diode

1. JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR
ANANTHAPURAMU – 515 002 , ANDHRA PRADESH
Electronic Devices and Circuits
11-05-2020 to 23-05-2020
Prof. S. Srinivas Kumar
Vice Chancellor
GATE Coaching Classes as per the Direction of
Ministry of Education
GOVERNMENT OF ANDHRA PRADESH

2. Content of the Lecture
Fourth class (Prof. S.Srinivas Kumar)
1. The Open-Circuited p-n junction
2. The p-n Junction as a Rectifier
3. The current components in a p-n diode
4. V-I Characteristic of semi-conductor diode
5. Diode Equation
6. Temperature dependence of the V/I characteristic
7. Exercise Problems & Objective Type Questions

3. Extrinsic Semiconductor (n type )
Crystal lattice with a germanium atom
displaced by a pentavalent impurity atom
Donor Impurity atoms: Antimony, Arsenic , Phosperous
Acceptor Impurity atoms: Boron, Gallium, Indium
Crystal lattice with a germanium atom
displaced by a Trivalent impurity atom

5. The Open Circuited p-n Junction
If donor impurities are introduced into one side and acceptors into the
other side of a single crystal of a semiconductor, a p-n junction is formed.
 The donor ion is represented by a plus sign because, after this impurity
atom "donates" an electron, it becomes a positive ion.
 The acceptor ion is indicated by a minus sign because, after this atom
"accepts" an electron, it becomes a negative ion.
 Space-charge Region: Because there is a density gradient across the
junction, holes will initially diffuse to the right across the junction, and
electrons to the left.

6.  The general shape of the charge density ρ, depends upon how the
diode is doped. Since the region of the junction is depleted of mobile
charges, it is called the depletion region, the space-charge region, or
the transition region. The thickness of this region is of the order of the
wavelength of visible light (0.5 micron = 0.5 Am).
 Within this very narrow space-charge layer, there are no mobile
carriers. To the left of this region the carrier concentration is p ≈NA,
and to its right it is n ≈ ND.

7. Electric Field Intensity: The space-charge density ρ is zero at the junction. It
is positive to the right and negative to the left of the junction.
Under steady-state conditions the drift hole (electron) current must be
equal and opposite to the diffusion hole (electron) current so that the net hole
(electron) current is reduced to zero—as it must be for an open-circuited
device. In other words, there is no steady-state movement of charge across
the junction.
The field intensity curve is proportional to the integral of the charge density
curve. This statement follows from Poisson's equation
where ɛ is the permittivity. If ɛr is the (relative) dielectric constant and ɛo, is
the permittivity of free space, then ɛ = ɛrɛo.
 Integrating Eq. and remembering that ɛ = —dV/dx gives where ɛ = 0 at
x = xo. Therefore the curve plotted in Fig. is the integral of the function drawn
in Fig. (divided by ɛ).

8. The electrostatic-potential variation in the depletion region is shown in Fig. and
is the negative integral of the function ɛ of Fig.
This variation constitutes a potential-energy barrier against the further
diffusion of holes across the barrier.
The form of the potential-energy barrier against the flow of electrons from the
n side across the junction is shown in Fig.
Under open-circuited conditions the net hole current must be zero. If this
statement were not true, the hole density at one end of the semi-conductor
would continue to increase indefinitely with time, a situation which is obviously
physically impossible.
Since the concentration of holes in the p side is much greater than that in the n
side, a very large hole diffusion current tends to flow across the junction from the
p to the n material. Hence an electric field must build up across the junction in
such a direction that a hole drift current will tend to flow across the junction from
the n to the p side in order to counterbalance the diffusion current.
This equilibrium condition of zero resultant hole current allows us to calculate
the height of the potential barrier Vo in terms of the donor and acceptor
concentrations. The numerical value for Vo is of the order of magnitude of a few
tenths of a volt.

9. (a) A p-n junction biased in the reverse
direction
(b) The rectifier symbol is used for the p-n
diode
(a) A p-n junction biased in the forward
direction
(b) The rectifier symbol is used for the p-n
diode
The p-n Junction as a Rectifier

10. The Volt- Ampere Characteristic
In the p-n junction, the current I is related to the voltage V by the
equation
A positive value of I means that current flows from the p to the n side. The
diode is forward-biased if V is positive, indicating that the p side of the
junction is positive with respect to the n side. The symbol η is unity for
germanium and is approximately 2 for silicon at rated current.
The symbol VT stands for the volt equivalent of temperature, and is given by
Eq. repeated here for convenience:
At room temperature (T = 300°K), VT = 0.026 V = 26 mV.

12. V-I characteristic of Semiconductor diode

13. Ideal diode characteristic
(Second quadrant)
V (milli volts)
I (mA)
I (μA)
V (volts)
For forward bias, Rf = 0 and cutin voltage is 0
For reverse bias Rr = Infinite

14. The p-n Junction as a Rectifier
The essential electrical characteristic of a p-n junction is that it constitutes a
rectifier which permits the easy flow of charge in one direction but restrains
the flow in the opposite direction. We consider now, qualitatively, how this
diode rectifier action comes about.
Reverse Bias A battery is shown connected across the terminals of a p-n
junction. The negative terminal of the battery is connected to the p side of the
junction, and the positive terminal to the n side.
The polarity of connection is such as to cause both the holes in the p type and
the electrons in the n type to move away from the junction.
Consequently, the region of negative-charge density is spread to the left of the
junction and the positive-charge-density region is spread to the right.
However, this process cannot continue indefinitely, because in order to have a
steady flow of holes to the left, these holes must be supplied across the
junction from the n-type silicon. And there are very few holes in the n-type
side. Hence, nominally, zero current results.

15. Actually, a small current does flow because a small number of hole-
electron pairs are generated throughout the crystal as a result of
thermal energy. The holes so formed in the n-type silicon will
wander over to the junction. A similar remark applies to the
electrons thermally generated in the p-type silicon.
This small current is the diode reverse saturation current, and its
magnitude is designated by Io. This reverse current will increase
with increasing temperature.

16. Forward Bias
An external voltage applied with the polarity shown in Fig. (opposite to that
indicated in Fig.) is called a forward bias. An ideal p-n diode has zero ohmic
voltage drop across the body of the crystal.
For such a diode the height of the potential barrier at the junction will be
lowered by the applied forward voltage V.
Hence, for a forward bias, the holes cross the junction from the p-type into
the n-type region, where they constitute an injected minority current.
Similarly, the electrons cross the junction in the reverse direction and
become a minority current injected into the p side.
Holes traveling from left to right constitute a current in the same direction
as electrons moving from right to left. Hence the resultant current crossing
the junction is the sum of the hole and electron minority currents.

17. Large Forward Voltages
Suppose that the forward voltage V in Fig. is increased until V approaches
V0. If V were equal to V0, the barrier would disappear and the current could
be arbitrarily large, exceeding the rating of the diode.
As a practical matter we can never reduce the barrier to zero because, as
the current increases without limit, the bulk resistance of the crystal, as well
as the resistance of the ohmic contacts, will limit the current.
Therefore it is no longer possible to assume that all the voltage V appears as
a change across the p-n junction.
The forward voltage V becomes comparable with Vo, the current through a
real p-n diode will be governed by the ohmic contact resistances and the
crystal bulk resistance.
Thus the volt-ampere characteristic becomes approximately a straight line.

18. In the given Half wave Rectifier Circuit, with ideal diode, Sinusoidal signal is
given as input. The DC Current flowing through the circuit is Idc . The load is
RL. What is the DC Voltage across ideal diode.
Idc
a) 0V
b) ∞
c) Idc RL
d) - Idc RL

19. Notations
Pn Holes in n-type Semi Conductor
np Electrons in p-type Semi Conductor
Pp Holes in p-type Semi Conductor
nn Electrons in n-type Semi Conductor

20. The Current Components in a p-n Diode
When a forward bias is applied to a diode, holes are injected into
the n side and electrons into the p side. It was emphasized that
under low-level injection conditions such minority currents are due
almost entirely to diffusion, so that minority drift currents may be
neglected.
The hole diffusion current in the n-type material Ipn , decreases
exponentially with distance x into the n-type region and falls to 1/ɛth
its peak value in a diffusion length LP..
This current is also the corresponding electron diffusion current Inp,
in the p-type side. The doping on the two sides of the junction need
not be identical, and it is assumed in this plot that the acceptor
concentration is much greater than the donor density, so that the
hole current greatly exceeds

22. The Law of the Junction
In the preceding section it was pointed out that a forward bias V
lowers the barrier height and allows more carriers to cross the
junction. Hence pn(0) must be a function of V. From the Boltzmann
rela-tionship, Eq. it seems reasonable that pn(0) should depend
expo-nentially, upon V. It is found that
This relationship, which gives the hole concentration at the edge of
the n region (at x = 0, just outside of the transition region) in terms of
the thermal-equilibrium minority-carrier concentration No (far away
from the junction) and the applied potential V, is called the law of the
junction.
A similar equa-tion with p and n, interchanged gives the electron
concentration at the edge of the p region in terms of V.

23. Diffusion Currents
The minority (hole) diffusion current is IP = A Jp where A is the cross
section of the bar.

24. when x=0
Substituting the law of the junction in the above equation
This equation derivation will be explained later

25. The Total Diode Current Substituting into Eq. yields
The expression for the electron current Inp(0) crossing the junction into the p
side is obtained is given by the following equation
Electrons crossing the junction at x = 0 from right to left constitute a current
in the same direction as holes crossing the junction from left to right. Hence
the total diode current I at x = 0 is
Since the current is the same throughout a series circuit, I is independent of
x and is indicated as a horizontal line in Fig. The expression for the diode
current is

26. The Reverse Saturation Current
In the foregoing discussion a positive value of V indicates a forward bias.
The derivation of Eq. is equally valid if V is negative, signifying an applied
reverse-bias voltage. For a reverse bias whose magnitude is large compared
with VT (≈26 mV at room temperature), I → -Io, Hence Io is called the reverse
saturation, current.
Since the thermal-equilibrium concentrations pno and npo, depend upon
tem-perature T, then Io is a function of T.

27. The Majority-carrier Current Components
In the n-type region of Fig. the total current I is constant and the
minority (hole) current Ipn varies with x. Clearly, there must exist
a majority (electron) current Inn, which is a function of x because
the diode current I at any position is the sum of the hole and
electron currents at this distance.
Inn (x) = I - Ipn (x)
This majority current is plotted as the dashed curve in the n
region of Fig. where the narrow depletion region is also
indicated. The majority hole current Ipp is similarly shown dashed
in the p region of this figure. these majority currents are each
composed of two current components; one is a drift current and
the second is a diffusion current. the diffusion electron current is
—(Dn/Dp)Ipn in the n side.

28. The holes approach the junction, some of them recombine with the
electrons, which are injected into the p side from the n side. The current Ipp
thus decreases toward the junction what remains of Ipp at the junction
enters the n side and becomes the hole diffusion current Ipp.
Similar remarks can be made with respect to current Inn.
We emphasize that the current in a p-n diode is bipolar in character
since it is made up of both positive and negative carriers of electricity.
The total current is constant throughout the device, but the proportion
due to holes and that due to electrons varies with distance.
In the transition region the carrier recombination may be neglected.

29.  When the voltage V is positive and several times VT the unity in the
parentheses may be neglected.
Accordingly, except for a small range in the neighborhood of the origin,
the current increases exponentially with voltage. When the diode is
reverse-biased, and Vi is several times VT, I ≈ -Io. The reverse current is
therefore constant, independent of the applied reverse bias. Consequently,
Iois referred to as the reverse saturation current.
 Ordinarily, the range of forward currents over which a diode is operated
is many orders of magnitude larger than the reverse saturation current.
The volt-ampere characteristic shown in that figure has a forward-current
scale in milliamperes and a reverse scale in microamperes.
The dashed portion of the curve of Fig. indicates that, at a reverse-biasing
voltage Vz, the diode characteristic exhibits an abrupt and marked
departure from Eq. At this critical voltage a large reverse current flows, and
the diode is said to be in the breakdown region.

30. The Cutin Voltage Vϒ
 There exists a cutin, offset, break-point, or threshold, voltage Vϒ
below which the current is very small.
 Beyond Vϒ the current rises very rapidly. From Fig. we see that Vℽ is
approxi-mately 0.2 V for germanium and 0.6 V for silicon.
The reason for this difference is to be found, in part, in the fact that
the reverse saturation current in a germanium diode is normally larger
by a factor of about 1,000 than the reverse saturation current in a silicon
diode of comparable ratings.
I0 is in the range of microamperes for a germanium diode and nano
amperes for a silicon diode at room temperature.
 Since η= 2 for small currents in silicon, the current increases as ƐV/2VT
for the several tenths of a volt and increases as Ɛ V/VT. only at higher
voltages. This initial smaller dependence of the current on voltage
accounts for the further delay in the rise of the silicon characteristic.

32. The Temperature Dependence of the V/I Characteristic
The volt-ampere relationship contains the temperature
implicitly in the two symbols VT and Io. It is shown that the
theoretical variation of Io with T is 8 percent/°C for silicon and
11 percent /°C for germanium.
From experimental data we observe that the reverse
saturation current increases approximately 7 percent/°C for
both silicon and germanium.
Since (1.07)10≈ 2.0, we conclude that the reverse saturation
current approximately doubles for every 10°C rise in
temperature.

33. If the temperature is increased at a fixed voltage, the current
increases. However, if we now reduce V, then I may be brought
back to its previous value. In silicon or germanium (at room
temperature)
In order to maintain a constant value of I. It should also be
noted that |dV / dT| decreases with increasing T

35. Band Structure of An Open Circuit p-n Junction
 We here consider that a p-n junction is formed by placing p- and n-type mate-rials
in intimate contact on an atomic scale. under these conditions the Fermi level must
be constant throughout the specimen at equilibrium.
 If this were not so, electrons on one side of the junction would have an average
energy higher than those on the other side, and there would be a transfer of
electrons and energy until the Fermi levels in the two sides did line up.
Fermi level EF is closer to the conduction band edge Ecn in the n-type material and
closer to the valence band edge Evp in the p side. Clearly, then, the conduction band
edge Ecp, in the p material cannot be at the same level as Ecn, nor can the valence
band edge Evn in the n side line up with Evp.
 Hence the energy-band diagram for a p-n junction appear as shown in Fig., where a
shift in energy levels. E0 is indicated.
Note that This energy E0represents the potential energy of the electrons at the
junction, as is indicated in Fig.

36. The Contact Difference of Potential
We now obtain an expression for Eo. From Fig. we see that
and
Adding these two equations, we obtain
np = ni
2

37. Substituting from Eqs. and in Eq. yields
The E's are expressed in electron volts and k has the dimensions of electron
volts per degree Kelvin.
The contact difference in potential Vo is expressed in volts and is numerically
equal to Eo. Note that Vo, depends only upon the equilibrium concentrations,
and not at all upon the charge density in the transition region.

38. The p-n Diode Volt- Ampere Equation
Consider a p-n junction biased by an external voltage V in the forward
direction as in Fig. Under low-level injection conditions the minority diffusion
current. crossing the junction at x = 0 is, from Eq.
The injected carrier concentration at the junction depends upon the applied
voltage V. We now find this relationship.

39. The Law of the Junction
Across the junction the electric field is high, and hence so is the drift current.
Also, the diffusion current is large because of the high-concentration
gradient at the junction. In Eq. namely
the magnitude of each term on the right-hand side is large compared with
the low-level injection current Jp. If two large numbers are subtracted and we
obtain a small difference, these two quantities are almost equal. Hence we
may write approximately.
using the Einstein relationship, Eq. becomes

40. At the left-hand side of the p material the hole concentration equals the
thermal-equilibrium value ppo. At the right-hand edge of the depletion region
in Fig. (in the n side) the hole concentration is pn(0). The junction voltage Vj is
the barrier potential V0 decreased by the forward voltage V. Integrating Eq.
across the junction gives
Carrying out the integration yield
p1 =ppo , p2 =pno and V21 =Vo
Dividing Eq. by Eq. yields
This boundary condition is called the law of the junction. It indicates that for
a forward bias (V >0) and with V >> VT (~26 mV at room temperature) the
hole concentration pn(0) at the junction in the n side is greatly increased over
the thermal-equilibrium value pno. The argument given above is also valid for
a reverse bias, and Eq. indicates that for negative V with |V| >> VT, the
concentration pn(0) is essentially zero.

41. The Current Components
From eq. with
The electron current Inp(0) crossing the junction into the p side is obtained
from Eq.) by interchanging n and p, or
Finally, from Eq. the total diode current I is the sum Ipn(0), and Inp(0) or
where
If Wp and Wn are the widths of the p and n materials, respectively, the above
derivation has implicitly assumed that Wp>>Ln and Wn>>Lp. If, as some-times
happens in a practical (short) diode, the widths are much smaller than the
diffusion lengths, the expression for L0 remains valid provided that Ln and Lp
are replaced by Wp and Wn respectively.

42. The Reverse Saturation Current
For a reverse bias whose magnitude is large compared with VT, I ─> -I0.Hence
Io is called the reverse saturation current. Combining Eqs. we obtain
Where is as given by Eq.
where VGO is a voltage which is numerically equal to the forbidden-gap
energy EGO in electron volts, and VT is the volt equivalent of temperature. For
germanium the diffusion constants Dp, and Dn vary approximately inversely
proportional to T. Hence the temperature dependence of I0 is
where K1 is a constant independent of temperature.

43. We have neglected carrier generation and recombination in the space-charge
region. Such an assumption is valid for a ger-manium diode, but not for a
silicon device. For the latter, the diffusion cur-rent is negligible compared
with the transition-layer charge-generation current, which is given
approximately by
where η≈2 for small. (rated) currents and η≈1 for large currents.