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Excerpt Edition
This PDF is an excerpt from Chapter 7
of the Parametric Measurement Handbook.
The
Parametric Measurement
Handbook
Third Edition
March 2012
Chapter 7: Diode and Transistor Measurement
"Choose a job you love, and you will never have to work a day in your life"
-- Confucius
Introduction
It is not the intent of this handbook to teach a course on semiconductor device
physics as there are already an abundance of excellent textbooks available on
this subject. However, it is difficult to discuss making parametric diode and
transistor measurements without first spending a little time understanding their
operation. Therefore, we will give a brief review of pn junctions, diodes, and
MOS and bipolar transistor operation with an emphasis on how we characterize
them in parametric test as opposed to detailed theoretical derivations.
PN junctions and diodes
Review of PN diode operation
Intrinsic semiconductor materials (such as silicon) do not have an abundance
of either electrons or electron holes. However, silicon can be doped with other
materials such that it becomes either n-type (possessing excess electrons) or
p-type (possessing excess electron holes). When considered individually these
materials are not particularly interesting. However, consider the case shown
below when these two materials are brought into close contact.
p n
Q
+
xp
- xn x
E
Figure 7.1. The cross section of a pn junction assuming an abrupt change from p-doped
to n-doped material. The graph shows the fixed charge remaining after the mobile carrier
diffusion has stabilized.
Assuming the extremely idealized case of an abrupt junction (i.e. one that
instantaneously transitions from p to n material) as shown in Figure 7.1, we can
see that something very interesting happens. The force of diffusion causes holes
from the p-type material to flow into the n-type material (leaving behind fixed
negative charge), and similarly the force of diffusion causes electrons from the
n-type material to flow into the p-type material (leaving behind fixed positive
charge). This diffusion process will continue until the electric field created by the
fixed charge in what is normally called the space-charge region becomes strong
enough to exactly balance the diffusion tendencies of the mobile carriers.
126
The one-dimensional (x-axis) equations defining current flow in semiconductor
are shown below.
dn
Jn = qnx + qDn (Equation 7.1)
dx
dp
Jp = q p x - qD p (Equation 7.2)
dx
Where J is the current density of electrons (n) and holes (p)
q is the electron charge
xis the electric field in the x-dimension
is the mobility of electrons (n) and holes (p)
D is the diffusion constant for electrons (n) and holes (p)
n is the electron density
p is the hole density
These equations basically state what was alluded to in the previous discussion
of an abrupt pn junction. Namely, current flow in a semiconductor consists of
two parts: a drift current proportional to the applied electric field and a diffusion
current proportional to the spatial first derivative of the mobile carrier density. In
addition to the above current flow equations we also have the Einstein relation-
ship which relates the ratios of the mobility and diffusions constants as shown
below.
Dn Dp kT
= = (Equation 7.3)
n p q
Where q is the magnitude of the electron charge (1.602