Wave function penetration effects in double gate metal-oxide-semiconductor field-effect-transistors: impact on ballistic drain current with device scaling

Abstract

A study of the evolution of wave function penetration effects on ballistic drain current (ID) in nanoscale double gate (DG) metal-oxide-semiconductor field-effect-transistors (MOSFET) with the downscaling of device dimensions is presented. The electrostatics of the devices is calculated through the self-consistent solution of two dimensional Schrödinger and Poisson equations. HfO2/SiO2 stack is considered as the gate-dielectric material. It is observed that wave function penetration increases drain current in DG MOSFETs fabricated on (110) silicon, and the off-state current is more sensitive to the penetration effects than the on-state current. Numerical results show that the magnitude of the relative increase in ID due to wave function penetration increases sharply with the downscaling of silicon body thickness. On the other hand, the impact of the downscaling of gate length on the penetration effects depends on the gate bias. The relative increase in the off-state current due to wave function penetration decreases with the scaling of the gate length, while the variation in the relative increase in the on-state current with the gate length is insignificant. Drain-induced barrier lowering plays an important role in determining the effects of wave function penetration on the ballistic drain current with device scaling. Wave function penetration effect decreases the threshold voltage and increases the on-state transconductance. This phenomena becomes stronger with the scaling of the silicon body thickness. However, gate length scaling has little influence on these parameters. With the simultaneous scaling of the body thickness and the gate length, wave function penetration effects on all the parameters become more dominant. Physical explanation for these observations are provided.

A review of quantum transport in field-effect transistors

“…If there is no scattering, and the device transverse dimensions remain constant from one end to the other, then the various modes will be uncoupled, so one can simply use the Landauer formula. This provides a type of ballistic transport for a small device and has been used to study wave function penetration into the gate oxide [212], and to study a double-gate FET in TMDCs as a biological sensor [213]. A slightly different formulation, termed the quantum transmission boundary method [214], has been used to study the effect of defects in graphene nanoribbon FETs [215].…”

Self consistent simulation for C-V characterization of sub 10nm Tri-Gate and Double Gate SOI FinFETs incorporating quantum mechanical effects

“…For such small scaled devices, the potential wells become sufficiently narrow to give rise to splitting of the energy levels into subbands, which in effect quantizes the inversion layer carriers at the voltages of interest [11]. An important consequence of this carrier quantization is the penetration of wave functions into the gate oxide due to the finite conduction band offset at the Si/SiO 2 interface [12]. The aforementioned self-consistent model aptly considers the quantization effects whereas the application of an open boundary condition at the Si/SiO 2 interface guarantees that wave function penetration effects are included in our studies.…”

On the distinction between triple gate (TG) and double gate (DG) SOI FinFETs: A proposal of critical top oxide thickness

“…Wavefunction penetration is an unavoidable phenomenon in highly scaled devices [10]. To incorporate wavefunction penetration effect, Schrödinger's equation is solved with open boundary condition at the Si/SiO 2 interface.…”