This lecture is a short summary of what is going on
inside a diode and how it switches. We're going to cover reverse recovery and the basic mechanisms governing switching
of diodes. So here is a p-n junction, type diode.
we have p-doped material on the left side of the junction
and n-doped material on the right side. n-doped material, for example, means that
we have doped the, silicon lattice with [COUGH] impurities that, provide additional or
extra electrons to the lattice that are of high
energy state and easily able to conduct current by jumping from one atom
to the next, and we call these majority carrier
electrons in the n material. In a similar manner in the p material we
have majority carrier holes that can easily conduct current and jump
from one atom to the next. When these devices are at reasonable temperatures such as at room temperature
the, the thermal energy of the majority
carriers makes them bounce around inside the
lattice. So we can think of them as having thermally induced vibrations or jumping
around and bouncing around. Okay, at the p-n junction what happens then is, what's called a depletion region
is formed. And this happens because when these
majority carriers are bouncing around, they tend to defuse in directions, in the
direction of reduced concentration. And so right here at the junction we have
a high concentration of holes on the left
side and a high concentration of electrons on
the right. And so, what happens is that [COUGH], that the thermal energy will cause the
majority carriers to diffuse in the direction of reducing
concentration, until electrons will diffuse from right to left
across the junction, and holes will diffuse from left
to right. When these majority carrier's diffuse
across the junction, they become what are called minority carriers
on the opposite side. And in the process of, of moving across
the junction they leave behind ionized atoms or net charges on the
dopant atoms of the region that they left. And so when electrons diffuse into the p
region they leave behind plus charges or positively charged
atoms in the n region. And, likewise holes, when they defuse into
the n region they leave behind negatively
ionized atoms, in the p region. And as a result there's an electric field
between these charges. And, that electric field makes a voltage. The voltage is the integral of the
electric field. And so you can see there will be a net
voltage that is plus on the right side and lef, minus on the
left side of the junction. And this region here is called the depletion region or the space charge
there. Across this depletion region then, this
voltage actually opposes the diffusion. So, [COUGH] a positive charge, would have to basically diffuse uphill, voltage wise.
And what happens is that, this voltage across this
depletion region builds up, until in equilibrium the, the the voltage
completely stops these further diffusion of holes in
electrons across the junction. And at that point we are in steady state
or the devices in steady state. It has this built in voltage across the junction, and no further minor, majority
carriers will diffuse [COUGH]. Here's what happens under reverse bias
conditions. So, now we have conta, contacts to the
outside world, and we apply a voltage that's normally
re-considered a negative voltage across the device [COUGH]. So, this voltage is negative with respect
to the p material which is the anode and it's plus with respect to the n
material which is the cathode. Okay, when we do this, we have added
voltage. This adds voltage across the depletion
region and makes the depletion region get larger. Basically this entire voltage, externally
implied voltage is is blocked by the depletion region. [COUGH] You can see see that increase the
depletion region's size and have more voltage across it, you have to
add charge to it. And that charge actually comes from the external voltage source, or the external
circuit. So in this sense, the depletion region
acts as a capacitance. We have to add charge to it to increase
it's voltage. And we generally call this the junction
capacitance of the device. And it's a real capacitor that can store
energy in its electric field that you can get back later if you
change the voltage. Under forward bias conditions, what we do
is we, we increase the voltage of the p-region with respect to the n-region and that makes the depletion region get
smaller. When the depletion region is smaller, it
no longer stops the diffusion of, of majority
carriers across the junction. And so, we, we start to get, flow of
charge across the junction in each direction. So, that holes from the p region defuse
into the n region, where they become what we call
minority carrier holes. They're still at a high enough energy
state in the n-region that they can easily jump from one atom to the
next and conduct current. Similarly, electrons from the n-region
will diffuse into the p-region, where they become minority
carrier electrons and are able to conduct current there.
Under forward-biased conditions then here's what happens.
We have current coming in, the contact from the external circuit.
That in the p-region is gives us holes. Those holes can do one of two things.
One is, they can diffuse across the the junction, become minority carriers in the n-region, and eventually, they
recombine with electrons, majority carrier
electrons, in the n-region. And so, an electron from the negative
terminal may come in, [COUGH] and recombine with one of these holes. The other thing that the p in, what the
holes can do in the p-region, is to recombine with an electron
that has diffused in from the n-region. So, we can have them already carrier
electron that dif, recombines with a majority carrier
hole in the p-region [SOUND]. So those are the two things that can
happen and under forward-biased conditions that accounts
for the entire current of the diode. The entire current consists of
recombination on one side or the other of the junction. And as long as there are minority
carriers, in these regions, we continue to have
current. So what we have then is here's a plot of
the minority carriers, or the minority carrier
concentration on the two sides of the junction. So here for example, we have holes that
diffuse across the junction. And they diffuse at some rate that depends
on the slope of this concentration, characteristic, so they diffuse towards
regions of lower concentration. And, they they last in this region for
sometime that we call the lifetime and the, on average after the lifetime is
over, they will have recombined. And they, they recombine as they, they
diffuse and we get a concentration that reduces the further
away we get from the junction. And we have that on both sides of the p-n
junction. So if we want to turn off the diode, we have to remove these
minority carriers on the two sides of the junction, one, by one way or another, to stop their recombination and stop the current
from flowing. Thus, the diode is charge-controlled by
minority carriers in the, p-n-n regions of the
diode. Here is a classic first order
charge-control model for the diode. It, it relates first the voltage across
the depletion region v, to the minority carrier charge concentration
at the edge of the depletion region. So this q of t we can take as the charge of the
minority carrier holes, right here at this point, or the
minority carrier electrons at this point. [COUGH] And these are related to the voltage
basically the applied voltage of the diode but really the voltage across
the depletion region. So you're used to seeing perhaps the
steady state current versus voltage characteristics of the
diode that has the exponential function. That's a steady state relationship and in fact, the correct relationship is this
one. Okay, so the charge is charge
concentration at the edge of the depletion region, is, is this
quantity. given that quantity we can, turns out, we can find what this entire distribution of
charge is. And there is a total amount of charge or
area under these concentration curves. That is the total stored minority charge
in the device. In the charge control model, we can make
lumped element models of the device. And the, the simplest first order lumped element model, has a
single lump of charge that is this total amount of charge
stored here. And that charge then is, is related again
with some constant to the voltage across the depletion region with
the exponential characteristic. And the charge control equation says that
the total charge can increase if we put
current, more current into the diode which supplies more charge, or
it can decrease by recombination. And so this is actually a dynamic equation
of the diode that says how the stored minority
charged can vary. I should say also that these equations
don't include the capacitance across the junction which
we've talked about previously. That's a separate element and we're
talking simply about what happens with, with the holes and
electrons, moving across the junction. Okay, so if we look at the charge control
equation, in equilibrium the diode works in steady
state, the qdt is 0. And then we can solve this equation and
equate this to 0 and find that the current is equal to the storage charge over the
lifetime. And you can plug this stored charged
equation here, into there, [COUGH] like this.
And if you do, you'll find that the current follows the exponential diode
relation that we're all used to, which is the exponential iv, curve that, that
does this. But, this is an equilibrium equation, and
during transients in the diode, this doesn't have to happen, have
to, to be followed. The dqt term can be non-zero and we can
actually for example, have current that removes stored charge or adds stored
charge that deviates from this iv curve. And that's in fact what happens during the
switching times of the diode. Here in fact is a plot of what, or, a
sketch of what really happens. So, here we had the diode on, initially. So, there's some voltage, like
seven-tenths of a volt, across the diode. And we're conducting some current.
And there's some stored charge. So, here I've drawn, on one side of the
depletion region, the stored minority charge and,
what it looks like. So again we, we have a slope here that
determines the, the rate at which the carriers diffuse and that slope is
proportional to the current in the device and so will have charges moving this way
and conducting this current. Now, at some point, t0 then, this is the
initial condition. At this point, we start to try to switch
the diode off. So, the external circuit [COUGH] will switch, and as a result, we will
start removing charge from the, the diode. And so, what we'll observe in the external circuit is this, this current through the
diode and we can actually remove charge actively
from the diode by simply having a reverse
current. In our charge control equation, I becomes
negative, which makes dqdt be negative, and we
actively remove say the minor, minority carrier holes
backwards across the junction. And minority electrons backwards across
the junction that contribute to this current. Okay, so with this negative current, then
say, at time t1, we have negative current and we're
pulling charges backwards across the junction. The slope, by pulling these charges we
will reduce the concentration of charge. say in the end region, and with the slope
going on the different direction, you'll see charges actually moving the other
direction. A time t2, we've removed an off storage
charge, minor, a stored minority charge, that the the charge right at the edge of
the depletion region goes to 0. And that's what happens right here. Okay, at that point the voltage on the
depletion region can start to change. It's no longer this exponential function
that is, roughly 0.7 volts, but the diode voltage starts to
actually finally go negative. So before this point where we still have
positive minority charge at the edge of the, the depletion region, the diode
voltage remains positive and you can barely see the difference it's,
it's more or less 0.7 volts. and it looks like the diode really is
still on. So at this point, we start to see the
voltage change and see the volt, some negative voltage.
We continue to remove charge and what happens say at time t3, here, is that we
have removed this charge and, the charge is now 0 at, at this point x3 and the depletion region has actually
grown, and comes all the way out to x3 that, which is, consistent with having negative
voltage across the device. finally, out here at time t4, we've
removed all of the stored charge, there's no more
minority charge left. And finally, the diode is all the way off
and it can block the full negative voltage, the circuit imposes without
conducting current. Okay, let's look a little at the power
flow. So power is the voltage times the current. And the power in the diode, at this point,
before we switch the diode off, we had positive
current flowing into the diode. Positive voltage across it and we had some
power loss in the diode that is the conduction loss
of the diode. You can see, where the current goes negative and the voltage is still
positive, over this time. The diode actually supplies power. It has positive voltage and negative
current. And where actually, some of the energy of
these minority carrier charges is being extracted, where we actively pull
them out of the, the the diode. Now that, that amount of power bring
supplied is not very much and in fact, in a switching converter generally that
power is, is lost in the mosfet anyway. and so it's not a very significant amount
of power. But then for the next part, let's say
from, this time, we have negative voltage that is
substantial and we have negative current. And this is substantial power loss that
happens in the diode itself and it can make the diode
hot. So this is real switching loss in the
diode. And in fact we're going to see, in the
next lecture that, that we get substantial switching loss if we consider
both the mosfet and the diode, over this whole
time. And this is a significant amount of loss
and it's often, in what we call hard switched or, or
conventional switching converters. This is often the largest single source of
loss in the circuit, because you can see this is a lot
of current. In a typical diode this peak negative
current may be several times the on state current. And this is the full off state voltage. So the product of these is a very high
instantaneous power. So this is called the reverse recovery of
the diode. this time here is the turn off switching
time, which is often called the reverse recovery
time, and this charge, which is the minority charge
that is actively removed from the device is called
the recovered charge. Now, you can also switch the diode off by
simply stopping the current and waiting a long time for all
the charge to recombine. While we could do some combination, where we maybe, reduce the rate at which
the current change is and goes negative which lets more of the charge recombine in
diode, and less of it be actively removed. But if we switch the diode off quickly,
this is what happens. We basically actively pull all of the
stored minority charge out of the diode and it becomes
recovered charge. The familiar iv characteristic of the
diode is an equilibrium relationship, and it can
be violated during the switching times. In particular, to turn off a diode, we typically have this reverse recovery
trangent, in which the we have the large reverse current that
violates the x, the equilibrium exponential iv
characteristic of the diode. And this reverse recovery time and recovered charge can induce substantial
switching loss in the mosfet, and substantial loss in the diode
itself, as well. In the next lecture, we're going to
calculate what the switching masses are and model them in the
switching converter.