ELECTRONICS II VLSI DESIGN Fall 2013

1. ELECTRONICS II VLSI DESIGNFall 2013

2. The Hydrogen Atom

3. Allowable States for the Electron of the Hydrogen Atom

4. The Periodic Table

5. From Single Atoms to Solids

6. Energy bands and energy gapsSilicon

7. Band Structures at ~0K

8. Atomic Bonds

9. Electrons and holes in intrinsic [no impurities] semiconductor materials

10. Electrons and holes in extrinsic [“doped”] semiconductor materials

12. Some Terminology and Definitions

13. Electron and Hole Concentrations at Equilibrium

14. Calculating Concentrations

15. Some Calculations At room temperature kT = 0.0259eV At room temperature ni for Si = 1.5 x 1010/cm3 Solve this equation for E = EF Let find f(E<EF) and f(E>EF) Let T = 300K and EF = 0.5eV plot f(E) for 0 < E < 1 EC EV

16. Fermi-Dirac plus Energy Band

17. More Calculations At room temperature kT = 0.0259eV At room temperature ni for Si = 1.5 x 1010/cm3 If Na = 2 x 1015 /cm3 find po and no The band gap of Si at room temp is 1.1eV or EC – EV = 1.1eV What is the value of EC – EF for intrinsic Si at T= 300K The band gap of Si at room temp is 1.1eV or EC – EV = 1.1eV What is the value of Ei – EF if Na = 2 x 1015 /cm3 at T= 300K The band gap of Si at room temp is 1.1eV or EC – EV = 1.1eV What is the value of EF – Ei if Nd= 2 x 1015 /cm3 at T= 300K

18. Intrinsic Carrier Concentrations Which element has the largest Eg? What is the value of pi for each of these elements?

19. Si with 1015/cm3 donor impurity

20. Conductivity

21. Excess Carriers

22. Photoluminescence

23. Diffusion of Carriers

24. Drift and Diffusion

25. Diffusion Processes n(x) n1 n2 Since the mean free path is a small differential, we can write: x0 Where x is at the center of segment 1 and x0 + l x0 - l In the limit of small or

26. Diffusion Current Equations

27. Combine Drift and Diffusion

28. Drift and Diffusion Currents Electron drift Hole drift Electron & Hole Drift current E(x) n(x) Electron diffusion Hole diffusion Electron Diff current Hole Diff current p(x)

29. Energy Bands when there is an Electric Field E(x) E(x)

30. The Einstein Relation At equilibrium no net current flows so any concentration gradient would be accompanied by an electric field generated internally. Set the hole current equal to 0: Using for p(x) E(x) qE(x) 0 E(x) The equilibrium Fermi Level does not vary with x. Finally:

31. D and mu

32. Message from Previous Analysis An important result of the balance between drift and diffusion at equilibrium is that built-in fields accompany gradients in Ei. Such gradients in the bands at equilibrium (EF constant) can arise when the band gap varies due to changes in alloy composition. More commonly built-in fields result from doping gradients. For example a donor distribution Nd(x) causes a gradient in no(x) which must be balanced by a built-in electric field E(x). Example: An intrinsic sample is doped with donors from one side such that: Find an expression for E(x) and evaluate when a=1(μm)-1 Sketch band Diagram

33. Diffusion & Recombination Jp(x) Jp (x + Δx) x x + Δx Increase in hole conc In differential volume Per unit time Recombination Rate Rate of Hole buildup - =

34. If current is exclusively Diffusion And the same for holes

35. And Finally, the steady-stateDetermining Diffusion Length