Distribution of fields and charge carriers in cylindrical nanosize silicon-based metal–oxide–semiconductor structures

Pokatilov, E. P.; Fomin, V. M.; Balaban, S. N.; Gladilin, V. N.; Klimin, S. N.; Devreese, Jozef T.; Magnus, Wim; Schoenmaker, Wim; Collaert, N.; Rossum, M. Van; Meyer, K. De

doi:10.1063/1.370171

Cited by 19 publications

(25 citation statements)

References 10 publications

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“…The study of the charge distribution in the cylindrical MOSFET with closed gate electrode in the state of the thermodynamical equilibrium (see Ref. 31 ) has shown that the concentration of holes is much lower than that of electrons, so that electron transport is found to provide the main contribution to the current flowing through the SOI MOSFET. For that reason, holes are neglected in the present transport calculations.…”

Section: The Hamiltonian Of the Systemmentioning

confidence: 99%

Quantum transport in a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistor

Croitoru

Gladilin

Fomin

et al. 2003

Journal of Applied Physics

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An approach is developed for the determination of the current flowing through a nanosize siliconon-insulator (SOI) metal-oxide-semiconductor field-effect transistors (MOSFET). The quantum mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation. Accounting for electron scattering due to ionized impurities, acoustic phonons and surface roughness at the Si/SiO2 interface, device characteristics are obtained as a function of a channel length. From the Wigner function distributions, the coexistence of the diffusive and the ballistic transport naturally emerges. It is shown that the scattering mechanisms tend to reduce the ballistic component of the transport. The ballistic component increases with decreasing the channel length.

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Section: The Hamiltonian Of the Systemmentioning

confidence: 99%

Quantum transport in a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistor

Croitoru

Gladilin

Fomin

et al. 2003

Journal of Applied Physics

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“…(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):…”

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confidence: 99%

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

Amakawa

Nakazato²,

Mizuta³

2003

Extended Abstracts of the 2003 International Conference on Solid State Devices and Materials

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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...

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“…The main elements of such model are described in the next section. We refer to the original papers for more details [18,19].…”

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confidence: 99%

“…5 The quantum MOSFET model Calculations were performed in [18,19] for a cylindrical MOS structure, with the gate covering the cylinder mantle and the source/drain contacts at both ends (Fig. 3a).…”

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confidence: 99%

“…6 Discussion In the model [18,19] outlined above three equations are solved self-consistently: (i) the Poisson equation, (ii) the radial Schrödinger equation, and (iii) the equation for the Wigner distribution function. In this way, the dynamical behaviour of the device is linked to the description of its equilibrium state and therefore (through the spatial boundary conditions) to its geometry.…”

mentioning

confidence: 99%

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Moore's law: new playground for quantum physics

Rossum¹,

Schoenmaker²,

Magnus³

et al. 2003

Physica Status Solidi (b)

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Dedicated to Professor Jozef T. Devreese on the occasion of his 65th birthday PACS 05.60.Gg, 85.30.Tv CMOS technology has been proven as one of the most important achievements in modern engineering history. In less than 30 years, it has become the primary engine driving the world economy. Device scaling makes this possible. For decades, progress in device scaling has followed an exponential curve: this has come to be known as Moore's law. Downscaling such devices like MOSFETs to their limiting sizes is a key challenge of the semiconductor industry now. Therefore device simulation requires new theory and modeling techniques, what helps to improve the understanding of device physics and design, for structures at the sub-100 nm scale, and complements experimental work in addressing this challenge. We present a new approach, which allows us to make predictions about performance of future MOSFETs. The quantum-mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation.1 Introduction Ever since the first observation of the Quantum Hall Effect in MOS inversion layers [1], it has been known that a MOS transistor can display quantum properties. But quantum MOS structures were soon overshadowed by the spectacular progress in the fabrication of epitaxial layers, which for many years established semiconductor heterostructures as the most popular man-made quantum objects. During this period, the MOSFET was relegated to the practical playgrounds of microelectronics engineering, whereas heterostructure devices raised considerable excitement in the physics community. In the last decade however, a remarkable change of perspective has taken place, and the MOSFET has been gradually reintroduced into the realm of physics, drawing attention from theorists and experimentalists alike. Much of this is the result of "Moore's law", a complex technological and industrial process thanks to which the semiconductor industry has enjoyed exponential growth over a prolonged period. The main physical impact of this law is the relentless downscaling of transistors and interconnects, which are now entering the nanometer regime. This fast evolution has raised concern over the soundness

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Distribution of fields and charge carriers in cylindrical nanosize silicon-based metal–oxide–semiconductor structures

Cited by 19 publications

References 10 publications

Quantum transport in a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistor

Quantum transport in a nanosize silicon-on-insulator metal-oxide-semiconductor field-effect transistor

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

Moore's law: new playground for quantum physics

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