You are planning to create an ohmic contact for your newsemiconductor device. Unfortunately, in your first attempt thecontact shows a diode-like current-voltage characteristic, whichindicates that the electrons must overcome a barrier.
(a) Show, using the WKB approximation for a parabolic barrier,that at a doping density of ?? = 1 â‹… 1016cm-3 the tunnelingcoefficient T is so small that no carriers are crossing the barriervia the tunnel effect.
(b) To what level do you need to raise the doping concentrationso that your barrier thickness will be reduced to 3 nm? What is theTunneling coefficient for this doping concentration? Hint: Thematerial that was used is Silicon4 (Si) with an effective electrontransport mass of m* = 0.26 me and a dielectric constant of ε = 12.The barrier height of the contact is given by ΦSB = 0.6 eV. Theproblem has been simplified as to not use barrier lowering anddoping dependence of the Fermi level in the semiconductor.
