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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 05, 17 Jan 14. Chp. 01 Crystals: HW01 solutions Energy levels: E- k Effective mass m ij * v group E gap is a function of temperature T. R ’ ≠ R.

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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 05, 17 Jan 14 • Chp. 01 • Crystals: • HW01 solutions • Energy levels: E-k • Effective mass mij* • vgroup • Egap is a function of temperature T VM Ayres, ECE875, S14

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  9. R’ ≠ R VM Ayres, ECE875, S14

  10. math except 0 physically: to describe |R’|: Z = a whole number ≠ 0 VM Ayres, ECE875, S14

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  15. Pr. 1.04 and 1.05: Useful for electron on x-ray diffraction: k-space SAED diffraction pattern VM Ayres, ECE875, S14

  16. Pr. 1.05: Useful for y(r,k): Electronics: Transport: e-’s moving in an environment Correct e- wave function in a crystal environment:Bloch function: Sze:y(r,k) = exp(jk.r)Ub(r,k) = y(r + R,k) Correct E-k energy levels versus direction of the environment: minimum = Egap Correct concentrations of carriers n and p Correct current and current density J: moving carriers I-V measurement J: Vext direction versus internal E-k: Egap direction Fixed e-’s and holes: C-V measurement (KE + PE) y(r,k) = E y(r,k) x Probability f0 that energy level is occupied q n, p velocity Area VM Ayres, ECE875, S14

  17. HW01: VM Ayres, ECE875, S14

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  24. Why assigned: fcc bcc Get similar Start: Find a*, b*, c*: VM Ayres, ECE875, S14

  25. This Wigner-Sietz cell of bcc reciprocal space ‘structure’ = is the 1st Brillouin zone for all fcc primitive cell-based crystals: The fcc a*, b*, c* looks like a bcc arrangement. Take ┴ bisector planes midway between the atoms VM Ayres, ECE875, S14

  26. fcc-type Wigner Seitz cell is useful for HW02 Pr. 1.08: Si: VM Ayres, ECE875, S14

  27. Lecture 05, 17 Jan 14 • Chp. 01 • Crystals: • HW01 solutions • Energy levels: E-k • Effective mass mij* • vgroup • Egap is a function of temperature T VM Ayres, ECE875, S14

  28. E k VM Ayres, ECE875, S14

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  30. Given: Can you find an effective mass? A group velocity? VM Ayres, ECE875, S14

  31. Egap as a function of temperature T: Sze, p. 15: Stated without proof: This approximation in eq’n (12) works well in Si and GaAs: VM Ayres, ECE875, S14

  32. Egap as a function of temperature T: Sze, p. 15: Stated without proof: This approximation in eq’n (12) works well in most cases: VM Ayres, ECE875, S14

  33. Egap as a function of temperature T: Sze, p. 15: Stated without proof: This approximation in eq’n (12) works well in most cases: VM Ayres, ECE875, S14

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  35. Egap (0 K) is in Appendix F; a an b are not Note that everything is 300 K except Egap (0 K) Note differences between Egap (300 K) and Egap (0 K) VM Ayres, ECE875, S14

  36. Extrapolated Egap (0 K) a and b for Si and GaAs are given in Sze Fig. 06 Literature Ioffe VM Ayres, ECE875, S14

  37. Example problem: A satellite in low earth orbit experiences a temperature swing of +200oC sun side to – 200oC dark side. Its electronics are Si-based. Find the range of Egap and compare it to operation on earth. VM Ayres, ECE875, S14

  38. Example problem: A satellite in low earth orbit has a temperature swing of +200oC sun side to – 200oC dark side over 24 h. Its electronic are Si-based. Find the range of Egap and compare it to operation on earth. Calculated solution or graphical solution T = 200oC = 473 K T = - 200oC = 73 K Egap (73 K): graph estimate: 1.16 eV Egap (300 K): on graph: 1.12 eV Egap (473 K): graph estimate: 1.08 eV VM Ayres, ECE875, S14

  39. Will explore further in photodetector sensitivities in Chp. 13 VM Ayres, ECE875, S14

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