Semiconductor Physics

Transcription

1 10p PhD Course Semiconductor Physics 18 Lectures Nov-Dec 2011 and Jan Feb 2012 Literature Semiconductor Physics K. Seeger The Physics of Semiconductors Grundmann Basic Semiconductors Physics - Hamaguchi Electronic and Optoelectronic Properties of Semiconductors - Singh Quantum Well Wires and Dots Hartmann Wave Mechanics Applied to Semiconductor Heterostructures - Bastard Fundamentals of Semiconductor Physics and Devices Enderlein & Horing Examination Homework Problems (6p) Written Exam (4p) Additionally Your own research area. Background courses (Solid State Physics, SC Physics, Sc Devices)

2 Course Layout 1. Introduction 2. Crystal and Energy Band structure 3. Semiconductor Statistics 4. Defects and Impurities 5. Optical Properties I : Absorption and Reflection 6. Optical Properties II : Recombinations 7. Carrier Diffusion 8. Scattering Processes 9. Charge Transport 10. Surface Properties 11. Low Dimensional Structures 12. Heterostructures 13. Quantum Wells/Dots 14. Organic Semiconductors 15. Graphene 16. Reserve and Summary

3 Crystal and Energy Band structure Crystals structure Basic Lattice Types Basic Crystal Structures Polytypism Reciprocal Lattice Miller indices Point Defects Extended Defects Bandstructure Bloch Theorem Tight Binding Method Spin-Orbit Coupling k-p Model Effective Mass Semiconductor Band Structures

4 Basic Lattice Types Basis a building block of atoms Lattice a matematically periodic structure Lattice defined by three translation vectors a 1, a 2, a 3 Any lattice point R can be obtained from any other point R Bravais Lattice Lattice + basis = crystal structure. R = R + m 1 a 1 + m 2 a 2 + m 3 a 3 a 1 shortest period of the lattice a 2 shortest period not parallel to a 1 a 3 shortest period not coplanar to a 1 and a 2

5 Basic Lattice Types Unit Cell formed by the translations vectors. Unit cells are not unique The smallest possible unit cell is called primitive unit cell. The property of the unit cell determines the property of the solid. The Wigner-Seitz primitive cell Choose a reference atom Connect to all neighbours Draw perpendicular lines (2D) or planes at the midpoint.

6 Basic Lattice Types Unit cells in one-dimensionell crystals

7 Chemical Bonding in Semiconductors Diamond Crystals Si and Ge (and diamonds) has covalent bonds. Each atom in the center of a tetrahedron with four nearest neighbours. In all cases four valence electrons, 2 s-electrons and 2 p- electrons. One s-electron excited to p-state forming sp 3 hybrid orbitals

8 Basic Lattice Types 14 3D Bravais Lattices sc simple cubic bcc body centered cubic fcc face centered cubic

9 Basic Crystal Structures Diamond Structure fcc lattice Base ot two identical atoms at (0,0,0) and (¼, ¼, ¼)a C, Si, Ge

10 Basic Crystal Structures Zincblende Structure fcc lattice Diatomic base atom (A) at (0,0,0) and atom (B) at (¼, ¼, ¼) a GaAs, InAs, AlAs, InP, GaP and their alloys. ZnS, ZnSe, ZnTe, HgTe, CdSe and CdTe Cubic structure of GaN, SiC and ZnO

11 Basic Crystal Structures Wurtzite Structure (Aka hexagonal ZnS) hcp lattice with diatomic base Many semiconductors with high bandgap GaN, AlN, InN, ZnO, SiC, ZnS CdS and CdSe

12 Basic Crystal Structures Chalcopyrite Structure (CuFeS 2 ) Tetrahedral structure with triatom base. I-III-VI 2 (Mg, Zn, Cd) (S, Ge, Sn) (As, P, Sb) 2

13 Basic Crystal Structures Cubic SiC, GaN, ZnO is Zinc Blende Hexagonal SiC, GaN, ZnO is wurtzite

14 Polytypism Stacking sequence not only hcp or fcc But takes different sequences. SiC typical example Each hexagonal atomic layer have three different possible relative positions A, B, and C 3C-SiC : ABC ABC 4H-SiC : ABCB ABCB 6H-SiC : ABCACB ABCACB A Polytypes is a large number of repetition of the same stacking sequence About 45 different observed in SiC Theoretically > 200 Every polytype has different electrical and optical properties

15 Reciprocal Lattice Reciprocal lattice is important to understand and to study the periodic structure of a crystal. X-ray diffraction phonons band structure It is a quasi-fourier transformation of the direct lattice. R are translations vectors for the direct lattice. G are the corresponding reciprocal lattice vectors. exp( igr ) = 1 Therefore, for all vectors r and the reciprocal lattice vector G exp( ig(r+r) ) = exp( igr ) Each Bravais lattice has a certain reciprocal lattice, which also is a Bravais lattice.

16 Reciprocal Lattice Reciprocal lattice vectors b 1 = 2π ( a 2 x a 3 ) / V a b 2 = 2π ( a 3 x a 1 ) / V a V a = a 1 ( a 2 x a 3 ) volume of unit cell b 3 = 2π ( a 1 x a 2 ) / V a Any arbitrary set of primitive vectors a 1, a 2 and a 3 of a given crystal lattice gives a set of reciprocal lattice points. G = h b 1 + k b 2 + l b 3 h,k,l are integers Every crystal has two lattices, one direct and one reciprocal. The reciprocal of the reciprocal lattice is again the direct lattice. The reciprocal of a bcc is the fcc, and vice versa. The reciprocal lattice of the Wigner-Zeits unit cell is called Brillouin zone

17 Brilloun Zone fcc For fcc hcp

18 Miller indices A lattice plane is determined by the intercept of that plane on the crystallografic axis and specified by Miller indices. One use the axes that coincide with the edges of the conventional unit cell and express the intercept in units n 1, n 2 and n 3 of the lattice vectors a 1, a 2 and a 3. The Miller indices h,k,l are obtained from the reciprocal of n 1, n 2 and n 3 and multiplying them by the smallest number that clears the fraction n 1, n 2 and n 3 = 3, 2, 2 reciprocal = 1/3, 1/2, 1/2 Mult with 6 = 2,3,3 = (233)

19 Miller indices Cubic crystals a 3 a 1 a 2

20 Miller indices

21 Miller indices Hexagonal Lattice In hexagonal lattice four indices (hkil). i = -(h+k) (110) = (11-20)

22 Point Defects Intrinsic Defects Vacancy Self Interstitial Anti-site Substitutional Extrinsic Defects Substitutional Interstitial Complexes

23 Structural Defects Dislocations Edge dislocations Screw dislocations Threading Edge dislocations Grain boundaries Stacking Faults

24 Structural Defects Stacking Faults : An error inte normal stacking sequence (ABCABC ). Intrinsic Fault : Missing atomic plane (ABCACABC ) Extrinsic Fault : Extra atomic plane (ABCABACABC..) Twin lamella : reversed sequence (ABCABCBACBAC )

25 Structural Defects Xray Topography Synchrotron White Beam Xray Topography SWBXT Reflection Transmission

26 Structural Defects Dislocation densities Si cm -2 SiC cm -2 GaN 10 7 cm -2

27 Polycrystalline Semiconductors Randomly oriented crystal grains. Used in : Cheap, large area applications. Solar cells Thin film transistors

28 Bloch Theorem Schrödinger equation

29 Bloch Theorem

30 Bloch Theorem

31 Empty Lattice U(r) = 0 One-dimensional Reduced zone scc

32 Kronig Penney Model Schrödinger Equation En-dimensionell periodic potential Well Barrier Bloch s teorem Uo b 0

33 Kronig Penney Model

34 Tight Binding Method TBM an empirical technique, i.e. experimental inputs, are used to fit the bandstructure. Uses atomic functions as basis set for the Bloch functions.

35 Tight Binding Method Does not describe the valence band without including spinorbit interaction

36 Spin-Orbit Coupling Most semiconductor has similar valence bandedge. Without s-o coupling 6-fold degenerate. S : Spin angular momentum L : Orbital angular momentum J : Total angular momentum S-O coupling 4-fold degenerate 2 HH Heavy Hole 2 LH Light Hole 2 split-off bands

37 Other Methods Ortogonalized Plane Wave (OPW) Uses the valence and conduction band states ortogonal to the core states. Simplifies calculations and reduces number plane wave states. Pseudopotential Method The background periodic potential is replace by a new pseudopotential, subtracting the core contribution and constant background perturbation potential. k p Method Accurate close to bandedges. Used also for low dimensional structures. Starts at bandedges and uses perturbation theory to describe the bands away from high symmetri points.

38 Semiconductor Band Structures

39 Effective Mass For the conduction band Effective mass decreases with bandgap

40 Selected Bandstructures : Si Indirect bandgap Small E G = 1.1 ev Limited used for optical applications. Limited use as Semi-Insulating applications (Isolator). Six equivalent conduction band valleys.

41 Selected Bandstructures : GaAs Direct bandgap E G = 1.43 ev Optical application.

42 Selected Bandstructures : Nitrides Direct bandgap InN : GaN : AlN : E G = 0.70 ev E G = 3.40 ev E G = 6.2 ev

43 Selected Bandstructures :