1. Semiconductor Materials and Devices
Spring Semester, 2014
Goals: The purpose of this course is to provide a concrete framework for understanding basic principles and physical properties of semiconductors, semiconductor processing and the characteristics of pn junction devices.                
Instructor: Prof. Sang Yeol Lee (07-216A, Tel: ,
Textbook: Semiconductor Device Fundamentals
          by Robert F. Pierret
References: Solid State Electronic Devices by B.G. Streetman
            Introduction to Microelectronic Fabrication
               by R.C. Jaegar

2. Grading Guideline Midterm Exam : 40% Final Exam : 40% Assignment: 10%
Attendance: %
Total:                100%

3. Chapter 1. General Introduction
General material properties(물질의 일반적 성질)
Crystal structure(결정구조)
Crystal growth(결정성장)

4. Composition of Semiconductor Materials
(반도체물질의 구성)
Semiconductor materials : groups of materials having electrical conductivities intermediate between metals & insulators

5. Elemental semiconductors(원소형반도체) : column Ⅳ semiconductors - Si, Ge
- Widely used : rectifiers, transistors, integrated circuit
B. Compound(Intermetallic) semiconductors(화합물반도체)
: Compounds of Ⅲ and Ⅴ, compounds of Ⅱ and Ⅳ
- GaAs, InP, ZnS
- High-speed devices and optoelectronics device
Ex) binary compounds(2원화합물) : two - element : GaAs, GaP
     ternary compounds(3원화합물) : three - element : GaAsP
    quaternary compounds(4원화합물) : four - element : InGaAsP

7. Crystal Structure(결정구조)
                                                                                                          
Fig 1.1 Tree types of solids, classified according to atomic arrangement :
(a) crystalline and (b) armorphous materials are illustrated by microscope views of the atoms, whereas (c) polycrystalline structure is illustrated by a more macroscopic view of adjacent single-crystalline regions, such as (a)
(결정질)
(비정질)
(다결정질)

8. Periodic arrangement of atoms in a crystal 2. Unit cell(단위셀)
1. Lattice(격자)
Periodic arrangement of atoms in a crystal
2. Unit cell(단위셀)
Volume which is representative of the entire lattice
3. Basis vectors : a, b, c
r = pa + qb + sc where p, q, s : integers
4. Primitive cell(기본셀)
Smallest unit cell that can be repeated to form the lattice
Fig 1.2 A two-dimensional lattice showing translation of a unit cell by
r = 3a + 2b

9. (단위 셀의 기하학적 구조)
Fig 1.9 Parallelepiped is chosen to describe geometry of a unit cell. We line the x, y and z axes with the edges of the parallelepiped taking lower-left rear corner as the origin

10. Simple 3-D Unit Cells
Fig 1.3 Simple three-dimensional unit cells. (a) Simple cubic unit cell. (b) Pedantically correct simple cubic unit cell including only the fractional portion (1/8) of each corner atom actually within the cell cube. (c) Body centered cubic unit cell. (d) Face centered cubic unit cell.

11. Cubic lattice(입방격자)
1. SC (Simple Cubic - 단순입방) structure
atoms at each corner of the unit cell
2. BCC (Body Centered Cubic - 체심입방)
SC + atom at center.
3. FCC (Face Centered Cubic - 면심입방)
SC + atom at the center of each faces. 
4. Lattice constant(격자상수)
side a, b, c in a unit cell.
5. Number of atoms/unit cell.

12. Example.1-1 )
Find the fraction of the fcc unit cell volume filled with hard spheres as Fig. 1-3.(다음 면심입방에서 구체가 갖는 부피의 분률을 구하여라.)
Fig 1.4 Packing of hard spheres in an fcc lattice.

13. Solution : Each corner atoms in a cubic unit cell is shared at each of the neighboring cell ; thus each unit cell contains of a sphere at each corners for total of one atom. Similarly, the fcc cell contains half an atom at each of the six faces for a total of three. Thus we have
Therefore, if the atoms in an fcc lattice are packed as density as possible, with no distance between the outer edges of nearest neighbors, 74 percent of the volume is filled.
This is a relatively high percentage compared with some other lattice structures.

14. Planes and Directions(평면과 방향)
a set of three integers to describe the position of a plane or the direction of a vector within the lattice.
Miller indices(밀러지수)
- specify the plane in a crystal.
(1) find intercepts of the plane or the crystal axes: p, q, r
(2) take reciprocals of the intercepts & clear fractions.
              
(3) divide by the same ratio
            
(4) (hkl) for a plane.

15. Fig 1.5 A (214) crystal plane Example 1-2 )
The plane illustrated in Fig. 1-5 has intercepts at 2a, 4b, and 1c along the three crystal axes. Taking the reciprocals of these intercepts. we got 1/2 , 1/4, and 1. These three fractions have the same relationship to each other as the integers 2, 1, and 4 (obtained by multiplying each fraction by 4). Thus the plane can be referred to as (214) plane.

16. Set of Miller Indices(밀러지수 규정요약) (1) { hkl } : equivalent planes.
(2)  ( hkl ) : plane.
(3)〈 hkl 〉: equivalent directions indices.
(4)〔 hkl 〕: direction indices.
Fig 1.6 Equivalence of the cube faces ({100} planes) by rotation of the unit cell within the cubic lattice.

17. Family of direction
The spacing of atoms along each direction is the same
(각 방향을 따라 원자간의 간격은 동일하다.)
ex) <100> : [100], [100], [010], [001], ….
 In tetragonal system [100] & [010] : same
[010] & [011] : different

18. Fig 1.7 Crystal directions in the cubic lattice.
(입방격자 내 결정 방향들)

19. Seven Crystal System 立方晶 正方晶 斜方晶 菱方晶 (三方晶) 六方晶 單斜晶 三斜晶 Crystal System
Axial Relationships
Interaxial Angles
Unit Cell Geometry
Cubic
a=b=c
α=β=γ=90°
Tetragonal
a=b≠c
Orthorhombic
a≠b≠c
Rhombohedral
α=β=γ≠90°
Hexagonal
α=β=90°, γ=120°
Monoclinic
α=γ=90°≠β
Triclinic
α≠β≠γ≠90°
立方晶
正方晶
斜方晶
菱方晶
(三方晶)
六方晶
單斜晶
三斜晶

21. Fig 1.8 The seven crystal system (unit cell geometries) and fourteen Bravais lattices.(7가지 결정계(단위셀의 기하학적구조)와 14가지 브라베이격자)

22. Hexagonal Crystals(육방정)
Four-axis or Miller-Bravais coordinate system(4개의 축 또는 밀러-브라베이 좌표축)
120°.
a1, a2, a3 on basal plane
z axis : perpendicular to this basal planes
Fig 1.10 Coordinate axis system for a hexagonal unit cell
(Miller-Bravais scheme)

23. Conversion (plane) (전환(평면))
Where n : a factor to reduce u, v, t & w to the smallest integers

24. Conversion (direction)
Fig 1.13 For the hexagonal crystal system, (a) [0001], [1100], and [1120] direction, and (b) the (0001), (1011), and (1010) planes.

26. Seven crystal system(7가지 결정계)

27. Fourteen Bravais lattices(14가지 브라베이 격자)

28. Fourteen Bravais lattices

29. FCC unit cell

30. BCC unit cell a b Examples : Alkali metals (Li, Na, K, Rb), Cr,
Mo, W, Mn, α-FE(<912℃), β-Ti(>882℃)

31. Diamond & Zinc blends crystal(섬아연광 격자구조)

32. Hexagonal close packing(육방최밀쌓임)

33. Cubic close packing(입방최밀충전)

34. Packing sequence & unit cell(패킹순서&단위셀)

35. Packing sequence & unit cell
Layer B
Layer A
Layer B
Layer C
Layer A
Layer A
(a)
(b)
(c) (d)
Examples : Be, Mg, α-Ti(<882℃), Cr, Cu, Zn, Zr, Cd

36. Crystallographic notation
(결정학상의 표기법)
- to specify a given direction or plane in a crystal
- use a, b, c which define the unit cell

37. Miller indices: plane ▷ Miller indices
- to specify the planer in a crystal
find intercepts of the plane on the crystal axes
take reciprocals of the intercepts & clear fractions
divide by the same ratio

38. Miller indices: plane

39. Miller indices: plane

40. Miller indices: direction
OP direction expression
OP : components : 1/2, 1, 1/2
remove fraction : 1, 2, 1 (reduce the smallest set of integers having the same ratio)
plane square brackets : [1 2 1]
for negative components : [ ]
family of directions : cube edges < >
ex) <1 0 0> : [1 0 0], [ ], [0 1 0]

42. Interplanar spacing(격자 면간격)
(in the cubic system)
the perpendicular distance between the plane closest
to the origin and a parallel plane that goes through the origin a c b α1 α3 α2
for an orthogonal coordinate system

43. Interplanar spacing - generally, for all axis angles = system
(cubic, tetragonal, orthorhombic)
where
for cubic system
for tetragonal system
for orthorhombic system

44. Interplanar spacing
Rhombohedral
monoclinic
Triclinic

45. Note : spacing between planes of different order is different
Interplanar spacing
- family of planes
(111),
Note : spacing between planes of different order is different
ex) (111) & (222)

46. Hexagonal Crystals
Direction conversion

47. Hexagonal Crystals
Plane conversion
(h k l) → (h k i l)
-i = h + K

48. Crystal structure analysis(결정구조)
2dsinΘ = nλ

49. Xray-Diffraction(X선 회절현상)◑
sample
detector ◑ 2Θ

50. X-ray Diffraction ◑
ex) in a cubic system (100) peak position for CsCl (4,1 Å )
If x-ray wavelength is 1.54 Å ,
(100) peak is at
detected between position

51. Semiconductor lattices
1. Basic lattice structure for many important semiconductors
- Si, Ge : diamond lattice
- Ⅲ-Ⅴ compounds : zincblende lattice
- diamond but are different on alternating sites
- vary the mixture of elements : AlxGa1-xAs
2. Diamond structure
- fcc + an extra atom placed at a/4 + b/4+ c/4 from each of fcc atoms.

52.                                                                                                           
Fig 1.11 Diamond lattice structure : (a) a unit cell of the diamond lattice constructed by placing atoms 1/4, 1/4, 1/4 from each atom in an fcc; (b) top view (along any <100> direction) of an extended diamond lattice. The colored circles indicate one fcc sublattice and the black circles indicate the interpenetration fcc.

53. 3. Property of diamond structures :
(1) varying the mixture of elements.
(2) preferential chemical etching
directions.
4. Si at RT
a = 5.43 Å (1Å = 10-8㎝)
5.       
Fig 1.12 Diamond lattice unit cell

54. Family of equivalent planes
- Same atomic packing
- Depending on the symmetry of the particular structure
ex) {111} : (111), (111), (111), (111), ….
{123} : (123), (312), ….

55. ◆ Bulk Crystal Growth(결정성장)
1. Bridgman method : contact problem.
Fig.1-15 Crystal growing from melt in a crucible : (a) solidification from one end of the melt (horizontal Bridgman method); (b) melting and solidification in a moving zone

56. 2. Czochralski method (쵸크랄스키법)
Fig 1.16 Pulling of a Si crystal from the melt (Czochralski method):
(a) schematic diagram of the crystal growth process; (b) view through a port in the furnace showing Si crystal being pulled from the melt.

57. 3. Zone refining(구역정제) : 1-15(b) and 1-17.
4. Floating - zone growth : Fig.1-17
does not touch the crucible walls.
Fig 1.17 Floating-zone crystal growth : schematic diagram of the growth process