The childlangmuir law has many diverse applications, and one of them is to semiconductors 1,4,7,9, and we will focus on this application. Graph of child langmuir law is shown, namely dependence of anode current on anode voltage in an idealized vacuum diode. As a result, the currentvoltage characteristic of the diode is expressed in the form of a new generalization of the child langmuir law. Quantum extension of childlangmuir law quantum extension of childlangmuir law lau, yue y chernin, david p colombant, denis g ho, pingtong 19910401 00. Child originally derived this equation for the case of atomic ions, which have much smaller ratios of their charge to their mass. Childlangmuir law applicability for a cathode sheath. Pdf generalization of the childlangmuir law for nonzero. While there exist crosssection values for momentumtransfer collisions, it is assumed the dominant interaction in the sheath is the chargetransfer collision3.
Apr 29, 2009 in this paper, the childlangmuir law and langmuirblodgett law are generalized to the relativistic regime by a simple method. We derive the limit problem associated with these asymptotics, and prove the existence of the childlangmuir current. The physics of electrokinetic devices applying and. While it is known that the peak current density can surpass this limit when the boundary conditions vary in time, it remains an open question of whether the average current can violate the childlangmuir limit under timedependent conditions. We perform the asymptotic analysis of the onedimensional vlasovpoisson system when singular boundary data are prescribed. The child langmuir law may be obtained when the current density j is so high that the e, term in both eqs. A cathode area 1 cm2, d cathodeanode distance 1 cm. Irving langmuir published the application to electron currents in 19, and extended it to the case of cylindrical cathodes and.
The childlangmuir law and analytical theory of collisionless. The problems are incredibly rich, and the physics deceptively subtle, but the caveats and special conditions even for the simple diode. Simple derivation of quantum scaling in child langmuir law. Again note paper 39, in which the author has treated the analytical models describing the space charge sheaths in a multitude of cases. Pdf we analyze the motion of charged particles in a vacuum tube diode using a new set of variables. The childlangmuir cl law is one of the most well known and often applied laws of plasma physics which states that the behavior of the current. Ultrashortpulse child langmuir law in the quantum and relativistic regimes l. By using this approach, we can derive a one dimensional expression for the characteristic properties of lifters and related electrokinetic devices and by drawing an analogy to the vacuum diode, gain insights into the lifters subtle properties. Introduction to direct variational and moment methods and. Validating the collisiondominated childlangmuir law for a dc discharge cathode sheath in an undergraduate laboratory v lisovskiy and v yegorenkov kharkov national university, svobody sq. It is often called the threehalves power law, and is expressed by the equation below. This is done by deriving the child langmuir law for a dc diode and the space charge limit for the short pulse of a photocathode gun. The number 1 should be added to the righthand side of eq.
A simple physical derivation of childlangmuir spacecharge. An asymptotic analysis of the onedimensional vlasov. Generalization of the langmuirblodgett laws for a nonzero. The childlangmuir cl law is one of the most well known and often applied laws of plasma physics which states that the behavior of the current density in a. We found what we call the microsocopic child langmuir law, which states that the change in electro. Ion energy distributions for collisional ion sheaths at an. Berkeley, ca 94720university of californiadepartment of. A simple physical derivation of childlangmuir space. The langmuirblodgett laws for cylindrical and spherical diodes and the childlangmuir law for planar diodes repose on the assumption that the electric. Childlangmuir law, or childs law, or the threehalves power.
Childlangmuir law article about childlangmuir law by the. We derive the limit problem associated with these asymptotics, and prove the existence of the child langmuir current. He was the third of the four children of charles langmuir and sadie, nee comings. The childlangmuir law limits the steadystate current density across a onedimensional planar diode. The equation is also known as the threehalvespower law or the childlangmuir law. Validating the collisiondominated childlangmuir law for. Simple theory for the twodimensional childlangmuir law. Its analogy in a trapfree solid or dielectric is known as mott gurney mg law. An exact numerical solution describing the child langmuir law appropriate to the relativistic regime is obtained for the case of a parallel plane diode. This problem has a simple explicit solution in the onedimensional case. Child langmuir law avoids the need of solving a nonlinear differential equation and presents a new insight into the way of approaching the problem of the charge dynamics inside a vacuum tube diode.
The childlangmuir law may be obtained when the current density j is so high that the e, term in both eqs. Generalization of childlangmuir law for nonzero injection. The child langmuir law is a statement on the maximum steady state current that can be transported in a planar diode when the initial velocity of the electrons at the cathode is zero. The equation is also known as the threehalvespower law or the child langmuir law.
The physics of electrokinetic devices applying and adapting. Ultrashortpulse childlangmuir law in the quantum and relativistic regimes l. Child langmuir law a law governing spacechargelimited flow of electron current between two plane parallel electrodes in vacuum when the emission velocities of the electrons can be neglected. During his childhood, langmuirs parents encouraged him to carefully observe nature and to keep a detailed record of his various observations. The childlangmuir law determines the maximum current that can be drawn from an electron emitting surface. Formula used is from child s law section in space charge article on english wikipedia. Sheath thickness evaluation for collisionless or weakly collisional bounded plasmas shiangbau wang and amy e. The childlangmuir law the childlangmuir cl law1,2 is a statement on the maximum steady state current that can be transported in a gap, subject to the constraint imposed by the poisson equation r2. Child s original paper was cited in scientific papers more than 600 times in the century following its publication. Child langmuir law for a collisionfree sheath, the sheath with frequent collisions, the ionelectron sheath etc. Child s law or the child langmuir law or threehalvespower law gives the maximum spacechargelimited current in a planar diode of infinite radius i.
The childlangmuir law describes the characteristics of a parallel plate vacuum diode. Simple solutions for relativistic generalizations of the. University of california, berkeley p l a s m a electron emission from surfaces. Sheath thickness evaluation for collisionless or weakly.
The fundamental childlangmuir limit on the maximum current density in a vacuum between two infinite parallel electrodes is one of the most well known and often applied rules of plasma physics. Unlike the standard generalized child langmuir law, the latter result provides an explicit functional dependence of the diode current on the external diode parameters. Graph of childlangmuir law is shown, namely dependence of anode current on anode voltage in an idealized vacuum diode. Is called childs law1 or the childlangmuir law, including langmuir who independently. Volume 246, issues 34, 14 september 1998, pages 318324. Revised generalized childlangmuir law sciencedirect. Simple derivation of quantum scaling in childlangmuir law. In this experiment you will measure both childs law and the richardson e. The childlangmuir law is a statement on the maximum steady state current that can be transported in a planar diode when the initial velocity of the electrons at the cathode is zero. Wendt abstract the widely used childlangmuir law for sheath thickness evaluation in semiin. Results show, in particular, that the classical value for the limiting current in. Pdf simple derivation of quantum scaling in childlangmuir. We develop a simple model using vacuum capacitance, conservation of energy, and conservation of charge to derive the childlangmuir spacechargelimited emission.
Current density and charge density are related by jz. Jun 24, 2015 the child langmuir law is a statement on the maximum steady state current that can be transported in a planar diode when the initial velocity of the electrons at the cathode is zero. In the case of ion beam extraction from a plasma, the langmuirblodgett relations are the typical tools of. He is noted particularly for childs law 1911, which is an equation that describes the electric current that flows between the plates of a vacuum tube. Childlangmuir law in the relativistic regime sciencedirect. The childlangmuir law for the boltzmann equation of. Child langmuir law pdf include the childlangmuir law and model of a collisionless ion sheath, the. Ballistic transport in semiconductors have been studied for practical purposes in 2,18,19. Generalization of the childlangmuir law for nonzero injection velocities in a planar diode.
Childlangmuir law applicability for a cathode sheath description of glow discharge in hydrogen v a lisovskiy1,2,3, k p artushenko1 and v d yegorenkov1 1kharkov national university, 61022, kharkov, svobody sq. Gilgenbach, twodimensional childlangmuir law, phys. Childs law consider a planar interface between a metal x 0. Ion energy distributions for collisional ion sheaths at an rfbiased plasma electrode 4 the published argonargon chargetransfer collision crosssections2.
Such a singular perturbation problem arises in the modelling of vacuum diodes under very large applied bias. Two classical laws suitable for the nonrelativistic regime are modified to simple approximate expressions applicable for calculating the spacechargelimited currents of onedimensional steadystate planar diodes and coaxial diodes under the relativistic regime. Langmuir himself considered how the relation was modified for current flow between coaxial cylinders and concentric spheres. Raviart, an asymptotic analysis of the onedimensional vlasovpoisson system. We investigate the socalled childlangmuir asymptotics of the onedimensional stationary boltzmannpoisson system. Another topic discussed in section 4 is the mathematical sense of models of ion sheaths from the point of view of modern theoretical physics. Vacuum tubes were the main components in electronics from about 1905 to 1960, when transistors and integrated circuits mostly supplanted them. In this paper, the childlangmuir law and langmuirblodgett law are generalized to the relativistic regime by a simple method. Ultrashortpulse childlangmuir law in the quantum and. The numerical solution is carried out for anode voltages up to about one hundred million volts.
Quantum extension of childlangmuir law, proceedings of. Also, some comments are made regarding the child langmuir law applicable to other geometries. When either v 0 or e 0 is sufficiently large, however, the exact solution may differ appreciably from the childlangmuir law. Explicitly, the childlangmuir law states that the maximum current density in am2 in a onedimensional diode is given by 12 32 0 2 42, 9 a cl q v j md. We investigate the socalled child langmuir asymptotics of the onedimensional stationary boltzmannpoisson system. Jan, 2005 the fundamental childlangmuir limit on the maximum current density in a vacuum between two infinite parallel electrodes is one of the most well known and often applied rules of plasma physics. However, the twodimensional case of a cylindrical diode has proved more dif. On the childlangmuir law for semiconductors springerlink. This is done by deriving the childlangmuir law for a dc diode and the space charge limit for the short pulse of a photocathode gun. For scl current in free space, the governing law is known as the child langmuir cl law. Irving langmuir was born in brooklyn, new york, on 31 january 1881.
Then the richardsons and childs laws are recalled since they provide the basins to understand the hypothesis and the developments of the theory pre sented in. Two dimensional electromagnetic childlangmuir law of a shortpulse electron flow. An upper bound to timeaveraged spacecharge limited diode. Theoretical and experimental investigations on the childlangmuir.
The childlangmuir law and analytical theory of collisionless to collisiondominated sheaths. The space charge limit is applied to the observed operation of rf photocathode guns. The application to electrons was made in 19 by irving langmuir, and the equation is also called the child langmuir law because of this. The asymptotics apply when the lattice temperature is small and leads to a singular perturbation problem. Bollen stanford research institute, menlo park, california, u.
In this experiment you will measure both child s law and the richardson e. Zhang school of electrical and electronic engineering, nanyang technological university, singapore 639798 received 3 january 2007. Child 1868 1933 was an american physicist and educator. Pdf this work presents a selfconsistent model of space charge limited. The childlangmuir law relates the voltage applied across a planar diode to the saturation value. Published 14 november 2008 2009 iop publishing ltd plasma sources science and technology, volume 18, number 1. Pdf a new approach to the childlangmuir law researchgate. Childlangmuir law introduction to the physics of electron.
Introduction to direct variational and moment methods and an. Pdf fractionaldimensional childlangmuir law for a rough cathode. For scl current in free space, the governing law is known as the childlangmuir cl law. Childlangmuir law a law governing spacechargelimited flow of electron current between two plane parallel electrodes in vacuum when the emission velocities of the electrons can be neglected. Received 15 july 1969 an exact numerical solution describing the childlangmuir law appropriate to the relativistic regime is obtained for the case of a parallel plane diode. Generalization of the child langmuir law for nonzero injection velocities in a planar diode. Sc forcesrms envelope scchildlangmuir lawsccsimulation codeslebt simulation outline 1 the space charge. Childlangmuir law article about childlangmuir law by. Formula used is from childs law section in space charge article on english wikipedia. Child s law consider a planar interface between a metal x 0. The childlangmuir law in the quantum domain internet archive.