1. ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

2. VM Ayres, ECE875, S14 Chp 03: metal-semiconductor junction Currents: I-V / J-V measurements: discussion of part b (not assigned) in Pr. 3.08 on board to introduce thermionic emission model for I-V (or J-V) Thermionic emission model: where from Lecture 23, 10 Mar 14

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

4. Thermionic emission model for J

5. VM Ayres, ECE875, S14 Chp 03: metal-semiconductor junction Currents: I-V / J-V measurements: discussion of part b (not assigned) in Pr. 3.08 on board to introduce thermionic emission model for I-V (or J-V) Thermionic emission model: where from Lecture 23, 10 Mar 14

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

7. 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

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

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

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

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

12. N(E): 3Df(E): “hot”: non-degenerate

13. So far: dn is now in terms of dv

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

15. See next slide for helpful integrals Note that k = k B = 1.38 x 10 -23 J/K

17. 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:

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

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