Electrical conductivity in solids

Transcription

1 Electrical conductivity in solids Name : ID :

2 Table of contents Introduction... 3 Experiment 1: Temperature Dependence of a Noble Metal Resistor...4 Experiment 2: Temperature Dependence of a Semiconductor Resistor 6 2

3 Introduction Band Theory for Electrical Conductivity In an atom, electrons revolve in the orbits around the nucleus. The electrons are revolving in different orbits. Some orbits are closer to the nucleus some are away from the nucleus. The electrons closer to the nucleus posses lower energy than those farther from nucleus. If the distance between electrons and nucleus increases, the potential energy of the electrons is increased. Thus it can be said that the position occupied by an electron in an atom signifies a certain energy level of that electron. Due to opposite charges in electron and nucleus, there will be an attraction force between them. Naturally this attraction force becomes weaker as the distance between nucleus and electrons increase. So the outermost atom can easily be detached from the parent atom. When a number of atoms are brought together, the electrons of one atom experience forces of other atoms. This effect is most pronounced in outer most orbits. Due to this force, the energy levels, which were sharply defined in an isolated atom, are now broadened into energy bands. Due to this phenomenon generally two bands result, namely valance band and conduction band. Valance Band: The outermost orbital of an atom, where electrons are so tightly bounded that, they can not be removed as free electron. Conduction Band: This is the highest energy level or orbital in outer most shell, in which electrons are free enough to move. Band Gap: There is one energy gap separates these two bands, - the valance band and conduction band. This gap is called forbidden energy gap. 1- Electrical Conductivity of Metal In metals, the atoms are so tightly packed that electrons of one atom experience sufficiently significant force of other closed atoms. That result, the valance band and conduction band in metals come very closer to each other may even overlap. Consequently, by receiving very small amount of energy from external heat or electrical energy source, the electrons readily ascend to higher levels in the metal. Such electrons are known as free electrons. These free electrons are responsible for current flows through a metal. When external electric source is connected to a piece of metal, these free electrons starts flowing towards higher potential terminal of the source, causing current to flow in the metal. So metal is good electrical conductor. In metal density of free electrons in conduction band is much higher than other materials, hence metal is referred as very electrical conductor. In other words electrical conductivity of metal is very good. 2- Electrical Conductivity of Semiconductor In semiconductor the valance band and conduction band are separated by a forbidden gap of sufficient width. At low temperature, no electron possesses sufficient energy to occupy the conduction band and thus no movement of charge is possible. But at room temperature it is possible for some electrons to give sufficient energy and make the transitions in conduction band. The density of electrons in conduction band at room temperature is not as high as in metals, thus can not conduct electrical current as good as metal. 3

4 Experiment 1: Temperature Dependence of a Noble Metal Resistor Objective: Measuring the Ohmic resistance of a noble metal as a function of temperature at various points. Determining the temperature coefficient of resistance α. Apparatus: 1 Sensor-CASSY 1 CASSY Lab 2 1 Current source box 1 Temperature box 1 NiCr-Ni adapter S 1 Temperature sensor NiCr-Ni, type K 1 Noble metal resistor 1 Electric oven 1 Safety connecting box 2 Connecting leads 1 PC with Windows XP/Vista/7/8 Theory: In a metal, the valence electrons are thought of as being shared by all the positive ions. Therefore, the electrons are free to move throughout the crystalline lattice. The electrons move randomly throughout the crystal, until an electric field is applied to the material. Then the electric field forces the electrons to move in a direction opposite to the field. Actually, the electrons still move somewhat randomly, but with a superimposed "drift". This produces current. As the temperature increases, the positive ions in the crystal vibrate more, and more collisions occur between the valence electrons and the vibrating ions. These collisions hinder the "drift" motion of the valence electrons, thus reducing the current. In summary, for a metal, an increase in temperature causes an increase in resistance. The following equation applies to the resistance of normal metals within the first degree of approximation: where : Resistance at 0 0 C θ : Temperature in 0 C : Resistance at the temperature θ 0 C α: is the temperature coefficient of the resistor (resistance change per degree). If is plotted against on a coordinate system, we obtain a straight line with the gradient It is thus possible to determine temperature coefficient of the resistor: 4

5 Carrying out the experiment: Experiment setup is shown in the figure. The temperature box at Sensor-Cassy input A measures the temperature of the sensor in the electric oven. Insert the measuring tip into the hole in the back of the oven so that the tip is in direct proximity to the resistor element. The current supply box at input box at input B register the electrical resistance. 1. Load settings. 2. Start measurement (a value pair is recorded for every temperature increase of 5K). 3. Switch on the oven. 4. Stop measurement when the temperature reaches 470 K (approx C) 5. Switch off the oven. 6. Repeat the measurements during the cooling phase. 9. Plot R θ versus θ. 10. Calculate the slope. 11. Calculate the intercept (it represents the resistance at zero temperature) and hence the temperature coefficient of resistance α. Note: The material used for the noble metal resistor is platinum. Values between and are specified for α depending upon degree of purity. 5

6 Experiment 2: Temperature Dependence of a Semiconductor Resistor Objective: Determining the resistance R of a semiconductor as a function of temperature T. Determining the band gap. Apparatus: 1 Sensor-CASSY 1 CASSY Lab 2 1 Current source box 1 Temperature box 1 NiCr-Ni adapter S 1 Temperature sensor NiCr-Ni, type K 1 Semiconductor resistor 1 Electric oven 1 Safety connecting box 2 Connecting leads 1 PC with Windows XP/Vista/7/8 Theory: In a semiconductor, at 0 K, valence electrons are in filled energy levels (bonds are formed by electron pairs filling the energy levels). They do not respond to an applied electric field to produce current flow. In the presence of an electric field, the electron motion is still random; no net motion in one direction occurs (no current flows). These filled energy levels, which the valence electrons occupy, form the valence band. In order for current to flow, electrons must move from the filled valence band to the empty conduction band. To make this move requires energy, which can be in the form of heat. (Important: the electrons do not move from a "place" in the crystal called the valence band to another "place" called the conduction band. The electrons have the energy associated with the valence band and acquire enough energy to have the energy associated with the conduction band. An energy change occurs, not a position change.) At room temperature, many electrons will have the energy needed to jump to the conduction band. As one electron moves out of the valence band and into the conduction band, a hole is produced in the valence band. Both the electrons in the conduction band and the corresponding holes in the valence band are considered charge carriers. When an electric field is applied to the material, these electrons and holes "drift". The electrons in the conduction band drift in the direction opposite to the applied field, and the holes drift in the same direction as the applied field. Thus, current is produced. As the temperature of the material is increased, more valence electrons acquire sufficient energy to move to the conduction band (producing holes), so more current flows. It is still true that as the temperature is increased, the atoms vibrate more and cause more collisions with the drifting electrons. However, this opposing effect is negligible, compared to the increase in charge carriers. The temperature dependence follows an exponential relation with temperature, Where : Resistance at 0 k T : Temperature in Kelvin 6

7 : Resistance at the temperature T k : is the band gap K = 1.38 x J.k -1 ) the Boltzmann constant ). If is plotted against 1/T on a coordinate system, we obtain a straight line with the gradient It is thus possible to determine the band space semiconductor resistor: form the temperature dependence of the Carrying out the experiment: Do the steps 1to 6 from Experiment 1. CAUTION: The semiconductor resistance temperature must not exceed 180 o C. Note: 8. Plot graph 1: versus T. 9. Plot graph 2: versus 1/T. 10. From graph 2, calculate the slope. 11. Calculate the intercept (it represents the at zero temperature) and hence the band gap. The semiconductor resistance decreases non-linearly with increasing temperature. In the case of non-pure semiconductors, as a function of 1/T is a linear relation only at higher temperatures, use intrinsic conduction is dominant there. For the semiconductors used in this experiment, Semiconductor resistor (586 82): Semiconductor resistor ( ): = 7.5x10-20 J = 0.47 ev = 11x10-20 J = 0.69 ev 7