# Contact resistance in transistors
### Background

Contact resistance in transistors is the resistance between the metal and silicon in a contact. This is due to the difference in the bandgap energies between the two materials. The closer the bandgap the less resistance.
Early on in the semiconductor world, Aluminium was used as the metal, however this was replaced by copper which provided a better contact resistance.
If the example of a 1 micron and a 0.1 micron manufacturing process with aluminum contacts is taken into consideration it will become apparently clear how important this is becoming. The resistance of the device (R) is equal to the contact resistance (PC) divided by the area (A). For aluminum to heavily doped silicon the contact resistance is around 1x10-6 ohms cm2.
For the 1 micron example the area will be (1x10-4)2 which equals 1x10-8 cm2 thus the resistance will equal 1x10-6 / 1x10-8 which will equal 100 ohms. The 0.1 micron example the area will be (1x10-5)2 which equals 1x10-10 cm2 thus the resistance will equal 1x10-6 / 1x10-10 which will equal 10,000 ohms.
Measurements on the metal to find the contact resistance has been the Cross bridge Kelvin Resistor, however in small devices it has been noted that the results have not been very acurate using the standard calculation. Understanding, better calculations and a new measuring technique was introduced in a 2002 paper "A simple approach to understanding measurement errors in the cross-bridge Kelvin resistor and a new pattern for measurements of specific contact resistivity (Mizuki Ono, Akira Nishiyama, Akira Toriumi : Solid-State Electronics 46 (2002) 1325-1331)".

### Cross Bridge Kelvin Resistor (CKR)

Above shows the structure of the CKR. In an ideal situation the arm's of the silicon and metal layers would be the same width of the contact but due to alignment margins this is impossible under normal manufacturing processes. It was seen that by moving the contact area around the arm's would provide different resistance measurements which has provided a lot of mystery around the device until the 2002 paper by Mizuki Ono. This paper showed how the effect of the extra silicon affected the results and hence why the measurements changed when the contact area was moved around.

### Ono Equation

Pc= specific contact resistivity Ps= sheet resistance
Using this equation, we can more accuratly calculate the contact resistance for the metal's using the standard CKR and hence are able to use premade version by accuratly finding out the measuremnets required using an appropriate electron microscope.

### Ono Design

This design was created as a replacement to the CKR, due to the large length the design irradicates a lot of the errors, the CKR is prone to, and thus gives a more accurate result. For this to work, the length L must be longer than (Pc/Ps)1/2 in which case the equation I=(W.Vo)/sqrroot(PcPs) where Vo is the voltage at the right edge of the contact hole. Vo can be found by extrapolating the ratio of voltage between the potential terminal of the metal and each potential terminal in the silicon active layer (ie Vsa, Vsb and Vsc).

### Additional files

Media:contactresistance.sxw - my Final year project report on contact resistance (At Queens University, belfast) in open office format Contact resistance tool mentioned in final year project is avaible upon request