ENERGY GAP OF A SEMICONDUCTOR
I. Introduction
Electrons moving within a crystal are confined to discrete energy levels or “bands,” separated by regions for which there is no allowed state of motion for the electron, called energy gaps. The energy gap to be measured in this experiment is that between the valence and conduction bands of a semiconducting material. It is the size of this gap which, in part, determines the electronic properties of semiconductors.
The current passed by a semiconductor varies with temperature according to the relation
where I is the current of the device at a temperature T (K), Io is the current at some reference temperature, Ee is the effective energy gap of the material and k is Boltzmann’s constant. Strictly speaking, Ee is not independent of temperature, but its variation is very small over the temperature range 20 to 90°C that is to be used in this experiment.
From the equation, a plot of ln(I) versus 1/T will yield a straight line with a slope (-Ee/2k) from which the Ee may be derived. In this experiment we are determining the current passed by a forward biased junction in which case Ee is the difference between the actual energy gap Eg and the applied potential eV so that
In your discussion of this report show, using an energy level diagram that this is in fact true.
II. Experimental
Each group will be given a different colored light emitting diode. The diodes have the following maximum ratings:
|
Color
|
Voltage (V)
|
Max. Current (mA)
|
|
Red
|
1.6
|
50
|
|
Yellow
|
1.8
|
50
|
|
Green
|
2
|
50
|
Connect the constant voltage source provided to one of the LEDs and set a voltage such that the diode operates. Measure this voltage as accurately as possible using the digital voltmeter. Immerse the LED in the water bath at 20°C and measure both the actual temperature of the bath using the thermometer and the current. Take readings every 5°C as the water bath is heated between 20 and 100°C. Calculate Eg for the diode.
III. Results
Your results should tabulate the values of temperature and current that you measured and be accompanied by an accurately drawn graph showing the variation of current versus temperature appropriate to determining the band gap. The error associated with the measurements should be estimated and, if large enough, indicated on the graph. A regression analysis is required in order to determine both the slope and the error in the slope of the line. In collaboration with the other groups you should provide a table indicating the band gap of each of the variously colored LEDs.
IV. Discussion
(a) From your calculated energy gaps you should be able to determine which material the LED was fabricated from. If the band gap does not exactly match that of a pure semiconductor how might the band gap be modified.
(b) What other simple method can be used to determine the band gap by examining the light emitted from the diode.
Useful Data
1eV = 1.602 x 10-19 J
h = 6.625 x 10-34 Js
c = 2.998 x 108 ms-1
k = 1.38 x 10-23 JK-1
References
The Structure and Properties of Materials, Vol. 4, Electronic Properties, L. F. Pease, R. M. Rose and J. Wulff, Wiley 1966.
Electronic Processes in Materials, L. V. Azaaroff and J. J. Brophy, McGraw-Hill 1963.
