thickness. The electric charge from the buried oxide was poorly investigated, because the interesting conduction occurs in the vicinity of the front oxide. But the pseudo-MOS transistor, used as a dedicated device for electrical characterization, exclusively works with buried oxide. The classical model of VFB, deduced for the pseudo-MOS transistors with micronic sizes, presents some deficiencies in the nanodevice area. The downscaling consequences of the SOI wafers on the flat band voltage modeling were studied in this paper. The simulations and modeling were focused on the electric charges arisen at Si/SiO2 /Si interfaces. This reference model will be confronted with others, analytically deduced in the following paragraph. The discrepancies between the classical model (1) and the simulations increase with the SOI sizes downscaling. 2. The interface charges At the interface Si/SiO2 exists two types of charges: the interface charge Qit [e/cm2 ] representing the electrons trapped on the Tamm-Shockley fast surface states and the fixed charge Qf [e/cm2 ] representing an excess of the ionic silicon solved in oxide and frozen at the Si/SiO2 interface during the end of the annealing. Usual values are: Qit1=109 ÷1010 e/cm2 , Qit2=1010 ÷1011 e /cm2 , Qf1=1010 e/cm2 , Qf2=1012 e/cm2 =10-2 e/nm2 , [3]; where the index “1” is used for the upper SOI interface and “2” for the bottom SOI interface. Frequently, the effect of Qit on VFB is neglected. For example, the contribution of Qit charge is just 0,01V in VFB value for the densisty of states Dst=1010 eV-1 cm-2 in a bulk MOSFET with NA=1015 cm-3 and xox=100nm, [4]. In a second discussion will be approached this kind of charge.

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