ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

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

VM Ayres, ECE874, F12 Motivation: Show order: Show real wafers: plain and with circuits

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 -

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

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

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

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

VM Ayres, ECE874, F Miller indices Ii, iii, iv

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

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

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

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

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

VM Ayres, ECE874, F12

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

VM Ayres, ECE874, F12

6 equivalent {100} planes:

VM Ayres, ECE874, F12 6 equivalent directions:

VM Ayres, ECE874, F12 [110]

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:

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:

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

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

VM Ayres, ECE874, F12 [110]

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

VM Ayres, ECE874, F12 (a)

VM Ayres, ECE874, F12 (b)

VM Ayres, ECE874, F12 (c)

VM Ayres, ECE874, F12 (d)

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?

VM Ayres, ECE874, F12