Section B3: The Practical Diode
OK, the ideal diode is an extraordinarily well-behaved creature that allows
us to deal with its nonlinearities in unbelievably reasonable terms. But...and
there’s always a but... we have to look at the deviations from ideal that
materials, fabrication and miscellaneous stuff introduces. We’re going to
approach this by removing some of the ideal approximations to define a
semi-ideal case. Then, as promised by the title of this section, practical
considerations will be introduced and we’ll end up with a pretty realistic
device.
To begin, recall from our discussion of diffusion that the free electrons in
the n-type material and the free holes in the p-type material will move
across the junction until equilibrium is reached. The width of the resulting
depletion region is related to the barrier potential and is a function of
applied bias.
I realize that all these terms are somewhat overwhelming, but if
they are not comfortable, please review The pn Junction discussion.
These concepts are fundamental to the design, operation and
manipulation of all semiconductor devices and the sooner they are
internalized, the less “painful” future material will be!
Now, with that said, let’s look at how a diode actually works...
The diode current equation presented in Equation 3.26 defines an
exponential relationship between the diode current (the dependent variable)
and the diode voltage (the independent variable) and is derived from the
physics of Section A. This equation holds over at least seven orders of
magnitude of current and is truly valuable in defining the behaviors of
semiconductor diodes (and later bipolar junction transistors). NOTE: Please
refer to notation conventions for a description as to significance of upper and
lower case characters.
vD
iD = IO (e
where:
iD
vD
IO
nVT
− 1)
(Equation 3.26)
is the current through the diode
is the voltage (potential difference) measured across the diode
terminals
is the reverse saturation current
n
VT
is a device constant between 0.5 and 2 that is dependent on
material, diode
construction, and operational considerations.
Unless otherwise explicitly stated, the standard simplification of
n=1 will be used for all examples and may be made for all
analyses.
is defined as the thermal voltage and is approximately 26mV at
room temperature (25oC).
Note: VT=kT/q where k is Boltzmann’s constant (1.38x10-23 J/oK), T is the
absolute temperature in degrees Kelvin (oK=273 + the temperature in oC),
and q indicates the fundamental charge of an electron (1.60x10-19 Coulombs
(C=J/V)).
The general shape of the IV curve based on Equation 3.26 is illustrated in
the figure below:
Let’s look more closely at this figure and Equation 3.26. From observation
(and quick-and-dirty-math), we can define three distinct regions for the
diode:
1. For zero bias, or the portion of the curve about vD ≈ zero, iD is
approximately equal to zero. The curve is approximated by a straight line
with a slope close to zero. This results in a near zero conductance (g=i/v)
or an infinite resistance (r=v/i).
2. For the reverse bias situation, vD < 0 and the exponential term is less
than one. If the reverse bias magnitude is greater than a few VT, the
exponential term becomes negligible and iD≅-I0. The slope is still
essentially zero, so the conductance remains close to zero and the diode
resistance is considered infinite.
3. For any forward bias greater that a few VT (i.e., 50mV or so at room
temperature), the exponential term in Equation 3.26 becomes much
larger than one and may be considered dominant. In this case, the diode
current expression may be simplified to iD≅I0exp(vD/nVT). The curve
quickly becomes a straight line with a very large slope. At any point on
this section of the curve, the dynamic resistance (which is
approximately equal to the diode forward resistance, Rf) of the diode is
defined by
rd ≈ Rf =
nVT
.
iD
(Equation 3.31)
So…now we’ve got a semi-ideal diode that’s based on physics and is still
pretty well behaved. Since we can never let well enough alone, let’s goof
with it, shall we?
The first change that must be made when discussing practical devices is the
removal of the assumption of the ideal, instantaneous change of material
type at the pn junction. Instead of an ideal junction, the doping near the
junction may be graded – that is, doping concentrations are a function of
distance from the junction definition. This arises from the use of diffusion
and implantation techniques – we don’t actually have two distinct material
types and “stick” them together. We’re not actually going to do anything
with this here (ah, for a solid state class), but I just wanted to bring it to
your attention.
The most important modification we must make in the forward bias region
is the applied voltage required to get a measurable diode current (known as
turn-on voltage). Rather than the few VT we used in the semi-ideal diode
discussion above, this value (called VON) is approximately 0.7 V for silicon,
0.2 V for germanium, and 1.2 V for gallium arsenide diodes. Yep, this is the
potential barrier voltage, Vo, of the pn junction we talked about in Section
A6.
There is also a difference in the reverse bias region due to both material
characteristics and fabrication of the diode junction. The semi-ideal diode
had a leakage current across the junction (the reverse saturation current,
shown by –Io in the figure above), but had no restrictions on the magnitude
of the applied reverse voltage. Practical devices have a breakdown voltage
VBR (also called the peak inverse voltage (PIV) on manufacturer’s spec
sheets). For magnitudes less than this breakdown voltage, the IV
characteristics of the diode have a slope of 1/Rr. If the magnitude of the
reverse bias approaches VBR, avalanche breakdown occurs. In this case,
the junction breaks down, a large current flows, the device overheats, and a
normal diode may be destroyed.
These practical considerations are illustrated in Figure 3.18 of your text
(reproduced below). For illustration, compare this figure to that for the semiideal (and ideal) diode.
The last effect on diode operational characteristics we’re going to look at has
to do with temperature. Going back to the thermal effects at the material
level (Remember? More free carriers through EHP generation with increasing
temperature?), there is more current, both for the forward and reverse
operating regions, as the temperature increases. Therefore, the turn on
voltage of the diode is directly related to the device temperature – as T
increases, VON decreases and vice versa. Although there are numerous
components to this dependence, it is standard practice to express the
temperature dependence as a constant kT (see below). Equation 3.32
defines this temperature dependence numerically in terms of the relationship
between room temperature parameters and a “new” temperature, which
may be greater than or less than room temperature.
VON (TNew ) − VON (Troom ) = kT (TNew − Troom )
(Equation 3.32)
where:
Troom
VON(Troom)
TNew
VON(TNew)
kT
is generally considered approximately 25oC
is 0.7V for Si, 0.2V for Ge, and 1.2V for GaAs
is the new diode temperature in degrees Centigrade (oC)
is the diode turn-on voltage at new temperature
is a temperature coefficient (kT = -2.0 mV/oC for Si and
− 2.5 mV/oC for Ge)
Finally, we can quantify the effect of temperature on the reverse saturation
current. Equation 3.33 allows us to calculate the change in I0 at two
temperatures T1 and T2 (Note: temperatures must be expressed in degrees
Celcius!). The constant ki in equation 3.33 is material dependent and is
defined at 0.15/oC for silicon.
I0 (atT2 ) = I0 (atT1 )e k i (T2 −T1 )
(Equation 3.33)
Figure 3.19 in your text illustrates the temperature dependence of a
standard silicon diode in the forward bias region as a sequence of curves
generated for temperature increments of 25oC.
This figure should be no surprise – again, it comes back to the physics of the
junction. Remember that EHP generation is directly related to thermal
excitation – as the temperature increases, the more free carriers are
generated. So…with an increase in temperature the curves in forward bias
shift left since less applied potential is required for the same current.
Likewise, as temperature decreases, the curves will shift right. Regardless of
the temperature change, the overall shape of the curve remains the same
since it is controlled by the exponential relationship defined in equation 3.26.