You are planning to create an ohmic contact for your new semiconductor device. Unfortunately, in your...

You are planning to create an ohmic contact for your new semiconductor device. Unfortunately, in your first attempt the contact shows a diode-like current-voltage characteristic, which indicates that the electrons must overcome a barrier.

(a) Show, using the WKB approximation for a parabolic barrier, that at a doping density of ?? = 1 ⋅ 1016cm-3 the tunneling coefficient T is so small that no carriers are crossing the barrier via the tunnel effect.

(b) To what level do you need to raise the doping concentration so that your barrier thickness will be reduced to 3 nm? What is the Tunneling coefficient for this doping concentration? Hint: The material that was used is Silicon4 (Si) with an effective electron transport 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. The problem has been simplified as to not use barrier lowering and doping dependence of the Fermi level in the semiconductor.

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genius_generous answered 1 year ago

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