by Casey Chiang and Patten Priestley

February 12, 2002

Abstract:

In the following experiments we verified the canonical distribution through the use of an NPN silicon semiconductor in a thermal reservoir, and compared the spectra of InP at several laser intensities, to see if increasing power resulted in a variance from the Boltzmann distribution, expecting it to resemble a Fermi distribution for higher intensities.  We found the slope of our log(I) vs. V curve to be within 10% error of the expected value.  Our results were in accordance with the Ebers-Moll equation.  We found a band gap of 1.2eV for silicon (1.2eV actual value).  Through laser spectroscopy we found the general broadening of the spectra as the power of the laser was increased.  We also found the band gap within reasonable error as well as a value for the temperature of the sample.

Semiconductor Theory:

Within a semiconductor, there are multiple energy bands in which electrons can exist.  These are formed by the wave functions of multiple electrons being close together.  A band gap is formed between these two bands due to forbidden zones in which the wave functions are not allowed.

(Thornton and Rex, p.364)

The lowest state band is commonly referred to as the valence band, and this band is usually full.  The band gap separates the valence band from the conduction band.  For small band gaps (on the order of a few eVs), it is possible for a modest voltage to provide enough energy to place electrons in the conduction band, thus allowing for a modest current through the semiconductor.  When the electrons are excited from the valence band to the conduction band, they leave behind “holes” in the valence band, which we can think of as positive charges.  There is always an equal number of holes in the valence band as electrons in the conduction band. 

Semiconductor performance can also be improved through a process called doping.  When a semiconductor is doped, a small amount of an element with one more or less electron in the valence shell is added to the semiconductor.  This creates additional allowed energy levels in the band gap of the semiconductor.  If the element is a type III element, additional levels called acceptance levels are created just above the valence band.  If the element is a type V element, additional levels just below the conduction band called donor levels are created.  The reason behind this is that type III elements have one less electron than the semiconductor (which is typically a group IV element).  The type III material creates initial “holes” in the valence band, allowing for travel of electrons within the valence band.  Type V elements have one extra electron, making it possible for this electron to travel to the conduction band with less energy because it is not part of the lattice.  Addition of a type III element creates a p-type semiconductor, because of a surplus of holes.  Addition of a type V element creates an n-type semiconductor, because of a surplus of electrons not within the crystal lattice.  Another way to increase the electrical conductivity of semiconductors is to combine a type III and type V element, such as our InP sample.  In this case, the compound has a large number of both holes and electrons available for conduction. 

Semiconductors can be used as transistors, such as the silicon n-p-n-junction transistor used in the first part of our experiment.  The premise behind such a device is that a p-type material (called the base) is sandwiched between two n-type semiconductors (called the collector and emitter).  In our circuit, the emitter and base form a diode in forward bias, and the base and collector form a diode in reverse bias.  The electrons flow from the emitter through the base and up to the collector.  

(Thornton and Rex, pp. 361-389)

Introduction:

In each experiment we added energy to the system to excite the electrons from the valence band to the conduction band.

We looked at two ways of measuring the probability density of the electrons overcoming the energy barrier of the band gap and ending up in the conduction band.  The first was a measurement of current.  We excited the electrons by applying a voltage to the system.  When the conduction band is populated by electrons, the valence band has holes.  Both electrons and holes are free to move about and their movement produces a current.  We measured this current with an ammeter.

The second experiment measured the light the semiconductor gave off.  We excited the system by shining a laser at the sample.  The electrons were excited to the conduction band and then relaxed to the valence band, giving off a photon of light.  We measured the wavelength and intensity of these photons with a spectrometer.