ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

VM Ayres, ECE875, S14 Chp 03: metal-semiconductor junction Currents: I-V / J-V measurements: discussion of part b (not assigned) in Pr on board to introduce thermionic emission model for I-V (or J-V) Thermionic emission model: where from Lecture 23, 10 Mar 14

Pr. 3.08: Use: X 1/10 10 VM Ayres, ECE875, S14

Thermionic emission model for J

VM Ayres, ECE875, S14 Chp 03: metal-semiconductor junction Currents: I-V / J-V measurements: discussion of part b (not assigned) in Pr on board to introduce thermionic emission model for I-V (or J-V) Thermionic emission model: where from Lecture 23, 10 Mar 14

Width Height Barrier width versus height maximally affect different types of transport which are energy-dependant VM Ayres, ECE875, S14

1. Thermionic emission (enough energy compared with height: q  Bn is critical) 2. Tunnelling (W D is critical) Dotted line: Both 1. and 2. can be going on at the same time VM Ayres, ECE875, S14

3. J rec 4. diffusion of electrons 5. diffusion of holes VM Ayres, ECE875, S14

5. diffusion of holes VM Ayres, ECE875, S14 4. diffusion of electrons

Thermionic emission model for transport: VM Ayres, ECE875, S14 enough energy above E C compared with barrier height q  n is critical

Start: ECEC Need to put dn in terms of v x

N(E): 3Df(E): “hot”: non-degenerate

So far: dn is now in terms of dv

v is 3D: e- moving in any direction. Still need to pick out the transport direction in x

See next slide for helpful integrals Note that k = k B = 1.38 x J/K

Are you done? No. You need to re-write the contact potential in terms of the barrier height Requirement on the KE/velocity in the transport direction x:

Note: current direction is going the other way. No bias on metal side: V = 0 Current density from metal into semiconductor:

J TE = J TE-sat = J TE = J s->m + J m->s Total Thermionic Current density: = {J TE-sat } Now you are done.