Field and thermionic-field emission in Schottky barriers
TL;DR: In this article, the authors derived voltage-current characteristics for field and T-F emission in the forward and reverse regime of Schottky barriers formed on highly doped semiconductors.
Abstract: Field emission and thermionic-field (T-F) emission are considered as the phenomena responsible for the excess currents observed both in the forward and reverse directions of Schottky barriers formed on highly doped semiconductors. Voltage-current characteristics are derived for field and thermionic-field emission in the forward and reverse regime. The temperatures and voltages where these phenomena are predominent for a given diode are discussed. Comparison with experimental results on GaAs and Si diodes shows good agreement between theory and experiments.
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TL;DR: In this paper, the 2D counterpart of layered black phosphorus, which is called phosphorene, is introduced as an unexplored p-type semiconducting material and the authors find that the band gap is direct, depends on the number of layers and the in-layer strain, and significantly larger than the bulk value of 0.31-0.36 eV.
Abstract: We introduce the 2D counterpart of layered black phosphorus, which we call phosphorene, as an unexplored p-type semiconducting material. Same as graphene and MoS2, single-layer phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct, and appreciable band gap. Our ab initio calculations indicate that the band gap is direct, depends on the number of layers and the in-layer strain, and is significantly larger than the bulk value of 0.31–0.36 eV. The observed photoluminescence peak of single-layer phosphorene in the visible optical range confirms that the band gap is larger than that of the bulk system. Our transport studies indicate a hole mobility that reflects the structural anisotropy of phosphorene and complements n-type MoS2. At room temperature, our few-layer phosphorene field-effect transistors with 1.0 μm channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm2/V·s, and an...
5,233 citations
TL;DR: In this article, a few-layer phosphorene has been introduced as a 2D p-type material for electronic applications, which has an inherent, direct and appreciable band gap that depends on the number of layers.
Abstract: Preceding the current interest in layered materials for electronic applications, research in the 1960's found that black phosphorus combines high carrier mobility with a fundamental band gap. We introduce its counterpart, dubbed few-layer phosphorene, as a new 2D p-type material. Same as graphene and MoS2, phosphorene is flexible and can be mechanically exfoliated. We find phosphorene to be stable and, unlike graphene, to have an inherent, direct and appreciable band-gap that depends on the number of layers. Our transport studies indicate a carrier mobility that reflects its structural anisotropy and is superior to MoS2. At room temperature, our phosphorene field-effect transistors with 1.0 um channel length display a high on-current of 194 mA/mm, a high hole field-effect mobility of 286 cm2/Vs, and an on/off ratio up to 1E4. We demonstrate the possibility of phosphorene integration by constructing the first 2D CMOS inverter of phosphorene PMOS and MoS2 NMOS transistors.
3,846 citations
Book•
IBM1
TL;DR: In this article, the authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices.
Abstract: Learn the basic properties and designs of modern VLSI devices, as well as the factors affecting performance, with this thoroughly updated second edition. The first edition has been widely adopted as a standard textbook in microelectronics in many major US universities and worldwide. The internationally-renowned authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices. Equations and parameters provided are checked continuously against the reality of silicon data, making the book equally useful in practical transistor design and in the classroom. Every chapter has been updated to include the latest developments, such as MOSFET scale length theory, high-field transport model, and SiGe-base bipolar devices.
2,680 citations
01 Jan 2014
TL;DR: The found phosphorene to be stable and to have an inherent, direct, and appreciable band gap, which depends on the number of layers and the in-layer strain, and is significantly larger than the bulk value of 0.31-0.36 eV.
Abstract: We introduce the 2D counterpart of layered black phosphorus, which we call phosphorene, as an unexplored p-type semiconducting material. Same as graphene and MoS2, single-layer phosphorene is flexible and can be mechanically exfoliated. We find phosphorenetobestableand,unlikegraphene,tohaveaninherent, direct, and appreciable band gap. Our ab initio calculations indicate thatthebandgapisdirect,dependsonthenumberoflayersandthe in-layer strain, and is significantly larger than the bulk value of 0.31� 0.36 eV. The observed photoluminescence peak of single-layer phosphorene in the visible optical range confirms that the band gap is larger than that of the bulk system. Our transport studies indicate a hole mobility that reflects the structuralanisotropyofphosphoreneandcomplementsn-typeMoS2.Atroomtemperature,ourfew-layerphosphorene field-effecttransistorswith1.0 μm channellengthdisplayahighon-currentof194mA/mm,ahighhole field-effectmobilityof286cm 2 /V 3 s,andanon/offratioofupto10 4 .Wedemonstrate the possibility of phosphorene integration by constructing a 2D CMOS inverter consisting of phosphorene PMOS and MoS2 NMOS transistors.
2,675 citations
TL;DR: In this article, a double-barrier structure with a thin GaAs sandwiched between two GaAlas barriers has been shown to have resonance in the tunneling current at voltages near the quasistationary states of the potential well.
Abstract: Resonant tunneling of electrons has been observed in double‐barrier structures having a thin GaAs sandwiched between two GaAlas barriers. The resonance manifests itself as peaks or humps in the tunneling current at voltages near the quasistationary states of the potential well. The structures have been fabricated by molecular beam epitaxy which produces extremely smooth films and interfaces.
1,633 citations
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TL;DR: In this paper, a general expression for the emitted current as a function of field, temperature, and work function is set up in the form of a definite integral, and each type of emission is associated with a technique for approximating the integral and with a characteristic dependence on the three parameters.
Abstract: Although the theories of thermionic and field emission of electrons from metals are very well understood, the two types of emission have usually been studied separately by first specifying the range of temperature and field and then constructing the appropriate expression for the current. In this paper the emission is treated from a unified point of view in order to establish the ranges of temperature and field for the two types of emission and to investigate the current in the region intermediate between thermionic and field emission. A general expression for the emitted current as a function of field, temperature, and work function is set up in the form of a definite integral. Each type of emission is then associated with a technique for approximating the integral and with a characteristic dependence on the three parameters. An approximation for low fields and high temperatures leads to an extension of the Richardson-Schottky formula for thermionic emission. The values of temperature and field for which it applies are established by considering the validity of the approximation. An analogous treatment of the integral, for high fields and low temperatures, gives an extension of the Fowler-Nordheim formula for field emission, and establishes the region of temperature and field in which it applies. Also another approximate method for evaluating the integral is given which leads to a new type of dependence of the emitted current on temperature and field and which applies in a narrow region of temperature and field intermediate between the field and thermionic emission regions.
1,242 citations
TL;DR: The electron current in a semiconductor at uniform lattice temperature, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion as discussed by the authors.
Abstract: The electron current in a semiconductor at uniform lattice temperature ${T}_{0}$, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion. The first two terms involve the mobility and diffusion coefficient which are functions of the electron temperature $T$ or, more generally, depend on certain averages over the nonequilibrium, field-dependent electron energy distribution function. The third term is due to the electron temperature gradient and is analogous to conventional thermal diffusion of a gas in a temperature gradient. In conventional theory, which neglects electron heating or cooling, the mobility and diffusion coefficient are material constants and thermal diffusion is absent. Contrary to the case of uniform fields, $T$ is not a unique function of the local field; it also depends on the current and can only be determined by a simultaneous solution of the equations for current flow and conservation of energy with boundary conditions for a particular structure. As an example, a one carrier metal-semiconductor contact rectifer has been analyzed in detail including a discussion of the Peltier effect. In the barrier region $T$ is greater than ${T}_{0}$ (i.e., hot electrons) for a reverse bias but less than ${T}_{0}$ (i.e., cold electrons) for a forward bias. Computer solutions have been obtained for a Schottky barrier and electron scattering due to acoustic phonons only.
472 citations
TL;DR: In this paper, the effects on the volt-current characteristic of a non-parabolic energy momentum relation in the insulator, and a conduction-band-edge effective electron mass in the inner metal layers, have been derived.
433 citations
TL;DR: In this article, the Richardson equation appropriate to thermionic emission in Schottky barrier diodes is derived for a semiconductor having an energy band with ellipsoidal constant-energy surfaces in momentum space.
Abstract: The Richardson equation appropriate to thermionic emission in Schottky barrier diodes is derived. For a semiconductor having an energy band with ellipsoidal constant-energy surfaces in momentum space, the Richardson constant A 1 ∗ associated with a single energy minimum is A ∗ 1 =4φ qk 2 h 3 (l 2 m y m z +m 2 m z m x +n 2 m x m y ) 1 2 where l, m and n are the direction cosines of the normal to the emitting plane relative to the principal axes of the ellipsoid and mx, my and mz are the components of the effective mass tensor. In the Ge conduction band, summation of emission from all the energy minima gives maximum and minimum ratios of A∗ to the free electron value A (= 120 A/cm2/°K2) of 1·19 and 1·07 for the 〈100〉 and 〈111〉 directions respectively. In the silicon conduction band, maximum and minimum ratios of 2·15 and 2·05 occur for the 〈111〉 and 〈100〉 directions respectively. The theoretical predictions are in good agreement with experimental results from W-Si and Au-GaAs diodes.
364 citations
TL;DR: In this article, the authors derived the field emission current density for an arbitrary degeneracy (i.e., Fermi energy) at the surface of a germanium surface.
Abstract: The field emission current density ${j}_{c}$, originating from the conduction band, is derived for an arbitrary degeneracy (i.e., Fermi energy) at the surface. The theory allows for a difference between the effective and free electron masses; detailed results being worked out for spherical energy surfaces. Simple formulas for ${j}_{c}$ are presented which involve correction factors that are slowly, varying functions of the temperature, field $F$, and Fermi energy, and have been computed numerically; ${j}_{c}$ is approximately proportional to the emission probability of an electron either at the Fermi level or at the bottom of the conduction band for positive or negative Fermi energies, respectively. Strong deviations from linearity, of a $\mathrm{ln}{j}_{c}$ versus ($\frac{1}{F}$) plot, require that the Fermi energy at the surface depend markedly on $F$. The emission current for the intermediate, or $T\ensuremath{-}F$, range is also considered. The field emission current density ${j}_{v}$ originating from the valence band is also discussed. As an example, numerical results are given for germanium. For this case, ${j}_{v}$ exceeds ${j}_{c}$ at room temperature, except when the surface is strongly degenerate $n$ type. The theory is qualitatively consistent with Allen's experimental results for a clean germanium surface.
219 citations