GeSi Quantum Dot Superlattices

GeSi Quantum Dot Superlattices ECE440 Nanoelectronics Zheng Yang Department of Electrical & Computer Engineering University of Illinois at Chicago

Nanostructures & Dimensionality Bulk Quantum Walls Quantum Wires Quantum Dots ρ 3D (E) ρ 2D (E) ρ 1D (E) ρ 0D (E) Energy Energy Energy Energy 2 ρ 3D (E) ~ E 1/2 ρ 2D (E) ~ E 0 ρ 1D (E) ~ E -1/2 ρ 0D (E) ~δ(e)

Contents Growth of GeSi QDSLs Molecular-beam epitaxy; S-K growth mode; Raman Spectra of QDSLs Background on Raman scattering; Optical phonons; Acoustic phonons. PL Spectra of QDSLs 3 QDSL: Quantum Dot Superlattice

Applications of Ge/Si Quantum Dot (Superlattices) Electronic Applications such as resonant tunneling diodes with improved quality. Optoelectronic Applications such as photo-detectors, photo-emitters, and lasers in mid-infrared range. Thermoelectric Applications such as novel thermoelectric materials with large ZT values. 4 Quantum Information Applications

Molecular-Beam Epitaxy (MBE) F-vdM: Frank-van der Merwe V-W: Volmer-Weber 6 S-K: Stranski-Krastanow

Self-Assembled Growth of GeSi Quantum Dot Superlattices Schematics of GeSi QDSLs 7 Si spacer layer Self-assembled Ge quantum dots Ge wetting layer Si buffer layer Si substrate

TEM Image of Ge/Si Quantum Dot Superlattices Vertical correlation of the quantum dots is evident!! 10-period, 540 C Ge 1.2 nm/si 20 nm Si spacer layer 8 210 Self-assembled Ge quantum dot

AFM Images of Ge/Si Quantum Dot Superlattices 0 0.2 0.4 0.6 µm 9 Growth temperature: 600 o C; Ge nominal thickness: 1.5 nm. Base size of the dots ~ 70 nm; Height of the dots ~ 15 nm.

The Samples Used in the Following Experiments 10

More AFM Images of Ge/Si Quantum Dot Superlattices (1) 137 210 187 0.5μm 0.5μm 0.5μm 226 226 11 0.25μm

More AFM Images of Ge/Si Quantum Dot Superlattices (2) 266 50 nm 12

More TEM Images of Ge/Si Quantum Dot Superlattices 20 Periods 265 13

Discovery of Raman Spectroscopy In 1928, Raman discovered that the spectrum of scattered lines of CCl 4 liquid not only consisted of the Rayleigh lines but a pattern of lines of shifted frequency the Raman spectrum. Mr. Raman won the Nobel Prize of Physics in 1930, for his work on the scattering of light and for the discovery of the effect named after him. 15 C.V. Raman (1888-1970)

Stokes S Anti-Stokes S S L S L q q 16 S L q S L q

Raman Spectra of Ge/Si Quantum Dot Superlattices Acoustic Mode From Sample 226 Si-Si Raman Intensity (arb.unit) Ge-Ge Optical Mode Si-Ge 17 0 10 20 30 40 250 300 350 400 450 500 550 Raman Shift (cm -1 )

Raman Spectra of Optical Phonon Modes (1) From Samples 137 and 136 Si-Si Raman Intensity (a.u.) Ge-Ge Ge QDs Si-Ge Si-Si LOC WLs 18 250 300 350 400 450 500 550 600 Raman Shift (cm -1 ) WL: wetting layer

Raman Spectra of Optical Phonon Modes (2) 298 From Samples 210, 226, and 187 Raman Intensity (a.u.) 297 299 Sample 226 Sample 210 Sample 187 Bulk Ge: 300 cm -1 19 250 300 350 400 450 Raman Shift (cm -1 )

Frequency Shift of Optical Phonon Modes Redshift Ge-Ge optical phonon frequency Blueshift Phonon Confinement ~1cm 1 Strain Linear Chain Model 1 or RWL Model 2,3 Biaxial Strain Model 1,2 20 1 Liu J L et al, JAP 92, 6804 (2002) 2 Yang Z et al, Chin. Phys. Lett. 20, 2001 (2003) 3 Richter H et al, Solid State Commun. 39, 625 (1981)

Red Shift from Phonon Confinement Phonon Confinement phononconfinement A a d Ge Richard, Wang and Ley Model: Solid State Communication, 39, 625 (1981); APL, 69, 200 (1996); PRB, 55, 9263 (1997); JAP, 86, 1921 (1999) a Ge 0.566nm Lattice constant of germanium 21 A -1 52.3cm 1.586 Red shift ~ 1 cm -1 Constant parameters d the height of the Ge dot nearly same as the result of Linear Chain Model!

Blue Shift from Compressive Strain Effect (1) Strain induced blue shift strain 1 2 0 p zz q( xx yy ) 0 5.6510 13 s 1 (~ 300cm 1 ) Frequency of the bulk Ge zone center LO phonon p 4.710 27 q 6.16710 s 2 27 s 2 Ge deformation potentials 22 zz yy 2C C xx 12 11 xx C C 11 12 1288kbar Biaxial strain model PRB, 59, 4980 (1999) 482.5kbar

Blue Shift from Compressive Strain Effect (2) Strain induced blue shift strain 1 C12 1 q p xx xx 414.5(cm 0 C11 ) 23 Fully Strained a a Si Ge 0.543nm 0.566nm Partially Strained (due to the strain relaxation from the atomic intermixing at the Si/Ge interface) xx a Si a a Si Ge 1 0.042 17.4(cm ) xx xge 1- x 1- x x strain asi age xx x? a Si Ge

Composition of the Ge/Si Quantum Dots I I GeGe SiGe a Vegard s Law Si Ge xage (1 x) a 1- x x x B x 2(1 x) 1 B 3.2 I Si 1 1.6 I GeGe SiGe Raman Intensity (a.u.) 298 297 299 Sample 226 Sample 210 Sample 187 250 300 350 400 450 Raman Shift (cm -1 ) 24 I GeGe : Integrated Intensity of Ge-Ge peak; I SiGe : Integrated Intensity of Si-Ge peak; x ~ 0.5

Composition of the Ge/Si Quantum Dots Composition of the quantum dots APL, 62, 2069 (1993) I I GeGe SiGe x B 2(1 x) B 3.2 x 1 I 1 1.6 I GeGe SiGe Vegard s Law a Si Ge xage (1 x) a 1- x x Si xx a Si 1- x a Ge Si x 1- x a Ge x Ge 1 x 1 (1 x) a a Si Ge 1 1 0.96 0.04x a ( a Si Ge 0.96) 25 xx 0.02 when x 0.5 strain 8(cm 1 )

Summary (Raman optical phonon part) Optical phonon modes in MBE-grown self-assembled Ge/Si QDSLs were studied by Raman spectroscopy. Si-Si, Ge-Ge, and Si-Ge peaks were observed in the Raman spectra, arising from Si substrate, optical phonon modes of Ge in the QDs, and the SiGe alloys, respectively. The red-shift and blue-shift of the optical phonon modes in the Raman spectra induced by phonon confinement and strain within the Ge QDs were investigated. 26

(a) 10 periods 100 nm Raman Intensity (a. u.) Folded acoustic phonons Optical phonons 1 µm Ge-Ge Si-Ge Si-Si (b) 20 periods 100 nm Raman Shift (cm -1 ) 0 15 30 45 300 350 400 450 500 550 R am an Shift (cm -1 ) 45 40 35 30 25 20 15 10 Intensity d cos( qd) cos( V d )cos( V 0.0 0.3 0.6 0.9 2 k 1 d ) sin( 2k V 20 35 50 (c) 28 35 periods 100 nm Z. Yang, J. Liu, Y. Shi, Y. Zheng, and K. Wang, J. Nanoelectron. and Optoelectron. 1, 86 (2006). 1 1 q =0.10nm -1 2 2 45 40 35 30 25 20 15 10 Wave Vector (/d) Phonon Frequency (cm -1 ) Normalized Raman Intensity 1.0 0.8 0.6 0.4 0.2 1 1 d )sin( V 2 2 ) 1st order 2nd order 3rd order Superlattice Periods

Rytov s Elastic Continuum Theory 29 In the model, the acoustic phonon dispersion can be approximately written as 2 d1 d2 k 1 d1 d cos( qd) cos( )cos( ) sin( )sin( v v 2k v v where k v v v1 and v2 d 2 and d 1 1 and 2 1 2 1 2 1 2 and d d 1 d 2 sound velocity thickness in Ge and Si layers density 1 2 2 )

Raman Spectra of Acoustic Phonon Modes (1) Raman Intensity (a.u.) Sample 137 Sample 136 Sample 138 From Samples 136, 138, 137 (nm) 0.6, 1.2, 1.5 Folded Acoustic Phonons in Ge/Si superlattices. d cos( qd) cos( V Rytov s Model 1 1 d )cos( V 2 2 2 k 1 d ) sin( 2k V 1 1 d )sin( V 2 2 ) Si sub 30 5 10 15 20 25 30 35 40 45 Raman Shift (cm -1 )

Raman Spectra of Acoustic Phonon Modes (2) Raman Intensity (a.u.) Si Sub Sample 226 Sample 210 From Samples 210 and 226 (nm) 1.2, 1.5 10 15 20 25 30 Raman Shift (cm -1 ) 31 Intensity increase with the thickness of Ge layer.

Raman Spectra of Acoustic Phonon Modes (3) 32 Raman Intensity (a.u.) 5 2 3 1 4 1 2 3 4 5 Sample 269 (2) Sample 264 (10) Sample 265 (20) Sample 266 (35) Sample 183 (50) 5 10 15 20 25 30 35 40 45 Raman Shift (cm -1 ) Intensity increases with increased periods of QDSL layers. The amplitudes of the lowfrequency Raman scattering peaks associate with each QDs layer when the Ge QDs in different layers are vertical correlated!

Summary (Raman acoustic phonon part) Low-frequency Raman scattering spectra of selfassembled Ge/Si QDSLs were first time observed in experiments on non-resonant Raman scattering mode. These Raman peaks were arisen from the folded acoustic phonons in the Ge/Si QDSLs. It has been observed that the intensity of the lowfrequency Raman peaks is closely related to the Ge and Si layer thickness and the number of the periods of the Ge QDSLs. The smaller periods, the lower intensity of the Raman peaks. The results were discussed with Retov model. 33

Photoluminescence Spectroscopy Continuum states Electronic bound state Laser energy E CB k h excitation h emission VB PL Intensity 35 A laser excites electrons from the valence band into the conduction band, creating electron-hole pairs These electrons and holes recombine (annihilate) and emit a photon. The number of emitted photons (intensity) as a function of energy, which is photoluminescence (PL).

Photoluminescence E (Normal semiconductor vs. Quantum Well) E C E G laser emitted light emitted light hν=2.4 ev hν=1.5 ev (GaAs) hν 1.2 ev (QDs) E V 36

Photoluminescence in Ge/Si Quantum Dot Superlattices PL Intensity (arb. unit) T=10K Ge QDs From Sample 265 TO+NP Si-TO Ge WLs TO NP Si-TA or Si-NP 37 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev)

Temperature Dependent Photoluminescence Spectra From Sample 265 PL Intensity (arb. unit) 10K 30K 50K 80K 120K 160K 200K 38 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev)

Temperature Dependence of PL Intensity in Nano-Crystallines r Early Theory Arrhenius Type R exp( ) r r T T Recent Theory Combination of Arrhenius and Berthelot Type T T Berthelot Type Rhop B exp( ) B 39 I I T ) T 1 exp( T ( 0 B Tr T ) T B 2 2 2 a m * e 2 k B

Fitting of the PL Intensity 10K PL Intensity (arb. unit) 30K 50K 80K 120K 160K PL Intensity (arb. unit) 1 200K 40 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity 10K PL Intensity (arb. unit) 30K 50K 80K 120K 160K PL Intensity (arb. unit) 0.91 200K 41 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity 10K PL Intensity (arb. unit) 30K 50K 80K 120K 160K PL Intensity (arb. unit) 0.88 200K 42 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity 10K PL Intensity (arb. unit) 30K 50K 80K 120K 160K PL Intensity (arb. unit) 0.77 200K 43 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity 10K PL Intensity (arb. unit) 30K 50K 80K 120K 160K PL Intensity (arb. unit) 0.47 200K 44 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity PL Intensity (arb. unit) 10K 30K 50K 80K 120K 160K PL Intensity (arb. unit) 200K 0.20 45 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity PL Intensity (arb. unit) 10K 30K 50K 80K 120K 160K PL Intensity (arb. unit) 46 200K 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Photon Energy (ev) 0.06 0.7 0.8 0.9 1.0 Photon Energy (ev)

Fitting of the PL Intensity 47 I T / I 10K 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 I I T ) T 1 exp( T ( 0 B Tr ) T Experimental Data Fitted Curves 0 20 40 60 80 100 120 140 160 180 200 220 Temperature (K) Fitting Parameters T B = 31.6 K; T r = 0 K; ν = 0.025

Estimation of the Electron Effective Mass in the QDs T B 2 2 2 a m * e 2 k B a : the dimension of the quantum dots ; m e* : the electron effective mass in the quantum dots ; m 0 : the rest electron mass; T B : fitting parameters. 48 m e* 1.4. m a 0 2 a (nm)

Summary (Photoluminescence part) Photoluminescence experiments were performed on MBE-grown Ge/Si QDSLs. The temperature-dependence of the PL intensity has been reported and fitted. 49 Based on the analyses of the fitting parameters, the electron effective mass of the QDs was estimated.

References Z. Yang, Y. Shi, J. Liu, B. Yan, Z. Huang, L. Pu, Y. Zheng, and K. Wang, Chinese Physics Letters 20, 2001 (2003). Z. Yang, Y. Shi, J. Liu, B. Yan, R. Zhang, Y. Zheng, and K. Wang, Materials Letters 58, 3765 (2004). Z. Yang, J. Liu, Y. Shi, Y. Zheng, and K. Wang, Journal of Nanoelectronics and Optoelectronics 1, 86 (2006). 50