Question

Aluminum wires exposed to air form a layer of insulating Al2O3, through which electrons have to tunnel to get through an interconnect. A simple model of electrons tunneling through an Al2O3 barrier of thickness L between two Al wires implies the following: for small fixed voltage V, the current I is Ce^(-2KL), where C and K are constants. In other words, the resistance R=V/I increases proportional to e^(2KL). Solving the Schrödinger equation gives K=sqrt(2mU/ 2 ) where m is the electron mass and U is the barrier height, i.e. the energy required to move an electron from Al into Al2O3.

a) Say that a contact with L =0.1nm has resistance of 1 ohm, and for L=0.2 nm it has 3 ohms. When L grows to 1 nm how many ohms will it have?

b) Use that to calculate the barrier height U.

c) In a real circuit, L grows gradually as the aluminum connections oxidize. If the connections in a 120V outlet providing power to a 1200 W air conditioner were made of aluminum, and the tunneling resistance drifted up to 10 ohms, what value of L does this correspond to using your calculation from part (a)? What real-world consequences would occur at this resistance?

Answer 1