1. ELECTRIC CHARGE DETERMINATIONOF SEMICONDUCTORS: PN DIODE --- ANDREW J. HILLIER 09/25/2015
ABSTRACT
This experiment seeks to draw a meaningful relationship between current-voltage
curves and the chargeof a pn-diode. The chargeof the pn diode is dependent on
the amountof doping in the extrinsic semiconductors p and n, and which bias we
use (forward/positive, or reverse/negative), which directly influence the position
of the fermi energy in both the p and n semiconductors and the ability of the
fermi energy to allow morecurrent to flow through the pn junction when in
contact, which turns out to be an exponential function that can be replicated
easily through the use of our ATE via LabVIEW. Thenatural log of this function
shows a direct correlation between voltages and currentafter a certain barrier,
that being the volts causing forward bias in the diode. This experiment is useful in
that it allows us to further engineer circuits and devices in which currentcan only
flow in one direction.
INTRODUCTION
The purposeof this experiment is to test the experimental chargeof a pn diode. A
circuit will be set up with our two GPIBDMM’s and a pn diode. A voltmeter will be
set up in series with the diode so that we may measurethe forward bias over the
diode, both of which in turn will be connected to a constant power supply. After
running the experiment, LabVIEW VI willrecord the data fromthe DMM’s, graph
the data as a current versus voltagecurve, and create an excel spreadsheetof the
delimited ASCII codefromthe GPIBsuch that it presents a column for the current
and for the voltage. We will then use excel to process the curvesuch that it
represents ‘e’.
THEORY
A pn diode is the merging of two extrinsic semiconductors, onep type and one n
type. These semiconductors aredoped with group III and group V elements
respectively. This gives the p semiconductor an excess of protons and the n
semiconductor an excess of electrons. This is due to the introduction of the
elements into a lattice containing group IV materials, namely Si or Ge. The

2. ELECTRIC CHARGE DETERMINATIONOF SEMICONDUCTORS: PN DIODE --- ANDREW J. HILLIER 09/25/2015
introduction of these elements into the lattice while remaining neutral give it
either ‘gaps’ for electrons to fill or excess electrons outside the lattice to move
throughoutthe material. The excess or absence of electrons in the doped
material either increases or decreases the fermi energy of the material
respectively. The fermi energy of a material is the energy at which finding an
electron is 50%, and lies midway between the valence and conduction bands of
an element. According to the Band theory of solids, instead of energy levels, due
to the Pauli Exclusion Principle allowing only two electrons of opposite spin,
energy levels become n-fold degenerate, where n is the number of atoms. This
degenerate characteristic of energy levels gives rise to ‘bands’ of electron energy
levels. The outermost band is the conduction band, and the next-to-outermost
band is the valence band. A semiconductor is one in which the bands are
separated by a small amount of energy, but do not touch or overlap. An intrinsic
semiconductor is one in which the material is pure, and an extrinsic
semiconductor is one in which the material is doped with some other material,
such as As or Ga. Conduction in p materials are due to an excess of ‘gaps’ in the
valence band, whereas conduction in n type materials are due to an excess of
electrons present in the valence band. When a p and n type material touch, they
forma diode, and interact with each other over the pn junction, the junction
being the distance over which the doped materials overlap. When in contact, the
extrinsic semiconductors fusewell due to the qualities of their characteristics,
that being the electrons moving toward the gaps of the valence band in the p
material, and the protons moving toward the excess electrons in the n material.
The recombination at the junction forms a depletion region wherethe
characteristics become that of an intrinsic semiconductor. The fermi energy
remains constant across thedepletion region, although the location of the
conduction and valence bands becomes bent, creating what is essentially an
energy barrier of the difference of fermi energies. By moving a voltage across the
diode with reversebias, we can create a larger energy barrier. This essentially
prevents currentfrommoving through the diode in that direction. By moving
voltage across with forward bias, though, wecan lessen the energy barrier and let
exponentially (dueto the Fermi-Dirac quantum statistics) morecurrent through

3. ELECTRIC CHARGE DETERMINATIONOF SEMICONDUCTORS: PN DIODE --- ANDREW J. HILLIER 09/25/2015
with increasing voltage. By modifying the current I to I0
(ev/kT)
, which makes I
proportionateto the number of charge carriers in the exponential curve. We can
then find ‘e’ by taking the slope of the ln(I) versus V.
PROCEDURE
 Connect pn diode to GPIB DMM’s such that forward bias can be recorded
 Run the LabVIEW VI to record the data onto an excel spreadsheet and graph the curve with an
appropriateamount of iterations
 Increasethe voltage over the diode from 0 to around one, noting the about 0.6 voltenergy barrier
 Decrease Voltage back down to 0
 Repeat and average for increased accuracy if necessary
 Plota graph of ln(I) versus V usingExcel
DATA
CONCLUSIONS
The charge of the pn diode is dependent on the amount of doping in the extrinsic
semiconductors p and n, and which bias we use, which directly influence the
position of the fermi energy in both the p and n semiconductors and the ability of
the fermi energy to allow more currentto flow through the pn junction when in
contact, which turns out to be an exponential function that can be replicated
easily through the use of our ATE via LabVIEW. Thenatural log of this function
shows a direct correlation between voltages and currentafter a certain barrier,
that being the volts causing forward bias in the diode. I believe the data points
centered around 0.7V – 1.00V to be more reliable, as they do not include any
initial flux of current, and show the area over which the charge carriers increase
exponentially. Errors to this experiment could include a lack of consistency in the
increase of voltage over time, giving points that don’t reflect an increasing voltage
as such, a change in temperature due to a lack of perfect insulation of the diode,
an inconsistency in the quality of wires used to conduct, faulty soldering in the
circuit, among other electrical errors. Thesecould be minimized in the experiment

4. ELECTRIC CHARGE DETERMINATIONOF SEMICONDUCTORS: PN DIODE --- ANDREW J. HILLIER 09/25/2015
by insulating the diode very well, and carefully managing electrical wires and
connections to ensuremore perfect currentflow.