1. ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

2. VM Ayres, ECE874, F12 Lecture 03, 06 Sep 12

3. VM Ayres, ECE874, F12 Motivation: Show order: http://www.siwafers.com/100-mm.htmhttp://www.siwafers.com/100-mm.htm Show real wafers: plain and with circuits

4. VM Ayres, ECE874, F12 Motivation: Wafer with circuits: pn junctions are inside the wafer, only the interconnects are on tops and bottoms: Principles of Electronic Devices, Streetman and Bannerjee + Battery -

5. VM Ayres, ECE874, F12 Motivation: Moving in direction  ~ 2 eV Moving in direction  only ~ 1 eV

6. VM Ayres, ECE874, F12 These are directions to planes: A {100} plane Moving in direction  ~ 2 eV Moving in direction  only ~ 1 eV

7. VM Ayres, ECE874, F12 Moving in direction  ~ 2 eV Moving in direction  only ~ 1 eV These are directions to planes: A {111} plane

8. VM Ayres, ECE874, F12 These are directions to planes: A {100} plane To say which {100}, need a coordinate system and an origin O. z x y a a a

9. VM Ayres, ECE874, F12 1.2.5 Miller indices Ii, iii, iv

10. VM Ayres, ECE874, F12 +z +x +y a a a Intercepts Reciprocals Whole # conversion Miller indexed plane (hkl): O

11. VM Ayres, ECE874, F12 +z +x +y a a a Interceptsa ∞∞ Reciprocals1/a 1/∞ 1/∞ 1/a 0 0 Whole # Conversion: x a a/a 0 0 Miller indexed plane (hkl): (1 0 0) O

12. VM Ayres, ECE874, F12 +z +x +y a a a Intercepts∞∞ a Reciprocals1/∞ 1/∞1/a = 0 0 1/a Whole # Conversion x a 0 0 1 Miller indexed plane (hkl): (001) O

13. VM Ayres, ECE874, F12 +z +x +y a a a Intercepts Reciprocals Whole # conversion Miller indexed plane (hkl): O

14. VM Ayres, ECE874, F12 +z +x +y a a a Intercepts Reciprocals Whole # conversion Miller indexed plane (hkl): O

15. VM Ayres, ECE874, F12

16. +z -x +y a a a Intercepts-a ∞∞ Reciprocals-1/a 1/∞ 1/∞ = -1/a 0 0 Whole # Conversion x a -1 0 0 Miller indexed plane (hkl): O

17. VM Ayres, ECE874, F12

18. 6 equivalent {100} planes:

19. VM Ayres, ECE874, F12 6 equivalent directions:

20. VM Ayres, ECE874, F12 [110]

21. VM Ayres, ECE874, F12 Lecture 01, slide 19: Example problem: what is the distance d between the parallel {111} planes? Distance d between parallel planes:

22. VM Ayres, ECE874, F12 Lecture 01, slide 19: Example problem: what is the distance d between the parallel {111} planes? Distance d between parallel planes:

23. VM Ayres, ECE874, F12 Example problem: (a) find the Miller indices of the plane shown below (Fig. 1.7 (a)) (b) find the distance d between its parallel planes

24. VM Ayres, ECE874, F12 Intercepts2a 1a 3a Reciprocals1/2a 1/a 1/3a Whole # Conversion x 6a 3 6 2 Miller indexed plane (hkl): (3 6 2) (a)(b)

25. VM Ayres, ECE874, F12 [110]

26. VM Ayres, ECE874, F12 Example problem: (a) find the angle  between the [111] and [001] directions (b) find the angle  between the [111] and [110] directions (c) find the angle  between the [111] and [362] directions (d) find the angle  between the [111] and [001 bar ] directions

27. VM Ayres, ECE874, F12 (a)

28. VM Ayres, ECE874, F12 (b)

29. VM Ayres, ECE874, F12 (c)

30. VM Ayres, ECE874, F12 (d)

31. VM Ayres, ECE874, F12 Example problem: the surface of a Si wafer is a (001) plane. Which, if any directions are perpendicular to the Si wafer (001) plane direction?

32. VM Ayres, ECE874, F12