This piece of work is the further investigation of the 3B5 - Schottky Barrier Diode (SBD) experiment. It involves a comprehensive data error analysis to both the raw data from the experiment and the parameters derived from them. An in-depth probe to the SBD is also done by examining the fundamental theory of SBD with illustrative band diagrams and reference to the thermionic emission theory. The ideal SBD model is then compared with common p-n junction and their differences are discussed. Further analysis on the non-ideal behaviours of both the SBD and p-n junction diodes are performed as well.
Evac Metal eΦm EF n-type semiconductor Evac eχsc eΦsc Ec EF Ev Figure 1 – Band ...view middle of the document...
Before they are brought together into contact, they have independent band configuration and the uppermost energy band is the one for vacuum, Evac, which essentially marks the energy level for the electrons to go beyond the material surface, emitted into the vacuum. Intuitively, the Evac for both the materials should be at the same level and the work functions Φm, Φsc and electron affinity for the semiconductor χsc has been marked. Another feature of the typical band structures is the Fermi level EF for metal is lower than that of the semiconductor, i.e., as can see from the diagram. Thus, when these two materials are in contact with each other and reach thermal equilibrium, their EF will line up, and this effectively brings down all the energy levels of the semiconductor accordingly while the energy level remains the same as before at the metalsemiconductor interface, as shown in figure 2. This also causes a transfer of electrons to occur from the semiconductor to the metal, which creates a potential difference - the built in potential of the junction V0. Thus, in equilibrium, where e is the magnitude of the electronic charge.
Metal Evac eΦb,m = e(Φm - χsc) EF w
N-type semiconductor Evac eΦb,s = e(Φm - Φsc) Depletion Region EF Ev Ec
through this device is attributed to those two types of carriers flowing in opposite directions. The I-V characteristic equation under forward bias (Schockley equation) of the p-n junction diode can be found by considering the Law of Mass Action, and continuity equation for the electrons and holes, which is
Figure 2 – Band diagram of metal and n-type semiconductor when they are in contact
The junction capacitance can be found to be where Is is the reverse saturated current; V is the applied bias voltage; NA is the density of acceptor atoms; ND is the density of donor atoms in the conduction band; ni is the intrinsic carrier concentration. Detailed derivations of all these above equations are available in Appendix. This equation is based on the following assumptions: - The injected minority carrier concentration is much less than the majority carrier, - No recombination occurs in the depletion region, - Negligible fields outside the depletion region. These assumptions are, nonetheless, not applicable for modelling the I-V behaviour of a SBD because the SBD is a unipolar device with only electron flow being considered, and instead of simple diffusion, the electrons are injected into the metal from a higher energy level . Additionally, there is no stored carriers in the metal. Therefore, the current flow is determined by how fast the electrons can get from the semiconductor to the metal and Thermionic Emission Theory is applied to model this behaviour. This theory assumes that the mobility of the electrons is such that they can get across the barrier as fast as they are emitted, and if the mobility is too low then there would be a mobility limited process. The net current from the semiconductor to...