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ECE 875: Electronic Devices

ECE 875: Electronic Devices. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 20, 24 Feb 14. Chp. 02: pn junction: Info: Linearly graded junction Multiple charge layers Example.

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ECE 875: Electronic Devices

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

  2. Lecture 20, 24 Feb 14 • Chp. 02: pn junction: • Info: Linearly graded junction • Multiple charge layers • Example • Chp. 03: metal-semiconductor junction: Schottky barrier • Review • Examples • New VM Ayres, ECE875, S14

  3. Linearly graded junction: Why: Why: get a more uniform E (x) over a bigger x region VM Ayres, ECE875, S14

  4. Linearly graded junction: How: Q and r E (x) yi(x) VM Ayres, ECE875, S14

  5. Linearly graded junction: How: Q and r ~ a x E (x) ~ ax2 + B yi(x) ~ ax2 + Bx +C

  6. Linearly graded junction: How: VM Ayres, ECE875, S14

  7. VM Ayres, ECE875, S14

  8. Practical: The curvature of the initial C-V curve is different from that for an abrupt junction The slope gives the grading constant a The intercept gives the equilibrium built in potential ybi 1/ VM Ayres, ECE875, S14

  9. Lecture 20, 24 Feb 14 • Chp. 02: pn junction: • Info: Linearly graded junction • Multiple charge layers • Example • Chp. 03: metal-semiconductor junction: Schottky barrier • Review • Examples • New VM Ayres, ECE875, S14

  10. Example: Set up the answer: (a) Find ybi at equilibrium fro the following doping profile in si at 300 K (b) Draw the energy band-bending diagram p 1017 cm-3 n 1016 cm-3 p 1015 cm-3 VM Ayres, ECE875, S14

  11. VM Ayres, ECE875, S14

  12. 1st 2nd 3rd VM Ayres, ECE875, S14

  13. q q VM Ayres, ECE875, S14

  14. Lecture 20, 24 Feb 14 • Chp. 02: pn junction: • Info: Linearly graded junction • Multiple charge layers • Example • Chp. 03: metal-semiconductor junction: Schottky barrier • Review • Examples • New VM Ayres, ECE875, S14

  15. @ Interconnects: • Use energy band diagrams to describe what is happening • One question to answer: is it an Ohmic contact or a Schottky barrier contact? • Interconnect contacts are key for nanotechnology: • MOSFET: Ohmic contact = good • NanoFET: SB contact = good

  16. Individual energy band diagrams: Different nature of a metal Lots of e- and NO Egap EC = at EF

  17. Need 2 descriptions: Electron affinity qcs = where is EC relative to Evac Work Function qFs = where is EF relative to Evac Need 1 description: Work Function of the metal qFm: where is EF = EC relative to Evac

  18. When in physical contact EFm and EFs align:

  19. Four cases = the same approach: 1. metal with small work function/n-type semiconductor: Ohmic (barrier)2. metal with big work function/n-type semiconductor: Schottky barrier3. metal with small work function/p-type semiconductor: Schottky barrier4. metal with big work function/p-type semiconductor: Ohmic (barrier)In every case, use logic: do I need to make the metal more n-type (add e- from semiconductor) or less n-type (e- move into semiconductor)

  20. Four cases = the same approach: 1. metal with small work function/n-type semiconductor: Ohmic (barrier)2. metal with big work function/n-type semiconductor: Schottky barrier3. metal with small work function/p-type semiconductor: Schottky barrier4. metal with big work function/p-type semiconductor: Ohmic (barrier)In every case, use logic: do I need to make the metal more n-type (add e- from semiconductor) or less n-type (e- move into semiconductor)

  21. 2. metal with big work function/n-type semiconductor

  22. electrons move to metal side leaving Nd+ behind • Size of n-side strip is set by doping concentration and can be large --Nd+ Nd+ n --Nd+ Nd+ To bring the Fermi energy level of the metal up: make the metal more n-type

  23. Schottky Barrier: ND+ on n-side --Nd+ Nd+ n --Nd+ Nd+

  24. Schottky Barrier: Very narrow region with high concentration of e- similar to ionized NA = large --Nd+ Nd+ n --Nd+ Nd+

  25. 3. metal with small work function/p-type semiconductor

  26. electrons move to p-side and recombine with its large hole population. This leaves Na- strip • Size of p-side strip is set by doping concentration and can be large ++Na-Na- p ++Na- Na- To bring the Fermi energy level of the metal down: make the metal less n-type

  27. Schottky Barrier: NA- on p-side ++Na-Na- p ++Na- Na-

  28. Schottky Barrier: Very narrow region = high concentration exposed + nuclei similar to ionized ND = large NA- on p-side ++Na-Na- p ++Na- Na-

  29. Lecture 20, 24 Feb 14 • Chp. 02: pn junction: • Info: Linearly graded junction • Multiple charge layers • Example • Chp. 03: metal-semiconductor junction: Schottky barrier • Review • Examples • New VM Ayres, ECE875, S14

  30. Example from Exam:

  31. Answer: Ei

  32. EC – EF = Egap/2 – (EF – Ei) = EF – Ei = kT ln(ND/ni) Streetman ni EC – EF =

  33. --Nd+ Nd+ n --Nd+ Nd+ Made the metal more n-type to bring EFm up to EFs Electrons left the semiconductor and went into the metal. The semiconductor is n-type: Nd+ left behind. • Size WD of n-side depletion region is set by doping concentration and can be large

  34. Example:(a) Evaluate the energy barrier qV0 = q ybi for previous problem(b) Draw the band-bending diagram

  35. Answer: (a) qV0 = --Nd+ Nd+ n --Nd+ Nd+ q ybi =qV0 = 0.057 eV (a) Band-bending diagram: Find W:

  36. Equilibrium: metal contact to n-type Si when work functions qFm > qFs Junction metal n0= 1017 cm-3 Although the charges are balanced, the layer on the metal side is very thin, similar to ionized NA = large qV0 EF EF - - P+ P+ P P P P P P P Ei Neutral region n-side E (x) Depletion region W

  37. = 1.14 x 10-5 cm = 0.14 mm

  38. Answer: (a) qV0 = --Nd+ Nd+ n --Nd+ Nd+ q ybi =qV0 = 0.057 eV Also: qFB = 4.0 -3.8 eV = 0.2 eV (a) Band-bending diagram: W = 0.14 mm

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