Non Ohmic Conductor

6 Key excerpts on "Non Ohmic Conductor"

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  Electrons in Solids

  An Introductory Survey

  • Richard Bube(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  Electrical Properties The electrical conductivity of different types of material varies over a wide range, from values of the order of 19 6 (Ω cm) 1 for metals to less than 10 1 5 (Ω cm) 1 for insulators. Semiconductors usually have a room temperature conductivity of the order of 1 (Ω cm) 1 , although this value is strongly de-pendent on both the temperature and the purity of the semiconductor. Con-siderations that determine the magnitude, temperature dependence, and imperfection dependence of electrical conductivity constitute the principal topics of this chapter. OHM'S LAW AND ELECTRICAL CONDUCTIVITY In elementary discussions of Ohm's law, it is usually described in terms of circuit parameters : / = V/R, where / is the current flowing in a circuit with resistance R and applied voltage V. The current and voltage are the variables, and the resistance is the proportionality factor, constant indepen-dent of the magnitude of / or V, if Ohm's law holds. Ohm's law can also be written in an equivalent form, J = aß (C.23) (9.1) where J is the current density (current per unit area), σ is the electrical con-ductivity, and ê is the electric field. If A is the cross-section area of the 131 132 9. Electrical Properties material and / is the distance between electrodes with which the field is applied, the correlation between the two forms of Ohm's law is given by J = I/A, S = V/U and σ = (l/R)l/A. The conductivity can be a scalar, or in anisotropic materials it can be a tensor. In order for Ohm's law to hold, σ must be independent of J or S. The electrical current density is given by J = nqv d (9.2) where n is the density of free carriers contributing to the conductivity, q is their charge, and v d is their drift velocity induced by the electric field. The drift velocity must be distinguished from the thermal velocity v = (2kT/m*) 1/2 which has a random direction.

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  Physics, Volume 2

  • David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  A potential difference V is applied across a cylindrical conductor of length L and cross-sectional area A, es- tablishing a current i. L i i ∆V A field E  V/L. If the current density is also uniform over the area A, then j  i /A. The resistivity is then (29-11) The quantity V/i that appears in this equation is defined as the resistance R: (29-12) Combining Eqs. 29-11 and 29-12, we obtain an expression for the resistance R: (29-13) The resistance R is characteristic of a particular object and depends on the material of which it is made as well as on its length and cross-sectional area; the resistivity  is char- acteristic of the material in general. The units of resistance are ohms (). Equation 29-12 gives us another basis for stating Ohm’s law. For a particular object, we can measure the current i for various applied potential differences and plot i as a function of V. If this plot gives a straight line, then the ob- ject is ohmic and obeys Ohm’s law. An equivalent state- ment of Ohm’s law is: The resistance of an object is independent of the magni- tude or sign of the applied potential difference. Ordinary resistors that are found in electric circuits are ohmic for the range of potential differences that are normally used in circuits. Semiconducting devices, such as diodes and tran- sistors, usually are nonohmic. Figure 29-7 compares the cur- rent – voltage plots for ohmic and non-ohmic devices. Keep in mind that the relationship V  iR is not a statement of Ohm’s law. This equation defines the resis- tance and is true for both ohmic and nonohmic objects. Even for nonohmic devices, we can find a value of the re- sistance R for a particular value of V; for a different V, a different value of R will be obtained. For ohmic devices, we get the same value of R for any value of V. R   L A . R  V i .   E j  V/L i/A . V, i, and R are macroscopic quantities, applying to a particular body or extended region.

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  University Physics Volume 2

  • William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
  • 2016(Publication Date)
  • Openstax

    (Publisher)

  This is an empirical law, which is to say that it is an experimentally observed phenomenon, like friction. Such a linear relationship doesn’t always occur. Any material, component, or device that obeys Ohm’s law, where the current through the device is proportional to the voltage applied, is known as an ohmic material or ohmic component. Any material or component that does not obey Ohm’s law is known as a nonohmic material or nonohmic component. Ohm’s Experiment In a paper published in 1827, Georg Ohm described an experiment in which he measured voltage across and current through various simple electrical circuits containing various lengths of wire. A similar experiment is shown in Figure 9.19. This experiment is used to observe the current through a resistor that results from an applied voltage. In this simple circuit, a resistor is connected in series with a battery. The voltage is measured with a voltmeter, which must be placed across the resistor (in parallel with the resistor). The current is measured with an ammeter, which must be in line with the resistor (in series with the resistor). Figure 9.19 The experimental set-up used to determine if a resistor is an ohmic or nonohmic device. (a) When the battery is attached, the current flows in the clockwise direction and the voltmeter and ammeter have positive readings. (b) When the leads of the battery are switched, the current flows in the counterclockwise direction and the voltmeter and ammeter have negative readings. In this updated version of Ohm’s original experiment, several measurements of the current were made for several different 406 Chapter 9 | Current and Resistance This OpenStax book is available for free at http://cnx.org/content/col12074/1.3 voltages. When the battery was hooked up as in Figure 9.19(a), the current flowed in the clockwise direction and the readings of the voltmeter and ammeter were positive.

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  Electrons in Solids 2e

  An Introductory Survey

  • Richard Bube(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  9 Electrical Properties The electrical conductivity of different types of material varies over a wide range, from values of the order of 10 6 ( cm) 1 for metals to less than 10~ 16 (Qcm) 1 for insulators. Semiconductors usually have a room temperature conductivity of the order of 1 (Qcm) 1 , although this value is strongly dependent on both the temperature and the purity of the semiconductor. Considerations that determine the magnitude, temperature dependence, and imperfection dependence of electrical conductivity constitute the principal topics of this chapter. The temperature dependence of electrical conductivity is determined by the temperature dependence of the free carrier density and the temperature dependence of the free carrier mobility, defined as the velocity due to an electric field per unit electric field. Metals and semiconductors or insulators have different temperature dependences for a variety of reasons. The free carrier density in a metal is independent of temperature and therefore the temperature dependence of the conductivity for a metal arises totally from the temperature dependence of the mobility. The free carrier density in a semiconductor or insulator is thermally activated over a wide temperature range and therefore increases exponentially with temperature over this range. The temperature dependence of the mobility depends on the specific scatter-ing process. We consider particularly scattering by acoustic lattice waves and by charged imperfections and differences that occur between metals and semiconductors or insulators. 164 Ohm's Law and Electrical Conductivity 165 The occupation of both band and localized imperfection states in a semiconductor is described in terms of the location of the Fermi level. We see how the Fermi level can be determined for a non-degenerate semi-conductor, and how we can express the occupation of all other states in the material in terms of the energy of the state and the Fermi energy.

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  Engineering Electromagnetics

  Pergamon Unified Engineering Series

  • David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  This region is thus the most difficult to deal with effectively. Free Electron Model of Conductors In the model of dielectric materials developed in Chapter 4, the presence of an electric field caused polarization of the nucleus and electrons of the atoms. But, 183 184 Currents and Conducting Materials because of the considerable energy required to break loose an electron from the attraction of its ion or nucleus, the electron remained bonded to the nucleus. In metals or conductors, this bonding energy is very small. Thus, when small electric fields are applied to the material, the outer electrons (valence electrons) break away from their nucleus and float free in the conducting material. These conduction electrons or free electrons move through the conductor creating the current which is externally measured. Thus we have in a conductor, a fixed lattice of ions left by the electrons, and a free electron cloud or gas free to move through the material. This simplified model of the electron gas is not 100% accurate. Our sophis-ticated knowledge of quantum mechanics, wave mechanics and band theory of solids indicates a better model is possible. But, in this text we are concerned primarily with the material properties (particularly electromagnetic ones) and not the microscopic or atomic details of materials. Only those descriptions of mater-ials necessary for an understanding of their electromagnetic properties will be included. The remainder will be left for others to discuss in texts oriented toward materials. OHM'S LAW Probably the most fundamental law of electrical engineering is Ohm's Law. A basic question is what interpretation to place on Ohm's Law in light of free electron gas model of conductors? Ohm's Law formulated for electromagnetics problems is J =

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  Materials Science and Engineering

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  We opted to use (Ω·m) −1 on the basis of convention—these units are traditionally used in introductory materials science and engineering texts. 18.5 Energy Band Structures in Solids • 651 The demonstration of the equivalence of the two Ohm’s law expressions (Equations 18.1 and 18.5) is left as a homework exercise. Solid materials exhibit an amazing range of electrical conductivities, extending over 27 orders of magnitude; probably no other physical property exhibits this breadth of variation. In fact, one way of classifying solid materials is according to the ease with which they conduct an electric current; within this classification scheme there are three groupings: conductors, semiconductors, and insulators. Metals are good conductors, typically having conductivities on the order of 10 7 ( Ω· m) −1 . At the other extreme are materials with very low conductivities, ranging between 10 −10 and 10 −20 ( Ω· m) −1 ; these are electrical insulators. Materials with intermediate conductivities, generally from 10 −6 to 10 4 ( Ω· m) −1 , are termed semiconductors. Electrical conductivity ranges for the various material types are compared in the bar chart of Figure 1.8. metal insulator semiconductor An electric current results from the motion of electrically charged particles in response to forces that act on them from an externally applied electric field. Positively charged particles are accelerated in the field direction, negatively charged particles in the direc- tion opposite. Within most solid materials a current arises from the flow of electrons, which is termed electronic conduction. In addition, for ionic materials, a net motion of charged ions is possible that produces a current; this is termed ionic conduction. The present discussion deals with electronic conduction; ionic conduction is treated briefly in Section 18.16.

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