A surface-potential-based cylindrical surrounding-gate MOSFET model

Abstract

Conclusion:A surface-potential-based model 1,2 is developed for the cylindrical surrounding-gate MOSFET (Fig. 1), of which the (non-differential) equation for the surface potential had not been known because of the cylindrical structure. Unlike other surrounding-gate MOSFET models, this model includes both drift and diffusion currents, 3,4 and also there is no inherent distinction between saturation and non-saturation.3-5 Its accuracy is demonstrated by comparison with device simulation without arbitrary fitting. The model could potentially be useful as a basis for developing compact models, just as the planer single-gate counterpart 1 has formed the theoretical foundations for the development of compact planar MOSFET models. 6-8Details: We formulate the model for a uniformly doped nMOS device assuming nondegeneracy using the gradual channel approximation. The gate oxide capacitance per unit length is given by C ox = 2π ox / ln(1 + t ox /a). The semiconductor charge Q s per unit length iswhere V GS is the gate voltage (source grounded), V fb is the flat-band gate voltage, and ψ s (z) ≡ ψ(a, z) is the surface potential. The semiconductor charge consists of mobile charge (electrons) and immobile charge (acceptor ions):If we use the depletion approximation,A is the ionised acceptor density, and d is the surface depletion depth. Note that the expression of d for the planar MOSFET [Eq. (4) of Jang and Liu 5 ] cannot be used for the cylindrical MOSFET. 9 We hereafter assume that the channel is fully depleted of majority carriers (holes), leading to Q im −πa 2 qN − A . The drain current I D (z) is proportional to Q mo (z) and the gradient of the electron quasi-Fermi potential V n (z):, where µ n is the electron mobility, and ∂V n ∂r = 0 is assumed (charge-sheet approximation). This equation includes both drift and diffusion currents. In a steady state, the electron density is given by, where n i is the intrinsic carrier density, β −1 = k B T /q is the thermal voltage, and V n is the electron quasi-Fermi potential. After some algebraic manipulation, I D can be written aswhere µ eff is the effective mobility, 6 and ψ sL ≡ ψ s (L) and ψ s0 ≡ ψ s (0).The surface potentials ψ s0 and ψ sL are needed to use Eq. (2). We therefore derive an equation for the surface potential. The Poisson equation for the fully depleted channel is, within the gradual channel approximation,whereA /n i ) and V np = V n − V p is the difference between quasi-Fermi potentials (Fig. 2). The boundary conditions for Eq. (3) In deriving Eq. (4), we did not make the charge-sheet assumption, and therefore the electric flux should be continuous at the interface between the channel and the gate oxide (if there is no interface trapped charge): (r, z). Then, from the second boundary condition,In order to perform the integral in Eq. (4), we use a charge-sheet model. In the charge-sheet model, mobile charge Q mo (z) is localised to the surface, and the electric flux is discontinuous there. Note, however, that ψ(r, z) is still continuous at r = a. The Poisson e...

An approximate carrier-based compact model for fully depleted surrounding-gate MOSFETs with a finite doping body

“…The modelling of SRG MOSFETs requires a different approach compared with conventional bulk CMOS due to several unique physical effects of the SRG MOSFETs such as volume inversion and carrier energy level quantization. Recently, extensive study of SRG MOSFET device physics and transport mechanism has been performed and some preliminary core models have also been proposed [4][5][6][7][8][9][10][11]. For example, [4,9] developed different potential-based models for SRG MOSFETs.…”

Sub-threshold behavior of long channel undoped cylindrical surrounding-gate MOSFETs

“…To increase the design window for sub-45 nm devices, a number of non-classical MOSFETs such as double-gate (DG) MOSFETs, Pi-Gate (PG) MOSFETs, and cylindrical surrounding-gate (SRG) MOSFETs have been proposed to extend the scalability of the CMOS integrated circuits. In particular, undoped SRG MOSFETs provide the best control of short-channel effects and sub-threshold characteristics [2][3][4][5][6][7][8][9]. However, new physical phenomena in SRG MOSFETs such as volume inversion [10][11][12][13][14][15] results in more complicated behavior in the subthreshold region.…”

Improved Explicit Current–Voltage Model for Long-Channel Undoped Surrounding-Gate Metal Oxide Semiconductor Field Effect Transistor

“…5) Recently, various current-voltage (I-V) models for SG MOSFETs, which are based on potential, carrier concentration, or charge density, have been reported. [6][7][8][9][10][11][12][13][14] For the development of a compact model applicable to a circuit simulator, an explicit model is preferred over iteration computation for efficiency consideration. However, most of the proposed models require that an implicit equation for an intermediate parameter [e.g., eq.…”

“…8] should be solved by numerical iteration. [6][7][8][9][10][11] Only few explicit I-V models have been reported. [12][13][14] Among these explicit I-V models, potential-based models require complex threestep approximation procedures 12) or special functions, such as a Lambert-W function, 13) which are computationally expensive.…”