1. SEMI CONDUCTOR
The electrons in the valence band are bound to the atoms of the crystal. They need to have enough extra energy to go across the forbidden band gap to get into the energy levels of the conduction band. To quantify electron concentration, count the number of electrons in the conduction band per a unit volume, typically a cm3. This is shown by the symbol n. When the system is in equilibrium, it is shown by n0.
Similarly, the number of holes in the valence band per unit volume is called “hole concentration” and shown by the symbol p. In equilibrium, we use p0.
2. INTRINSIC AND EXTRINSIC MATERIALS
An intrinsic semiconductor is ideally a perfect crystal. When an electron in an intrinsic semiconductor gets enough energy, it can go to the conduction band and leave behind a hole. This process is called “electron hole pair (EHP) creation”. For the intrinsic material, since electrons and holes are always created in pairs,
n = p = ni
where ni is the symbol for ”intrinsic carrier concentration.”
The intrinsic carrier concentration in silicon at room temperature is approximately,
ni = 1.45 × 1010 [1 /cm3 ] silicon, 300 K
3. EXTRINSIC MATERIALS
Extrinsic semiconductor can be made by adding some impurities in to the pure semiconductor.
There are two types of extrinsic material:
The dopant atoms added to the semiconductor crystal in this case are donor atoms. For silicon, we can use phosphorus (P), arsenic (As) or antimony (Sb) as donors. These are column V elements, with five electrons in their outermost shell. When these atoms are included in the silicon crystal, one of the electrons in this shell can easily jump to the conduction band, leaving a positively charged atom behind. This process is sometimes called “activation” or “ionization” of the donor atoms.
The positively charged donor atom that is left behind after ionization is immobile and does not contribute to conduction. The electron leaving the atom by ionization does, and is counted in the electron concentration n. Because the activation energy is low, at room temperature almost all of the donor atoms included in the crystal will give an electron to the conduction band. So if ND the donor concentration, for an n-type material at equilibrium.
N0 = ND
The dopant atoms in this case are acceptor atoms. For silicon, we can use boron (B), Aluminium (Al) and Gallium (Ga) as acceptors. These are column III elements, with three electrons in their outermost shell. When these atoms are included in the silicon crystal, one of the electrons in the silicon valence band can easily jump to the valence shell of one of the acceptor atoms, leaving a hole behind and making the acceptor atom negatively charged.
The negatively charged acceptor atom after an electron joins its valence shell is immobile and does not contribute to conduction. The hole left behind by that electron does, and is counted in the hole concentration p. Because the activation energy is low, at room temperature almost all of the acceptor atoms included in the crystal will accept an electron from the valence band. So if NA is the acceptor concentration, for a p-type material at equilibrium.
For both intrinsic and extrinsic materials, at equilibrium,
For an n-type material,
For a p type material,
n0= ni2/NA (3)
If ND > NA , material is N type.
n0= ND – NA ; p0= ni2/n0
If NA> ND, material is P type.
p0= NA– ND ; n0= ni2/NA
4. CARRIER TRANSPORT IN SILICON
Any motion of free carriers in a semiconductor leads to a current. This motion can be caused by an electric field due to an externally applied voltage, since the carriers are charged particles. This transport mechanism is carrier drift. Carriers also move from regions where the carrier density is high to regions where the carrier density is low. This carrier transport mechanism is due to the thermal energy and the associated random motion of the carriers. This transport mechanism is carrier diffusion. The total current in a semiconductor equals the sum of the drift and the diffusion current.
As applies an electric field to a semiconductor, the electrostatic force causes the carriers to first accelerate and then reach a constant average velocity, v, due to collisions with impurities and lattice vibrations. The ratio of the velocity to the applied field is called the mobility.
The motion of a carrier drifting in a semiconductor due to an applied electric field, , The field causes the carrier to move on average with a velocity, v.
Assuming that all the carriers in the semiconductor move with the same average velocity, the current can be expressed as the total charge in the semiconductor divided by the time needed to travel from one electrode to the other, or:
where tr is the transit time of a particle, traveling with velocity, v, over the distance L. The current density, J, can then be rewritten as a function of the charge density, :
If the carriers are negatively charged electrons, the current density equals:
while for positively charged holes it is:
Where n and p are the electron and hole density in the semiconductor.
In the absence of an applied electric field, the carrier exhibits random motion and the carriers move quickly through the semiconductor and frequently changes direction.
When an electric field is applied, the random motion still occurs but in addition, there is on average a net motion along the direction of the field. Due to their different electronic charge, holes move on average in the direction of the applied field, while electrons move in the opposite direction.
Jp| Drift = q p vd and Jn | Drift = q n vd
Where Jp =Hole Drift current density
Jn = Electron Drift current density.
At low electric field values,
Jp = qpμpE and Jn = qnμnE
μ is the “mobility” of the semiconductor and measures the ease with which
carriers can move through the crystal.
Thus, the drift velocity increases with increasing applied electric field.
Nature attempts to reduce concentration gradients to zero.
Example: a bad odour in a room.
In semiconductors, this “flow of carriers” from one region of higher concentration to lower concentration results in a “diffusion current”.
Ficks law describes diffusion as the flux, F, is proportional to the gradient in concentration.
where η is the concentration and D is the diffusion coefficient.
For electrons and holes, the diffusion current density (flux of particles times -/+q) can thus, be written as,
Jp| Diffusion= -qD p ∇p or
Jn| Diffusion= qD n∇n
Jp= Jp |drift + Jp| diffusion= q µp p E – q D p ∇p
Jn= Jn |drift + Jn |diffusion = q µn n E – q D n ∇n
J= Jn +Jp
GENERATION AND RECOMBINATION
Generation: e.g., absorption of a photon generates a free electron and a free hole (an electron‐hole pair).
Recombination: can be radiative, in which case a photon is emitted as the electron returns to the valence band, or non‐radiative, in which case the energy associated with the e‐h pair is converted to heat, or transferred to another charge Carrier (Auger recombination) – non‐radiative corresponds to no photon.
Generation, under influence of light absorption for example, promotes electrons from the valence band to the conduction band, resulting in a new free electron in the CB, and a new hole in the VB.
Recombination is essentially the reverse process, in which an electron returns to the valence band, giving up it electronic potential energy to a photon, or a third carrier, or to phonons.
5. p- n JUNCTION DIODE
A diode is a dispositive made of a semiconductor material, which has two terminals or electrodes (di-ode) that act like an on-off switch. When the diode is “on”, it acts as a short circuit and passes all current. When it is “off”, it behaves like an open circuit and passes no current.
A p–n junction diode is made of a crystal of semiconductor. Impurities are added to it to create a region on one side that contains negative charge carriers (electrons), called n-type semiconductor, and a region on the other side that contains positive charge carriers (holes), called p-type semiconductor. When two materials i.e. n-type and p-type are attached together, a momentary flow of electrons occur from n to p side resulting in a third region where no charge carriers are present. It is called Depletion region due to the absence of charge carriers (electrons and holes in this case). The diode’s terminals are attached to each of these regions. The boundary between these two regions, called a p–n junction, is where the action of the diode takes place. The crystal allows electrons to flow from the N-type side (called the cathode) to the P-type side (called the anode), but not in the opposite direction.
A diode is simply a pn junction with the following characteristics:
• Under forward bias, it needs a small voltage to conduct. This voltage drop is maintained during conduction.
• The maximum forward current is limited by heat-dissipation ability of the diode. Usually it is around 1000 mA.
• There is a small reverse current.
• Every diode has a maximum reverse voltage (breakdown voltage) that cannot be exceeded without diode damage.
5.1 DIODE EQUATION
5.1.1 Reverse Bias
When the diode is reverse-biased, a very small drift current due to thermal excitation flows across the junction. This current (reverse saturation current, I0) is given, according to the Boltzmann equation, by the formula:
I0 = K0 e-ev0/kT
Where K0 is a constant depending on the pn junction geometry and V0 is the built-in voltage of the diode.
5.1.2 Forward Bias
When the diode is forward-biased through a voltage V, a small drift current flows again across the junction. In that case, however, there is an additional component, the diffusion current Vd, given by the formula:
Id = K0 e e(V −V0)/kT
These two currents have opposite directions, the total current is therefore given by:
I = Id − I0 = K0 e e(V −V0)/kT – K0 e-ev0/kT
5.2 General Diode Specifications
There are four diode ratings that apply in one way or another to all types of diodes and applications:
1. Forward voltage drop VF : is the forward-conducting junction level (0.7 V for Si diodes and 0.3 V for Ge diodes).
2. Average forward current IF: is the maximum amount of forward current that the diode can carry for an indefinite period. If the average current exceeds this value, the diode will overheat and, eventually, will be destroyed.
3. Peak reverse voltage VR, or reverse breakdown voltage: This is the largest amount of reverse-bias voltage the diodes’s junction can withstand for an indefinite period of time. If a reverse voltage exceeds this level, the voltage will punch through the depletion layer and allow current to flow backwards through the diode, which is a destructive operation (except for the case of a Zener diode).
4. Maximum power dissipation P: The actual diode power dissipation is calculated multiplying the forward voltage drop and the forward current. Exceeding the maximum power dissipation will result in thermal breakdown of the diode.
A semiconductor diode’s behavior in a circuit is given by its current–voltage characteristic, or I–V graph (see graph below). The shape of the curve is determined by the transport of charge carriers through the so-called depletion layer or depletion region that exists at the p–n junction between differing semiconductors. When a p–n junction is first created, conduction-band (mobile) electrons from the N-doped region diffuse into the P-doped region where there is a large population of holes (vacant places for electrons) with which the electrons “recombine”. When a mobile electron recombines with a hole, both hole and electron vanish, leaving behind an immobile positively charged donor (dopant) on the N side and negatively charged acceptor (dopant) on the P side. The region around the p–n junction becomes depleted of charge carriers and thus behaves as an insulator.
Junction Diode Ideal and Real Characteristics
There are two operating regions and three possible “biasing” conditions for the standard Junction Diode and these are:
- 1. Zero Bias – No external voltage potential is applied to the PN junction diode.
- 2. Reverse Bias – The voltage potential is connected negative, (-ve) to the P-type material and positive, (+ve) to the N-type material across the diode which has the effect of Increasing the PN junction diode’s width.
- 3. Forward Bias – The voltage potential is connected positive, (+ve) to the P-type material and negative, (-ve) to the N-type material across the diode which has the effect of Decreasing the PN junction diodes width.
Avalanche Breakdown(for V> 5 V)
Under very high reverse bias voltage kinetic energy of minority carriers become so large that they knock out electrons from covalent bonds, which in turn knock more electrons and this cycle continues until and unless junction breakdowns.
Zener Effect (for V<5V)
Under reverse bias voltage junction barrier tends to increase with increase in bias voltage. This results in very high static electric field at the junction. This static electric field breaks covalent bond and set minority carriers free which contributes to reverse current. Current increases abruptly and junction breaks down.