the expressions for total electron and hole densities is given by Eq. (17).
dn
dp
J = eμ nE + eD
A / m2
and
J = eμ pE − eD
A / m2
(17)
e
e
e dx
h
h
h dx
Activity 1.7.5 Recombination
(i) Recombination is also a phenomenon which occurs in semiconductors.
(ii) It results from the collision of an electron with a hole as free conduction
electron return to the valence band.
(iii) Recombination is accompanied by the emission of energy.
Besides all these, thermal generation of electron-hole pairs takes place continuously
in semiconductors. Hence, there is net recombination rate given by the difference
between the recombination and generation rates.
To learn more about diffusion, drift and recombination log to http://jas.eng.buffalo.
edu/education/semicon/diffusion/diffusion.htmlhttp://jas.eng.buffalo.edu/education/
semicon/diffusion/diffusion.html . 7th October 2007.
Activity 1.8
P-N Junction
In this section you will learn that:
(i) A P-N junction is formed by joining together a doped P-type semiconductor and
a doped N-type impurity semiconductor into a single piece of a semiconductor.
(ii) The plane that divides the P-type from the N-type semiconductors is called junction.
In addition to this you also learn that the following three phenomena take place:
1. A thin depletion layer or region (also called space-charge region or transition
region) is established on both sides of the junction and is so called because
it is depleted of free charge carriers. Its thickness is about 10−6 m. See Fig.
1.6.
2. A barrier potential or junction potential is developed across the junction.
3. The presence of depletion layer gives rise to junction and diffusion capaci-
tances.
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Activity 1.9
Formation of Depletion Layer
In this learning activity the key things to learn include:
(i) That at the onset of formation of P-N junction, the concentration of holes in
P-region is greater than electrons in the N-region (where they exist as minority
carriers).
(ii) This concentration differences establishes density gradient across the junction,
which leads to some of the free and mobile electrons in the N-region to diffuse
across the junction and combine with holes to form negative ions.
(iii) These free electrons leave behind positive ions on the N-region.
(iv) Consequently, a space charge builds up, thereby leading to creation of a narrow
region at the junction called depletion layer as shown in Fig.1.6.
(v) The depletion layer inhibits any further electron transfer unless the junction forward biased.
Figure 1.6.
Depletion region formed on both sides of the junction
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Activity 1.10
Origin of Junction or Barrier Voltage
The key concepts to learn are:
(i) An electric potential difference V known as junction or barrier potentialis
B
established across a P-N junction even when the junction is externally isola-
ted.
(ii) The establishment of barrier potential is due to the oppositely-charged fixed
rows of ions on either side of the two sides of the layer.
(iii) The existence of barrier potential, V , stops further flow of carriers across
B
the junction unless supplied by energy from an external source.
(iv) At room temperature of 300º K, V is about 0.3 V for Ge and 0.7 V for Si.
B
(v) Barrier potential is given by Eq. 18 as
⎛ N N ⎞
V = V log
a
d
(18)
B
T
e ⎜
⎟
⎝ n2
i
⎠
where
N is electron density,
is hole density, is electron denity before doping,
d
Na
ni
kT
1.38 × 10−23 × 300
V = V
=
=
= 26 mV
T
300 e
1.6 × 10−19
Activity 1.11
P-N energy band in equilibrium
Here you learn that:
(i) At equilibrium, the Fermi level match on the two sides of the junctions. Thus,
electrons and holes reach an equilibrium at the junction and form a depletion
region as in Fig.1.7.
(ii) The upward direction in Fig.1.7 represents increasing electron energy. This
means that energy has to be supplied in order for an electron to go up on the
diagram, and supply energy to get a hole to go down.
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Figure 1.7. Position of Fermi level in P-N energy band in equilibrium
Activity 1.11
P-N energy band in Forward biased
In this section you learn that when the p-n junction is forward biased, as shown in
Fig. 1.8:
the electrons in the conduction band in the n-type material on diffusing across the
junction find themselves at a higher energy than the holes in the p-type material.
As a consequence, they readily combine with those holes, making possible a conti-
nuous forward current through the junction .
For demonstration of P-N junction diode under bias, see
http://jas.eng.buffalo.edu/education/pn/biasedPN/index.html . 5th October 2007.
Figure 1.8.
P-N energy band in Forward biased
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Activity 1.12
Forward Biased Conduction
The following happens during forward biased conduction:
(i) The forward current in a p-n junction involves electrons from the N-type mate-
rial moving leftward across the junction and combining with holes in the p-type
material.
(ii) Electrons proceeds further leftward by jumping from hole to hole, making the
holes to be seen as moving to the right. See Fig.1. 9.
Figure 1. 9 Forward Biased Conduction
Activity 1.13
Reversed biased P-N Junction
(i) In a reversed biased P-N junction Fig. 1.10, a reverse voltage causes a tran-
sient current to flow as both electrons and holes are pulled away from the
junction.
(ii) The current will cease except for the small thermal current when the
potential formed by the widened depletion layer equals the applied
voltage.
Figure 1.10
Reversed biased P-N Junction
