Scale invariance of a diodelike tunnel junction

Cabrera, H.; Zanin, D.; Pietro, L. G. De; Michaels, Thomas C. T.; Thalmann, Peter; Ramsperger, U.; Vindigni, Alessandro; Pescia, D.; Kyritsakis, Andreas; Xanthakis, J. P.; Li, Fuxiang; Abanov, Ar.

doi:10.1103/physrevb.87.115436

Cited by 38 publications

(84 citation statements)

References 35 publications

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“…The data in fig. 6b of [26] are not accompanied by SEM or TEM pictures but the extracted radius 6.5 nm falls in the range of R values of the tips used by this group, i.e. 4-10 nm [27].…”

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 80%

“…In figure 5, we plot the FN curves of three different experimental groups [3,4,26] and (Cabrera H, Zanin DA, De Pietro LG, Ramsperger U, Vindigni A, Pescia D. 2014, private communication) together with our theoretical fits to them. The degree of reproduction of experimental results is more than satisfactory.…”

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 99%

“…If the traditional FN equation were to be used there would be an answer β = 0.79β exp . For our calculations we have used the work function values given by the corresponding experimental papers ϕ = 4.05 eV for Si in [4], ϕ = 4.35 eV for Mo in [3] and ϕ = 4.5 eV for ϕ in H Cabrera, DA Zanin, LG De Pietro, U Ramsperger, A Vindigni, D Pescia (2014, private communication) [26]. In the above analysis, we have assumed that the curvature in the FN plots is primarily due to emitter curvature and other factors such as series resistance and supply saturation play a minor role.…”

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 99%

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Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Kyritsakis

Xanthakis

2015

Proc. R. Soc. A.

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In this paper, we derive analytically from first principles a generalized Fowler-Nordheim (FN) type equation that takes into account the curvature of a nanoscopic emitter and is generally applicable to any emitter shape provided that the emitter is a good conductor and no field-dependent changes in emitter geometry occur. The traditional FN equation is shown to be a limiting case of our equation in the limit of emitters of large radii of curvature R. Experimental confirmation of the validity of our equation is given by the data of three different groups. Upon applying our equation to experimental FN plots complying with the above limitations, one may deduce (i) R and (ii) standard field emission parameters-e.g. enhancement factor-with better accuracy than by using the FN equation.

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“…The data in fig. 6b of [26] are not accompanied by SEM or TEM pictures but the extracted radius 6.5 nm falls in the range of R values of the tips used by this group, i.e. 4-10 nm [27].…”

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 80%

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 99%

Section: Comparison With Experiment-extraction Of Rmentioning

confidence: 99%

See 1 more Smart Citation

Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Kyritsakis

Xanthakis

2015

Proc. R. Soc. A.

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“…In fact, the connection between the morphology of irregular surfaces including sharp conducting tips and the field emission properties has been a subject of intense research [4,5]. In a recent work [6], Cabrera et al measured experimentally the current-voltage (I-V) of a tunnel junction consisting of a sharp electron emitting metallic tip at a variable distance ("∆") from a planar collector and emitting electrons using electric field assisted emission. Their results showed scale invariance of the tunnel junction with respect to changes in ∆ (from few mm to several nm), which means that the physical laws governing the flow of current are invariant with respect the changes of the length scale ∆.…”

Section: Introductionmentioning

confidence: 99%

Height distribution of equipotential lines in a region confined by a rough conducting boundary

Castro¹,

Assis²,

Castilho³

et al. 2014

J. Phys.: Condens. Matter

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Abstract.This work considers the behavior of the height distributions of the equipotential lines in a region confined by two interfaces: a cathode with an irregular interface and a distant flat anode.Both boundaries, which are maintained at distinct and constant potential values, are assumed to be conductors. The morphology of the cathode interface results from the deposit of 2 × 10 4 monolayers that are produced using a single competitive growth model based on the rules of the Restricted Solid on Solid and Ballistic Deposition models, both of which belong to the Kadar-Parisi-Zhang (KPZ) universality class. At each time step, these rules are selected with probability p and q = 1 − p. For several irregular profiles that depend on p, a family of equipotential lines is evaluated. The lines are characterized by the skewness and kurtosis of the height distribution. The results indicate that the skewness of the equipotential line increases when they approach the flat anode, and this increase has a non-trivial convergence to a delta distribution that characterizes the equipotential line in a uniform electric field. The morphology of the equipotential lines is discussed; the discussion emphasizes their features for different ranges of p that correspond to positive, null and negative values of the coefficient of the non-linear term in the KPZ equation.Height distribution of equipotential lines in a region confined by a rough conducting boundary2

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“…Very recently, in Cabrera et al [1], it has been shown that the experimental current-voltage (I- with d was observed over a range of several orders of magnitude for d, from millimetres to several nanometres, but it began failing when d was only a few nanometres. At the outset of this work, it must be said that if the emitting surface is either planar or of large radius of curvature R, then the interpretation of the above observations is elementary.…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of a non-Fowler–Nordheim tunnelling junction

2014

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We have theoretically explained the experimentally observed scaling properties of the current-voltage (I-V) characteristics of a field-emission tunnelling diode with respect to the tip-anode distance d. All the I-V curves for different d-values collapse onto a single curve by a scaling transformation that keeps the electrical field at a given direction constant for different d. Our proof is applicable to more than just the obvious case where the electrostatic potential varies linearly with the distance from the cathode x (and the Fowler-Nordheim plot is also linear). It applies to any general nonlinear potential encountered in emitting tips of small radii of curvature R. Furthermore, we explain why the scaling property is excellent at d R, but deteriorates when d ∼ R. The scaling property is shown to derive from the simultaneous action of two factors: (i) in a Taylor expansion of the potential in the tunnelling region, the second-order coefficient is found to be proportional to the first-order coefficient and their ratio independent of d. (ii) The angular variation of the electric field is independent of d for d R. Deviations from scaling at d ∼ R are attributed to both the dependence on d of the angular variation of the electrical field and/or the presence of a third-order term.

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Scale invariance of a diodelike tunnel junction

Cited by 38 publications

References 35 publications

Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Derivation of a generalized Fowler–Nordheim equation for nanoscopic field-emitters

Height distribution of equipotential lines in a region confined by a rough conducting boundary

Scaling properties of a non-Fowler–Nordheim tunnelling junction

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