Chemistry 140a

1. Chemistry 140a Lecture #5 Jan, 29 2002

2. Fermi-Level Equilibration • When placing two surfaces in contact, they will equilibrate; just like the water level in a canal lock. • The EF of the semi-conductor will always lower to the EF of the metal or the solution. This can be understood by looking at the density of states for each material/soln. Semi-Conductor Metal/Soln. Initial EF Eq. EF Initial EF Eq. EF

3. E E E E ECB ECB Vbi EF EF ECB Vbi Vbi Vbi EF EF ECB EF EF EVB EVB EVB x x x x EVB Fermi-Level Equilibration • Charge comes from the easiest thing to ionize, the dopant atoms. This leads to a large region of (+) charges within the semi-conductor. • In the metal all of the charge goes to the surface. (Gauss’s Law) • The more charge transferred the more band bending.

4. Depletion Approximation • All donors are fully ionized to a certain distance, W, from the interface. • W=W(ND,Vbi) - - - - - - - - - - +++++ +++++ X W

5. Final Picture E E EVac EVac m sc ECB Vbi EF ECB Vbi EF EF - - - Eg EVB EVB + ++ x x

6. Useful Equations E(x) = Electric Field (V/cm) (x) = Electric Potential (V) Poisson’s Eqn: (x) = Electric Potential Energy (J) E(x)

7. x) (x) qND +++++++ Q=qNDW x X - - - - - - - - - - W -qNDW2 (2K0) Vbi= quadratic Electric Potential (V) Integrate Poisson’s Eqn. B.C.’s Result:

8. Depletion Width • Rearranging for W: • As expected, W increases w/ Vbi and decreases w/ ND • If one accounts for the free carrier distribution’s tail around x=W

9. Typical Values

10. E Net = 0 @ Eq. e- (x) Vbi B ECB Vn EF x EVB h+ x Electric Potential Energy • E(x) = -q(x) • (0) = -Vbi • qVbi = (EF,SC-EF,M) • B = Vbi + Vn • Barrier height • Independent of doping • Vbi and Vn are doping dependent

11. E(x) Ex) W x Emax=-qNDW/(K Electric Field (V/cm)

12. I-V Curve No Band Bending I Low Band Bending High Band Bending V

13. Review • N-type P-type E E EVac EVac m sc sc Vbi __ m ECB ECB - EF Vbi - - - + + + EF Eg Eg EVB EVB + ++ x x

14. Solution Contact • 10^17 atoms in 1mL of 1mM solution • D.O.S. argument holds • Difference in exchange current across the interface A- A- A- A- A- A- Li+ Li+ Li+ Li+ Li+ Li+ ++++++++++++++++ *Significantly less than typical W ~ 10nm 5-10 Angstroms

15. Semiconductor Contacting Phase • No longer 1-Sided Abrupt Jxn. as the semi-conductor doesn’t have infinite capacity to accept charge • Assume ND(n-type)=NA(p-type), then Wn=Wp p-type n-type e- Diode directionalized current h+

16. Degenerate Doping • Dope p-type degenerately • NA>>ND --> 1-sided Abrupt Jxn. P-N Homojunction B N-type B B N-type P+-type Wn Wp

17. Heterojunctions • 2 different semiconductors grown w/ the same cyrstal structure (difficult) • Ge/GaAs ao~5.65 angstroms Broken Normal Staggered

18. LASERs • 3 Pieces --> 2 Heterjunctions • p-(Al,Ga)As | GaAs | n-(Al, Ga) As e- h h+ Traps electrons and holes

19. Slope Never works for Si Fermi-Level Pinning Sze p. 278 TiO2 SnO2 1 CdS Si GaAs A-B Fermi-Level Pinning • Ideal Case (only works for very ionic semiconductors like TiO2 and SnO2)  1 EF,M

20. E E EVac EVac vs. B B ECB ECB EF EF EVB EVB x x What’s Missing? • Fermi-Level pinning hurts • Hinders our ability to fine tune Vbi Vbi/Ni~Vbi/Pt~Vbi/Au • Why does this happen? *Solution contact for GaAs sees Fermi-level pinning, while the barrier height correlates well with the electro-chemical potential for solution contact to Si

21. E E EF,X-EF,M ECB ECB EF,X EF,X EVB EVB x x Devious Experimenter • Given a Si sample with a magic type of metal on the surface X • Thus the Fermi-level will alwaysequilibrate to the Fermi-level of X • Thin interface --> e-’s tunnel through it and no additional potential drop is observed

22. What is X? • Any source or sink for charge at the interface • Dangling bonds • Surface states • etc.

23. Questions • Questions • Abrupt 1-sided junction (What is it?) • Sign of Electric P.E. and Electric Potential (Are they correct? I put them as they were in the notes, but this doesn’t seem to agree with the algebra to me)