1. Electrons and Holes ECE 2204

2. Intrinsic Carrier Concentration Intrinsic carriers are the free electrons and holes that are generated when one or more chemical bonds between the Si atoms break. ▫The intrinsic carrier concentration, the number of broken bonds per cubic centimeter, is given by:

3. Electron and Hole Concentration When a bond breaks: ▫One electron is freed and can wander through the crystal, but can’t leave the crystal. Hence, it is called a nearly free electron.  A nearly free electron is also known as a conduction electron. ▫One hole is generated and is temporarily tied between the two atoms with the broken bond  A hole is the lack of an electron to fill the outer shell of the two Si atoms that were sharing the now ‘free’ electron.

4. A bond can break when a Si atom absorbs enough energy from phonons (packets of heat) to equal the bandgap energy. Or, if it absorbs a photon that has as much or more energy than the bandgap energy, the atom can use the energy to break one of the bonds with another Si atom.

5. Electron and Hole Concentrations For intrinsic (pure) semiconductors: ▫The electron concentration, n, is the number of free electrons per cubic centimeter ▫The hole concentration, p, is the number of outer shell electrons that are missing because a chemical bond between Si atoms broke.

6. Electrons and Holes All electrons with the same energy and momentum are considered to be equal. All holes with the same energy and momentum are considered to be equal. ▫However, this is not true in magnetic semiconductors, such as MnGaAs, where spin up electrons are different from spin down electrons and similarly spin up holes are different from spin-down holes.  We aren’t going to worry about this exception. ▫Magnetic semiconductors are being investigated as an alternative to Si.  The technology is called spintronics.

7. Energy Diagram distance An energy diagram is a schematic drawing of the positions of the bottom of the conduction band and the top of the valence band as a function of distance.

8. From www.ioffe.ruwww.ioffe.ru Direct Semiconductor In this energy vs. momentum diagram (also known as an E-k diagram), the lowest point in the conduction band is directly above the highest point on the valence band (the curves below 0 eV). The difference between these two points is the bandgap energy, Eg. It is also the minimum energy required to take a valence electron (an outer shell electron) and put it into the conduction band (break a bond). If the free electron drops down into the valence band, energy must be released using some particle that has no momentum. The only particle that meets this requirement is a photon (a packet of light).

9. Modified from www.ioffe.ruwww.ioffe.ru Si Indirect Semiconductor In this E-k diagram, the lowest point in the conduction band is not directly above the highest point on the valence band. The difference between these two points is still the bandgap energy, Eg. If the free electron drops down from the lowest point in the conduction band in the highest point in the valence band, energy must be released using some particle that has momentum. The particle that meets this requirement is a phonon (a packet of heat). The probability that Si will emit light is approximately 1 in 10 15 transitions of an electron from the conduction band to the valence band. For most direct semiconductors, the probability is greater than 99 times out of 100.

10. Bandgap Energy vs. Temperature

11. What is the temperature dependence of n i ? B depends on the properties of the semiconductor – how heavy are the electrons and holes and how many places are available in the conduction band for electrons and in the valence band for holes. The value of B has a very small temperature dependence.

12. Values for B MaterialB (K -3 – cm -6 ) Si1.08 x 10 31 Ge2.31 x 10 30 GaAs1.27 x 10 29

14. Trends in intrinsic semiconductors n i increases with increasing temperature. Thus, the electrons and holes concentration in an intrinsic semiconductor increases with increasing temperature. ▫The curves stop when every atom has one broken bond. This is the temperature where the semiconductor is about to melt. Almost always, smaller the bandgap energy, the larger n i is at a particular temperature. ▫As discussed in the Semiconductor Material slides, Eg decreases as one moves down the periodic table.