Exact analytical solution for current flow throughdiode with series resistance

Banwell, T.C.; Jayakumar, A.

doi:10.1049/el:20000301

Cited by 208 publications

(134 citation statements)

References 8 publications

Supporting

Mentioning

130

Contrasting

Order By: Relevance

“…Because the solution is not available in elementary functions, we apply the product-log function to the expression on the right hand side [27,28]:…”

mentioning

confidence: 99%

Theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes

Rotkin

et al. 2010

Nano Res.

View full text Add to dashboard Cite

We present theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes. A simple physical model, taking into account the basic physics of current rectification, can adequately describe the single-tube and array devices. We show that for as-grown array diodes, the rectification ratio, defined by the maximum-to-minimum-current-ratio, is low due to the presence of metallic-single-walled nanotube (SWNT) shunts. These tubes can be eliminated in a single voltage sweep resulting in a high rectification array device. Further analysis also shows that the channel resistance, and not the intrinsic nanotube diode properties, limits the rectification in devices with channel length up to 10 μm. KEYWORDSSchottky diodes, aligned arrays, single-walled carbon nanotubesSince the earliest days of work on semiconductor devices, diodes have played critically important roles. Theories of p-n Schottky diodes [1, 2] laid the foundations for understanding bi-polar transistor operation and contact phenomena at the metal/semiconductor interface. Even though the diode itself is not a main element of modern digital electronics, the physics of the diode structure is essential for many applications, including in optoelectronics [3]. Nanoscale diodes have been already demonstrated with carbon-based nanomaterials, such as graphene and individual nanotubes [4][5][6][7][8][9][10][11][12][13][14]. The work presented here focuses on diode structures made of parallel nanotube arrays, their rectification properties, and the physics of their electronic transport. The array format is advantageous because they deliver much larger currents than a single-tube device and have less noise, enabling them to operate at high frequency as we have demonstrated Nano Res (2010) 3: 444-451

show abstract

“…Because the solution is not available in elementary functions, we apply the product-log function to the expression on the right hand side [27,28]:…”

mentioning

confidence: 99%

Theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes

Rotkin

et al. 2010

Nano Res.

View full text Add to dashboard Cite

show abstract

“…In the context of a maximum entropy principle, the associated distribution functions of all systems (c, d) are shown to belong to a class of exponentials involving Lambert-W functions, given in Eq. (14). There are no other options for tails in distribution functions other than these.…”

Section: Discussionmentioning

confidence: 99%

What do Generalized Entropies Look Like? An Axiomatic Approach for Complex, Non-Ergodic Systems

Hanel¹

2013

Concepts and Recent Advances in Generalized Information Measures and Statistics

View full text Add to dashboard Cite

Shannon and Khinchin showed that assuming four information theoretic axioms the entropy must be of Boltzmann-Gibbs type, S = − i pi log pi. Here we note that in physical systems one of these axioms may be violated. For non-ergodic systems the so called separation axiom (Shannon-Khinchin axiom 4) will in general not be valid. We show that when this axiom is violated the entropy takes a more general form,, where c and d are scaling exponents and Γ(a, b) is the incomplete gamma function. The exponents (c, d) define equivalence classes for all interacting and non interacting systems and unambiguously characterize any statistical system in its thermodynamic limit. The proof is possible because of two newly discovered scaling laws which any entropic form has to fulfill, if the first three Shannon-Khinchin axioms hold. (c, d) can be used to define equivalence classes of statistical systems. A series of known entropies can be classified in terms of these equivalence classes. We show that the corresponding distribution functions are special forms of Lambert-W exponentials containing -as special cases -Boltzmann, stretched exponential and Tsallis distributions (power-laws). In the derivation we assume trace form entropies, S = i g(pi), with g some function, however more general entropic forms can be classified along the same scaling analysis. In this contribution we largely follow the lines of thought presented in [1].

show abstract

“…where I D is the current through the diode, I s is the reverse bias saturation current, V D is the voltage across the diode, V T is thermal voltage and η is the ideality factor of the diode [56]. For the p-n junctions inside transistors we can assume a reverse saturation current value I s = 10 −17 A and an ideality factor η = 1.…”

Section: Circuit Analysismentioning

confidence: 99%

“…The use of the Lambert-W function W() has been previously researched within the context of VA modeling. Several authors have used it to solve the implicit I-V relationship of diodes [56,58,59]. Parker and D'Angelo used W() to model the Buchla Lowpass-Gate, a synthesizer circuit that employs a resistive opto-isolator (also known as a vactrol) in its control path [16].…”

Section: Explicit Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Virtual Analog Models of the Lockhart and Serge Wavefolders

Esqueda

Pöntynen

Parker³

et al. 2017

Applied Sciences

View full text Add to dashboard Cite

Wavefolders are a particular class of nonlinear waveshaping circuits, and a staple of the "West Coast" tradition of analog sound synthesis. In this paper, we present analyses of two popular wavefolding circuits-the Lockhart and Serge wavefolders-and show that they achieve a very similar audio effect. We digitally model the input-output relationship of both circuits using the Lambert-W function, and examine their time-and frequency-domain behavior. To ameliorate the issue of aliasing distortion introduced by the nonlinear nature of wavefolding, we propose the use of the first-order antiderivative method. This method allows us to implement the proposed digital models in real-time without having to resort to high oversampling factors. The practical synthesis usage of both circuits is discussed by considering the case of multiple wavefolder stages arranged in series.

show abstract

Exact analytical solution for current flow throughdiode with series resistance

Cited by 208 publications

References 8 publications

Theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes

Theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes

What do Generalized Entropies Look Like? An Axiomatic Approach for Complex, Non-Ergodic Systems

Virtual Analog Models of the Lockhart and Serge Wavefolders

Contact Info

Product

Resources

About