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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 10, 03 Feb 14. Chp. 01 Concentrations Nondegenerate Degenerate Nondegenerate Intrinsic Contributed by impurities Wanted impurities: “dopants”

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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 10, 03 Feb 14 • Chp. 01 • Concentrations • Nondegenerate • Degenerate • Nondegenerate • Intrinsic • Contributed by impurities • Wanted impurities: “dopants” • Unwanted impurities: “traps” Concentrations n Effect of temperature VM Ayres, ECE875, S14

  3. Example Pr. 1.12: VM Ayres, ECE875, S14

  4. Example Pr. 1.12: Need this ✔ Use: ✔ VM Ayres, ECE875, S14

  5. General Info: will use figure next slide to do Pr. 1.12: Centripetal force = Coulomb force Average is defined as the harmonic mean not the geometric mean. Used when E-field is present P and B are shallow impurities in Si VM Ayres, ECE875, S14

  6. Tabulated: can get EC – ED @ 300 K from Sze Fig 10 (useful): For P in Si: EC – ED = 0.046 eV This is the “ionization energy” Pr. 1.12: Given: ionization energy doesn’t change as a function of T VM Ayres, ECE875, S14

  7. Have: EC – ED Need: EF – ED Note: (EC – ED) – (EC – EF) = EF – ED Given: ND = 1016 cm-3 = nondegenerate in Si Therefore: use Sze (21): Need: NC @ 77K In App G: NC @ 300K = 2.8 x 1019 cm-3 VM Ayres, ECE875, S14

  8. Use the ratio to something you know method: 2 VM Ayres, ECE875, S14

  9. VM Ayres, ECE875, S14

  10. Also: kT at 77K: Plug and chug method: OR Ratio to something you know method: VM Ayres, ECE875, S14

  11. ✔ @ 77K = 3.64 X 1018 cm-3 Thus far: Sze (21): Problem: n ≠ ND+ = 1016 cm-3 at 77K because not all ND are ionized VM Ayres, ECE875, S14

  12. VM Ayres, ECE875, S14

  13. VM Ayres, ECE875, S14

  14. Important part: NOT EQUAL VM Ayres, ECE875, S14

  15. Important step: COMPARE: VM Ayres, ECE875, S14

  16. Lecture 10, 03 Feb 14 • Chp. 01 • Concentrations • Nondegenerate • Degenerate • Nondegenerate • Intrinsic • Contributed by impurities • Wanted impurities: “dopants” • Unwanted impurities: “traps” Concentrations n Effect of temperature VM Ayres, ECE875, S14

  17. Summary: concentration as a function of temperature and doping:For: nondegenerate doping (n-type Si shown in figure): VM Ayres, ECE875, S14

  18. Summary: Freeze-out range: concentration  partially ionized dopants: DONORS: Neutral ND Electron occupies a local energy level ED, h = 1, gD = 2 Ionized ND+ A local energy level ED is empty and available ACCEPTORS: Neutral NA A local energy level EA is empty and available Ionized NA- Electron occupies a local energy level EA, h = 1, gA = 4 F(E) is probability of an electron occupying an energy level E. If energy level E = local level ED (neutral ND) or local level EA (ionized NA-) use: VM Ayres, ECE875, S14

  19. Summary: Intrinsic range: concentration  partially ionized dopants: n ≈ p ≈ VM Ayres, ECE875, S14

  20. Summary: Saturation range: concentration  fully ionized dopants AND some probability of valence-to-conduction band transitions: Fully ionized dopants: single doping: n-type: p = ni2/n, solve quadratic for n p-type: n = ni2/p, solve quadratic for p VM Ayres, ECE875, S14

  21. Summary: Intrinsic range: concentration  fully ionized dopants AND high probability of valence-to-conduction band transitions: n ≈ pi = ni VM Ayres, ECE875, S14

  22. Summary: For all ranges: Egap = f(T); also f(P): VM Ayres, ECE875, S14

  23. Fig. 14: (a) Silicon; (b – not shown: GaAs) VM Ayres, ECE875, S14

  24. Example: Sun-side for a LEO (low-earth orbit) satellite is 200oC = 473 K. What doping concentrations can’t be used in Si electronics because all pn junctions will act like intrinsic Si, causing device inoperability? VM Ayres, ECE875, S14

  25. 473 K Answer: n and p doping concentrations 1013 cm-3 and below can’t be used. VM Ayres, ECE875, S14

  26. Lecture 10, 03 Feb 14 • Chp. 01 • Concentrations • Nondegenerate • Degenerate • Nondegenerate • Intrinsic • Contributed by impurities • Wanted impurities: “dopants” • Shallow dopants • Deep level dopants • Unwanted impurities: “traps” Concentrations n Effect of temperature VM Ayres, ECE875, S14

  27. Donors and acceptors don’t have to be “shallow”. Many atoms can get into Si: reason for cleanrooms VM Ayres, ECE875, S14

  28. How to read graph: DONORS: Neutral ND Electron occupies a local energy level ED, h = 1, gD = 2 Ionized ND+ A local energy level ED is empty and available ACCEPTORS: Neutral NA A local energy level EA is empty and available Ionized NA- Electron occupies a local energy level EA, h = 1, gA = 4 Above Ei: read EC – ED Below EI: read EA - EV Generally for single substitutional impurities: Donor Levels/two charge states: ED (neutral 0, positive +1) Acceptor levels/two charge states: EA (neutral 0, negative -1)

  29. Can have donor levels below Ei and acceptor levels above Ei: VM Ayres, ECE875, S14

  30. Pr. 1.16 (a): gold dopant/impurity: Au: The acceptor level at EA-0.54 has two charge states: neutral 0 to start and -1 if it gets an e-. The donor level at ED-0.29 has two charge states: neutral 0 to start and +1 if it loses an e- At start: “state of charge of the Au levels in Si”: EA-.54 = neutral 0 ED-.29 = neutral 0 VM Ayres, ECE875, S14

  31. Pr. 1.16 (a): Add neutral B to Au dopant/impurity: The acceptor level at EA-0.54 has two charge states: neutral 0 to start and -1 if it gets an e-. The donor level at ED-0.29 has two charge states: neutral 0 to start and +1 if it loses an e- The acceptor level at EA-0.044 has two charge states: neutral 0 to start and -1 if it gets an e-. It does get e- from the ED-0.29 donor level. VM Ayres, ECE875, S14

  32. Pr. 1.16 (a): After neutral B addition to Si with Au dopant/impurities: The acceptor level at EA-0.54 is neutral 0 at start and WHAT at finish The donor level at ED-0.29 is neutral 0 at start and WHAT at finish The acceptor level at EA-0.44 is neutral 0 at start and WHAT at finish Neutrality is maintained overall. VM Ayres, ECE875, S14

  33. Pr. 1.16 (b): effect of Au impurities on electron concentration n and hole concentration p, both from Si: Consider what the acceptor level at EA-0.54 can do with n from Si Consider what he donor level at ED-0.29 can do with p in Si Result: Si e- and holes that would have participated in current I are both being tied up (“trapped”) instead by the Au impurity levels. They are NOT contributing to current I while they are in traps. VM Ayres, ECE875, S14

  34. Effect on currents: 1.5.4: Will show: recombination and generation due to deep level dopants has greatest effect on ordinary current Ordinary current: Current I is in an assumed pn junction device VM Ayres, ECE875, S14

  35. 1.5.4: Rate U is related to current I: VM Ayres, ECE875, S14

  36. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium Fig 25 (a) matches Fig. 4 (b) Note: Recombining e- must have a momentum value that matches the crystal momentum of the hole it is dropping into. Direct bandgap = OK all the way to the valence band Recombination with emission of photon Has a rate Re Generation with creation of e- hole pair Has a rate Gthermal VM Ayres, ECE875, S14

  37. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium Fig 25 (a) matches Fig. 4 (b) Recombination decreases both n and p by 1 Now: pn < ni2 Think: what if just recombination kept going? VM Ayres, ECE875, S14

  38. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium VM Ayres, ECE875, S14

  39. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium Fig 25 (a) matches Fig. 4 (b) Recombination rate Re depends on having: - Concentration of electrons in EC, - Concentration of holes in EV to take the e- - Probability of spontaneous recombination Rec Therefore: Re = Rec np = Rec ni2 VM Ayres, ECE875, S14

  40. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium VM Ayres, ECE875, S14

  41. What is U: Net transition rate driven by powerful pn = ni2 at thermal equilibrium General: Specific: pn junction VM Ayres, ECE875, S14

  42. Evaluate U: within 1 diffusion length of the junction on the n-side of a pn junction: VM Ayres, ECE875, S14

  43. Within 1 diffusion length Lp of the junction on the n-side of a pn junction: Review: For a pn junction with low level injection Dp on n-side and Dn on p-side: pp0 ≈ NA- nn0 ≈ ND+ pn0 ≈ ni2/n=ND+ Lp np0 ≈ ni2/p=NA- Ln excess holes: Dp electrons: Dn VM Ayres, ECE875, S14

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