Lasers and Semiconductors

Spontaneous emission: A process whereby a photon is emitted when an electron in an excited atom falls naturally to a lower energy level, i.e. without requiring an external event to trigger it.

Stimulated emission: A process whereby an incoming photon causes/induces another photon of the same frequency & phase (& direction) to be emitted from an excited atom.

Laser: A monochromatic, coherent, parallel beam of high intensity light.

Meta stable state: An excited state whose lifetime is much longer than the typical (10^-8s) lifetime of excited states.

Population inversion: A condition whereby there are more atoms in an excited state than in the ground state.

{A meta stable state is essential for laser production because it is required for population inversion to be achieved, which, in turn, increases the probability of stimulated emissions.}

Conditions to achieve Laser action:

1. Atoms of the laser medium must have a meta-stable state.
2. The medium must be in a state of population inversion.
3. The emitted photons must be confined in the system long enough to allow them to cause a chain reaction of stimulated emissions from other excited atoms.

Formation of Energy Bands in a Solid/Band theory for solids:

• Unlike the case of an isolated atom, in a solid, the atoms are very much closer to each other.
• This allows the electrons from neighbouring atoms to interact with each other.
• As a result of this interaction, each discrete energy level that is associated with an isolated atom is split into many sub-levels.
  {This is in accordance to Pauli Exclusion Principle which states that: no 2 electrons can be in the same energy state}
• These sub-levels are extremely close to one another such that they form an energy band.
  {In other words, an energy band consists of a very large number of energy levels which are very close together.}

Valence Band: The highest energy band that is completely filled with electrons.

Conduction Band: The next higher band; For some metals/ good conductors, it is partially-filled; For other metals, the VB & CB overlap {hence it is also partially-filled}

Energy Gap {Forbidden Band}: A region where no energy state can exist; It is the energy difference between the CB & VB

Properties of Conductors, Insulators and Semi-conductors at 0 K {“low temp”}:

	Conductors	Insulators	Semi-conductors
Conduction Band	Partially filled	Empty
Valence Band	Completely Occupied
Energy gap between the bands	NA	Large (≈10 eV)	Small (≈1 eV)
Charge Carriers	free electrons	-	free electrons & holes

How band theory explains the relative conducting ability of a metal, intrinsic semiconductor & insulator:

• For a (good) conductor {ie a metal}, when an electric field is applied, electrons in the partially-filled conduction band can very easily gain energy from the field to “jump” to unfilled energy states since they are nearby.

• The ease at which these electrons may move to a nearby unfilled/unoccupied energy state, plus the fact that there is a high number density of free electrons make metals very good electrical conductors.

• For an insulator, the conduction band is completely unoccupied by electrons; the valence band is completely occupied by electrons; and the energy gap between the two bands is very large.

• Since the conduction band is completely empty, and

• It requires a lot of energy to excite the electrons from the valence band to the conduction band across the wide energy gap,

• When an electric field is applied, no conduction of electricity occurs.
  {Thus, insulators make poor conductors of electricity.}

• For intrinsic semi-conductors, the energy gap between the two bands is relatively small {compared to insulator}

• As such even at room temp, some electrons in the valence band gain enough energy by thermal excitation to jump to the unfilled energy states in the conduction band, leaving vacant energy states in the valence band known as holes.

• When an electric field is applied, the electrons which have jumped into the conduction band and holes {in the valence band} act as negative and positive charge carriers respectively and conduct electricity.

• {Thus, for intrinsic semiconductors, the ability to conduct vary with temperature {or even light}, as light can cause photo-excitation}.

Doping:

• Refers to the addition of impurity atoms to an intrinsic semiconductor to modify the number and type of charge carriers.

• n-type doping increases the no. of free {NOT: valence } electrons; p-type doping increases the no. of holes.

• Note that, even with a very small increase in the dopants, the electrical resistivity of an extrinsic semiconductor decreases significantly because the number of charge carriers of the intrinsic semiconductor is typically very small.

Explain why electrical resistance of an intrinsic semiconductor material decreases as its temperature rises:

Based on the band theory, a semiconductor has a completely filled valence band and an empty conduction band with a small energy gap in between. Hence there are no charge carriers and the electrical resistance is high.

1. When temperature is low, electrons in the valence band do not have sufficient energy to jump across the energy gap to get into the conduction band.
2. When temperature rises, electrons in the valence band receive thermal energy to enter into the conduction band leaving holes in the valence band.
3. Electrons in the conduction band & holes in the valence band are mobile charge carriers and can contribute to current.
4. Increasing the number of charge carriers means lower resistance.

2 Differences between p-type silicon & n-type silicon:

1. In n-type Si, the majority charge carrier is the electron, its minority charge carrier is the hole.
   For p-type Si, the situation is reversed.
2. In n-type Si, the dopants are typically pentavalent atoms (having 5 valence electrons);
   In p-type Si, the dopants are typically trivalent atoms (valency = 3)

Origin of Depletion Region

How a p-n junction can act as a rectifier

• When a p-n junction diode is connected in reverse bias in a circuit, the negative terminal of the battery pulls holes from the p-type semiconductor leaving behind more negatively-charged acceptor ions. At the same time the positive terminal pulls electrons from the n-type semiconductor leaving behind more positively-charged donor ions.

• This results in the widening of the depletion region and an increase in the height of the potential barrier, and so no current flows.

• When a p-n junction diode is connected in a forward-bias connection in a circuit, the externally applied pd opposes the contact pd across the depletion region.

• If the externally applied pd is great enough, it supplies energy to the holes and electrons to overcome the potential barrier and, so a current will flow. {In general, a forward-bias connection narrows the depletion region and reduces the height of the potential barrier.}

{Thus a p-n junction {diode} allows current to flow in one direction only {when the p-n junction is in forward bias} and so, it can be used as a rectifier to rectify an ac to dc}

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