Department of Electronic & Electrical Engineering – Trinity College Dublin, 2014
3C3 – Analogue Circuits
Lecture 2:
The Diode
1
N- and P-Type Semiconductors
• To increase the number of conduction-band electrons in intrinsic silicon, pentavalent
impurity atoms are added. Extra electrons not involved in bonding become conduction
electrons. These are the majority carriers and their number can be controlled. A few holes
(minority carriers) are also thermally generated.
• Similarly, to increase the number of holes in intrinsic silicon, trivalent impurity atoms are
added. Holes are introduced and these are the majority carriers and their number can be
controlled. A few electrons (minority carriers) are also thermally generated.
• N- and P-Type Semiconductors are not negatively and positively charged
2
The PN junction
• If a piece of intrinsic silicon is doped so that part is n-type and the other part is p-type, a
pn junction forms at the boundary between the two regions and a diode is created, as
shown below.
• The p region has many holes (majority carriers) from the impurity atoms and only a few
thermally generated free electrons (minority carriers).
• The n region has many free electrons (majority carriers) from the impurity atoms and only
a few thermally generated holes (minority carriers).
Basic pn junction at the instant of
junction formation
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The PN junction – formation of the depletion region
• The free electrons in the n region are randomly drifting in all directions.
• At the instant of the pn junction formation, the free electrons near the junction in the n
region begin to diffuse across the junction into the p region where they combine with
holes near the junction, as shown below.
• Before the pn junction is formed, recall that there are as many electrons as protons in the
n-type material, making the material neutral in terms of net charge. The same is true for
the p-type material.
• When the pn junction is formed, the n region loses free electrons as they diffuse across
the junction. This creates a layer of positive charges near
the junction.
• As the electrons move across the junction,
the p region loses holes as the electrons and
holes combine. This creates a layer of
negative charges near the junction.
• These two layers of positive and negative
charges form the depletion region.
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The PN junction – formation of the depletion region
• The term depletion refers to the fact that the region near the pn junction is depleted of
charge carriers (electrons and holes) due to diffusion across the junction.
• The depletion region is formed very quickly and is very thin compared to the n and p regions.
• After the initial surge of free electrons across the pn junction, the depletion region has
expanded to a point where equilibrium is established and there is no further diffusion of
electrons across the junction.
• As electrons diffuse across the junction, more and more positive and negative charges are
created near the junction. A point is reached where the total negative charge in the
depletion region repels any further diffusion of electrons into
the p region and the diffusion stops.
• In other words, the depletion region acts as a
barrier to the further movement of electrons
across the junction.
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The PN junction – Barrier Potential
• Any time there is a positive charge and a negative charge near each other, there is a force
acting on the charges as described by Coulomb’s law.
• In the depletion region there are many positive and negative charges on opposite sides of
the pn junction. The forces between the opposite charges form an electric field, as shown
below by the blue arrows between the positive and negative charges.
• This electric field is a barrier to the free electrons in the n region, and energy must be
expended to move an electron through the electric field.
• That is, external energy must be applied to get the electrons to move across the barrier of
the electric field in the depletion region.
• The potential difference of the electric field
across the depletion region is the amount of
voltage required to move electrons through the
electric field.
• This potential difference is called the
barrier potential and is expressed in volts.
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The PN junction – Barrier Potential
• Stated another way, a certain amount of voltage equal to the barrier potential and with the
proper polarity must be applied across a pn junction before electrons will begin to flow
across the junction.
• The barrier potential of a pn junction depends on several factors which we won’t go into in
detail in this course.
• The factors include the type of semiconductive material, the amount of doping, and the
temperature.
• The typical barrier potential is approximately 0.7 V for silicon (at 25°C).
• For the sake of comparison, the typical
barrier potential for germanium is 0.3 V.
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The Diode
• A diode is made from a small piece of semiconductor material, usually silicon, in
which half is doped as a p region and half is doped as an n region with a pn junction
and depletion region in between.
• The p region is called the anode and is connected to a conductive terminal.
• The n region is called the cathode and is connected to a second conductive
terminal.
• The basic diode structure and schematic symbol are shown below
8
The Diode – Forward Bias
• To bias a diode, you apply a dc voltage to it.
• Forward bias is the condition that allows current through the pn junction.
• To forward bias a diode, two requirements need to be satisfied:
1.
one must connect the positive side of the dc voltage to the p region and the negative side
to the n region.
2.
The dc voltage (also known as the bias voltage, VBIAS) must be greater than the barrier
potential (i.e., greater than 0.7 V for silicon).
• As shown below, when a diode is forward-biased, the negative side of the bias-voltage source
“pushes” the free electrons, which are the majority carriers in the n region, toward the pn
junction. This is called the electron current.
• Also, note that the voltage source
supplies electrons into the n region.
• The bias-voltage source gives the
free electrons enough energy to
overcome the barrier potential
and to move into the p region.
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The Diode – Forward Bias
• Now the electrons are in the valence band in the p region, because they have lost too much
energy overcoming the barrier potential to remain in the conduction band.
• The positive side of the bias-voltage source attracts the valence electrons toward the left end of
the p region. The holes in the p region provide the “pathway” for these valence electrons to move
through the p region, i.e., the valence electrons move from one hole to the next toward the left.
• The holes, which are the majority carriers in the p region, effectively (not actually) move to the
right toward the junction. This effective flow of holes is the hole current.
• As the electrons flow out of the p region through the external connection (conductor) and to the
positive side of the bias-voltage source, they leave holes behind in the p region; at the same time,
these electrons become conduction electrons in the metal conductor.
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The Diode – Forward Bias
• As more electrons flow into the depletion region (on the n side), the number of positive ions is
reduced.
• As more holes effectively flow into the depletion region on the other side of the pn junction, the
number of negative ions is reduced.
• This reduction in positive and negative ions during forward bias causes the depletion region to
narrow, as shown below.
• As we mentioned earlier, the electrons lose some energy when they cross the pn junction.
• In fact, they give up an amount of energy equivalent to the barrier potential.
• This results in a voltage drop across the pn junction equal to the barrier potential (0.7 V) when the
diode is forward biased – we will see this again.
• The internal resistance of the p and n regions is called the dynamic resistance and is very small. As
such, we will often neglect it.
11
The Diode – Reverse Bias
• Reverse bias is the condition that essentially prevents current through the diode.
• To reverse bias a diode, we do the opposite of what we did for forward bias, i.e., we connect
the positive side of the voltage source to the n region and the negative side to the p region.
• The positive side “pulls” the free electrons (the majority carriers) away from the pn junction.
• This causes the depletion layer to widen as additional positive ions are created at the junction.
• In the p region, electrons enter from the negative side of the voltage source and move from
hole to hole toward the depletion region where they add negative ions.
• This results in a widening of the depletion region and a depletion of majority carriers.
• This flow of charge carriers is transitional and lasts only a very short time.
12
The Diode – Reverse Bias
• As the depletion region widens, the availability of majority carriers decreases.
• As more of the n and p regions become depleted of majority carriers, the electric field
between the positive and negative ions increases in strength until the potential across the
depletion region equals the bias voltage, VBIAS.
• At this point, the transition current essentially ceases except for a very small reverse
current that can usually be neglected.
• This small current is due to minority carriers (and the fact that the conduction band – see
last lecture – in the p region is higher than that in the n region – so minority electrons in
the p region can easily transition across the depletion region).
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The Diode – Reverse Breakdown
• A side note:
• if the external reverse-bias voltage is increased to a value called the breakdown voltage, the
reverse current will drastically increase.
• The high reverse-bias voltage imparts energy to the free minority electrons so that as they
speed through the p region (see last slide), they acquire so much energy that when they
collide with atoms they knock valence electrons out of orbit and into the conduction band.
• The newly created conduction electrons are also high in energy and repeat the process.
• The multiplication of conduction electrons in this way is known as the avalanche effect.
• The high-energy electrons created go through the depletion region and have enough energy
to go through the n region as conduction electrons, rather than combining with holes.
• Reverse current can increase dramatically if steps are not taken to limit the current, which
can heat and permanently damage the diode.
• Most diodes are not operated in reverse breakdown.
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The Diode – Voltage-Current Characteristic
So:
• Forward bias produces current through a diode
• Reverse bias essentially prevents current, except for negligible reverse current, unless the
reverse-bias voltage becomes equal to or greater than the junction breakdown voltage
• The forward current, IF , increases very little until the forward voltage across the pn junction
reaches approximately 0.7 V at the knee of the curve – see slide 8.
• After this point, the forward voltage remains nearly constant at approximately 0.7 V, but IF
increases rapidly.
• Note, in the expanded
view on the right, that the
resistance of the forwardbiased diode is not linear
over the entire curve.
Because the resistance
changes as you move along
the V-I curve, it is called
dynamic or ac resistance.
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The Diode – Voltage-Current Characteristic
• When a reverse-bias voltage is applied across a diode, there is only an extremely small
reverse current (IR) through the pn junction.
• With 0 V across the diode, there is no reverse current.
• As you gradually increase the reverse-bias voltage, there is a very small reverse current and
the voltage across the diode increases.
• When the applied bias voltage is increased to a value where the reverse voltage across the
diode (VR) reaches the breakdown value (VBR), the reverse current begins to increase rapidly.
• As you continue to increase the bias voltage, the current continues to increase very rapidly,
but the voltage across the diode increases very little above VBR.
• Breakdown, with exceptions, is not a normal
mode of operation for most pn junction devices.
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The Diode – Voltage-Current Characteristic
• The complete V-I characteristic curve.
• Incidentally, this is affected by temperature
(more thermally generated carriers when
it is warmer).
17
The Diode – Models
• So, we have seen how a diode works: how it is made and how it operates when we apply
various bias voltages to it.
• Now, imagine we have a diode in a circuit and different voltages are being applied to it.
• We want to be able to describe how the current will change in the diode under different
voltages.
• To do this, we will use a model of how the voltage relates to the current.
• There are several models to choose from.
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The Diode – The Ideal Diode Model
• One very simple model for diode behaviour is the ideal model which is shown below.
• It basically says, that when the diode is reverse biased, it is cut off and no current flows.
• And that when a positive current is applied, zero voltage drop appears across the diode, i.e.,
it is turned on.
• Given what we have seen on the previous slides, this is obviously a simplification of how
diodes really operate.
19
The Diode – The Exponential Model
• Let’s examine another model, known as the exponential model.
• In forward-bias, the i-v relationship is closely approximated by:
i = IS (ev=nVT ¡ 1)
• IS is usually called the saturation current (we will see why shortly).
• The voltage VT is a constant called the thermal voltage and is given by:
kT
VT =
' 25 mV at room temperature
q
k is Boltzmann’s constant, T is temperature in Kelvin.
q is charge on electron.
• n is a constant that depends on the material and structure.
• It is between 1 and 2.
• For standard IC fabrication
processes, n  1.
This was VBR a few slides ago.
Same thing, don’t worry about it.
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The Diode – The Exponential Model
• When i is large (i.e., i >> IS), then
i ' IS ev=nVT
• Because of this exponential relationship, even if current gets very large, the voltage doesn’t
change much.
• Thus, for a “fully conducting” diode the voltage drop lies in a narrow range, approximately
0.6 V to 0.8 V.
• This gives rise to a simple "model" for the diode where it is assumed that a conducting
diode has approximately a 0.7-V drop across it, as mentioned already.
• For example, let’s compare the voltage for two different currents I1 and I2.
I2
= IS e(V2 ¡V1 )=nVT
I1
which can be rewritten as:
I2
V2 ¡ V1 = nVT ln
I1
Or in terms of log base-10:
V2 ¡ V1 = 2:3nVT log
I2
I1
21
The Diode – The Exponential Model
• In reverse bias, the exponential term becomes negligibly small. So:
i ' ¡IS
• This is the reason that IS is given the name saturation current.
22
The Diode – The Exponential Model
• The exponential model is highly nonlinear which makes it tricky to use when analyzing a
circuit.
• For example, consider the circuit below:
• Assuming that VDD is greater than 5 V or so, the diode current will be much greater than IS,
and we can represent the diode i-v characteristic by the exponential relationship, resulting
in:
V =nV
ID ' IS e
D
T
• We can also see that ID =
VDD ¡ VD
R
23
The Diode – The Exponential Model
• We can solve this by drawing a graph:
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The Diode – The Exponential Model
• Or instead of using a graph we can solve by iterative analysis – for example:
Let’s assume VDD = 5 V and R = 1 k.
We will also assume that the diode has a current of 1 mA at a voltage of 0.7 V and that the
voltage changes by 0.1 V for every tenfold increase in current.
ID =
VDD ¡ VD
5 ¡ 0:7
=
= 4:3 mA
R
1
• We can then use the exponential equation to get a better estimate for VD.
• Using the equation from slide 22:
• Now for us 2.3nVT = 0.1 V
• Thus,
V2 ¡ V1 = 2:3nVT log
I2
I1
I2
V2 = V1 + 0:1 log
I1
• Substituting V1 = 0.7 V, I1 = 1 mA, and I2 = 4.3 mA results in V2 = 0.763 V.
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The Diode – The Exponential Model
• Putting these new value back into our first equation and iterating again gives:
5 ¡ 0:763
ID =
= 4:237 mA
1
·
and
V2 = 0:763 + 0:1 log
¸
4:237
= 0:762V
4:3
• The values from the second iteration are similar to the first, so we can stop there.
• The iterative analysis procedure shown here is simple and yields accurate results after two
or three iterations.
• Nevertheless, there are situations in which the effort and time required are still greater than
can be justified. Specifically, if one is doing a pencil-and-paper design of a relatively complex
circuit, rapid circuit analysis is a necessity.
• Through quick analysis, the designer is able to evaluate various possibilities before deciding
on a suitable circuit design.
• To speed up the analysis process one must be content with less precise results.
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What we covered in this lecture
• Recapped the main points underlying n-doping and p-doping.
• Introduced the PN junction highlighting the distribution of majority and minority
carriers throughout the material.
• Explained the generation of the depletion region and the barrier potential.
• Defined a diode as a PN junction with a conductive terminals attached to both the p
region and n region.
• Described the operation of the PN junction under forward and reverse bias (and in
reverse breakdown).
• Drew a schematic of the voltage-current characteristic.
• Introduced the need to model the v-i characteristic of a diode when considering its
operation as part of a circuit.
• Introduced the ideal diode model and pointed out its (over)simplicity.
• Introduced the exponential model highlighting that a large change in current can arise
with a very small change in voltage.
• Showed that modelling a diode in a circuit using the exponential model can be difficult
and time consuming.
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