Physics of Semiconductor Devices: 12.1.1 Direct Band Gap Semiconductors

12 PHYSICS OF SEMICONDUCTOR DEVICES
12.1 Introduction
12.1.1 Direct band gap semiconductors
The semiconductor materials for which maximum of valence band and minimum of conduction band lie for same
value of k, called direct band gap materials (i.e. satisfies the condition of energy and momentum conservation). In
case of the direct band gap semiconductors, the direct recombination of electron and hole will takes place and the
energy is liberated in the form of photon. Ex: GaAs, InP, CdS etc.
Figure 12.1 Direct & indirect band gap semiconductors
12.1.2 Indirect band gap semiconductors

The semiconductor materials for which maximum of valence band and minimum of conduction band do not occur
for same value of crystal momentum (k) are called indirect band gap semiconductors. The direct recombination of
electron and hole is not possible in these semiconductors and the energy is liberated in the form of heat. Hence
Indirect band gap materials are not suitable for fabricating LEDs and lasers.. Ex: Si and Ge
12.2 PN Junction Diode

A p–n junction is a junction formed by joining p-type and n-type semiconductors together in very close contact. The
term junction refers to the boundary interface where the two regions of the semiconductor meet.
The PN junction is not constructed by adding two separate p- type and n- type materials because this will reduce the
contact area between the two surfaces due to imperfections, grain boundaries etc. They are formed mainly by the
three methods i.e. ion implantation, diffusion of dopants or by epitaxial method.
12.2.1 Formation of the depletion region.

When the n-type semiconductor and p-type semiconductor materials are first joined together, a very large density
gradient exists between both sides of the pn junction. This results in the free electrons from the donor impurity
atoms to migrate across the junction to fill up the holes in the p-type material producing negative ions and vice versa.
This charge transfer of electrons and holes across the pn junction is known as diffusion.
This will result in positively charged donor ions (ND) on the n-side and negatively charged acceptor ions (NA) on the
p- side. This process continues until a point is reached where the negative charged accepter ions repels any further
diffusion of electrons and vice versa. These two layers of positive and negative charges form the depletion region,
as the region near the junction is depleted of charge carriers.
Figure 12.2 Formation of depletion region in a diode
12.2.2 Barrier potential.

The electric field formed in the depletion region acts as a barrier.
External energy must be applied to get the electrons to move
across the barrier of the electric field. The potential difference
required to move the electrons through the electric field is called
the barrier potential. Barrier potential depends on the type of
semiconductor material, amount of doping and temperature. This
is approximately 0.7 V for silicon and 0.3 V for germanium.
12.2.3 The Energy Level Diagram of a PN junction Figure 12.3: Formation of PN Junction
As diffusion occur, the depletion region forms and the energy
level of the n-region conduction band drops, causing alignment of the Fermi level. At this point the energy bands are
at equilibrium. There is an energy gradient across the depletion region so that a n-region electron must climb to get
in to the p-region.
Figure 4: Energy level diagram of a unbiased p-n junction diode.

12.2.4 Biasing the PN Junction.
12.2.4.1 Forward Bias.
When the anode of a diode is connected to a positive supply and the cathode to a negative supply, the diode is said to
be forward-biased. Bias voltage imparts sufficient energy to the free electrons so they overcome the barrier potential
and move into the p-region.
Figure 12.5 (a) p-n Junction with forward bias (b) Symbolic representation of p-n junction with forward bias.
Conduction occurs with electron current in the n-type material and hole current in the p-type material. As more
electrons and holes flow in the depletion region the number of positive and negative ions is reduced, causing the
depletion region to narrow.
The energy loss in overcoming the barrier potential results in a voltage drop across the pn junction equal to the
barrier potential. (0.7 V for Si, 0.3 V for Ge).
When a pn junction is forward biased the n-region conduction band is raised to a higher level that overlaps with the
p-region conduction band.
12.2.4.2 Reverse Bias

In a reverse bias condition, a positive voltage is applied to the n-side and a negative voltage is applied to the p-side
of semiconductor. Reverse bias prevents current flow through a pn junction.
Reverse bias potential attracts the majority carriers away from the pn junction, widening the depletion region. The
potential across the depletion region is equal to the bias voltage. Reverse current can flow through the pn junction
due to minority carriers. When a pn junction is reverse biased, the energy hill increases.
Figure 12.6 (a) p-n junction with reverse bias (b) Symbolic representation of p-n junction with reverse bias
12.2.5 I-V Characteristics of a PN junction diode
When a forward bias is applied, the electrons will acquire the energy and cross the pn junction resulting the current.
The forward voltage at which the current through the junction starts increasing rapidly is called the knee voltage or
cut-off voltage.
When reverse bias is applied, the majority carriers drift away from the junction hence no current is resulted due to
majority carriers. But a small current is produced due to minority charge carriers.
When reverse bias voltage exceeds certain voltage, a sharp increase in the reverse current is observed. This voltage
is known as breakdown voltage. The breakdown voltage may be due to the following mechanisms.
Figure 12.7 I-V characteristics of a PN junction
Zener breakdown.
Zener breakdown takes place in heavily doped p-n junction diode. In heavily doped pn junction diode, the depletion
laver is narrow (about 100 A0). This results a large electric field (about 10 8 Vm-1) even for small reverse
voltage. This electric field breaks the covalent bonds and produces electron hole pairs. Zener breakdown occurs in
the diodes with the breakdown voltage less than 6V.
The Zener breakdown voltage decreases with increase in temperature. This is due to increase in the temperature
increases the energy of valance electrons hence less field is enough to break the covalent bond.
Avalanche breakdown.
Due to high reverse voltage, the minority carriers get high kinetic energy. They collide with the valence electrons of
the atoms and break the covalent bonds creating new electron hole pairs. The new generated electron hole pairs will
generate further electron hole pairs. In this way large electron hole pairs will be created which result in sharp
increase in reverse current. This mechanism occurs to the diodes where the breakdown voltage is more than 6V.
The avalanche breakdown voltage increases with increase in temperature. This is due to increase in the temperature
increases the collisions of electron with lattice resulting the loss of electron energy.
12.2.6 PN Junction diode equation:
[ ( ) ]
is numerical constant and depends upon the diode material. For Ge and for Si

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12 PHYSICS OF SEMICONDUCTOR DEVICES

Figure 12.1 Direct & indirect band gap semiconductors

12.1.2 Indirect band gap semiconductors

12.2 PN Junction Diode

12.2.1 Formation of the depletion region.

12.2.2 Barrier potential.

Figure 4: Energy level diagram of a unbiased p-n junction diode.

12.2.4.2 Reverse Bias

Figure 12.7 I-V characteristics of a PN junction

12.2.6 PN Junction diode equation:

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