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Journal ArticleDOI

Operating regimes and contact resistance of side-bonded contacts to thin heavily doped semiconductor nanowires

13 Nov 2018-Journal of Applied Physics (American Institute of Physics Inc.)-Vol. 124, Iss: 18, pp 184502
TL;DR: In this article, a side-bonded contact is shown to get fully depleted at the contact edge for N d ≤ α F D [4 e s ψ 0 / q R 2 ].
Abstract: In many nano-wire (NW) devices and during NW characterization, the contact is bonded on the surface or the side of the NW. The prior model of such side-bonded contacts assumes partial NW depletion and purely radial tunneling, both restricted to the contacted region. However, the real space-charge extends to the non-contacted NW, aided by the fringing field, and depletes the contacted NW fully for small NW radius, R. In addition, there are non-radial tunneling and generation-recombination near the contact edge. Supported by numerical calculations, the present work shows that when all the effects are included, different regimes of operation manifest in a side-bonded contact, and the space-charge and contact resistance can differ widely from prior predictions. Our calculations span contacts with barrier height, ϕb0 = 0.4–0.8 V on n-type silicon NWs of R = 7.5–20 nm and doping Nd = 1018–1020 cm−3 and include the effects of dielectric confinement, NW length, surface defects, image force barrier lowering, and heavy doping. We find that a side-bonded contact gets fully depleted at the contact edge for N d ≤ α F D [ 4 e s ψ 0 / q R 2 ], where ψ0 = contact potential and αFD = 0.73 (0.88) for air (SiO2) ambient. Furthermore, the behavior of a side-bonded contact approaches that of an end-bonded contact for N d ≤ α E B [ 4 e s ψ 0 / q R 2 ], where αEB = 0.16 (0.30), while surface space-charge widths in the two contacts match over a much wider Nd range for SiO2 ambient. We express the radial depletion width in the NW as an explicit function of the contact potential based on an available implicit relation.In many nano-wire (NW) devices and during NW characterization, the contact is bonded on the surface or the side of the NW. The prior model of such side-bonded contacts assumes partial NW depletion and purely radial tunneling, both restricted to the contacted region. However, the real space-charge extends to the non-contacted NW, aided by the fringing field, and depletes the contacted NW fully for small NW radius, R. In addition, there are non-radial tunneling and generation-recombination near the contact edge. Supported by numerical calculations, the present work shows that when all the effects are included, different regimes of operation manifest in a side-bonded contact, and the space-charge and contact resistance can differ widely from prior predictions. Our calculations span contacts with barrier height, ϕb0 = 0.4–0.8 V on n-type silicon NWs of R = 7.5–20 nm and doping Nd = 1018–1020 cm−3 and include the effects of dielectric confinement, NW length, surface defects, image force barrier lowering, and h...
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors improved the physical understanding and theoretical estimate of the contact resistance of a side-bonded contact to heavily doped semiconductor nanowire by highlighting the edge effects.
Abstract: We significantly improve the physical understanding and theoretical estimate of the contact resistance of a side-bonded contact to heavily doped semiconductor nanowire by highlighting the edge effects. The contact can be made of metal or metal silicide . Prior model of a side-bonded contact to semiconductor nanowire (NW) estimates the contact resistance using radial tunneling in the contacted NW region, neglecting the edge tunneling and fringing field in the non-contacted NW region. Using realistic TCAD simulations, we show that: (i) edge tunneling dominates over radial tunneling as contact thickness, nanowire radius or ambient dielectric constant are reduced; hence a thin contact together with a low-k surrounding dielectric can yield a significantly lower contact resistance; (ii) fringing field reduces both radial tunneling and edge tunneling.
References
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Journal ArticleDOI
TL;DR: A new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W are presented.
Abstract: The LambertW function is defined to be the multivalued inverse of the functionw →we w . It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.

5,591 citations

Journal ArticleDOI
TL;DR: In this paper, an extension of sinc interpolation to algebraically decaying functions is presented, where the algebraic order of decay of a function's decay can be estimated everywhere in the horizontal strip of complex plane around the complex plane.
Abstract: An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider class of functions with the algebraic order of decay on $\mathbb{R}$. The second type of error estimates governs the case when the order of function's decay can be estimated everywhere in the horizontal strip of complex plane around $\mathbb{R}$. The numerical examples are provided.

1,000 citations

Journal ArticleDOI
TL;DR: In this article, the authors summarized some of the essential aspects of silicon-nanowire growth and of their electrical properties, including the expansion of the base of epitaxially grown Si wires, a stability criterion regarding the surface tension of the catalyst droplet, and the consequences of the Gibbs-Thomson effect for the silicon wire growth velocity.
Abstract: This paper summarizes some of the essential aspects of silicon-nanowire growth and of their electrical properties. In the first part, a brief description of the different growth techniques is given, though the general focus of this work is on chemical vapor deposition of silicon nanowires. The advantages and disadvantages of the different catalyst materials for silicon-wire growth are discussed at length. Thereafter, in the second part, three thermodynamic aspects of silicon-wire growth via the vapor–liquid–solid mechanism are presented and discussed. These are the expansion of the base of epitaxially grown Si wires, a stability criterion regarding the surface tension of the catalyst droplet, and the consequences of the Gibbs–Thomson effect for the silicon wire growth velocity. The third part is dedicated to the electrical properties of silicon nanowires. First, different silicon nanowire doping techniques are discussed. Attention is then focused on the diameter dependence of dopant ionization and the influence of interface trap states on the charge carrier density in silicon nanowires. It is concluded by a section on charge carrier mobility and mobility measurements.

721 citations

Journal ArticleDOI
TL;DR: In this paper, the contact resistance of Al and Pt on n-type Si over a wide range of doping concentrations (10 18 → 2 × 10 20 cm −3 ) has been measured at both room temperature and liquid nitrogen temperature.
Abstract: The contact resistance of Al and Pt on n -type Si over a wide range of doping concentrations (10 18 → 2 × 10 20 cm −3 ) has been measured at both room temperature and liquid nitrogen temperature. These experimental results are compared with theoretical calculations based on a model with electron tunneling through the potential barrier at the interface as the dominant mechanism of current flow. Good agreement is found. It is hoped that this physical model can be used as a guideline in developing ohmic contacts for various semiconductor devices.

508 citations

Journal ArticleDOI
TL;DR: The physics and materials science of electrical contacts to carbon nanotubes, semiconductor nanowires and graphene are discussed, and the main research and development challenges in the field are outlined.
Abstract: Existing models of electrical contacts are often inapplicable at the nanoscale because there are significant differences between nanostructures and bulk materials arising from unique geometries and electrostatics. In this Review, we discuss the physics and materials science of electrical contacts to carbon nanotubes, semiconductor nanowires and graphene, and outline the main research and development challenges in the field. We also include a case study of gold contacts to germanium nanowires to illustrate these concepts.

468 citations