Formation of a PN Junction Diode and its Band
Diagram !
 To initiate the junction formation:
 click the FormJunction button, or
 mouse drag one object toward the other.
 To return the PN junction to separate pieces:
 click the Separate button, or
 mouse drag one object away from the other


The red rectangle represents a ptype semiconductor and
the blue rectangle an ntype semiconductor. At the moment, three semiconductors,
Si, Ge and GaAs, have correct materials parameters. You can change the
doping level by typing in the value and clicking the 'setNewValue' button.

Equilibrium band diagrams appear below the semiconductor. The green
horizontal line is the Fermi level. Initiate the pn junction formation
by clicking the 'FormJunction' button or using mouse drag and watch the
physical system approach a new (electrothermal) equilibrium which is characterized
by a constant Fermi level throughout the material. The white region between
the red (ptype) and blue (ntype) regions is the transition (or depletion)
region where most of the free carriers are depleted. This white region
is the space charge region with uncompensated ionized impurity charges
which produce electric field in this region.
Repeat formation and separation of the PN junction several times
trying out different doping values. When you become sufficietly familiar
with the equilibrium band diagram and its formation principles, do the
following quiz.
Quiz:
 Depletion thickness
 The depletion thicknesses, xp and xn,
represent the distance of the depeletion edge from the junction.
 Change the doping level of one side at steps of a factor ten. Record
on paper both depletion thicknesses at each doping level.
 Based on your data, what is the mathematical relationship of xp
and xn to Na and Nd ? Write down
a single equation that involves all these four parameters. Check
your answer.
 What does this relation mean physically about the toal space charge
? Check your answer.
 Band diagram
 Hide the applet page by scrolling down the text or minimizing your
web browser.
 Draw on paper the band diagram of PN junction for Na = 1E16 and Nd
= 1E15. Make the band diagram correct both quantitatively (in the relative
depletion thickness of the two sides) and qualitatively (shape of band
diagram).
 Use the applet to check if your diagram is correct.
 Can you draw the band diagram for a PNP structure where Na = 1E18,
Nd = 1E17, and Na = 1E15 ? Assume that the Nlayer thickness is greater
than the sum of the depletion thicknesses from the two junctions.
PROBLEMS:
The pn junction band diagram : This
applet demonstrates how the band diagram of a pn junction diode is formed.
Answer the following questions.
 By mouse drag of the rectangles toward each other or clicking on the
"formTheJunction" button, you can bring the two 'bulk' semiconductors
to form the junction. This applet visualizes the hypothetical, initial
transient process during junction formation, and the band stabilizes when
the junction arrives at a new thermal equilibrium (for the combined physical
system).
 From observing the band as the junction is being formed, state the
condition for a new equilibrium of the combined
physical system (ie, the p and nmaterials
joined together) ? Is this condition
satisfied separately for the two semiconductor pieces before
the pn junction formation ?
 For a Si pn junction, keep the doping level constant for oneside and
vary the doping level for the other side. Make a record of (N, V_{0})
for a series of N (the varying doping level)values. From this record,
find (or verify) the Mathematical relationship between V_{0} and
N. Do it for the other dopant also, and combine the two results.
Did you verify the commonly found relationship between V_{0}
and the doping levels (such as eq.315 of Yang, p.74).
 Comment on how this problem can be better formulated to assist you
to learn better, conceptually and mathematically.
 Comment on what additions (ie, graphical presentations) to this applet
will be helpful for learning the space charge (and total charge = 0), electric
field, and potential drop on each side of the junction.
 Any other related applet programs do you desire ??
Copyright (c) C.R.Wie, SUNYBuffalo, 19961997
Space charge and electric field
Diffusion
and drift currents
Applied
bias and current
flow
Diffusion
currents and the recombination in the neutral regions
The SPICE device model
for junction diode
Answer to the quiz:
1.
 N_{d} x_{n}
= N_{a} x_{p}.
 Space charge neutrality: that is, the total
positive charge ( N_{d} x_{n })
due to the uncompensated ionized donors is equal to the total negative
charge ( N_{a} x_{p }) due
to the uncompensated ionized acceptors.