Lecture 2 - Advanced Semiconductor Physics PDF

Advanced Semiconductor Physics TUM Online – 0000000143, WS-2023/24 J. J. Finley Chair for Semiconductor Nanostructures and Quantum Systems Walter Schottky Institut, Am Coulombwall 4a, 85748 Garching [email protected]...

Advanced Semiconductor Physics TUM Online – 0000000143, WS-2023/24 J. J. Finley Chair for Semiconductor Nanostructures and Quantum Systems Walter Schottky Institut, Am Coulombwall 4a, 85748 Garching [email protected] Lecture 2 – 28.10.24, 10:15 HS-3  This week... Crystal structure of key semiconductors Cubic (fcc, bcc) Lecture 2 Diamond and zincblende Wurtzite (hcp, diamond, with a twist…) Pyroelectricity A case study : cubic and hexagonal SiGe Defects in semiconductors Point defects (vacancies) Lecture 3 Vacancy complexes Interstitials and anti-site defects Dislocations (edge and screw) A case study: strain driven epitaxy and nanowires  3 Crystal structure , defects and doping of the 14 Bravais lattices that differ from one another only vice their symmetry (7 lattice systems , 14 Bravais lattices) two relevant for crystalline semiconductor only are m o st - Face Centered Cubic (FCC) Hexagonal Packed (TCP) - Close In general , the major materials (see last lecture) crystallize in one of these two forms : Both have a atoms in BASIS Examples : Group (elementall semiconductor (C , Si , Ge... ↳) Two identical atoms in basis (DIAMOND) #-I (compound) Semiconductors (GaA , InP, (nAs) ↳ two different atoms in basis I H fec-zincblende nat--Wurtzite structure structure 3 1. the Diamond Lattice constructed from two inter-penetrating FCC lattices... ⑳. Atoms & positions (0 0 0) ⑩~... I "Is , , -(1 , 1 , 0). 7 ⑧ =(1 , 0 , 1) & (0 , 1 , 1) These Sites FCC lattice are the lattice of spanned by te lattice vectors listed on the previous page BODY DIAGONAL DIAMOND f lattice has G-ATOM BASIS with IDENTICAL atoms - is one of these atoms at = [1 , 1 , 1] (0 , 0 , 0) and a second is shifted by (1 , 1 , 1) along me (0 0) body diagonal , 0, => Repeating this unit (BASIS) for all points of me FCC lattice gives te DIAMOND STRUCTURE EACH ATOM is surrounded by 4-others arranged in 4 space as a tetrahedral config. 1 O 2 ⑧ " ⑩ ⑧.... ⑧ 3 · ④ Diamond Lattice IC , Si , Ge etz ) ! the physical origin of this tetrahedral arrangement of atoms in space can be traced to the sp3 hybridization of atomic orbitals when the bonds are formed between atoms. Atomic orbitals (reminder) # s " ! # " p ! Hybridization Bond angle EXAMPLE Group # elemental semiconductos - =14 - - 7 Si 1522522p6352p2 I CORE elections ↳x valence orbitals SEE SLIDE Atomic orbitals of Valence electrons ↑ For the 35 3p orbitals => and 2 1S) z2 x y2 IPx,y , < X z y + + , , The p-orbitals described equally be can well as : R -> = 1 1P-) , (1px) i1py)) = Me= 11 - -l = 1 , me = 0 When two si-atoms approach each other in te gas phase Si 0 si the is 0--7 spherical symmetry broken => orbitals interact mix and , hybridize. => can form new eigestates /hi) that are LINEAR combinations of atomic orbitals (LCA0)  (nix = [15 + 14x) + (Py) + 142)] (h) [15 1px) (Py) 1Pz)3 e = = + - - 14x = [15 - 1px) + (py) - 1P=)) (nx) = = [15) - 1Px) - (py) + (pz)) What do mese hybridized WE's look like ? I his 142] 1 inx> 13 / 4x sp hybridized Orbitals form 4x bonds with a) Why does hybridization ocur ? T ETRAMEDRAL Spatial ↳ Al since total energy of interacting Si-atoms grangement. reduced - by hybridization without hybridization (left) two atoms would interact I sev · & and form bonding + ↑ -Ive antibanding p-orbital states Sev -x414. (right) each with , a bunding energy VI PTO->  However , with HYBRIDIZATON The energetics is different ! 1 Interacting si-atoms have to pay "me energy cost of forming hybridized orbitals /hi) -> Eprom Epan = [sp3) - 2ECS)]] / Energy of 4e inhib Energy of Ze orbitals in 1S) and 2 in 1p> From figure on previous page : ECsp3) = E(s) + ↑ [E(p) - E(s]] I, [3E(p) E(s)] = + therefore : Epam = = (3E(p) + ElS) -2 E(p)-2E/S} = Elp) - Els)} 1. SeV per electron So , by spp hybridization the system will goin 4x sp3 having V2 bonds , each a bunding energy of is favorable : Hybridization energetically when (4 - 2)V= - 4 Eprom =) V2 > 2 Eprom 1 S d L I If ↳ because cost" we have energy ineq lattice a Si ⑧ 0 5. #O HETERONUCLEAR BOND EXAMPLES SiC GaAs , InAs InP InSb cubic BN , , , , cubic GaN , InS , InSe I Asot - =>) Ga and : two elements have different electronegativities bond has partial cation/anion character : bond has partial ionic character  It - Useful picture is that the basis has a total is group I like of 8 -electrons + the basis effectively 2x E - - = => Diamand structure - Due to hetropolar basis , the zinablende lattice has lower diamand lattice symmetry o zimablende lattice => No inversion symmetry around bond center - # ⑳ # 3 3 The. Wurtzile - - lattice [examples BN , GaN , cate , zn0] ~ This belongs to the hexagonal lattice type In the diamand Wortite lattices tetrahedra and , neighboring to each over (dihedral angle) with % 60 respect are rotated by 1 ZINCBLENDE" 1 WURZITE · -This 8 atom sits O" # /waawei - L..... ↑ above the gap - 1 : between atoms theetwo fo -... ⑧ -..... ⑧ ⑧ - ↳ - DIEDRAL Angle o s... · -- 600  The ideal Wurtzite lattice is a hexagonal lattice with a two atom basis : I atom e(0 , 0 , 0) I atom & 3 (0 , 0 , 1) CONVENTIONAL unit cell E S B c-axis I/ A ↑ Wurtzite lattice conventional unit Hexagonal nature of lattice be here cell can nicely seen Rings of neighboring batoms in the Workite lattice have a tub" form 9-- ⑧ d- - ⑧ "Form I⑧ ⑧ -> ·⑧ c. f. chair / I- E - 11 --⑧ in zB lattice 0 e] ((nx : Stacking sequence of tetrahedra in B and WE latticel / I ABCABC A BABAB stacking stacking Comparison zincblend and wurzite lattices “tub form” of 6-atom rings (WZ) “chair form” of 6-atom rings (ZB) Zincblend lattice Wurzite lattice Wurzite lattice (..ABABAB stacking..) WZ lattice showing clearly the hexagonal symmetry... stacking of different layers along the c-axis in a WZ lattice Tetrahedra are “directly above” one another... stacking sequence of ZB and WZ lattices  SEE PPT on Hexagonal/cubic SiGe Pyroelectricity of 3. 4 the Wurzite lattice x Due the Wortte there hexagonal the lattice to · symmetry of is a special axis called the c-axis along the ABAB stacking This has axis symmetrics lead x special and can to very Strong PYROELECTRIC (PlEZOELECTRIC) effects & spontaneous appearance of polarization fields => To understand this consider the tetrahedral , bond arrangement e. g. NO- GaN C I each bond partial ~ Ga has of the > 45x one polar nature more polar No En - vo , I F a # - sc's & 0 P3 No I pi = - " Generally in a perfect Wurtzite crystal a re BuT · the slightly positive Ga atom (84) will be no ne dipole " sees 3x No atoms below... and only one NO atom above => Gast atm moves down in the crystal. NO- P MovES" #! I Ga If -> UNIT CELL POLARIZED BECOMES + ACQUIRES · 7 --s ↑ 8 I 43 > No a NET DIPOLE moment N o Due to the ABABAB stacking of the WE lattice , these Up" macroscopic dipoles ADD a macroscopic polarizatio field to 1 I = + P = Pi -unit vector along craxis of WE crystal. ⑦ What do mink will happen in ZB lattice ? you a ↳ A microscopic cancel dipoles each other microscopically due cubic to symmetry.... => NO spontaneous polarization in cubic crystals ! * macroscopic polarization can be induced by squeezing crystal to reduce symmetry (below cubicl - this is called PIEZOELECTRICITY (of PYROELECTRICITY in WES P Electrostatically , the existence of a macroscopic - polarization is internal equivalent to an electric field Eint generated by surface charges V volume dipole moment - 1 (p] (m) - I' --...... - - E I I ---- = [m3] = -= / I-ax is - > Xvolume dipoles/unit cell - o ** apparent polarization / + o - - P1 = 0 charges surface of on semiconductor. internal pol. generates internal, polarization due field => to => Io I = EE-E = E. Eit P = E. Ein + O :. El-I so internal electric field.  In highly ionic materials such as GaN and EnO , /Eur is very large , of the order of wIMV/cm - it strongly interiences the electronic structure of METEROSTRUCTURES Example 1 e g piezoelectrically induced HEMT @ c-plane GaN-AlGoN.. interface - Quantum well" I ⑦ #- - V -> 11 at AlGaN trapping - GaN - > Eg-beV & interface - - Eg-3. 40V NO T PYROELECTRIC effects I Example 2 ⑫ GaN-AlGaN LED's ↳e , - AlGaN -> - GaN ↓ emit me light aa bandgap of - GaN dre to the ht ⑰ quantum confined Starte effect. NO PYROELEC. effects.  14 28 Si S ilic o n 32 73 Ge Hexagonal SiGe : A new direct G e rm a n iu m bandgap semiconductor Case study 1 - zincblende and wurtzite SiGe… © Photo-ARPA-E Slides 19-35 are not examinable - they provide context for our discussion  Good arguments for integration…. 8750TWh globally (10% data-centers) Silicon Integrated Nanophotonics | IBM Research D. A. B. Miller et al. , Proc. IEEE 97, 1166 (2009) Data systems approaching 100 Terabit/second within 5 years at internet switches A. S. G. Andrae et al, Challenges, 6, 117-157, (2015) From system-to-system move to chip-to-chip and finally to on-chip N. Jones. Nature 561, p164, (2018) … Requires a redesign of electronic/photonic interface  Opto-eletronic integration on silicon ? M. Smit, K. Williams H. Sigg et al. (2019) V. Reboud et al., APL (2017) (1) InP on Si (2) Strained Ge (3) GeSn (IMOS) Looking for CMOS compatible technologies Y. Jiao et al , Semicond. Sci. Technol. 36 013001, (2020) F.T.A. Pilon et al. Nature Comm. 10, (2019) This talk à Hexagonal SiGe S. Wirths et al. Nature Photonics, 88, 9 (2015)  Cubic and hexagonal crystal symmetry Lonsdaleite Si A little change makes a big difference.. Wurtzite Si Γ − # Si 2H-4 {0001} … Hexagonal Wurtzite (WZ) Cubic Zincblende (ZB) B Diamond (A=B) A 2 atoms/unit cell (A & B) J. Joannopoulos & M. Cohen, Phys. Rev. B7, 2644, (1973) C. Raffy, J. Furthmueller, F. Bechstedt, Phys. Rev. B66,1–10 (2002) 4 atoms/unit cell A. De & C.E. Pryor, J. Phys. Condens. Matter 26, 045801 (2014) P.S. Chen et al. C. W. Liu et al. J. Phys. D. Appl. Phys.50 (2017) ABC-ABC-… stacking AB-AB-AB-… stacking M. R. Salehpour et al. , Phys. Rev. B41,3048–3052 97, (1990) T.K. Bergstresser, M.L. Cohen et al. Rev.164,1069–1080 (1967)  Hexagonal silicon (hex-Si): band folding ! → # Cubic Silicon Hexagonal Silicon See lecture 4 C. Rödl et al. Phys. Rev. B92, 045207, (2015) Hexagonal germanium (hex-Ge): band folding ! → # Cubic Germanium Hexagonal Germanium See lecture 4 C. Rödl et al. Physical Review Materials 3, 034602 (2019)  Tunable direct bandgap in Ge-rich hex-SiGe alloys Indirect BG Direct BG Tunable direct bandgap 60%) DFT by Rene Suckert, Friedhelm Bechstedt, Silvana Botti (Jena University)  1. MOVPE Growth of Wurtzite GaAs Core Nanowires 2. Crystal Structure Transfer: Growth of Hex-SiGe shells 500 nm  Hexagonal Wurtzite (WZ) Cubic Zincblende (ZB) Hex Hex Cubic Cubic (33ML) (12ML) Hex Hex WZ/ZB GaP S.Assali et al. Nano Letters 17, 6062 (2017) Crystal structure transfer in core/shell NWs R. E. Algra et al. Nano Letters 11, 1690 (2011) Transfer Wurtzite structure from III-V to group IV Hexagonal Si realized … a c d A b c e B 27000 Si HAADF Intensity (a.u.) 100 A 26000 B A 25000 80 B A 24000 60 23000 at.% 0.0 40 c e 26600 b P HAADF Intensity (a.u.) 26500 20 Ga 26400 26300 hcp 26200 0 26100 0.0 0.1 0.2 [1-100]hcp 0.3 26000 Distance (µm) 25900 [11-20]hcp 0.0 ABAB stacking demonstrated XRD: lattice parameters Raman: Hydrostatic stability H. I. T. Hauge et al. Nano Letters 15, 5855 (2015) Ge-shells on wurtzite GaAs NW cores GaAs 500 nm 500 nm And..hexagonal Ge ! HAADF-STEM Ge GaAs 5 nm  Tunability of the hex-SiGe emission Direct gap tunable over the range 1.8 – 3.5 µm Excellent agreement with theory! EMT Fadaly et al. Nature 580 (7802), 205-209 (2020)  Current directions of Hex-SiGe Lasing Photonic bandgap structures Single wire cavities InGaN pillars Perovskite wire S.W. Eaton, et al. PNAS 23, 2016 113 (8) 1993 J.B. Wright, et al. Sci. Rep. 3, 2982 (2013) Future directions of hex-SiGe New strategies for large-are WZ epitaxy Combination of SAG and ELO induces well defined WZ growth Staudinger, P. et al. Nano Lett. 20, 686 (2019)