Purdue PHYS 34200 - Electrical Resistance as a Function of Temperature

Unformatted text preview:

B. Analyzing data from the semiconductor resistorRR 9/00SS 12/01 Physics 342 LaboratoryThe Electronic Structure of Solids: Electrical Resistance as a Function of TemperatureObjective: To measure the temperature dependence of the electrical resistance of a metaland semiconductor and to interpret the observed behavior in terms of the underlying bandstructure of the solids. Apparatus: Electrical furnace, NiCr-Ni thermocouple, variac power supply for furnace,CASSY power/interface, current module (524-031), thermocouple module (524-045),computer, Pt resistor, semiconductor resistor.References: 1. W. Pauli, Z. Physik 31, 373 (1925). 2. E. Fermi, Z. Physik 36, 902 (1926). 3. P.A.M. Dirac, Proc. Roy. Soc. London A 115, 483 (1926). 4. E. Wigner and F. Seitz, Phys Rev. 43, 804 (1933) and Phys. Rev. 46, 509 (1934). 5. N.F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys,Oxford University Press, Oxford, 1936. 6. D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics; 5th Edition,Wiley and Sons, New York, 1997; Part 5, pgs. 1053-69. 7. K. Krane, Modern Physics, 2nd Ed., Wiley and Sons, New York, pgs. 309-29 andpgs. 344-62. IntroductionAn understanding of how much current flows through a conductor for a given appliedvoltage resulted from Georg Ohm’s thorough work in 1827. The empirical relationshipknown as Ohm’s Law has remained valid over the years and is still widely used today.Although Ohm’s work focussed primarily on metals, studies by Seebeck in 1821 and byFaraday in 1833 reported anomalies in current flow through a class of materials we nowknow as semiconductors. Interestingly, the temperature dependence of current flowmeasured by Faraday in semiconductors was quite different than the temperaturedependence of current flow in metals first reported by Davy in 1820. The fundamentalorigin of this difference remained unexplained for about a century until the developmentof quantum mechanics.Following the successful quantum theory of electronic states in isolated atoms,attention turned toward a better understanding of electronic states in molecules and solids.1Only with the completion of this effort was it possible to understand the implications ofthe simple observations about the temperature dependence of current flow made in theearly 1800s.It is now well established that any property of a solid, including its electricalresistance, is in some way controlled by the electronic states of that solid. As a way ofintroducing the important differences between the electronic structure of metals andsemiconductors, you will measure the temperature dependence of the electrical resistanceof samples made from these two important classes of materials. Before beginning thesemeasurements, it is useful (without paying undue attention to many of the details) toreview i) the modifications to electron states as we move from the atomic to the molecularto the solid state and ii) a simple physical model for current flow in solids.Theoretical ConsiderationsA. Electronic StructureThe important features of an isolated atom are a nucleus surrounded by a complementof electrons that are associated with it in a specifically defined manner. The Pauliexclusion principle requires these electrons to be non-uniformly distributed around thenucleus in regions of space, forming ‘shells’ of charge known as atomic orbitals. Thetotal negative charge of the electrons exactly balances the total positive charge containedin the nucleus. Most importantly, the electrons, because they are confined to a limitedregion of space, acquire quantized energy levels.As atoms are brought together to form a molecule, the outermost electrons from oneatom will interact with the outermost electrons of a neighboring atom. This interaction issubtle and a variety of theories have been devised to explain it accurately. The end resultis a profound modification to the allowed energies and spatial arrangement of theelectronic states. 2Figure 1: In a), a schematic diagram of a butadiene molecule C4H6. The bondingelectrons are indicated by the heavy sticks between atoms. The delocalized electrons,which extend both above and below the plane of the diagram, are schematically indicatedby the dotted path along the length l of the butadiene molecule. In b), the allowedenergies for the electrons in the molecule assuming l is 0.55 nm. The two lowest statesare filled. Higher vacant energy states (n=3, 4, 5 . . ) are available for occupation. TheHOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupiedmolecular orbital) are also labeled. To understand the nature of these modifications, it is useful to briefly consider asimple molecule like butadiene (C4H6). This molecule is a coplanar arrangement of 4carbon atoms combined with six hydrogen atoms. Each carbon atom contributes 4electrons; each hydrogen atom contributes 1 electron. During the synthesis of thismolecule, interactions between electrons cause a significant rearrangement of negativecharge. Many of the electrons become localized in regions of space that lie between twoatoms, forming states known as  bonds. These states are covalent in nature and are fullyoccupied, containing a charge equivalent of two electrons. The negative charge carried bythese  bonds effectively screens the electrostatic repulsion that is present between theatomic nuclei.Each carbon atom brings one more electron than required to form the 9  bonds inbutadiene. These extra electrons assume the lowest energy configuration possible whichresults in a delocalized occupied state referred to as a  orbital in the molecule. Aschematic picture of these two different electron states is given in Fig. 1(a). As willbecome clear below, because of the delocalized nature of these  states, one mightconclude that the butadiene molecule forms an extremely simple example of a tiny one-dimensional metal. If one could somehow connect clip leads to either end and apply apotential across it, one might expect current to flow through a single butadiene moleculein much the same way as it does through a copper wire! As suggested in Fig. 1(a), the 


View Full Document

Purdue PHYS 34200 - Electrical Resistance as a Function of Temperature

Download Electrical Resistance as a Function of Temperature
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Electrical Resistance as a Function of Temperature and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Electrical Resistance as a Function of Temperature 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?