Junctions and Semiconductors

Theories and practical devices

Metallic and Semiconductor Junctions

Each conductor has a unique quantity of energy that is required to free an electron. This energy is called the work function energy, qValues for qfor various metals are given in the table below:

In figure A, two dissimilar metals are not in contact. When they come into contact as shown in B, their respective Fermi energies must equilibrate throughout. To do this, electrons transfer from B to the lower unfilled levels of A until the level of the electron “sea” in both metals is equal. This causes A to become negatively charged, and B to become positively charged. The resulting potential is called the contact potential (qVC)

The Contact Potential, qVC, is equal to the difference in the respective work functions:

qVC = EF(B)-EF(A), or qVC=q(A)-q(B)

Although a potential exists, no work can be extracted, because when we attach leads, (i.e., metal C) the sum of the work functions is zero:

qFnet = q(C-A)+(A-B)+B-C)] = 0

If we join an “n” type region, which has excess negative charges, with a “p” type region, i.e. a “p-n” junction” a charged region develops a the interface:

Electrons and holes recombine at the interface, depleting the available electrons in the n material making it more positive, and holes in the p material, making it more negative. This creates a built-in electric field that discourages further transfer across the interface.

Electron band diagrams are a way to visualize what happens at a p-n junction, using the following rules:

1. The Fermi level must be at the same level on both sides of the junction when there is no applied field

2. Far from the junctions, the materials inherent electrical structure exists

3. He bands are bent, or curved, where the built-in electric fields exist at the junction

4. A potential energy step, qVo, due to contact potential Vo, develops at the junction. It is equal in magnitude to EF(n)-EF(p) or, equivalently q(p)-q(n)

5. Externally applied electric potentials displace the relative positions of EF and the band edges by amounts over and above those produced by the above rules.

If we apply a “reverse bias”, as depicted in A above and in figure B on the left, the barrier at the junction increases to q(Vo+V), thus increasing the barrier to current flow. If we apply a forward bias, as in B above and C, left, we annihilate EHPs and have a positive current flow

Forward biasing causes current to flow; reverse biasing causes it to stop flowing in a p-n junction. This can be represented in the following equation:

j = jR[exp (eV/kT)-1]

V is positive for forward biasing, and negative for reverse biasing.

jR is the reverse biased current

The Junction Equation

DIODES are p-n junctions that act as rectifiers, allowing current to pass only in one direction

Tunnel Diodes

Tunnel diodes act as oscillators. Current increases up to Vp, decreases between Vp and Vc, then increases beyond Vc

As shown at left, the Fermi level exists in the conduction zone of the n-type material and the valence zone of the p-type material. When a biasing voltage is applied, the electrons jump, or “tunnel” across the forbidden gap at the junction. When Vp<V<Vc, the gap widens and tunneling becomes small. Then, when V>Vc, tunneling can begin again.

Zener diodes

Zener diodes are used to regulate voltages in circuits. When the voltage becomes sufficiently large (10-1000V, depending on doping level), it reaches a “limiting” or “break down” voltage, and current is shunted to ground.

Transistors: triodes, npn and pnp junctions

MOS-FET

Current flow in a transistor vary with emitter voltage, Ve:

I = Ioexp(Ve/B)

Where Io and B are constants

Numerous transistors, resistors and electronic elements can be incorporated on a single wafer of semiconductor material, thus creating the integrated circuit

Thermocouples and other thermoelectric devices

If opposite ends of a metal bar are maintained at different temperatures, electrons will flow from the hot end to the cold end. As electrons pile up at the cold end, it creates a net electromotive force, or Seebeck voltage, opposing further charge transfer.

Seebeck voltage varies sensitively with temperature, and are 1000-fold larger in semiconductors than in metals. Using semiconductors used to measure changes in voltage are called thermistors, and can very accurately measure temperature

Other devices that measure temperature or have thermoelectric properties include thermocouples, Peltier effect and thermoelectric refrigerators.

When current flows through a junction, heat may be generated or absorbed, depending on current polarity. This enables the design of electric refrigerators

When metals with different work functions are joined, they generate a voltage that varies with temperature. Thermocouples accurately measure temperature by measuring this voltage difference.