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

2. VM Ayres, ECE875, S14 Chp. 01 Energy levels: E-k Effective mass m ij * v group Density of States Concentrations Effective DOS Lecture 06, 22 Jan 14

3. VM Ayres, ECE875, S14 Electronics: Transport: e-’s moving in an environment Correct e- wave function in a crystal environment: Bloch function: Sze:  r,k) = exp(jk.r)U b (r,k) =  (r + R,k) Correct E-k energy levels versus direction of the environment: minimum = E gap Correct concentrations of carriers n and p: contributions of (1) degeneracy and (2)traps Correct current and current density J: moving carriers I-V measurement J: V ext direction versus internal E-k: E gap direction Fixed e-’s and holes: C-V measurement Motivation: x Probability f 0 that energy level is occupied q n, p velocity Area (KE + PE)  (r,k) = E  (r,k)

4. VM Ayres, ECE875, S14 Carrier concentration: example: electron concentration n:

5. VM Ayres, ECE875, S14 Review: DOS:

6. VM Ayres, ECE875, S14 Typically you don’t know N T (E) or dE. To deal with this, note that E and k are related. Simple example: 1. Find N T (k): 2. Find/use the connector E = f(k) to convert N T (k) to N T (E) 3. Finish expression for DOS N(E)

7. VM Ayres, ECE875, S14 1. Find N T (k): An electron described by a wave fits into Volume (or Area, Line) in a a way that is bounded: a b c Macroscopic Volume in real space Bounded wave in reciprocal space OR

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11. GaAsGeSi Pierret

12. VM Ayres, ECE875, S14 GaAsGeSi Sze Pr. 1.07

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14. Lecture 04, Pr. 1.07: The parabola approximation and the equivalent constant energy surface ellipsoid (“cigar shaped minima”) description are the same: Parabola: Ellipsoid: Wikipedia: ellipsoid. Set b = c

15. VM Ayres, ECE875, S14 GaAsGeSi Vol-ellipsoid =Vol-sphere =

16. VM Ayres, ECE875, S14 GaAsGeSi M C = 8/2 = 4 Conduction band M C = 6M C = 1 Ge: lowest valley at the zone boundary along [111]

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18. GaAsGeSi Effective k-space volumeActual k-space volumes:

19. VM Ayres, ECE875, S14 Sze equation 14:

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22. Carry out the integration:

23. VM Ayres, ECE875, S14 This part is called N C : the effective density of states at the conduction band edge. MCMC Result: Use in Pr. 1.08 Note: m de ’s are given in this problem