Epitaxial and endotaxial semiconductor quantum dots Peter Moeck

Epitaxial and endotaxial semiconductor quantum dots Peter Moeck Department of Physics Portland State University P. O. Box 751, Portland, Oregon 97207 -0751 collaborations with Yuanyuan Lei, Teya Topuria, Nigel D. Browning, (University of Illinois at Chicago at that time), Robin Nicholas, Nigel Mason, Roger Booker, (University of Oxford), Klaus Pierz (PTB, Germany), Harry A. Atwater (CALTEC), Jacek K. Furdyna (University of Notre Dame) are kindly acknowledged

Outline 1. Introduction to quantum dots (QDs) 2. Stranski-Krastanow grown QDs 3. Sn QDs in Si 4. Summary and Conclusions

1. Introduction to quantum dots What are semiconductor quantum dots (QDs)? Traps for matter waves, artificial pseudo-atoms, entities with discrete energy levels one-dimensional, time independent Schrödinger’s equation Electron in atom: ΔE = 1 -10 e. V, L = 0. 1 nm Exciton in semiconductor quantum dot: ΔE ≈ 0. 1 e. V, L ≈ 10 nm,

QDs should be self-assembled (for economic gains, not quite in reach of nanolithography) 1) semiconductor with smaller bandgap embedded into matrix with large bandgap 2) just right size, large enough to accommodate an exciton, small enough in all directions for quantum confinement 3) no structural defects such as dislocations KEY ISSUE: uniformities of size, shape, chemical composition, strain distribution, crystallographic phase, mutual alignment, … optoelectronics (no contacting problem, only problem QD array homogeneity) - active medium in lasers, (In, Ga, Al)As based 1. 3 μm! - far infrared detectors - novel device concepts such as quantum cellular automata

Section Outline: Epitaxial QDs 2. Stranski-Krastanow grown quantum dots 2. 1. Problems and opportunities 2. 2. Thermodynamical argument for structural transformations 2. 3. Implications and experimental support

2. Stranski-Krastanow grow QDs 2. 1. Problems and opportunities deposition, surface diffusion, interdiffusion are random events, → random alloy quantum dots, cake with raisins smaller bandgap semiconductor (alloy) usually larger lattice constant

What structure results from this process? epitaxially grown QDs compressively strained, random distribution of atoms in adamantine host structures → ordinarily strained QDs examples (In, Ga)Sb islands/quantum dots on/in Ga. Sb substrate/matrix 100 nm AFM image, different types of islands, result in different types of quantum dot when overgrown CTEM 220 dark field close to [001], plan view, Ashby-Brown type Black-White (BW) contrast if strained 10 nm HRTEM, <110> cross section, Moiré’ fringes if relaxed, shape: “convex lenses with varying degrees of curvature”

Semiconductor superlattices → smaller bandgaps! since compound semiconductor alloys are not regular substitutional solid solutions, there is always some anticlustering and clustering (short range order) A. H. Cottrell, Theoretical Structural Metallurgy, Edward Arnold Publ. , 1954, p. 98 heteroepitaxy: “external strain enthalpy” due to elastic deformation of deposit calculated (In, Ga)As phase diagrams, bulk or completely relaxed (left); single layer pseudomorphically constrained to In 0. 5 Ga 0. 5 As substrate (right) J. Y. Tsao, Materials Fundamentals of Molecular Beam Epitaxy, Academic Press, 1994, p. 93 -150 similarities to intermetalics, e. g. Al 2 Cu, Guinier-Preston zones, understood as aging effects, age hardening, observed 1906, explained 1938

We know: Epitaxially grown quantum dots: - are always alloyed - possess same structural prototype as constituent elements or compounds - random distribution of atoms in respective sublattices - usually compressively strained (a few GPa!) – just as endotaxially grown QDs, “ordinarily strained” QDs -------------------------------- We also know: semiconductor alloys have propensity to atomic ordering and phase separation, i. e. formation of crystallographic or chemical superlattices, which also have the smaller band gaps we desire Are there structural transformations ? Can atomically ordered QDs be created at will ?

2. 2. Thermodynamic arguments minimization of Gibbs free energy G = E – T S + p V (compressively strained) OS-QDs, subscript OS p V = BOS ΔVOS accurate to within 10 % ! sphalerite → atomically ordered (subscript AO) negligibly strained, ΔVAO ≈ 0, p ≈ 0 EOS – T SOS + BOS ΔVOS > EAO – T SAO larger BOS ΔVOS → larger Tc (neglecting interfaces)

What does enhanced Tc mean? classical theories (Bragg-Williams, Bethe, Kikuchi) of long and short-range atomic ordering as cooperative phenomena (also called critical phenomena) higher Tc, more atomic ordering, shorter thermal treatments at higher temperatures ------------------------------------ quenched-in vacancies FV ≈ 1 e. V, fast quench from growth temperature (500 ºC) to room temperature → up to ten order of magnitude higher vacancy concentration, in strain gradients, vacancies move to places of higher compressive strain more quenched in vacancies at OS-QDs, faster atomic ordering !

2. 3. Implications and experimental support ordinarily strained In 0. 75 Ga 0. 25 P QD in Ga 0. 75 In 0. 25 P matrix, 3. 6 % compressive strain EOS – T SOS + BOS ΔVOS > EAO – T SAO (famatinite) for T = 300 K, strain evenly distributed - 0. 66 e. V/atom + 0. 6 e. V/atom > - 0. 33 e. V/atom hydrostatic pressure (GPa) → negligibly strained (atomically ordered) crystallographic superlattice(s) (without hydrostatic pressure, i. e. lattice mismatch strain → sphalerite structure)

→ Prediction 1: many different phases may exist (Zn, Mn)Se matrix 2 3 5 nm 1 a b Atomically ordered (Cd, Mn, Zn)Se QDs and agglomerates in (Mn, Zn)Se matrix, a) Atomic resolution Z-contrast image. All large agglomerates posses orientation relationship (020)agglomerate║(2 -20)matrix, (110)agglomerate║(1 -13)matrix. Although quite large, free of structural defects, except occasionally antiphase boudnaries, indicating negligible external lattice mismatch strains b) Selected area electron diffraction pattern (at least two agglomerates)

Tc ≈ 486 K, if stain evenly distributed between QD and matrix but, if all external lattice mismatch strain accommodated by quantum dot alone Tc ≈ 852 K, i. e. in range of growth T For this materials system actually observed by U. Håkanson et al. , Phys. Rev. B 66, 235308 (2002), Appl. Phys. Lett. 82, 627 (2003) Also short range order in (In, Ga)Sb in Ga. Sb matrix right after MOVCD growth observed by TEM, so it probably originated right after growth

→ Prediction 2: Tc may be in order of magnitude of growth temperature a b Atomically ordered (In, Ga)Sb quantum dot in Ga. Sb matrix a) High-resolution TEM, b) Selected area electron diffraction pattern Images recorded at 500 C, at which specimen was held for 2 h (and previously held at 475 C and 350 C for 2 h each), suggesting atomically ordered QD is structurally stable and Tc is of order of magnitude of growth temperature

→ Prediction 3: long and short range order may arise when samples are stored at room temperature a b Atomic order in Stranski-Krastanow grown (Cd, Zn)Se quantum dots in Zn. Se matrix after ≈ 38 month storage at room temperature; high-resolution TEM, a) Long-range order, b) Short-range order neither did appear to exist earlier, C. S. Kim et al. , Phys. Rev. Lett. 85, 1124 (2000)

Atomically ordered II-VI quantum dots possess their own photoluminescence (PL) spectra, i. e. could indeed by employed as QDs, here (Cd, Mn, Zn)Se QDs in (Mn, Zn)Se matrix as shown earlier in TEM/STEM images, PL excitation spot is 106 larger than TEM analysis area, so there is lots of atomic ordering, full line: nonresonant excitation over band gap

10 nm left: Resonant PL excitation is specific to certain structures, variations in peak heights as a function of excitation power density strongly suggests that the 2 e. V peaks arises from tunneling of excitons from “zero dimensional entities”, i. e. the about 25 nm diameter atomically ordered quantum dots shown in right: HRTEM image from the same (Cd, Mn, Zn)Se QDs in (Mn, Zn)Se sample

Section Outline: Endotaxial QDs 3. Sn quantum dots in Si 3. 1. Problems and opportunities 3. 2. Void filling and phase separation 3. 3. Shape transition with -Sn precipitate size 3. 4. β-Sn and its orientation relationship 3. 5. Thermodynamics -Sn → β-Sn

3. Sn quantum dots in Si 3. 1. Problems and opportunities bulk α-Sn (grey tin) direct, 0. 08 e. V, band gap, bulk substitutional Snx. Si 1 -x solution direct band gap for 0. 9 < x < 1 41. 8 % bulk unit cell volume mismatch, solid solubility 0. 12 %, conventional molecular beam epitaxy (c-MBE) restricted to ≤ 10 % Sn, ≤ 10 nm temperature and growth rate modulated MBE (tm-MBE), as pioneered at CALTECH: Snx. Si 1 -x/Si quantum well structures, x = 0. 02 to 0. 1, 1 - 2 nm, annealed endotaxial growth of quantum dots, Sn content raises significantly

tm-MBE at CALTECH: 100 nm Si 550 ºC, 0. 05 nm s-1 4 -6 nm Si ≈ 140 – 170 ºC, 0. 01 – 0. 03 nm s-1 1 -2 nm Snx. Si 1 -x x = 0. 02 - 0. 1 ≈ 140 – 170 ºC, 0. 02 nm s-1 100 nm Si 550 ºC, 0. 05 nm s-1 4 -6 nm Si, ≈ 140 – 170 ºC, 0. 01 – 0. 03 nm s-1 1 -2 nm Snx. Si 1 -x x = 0. 02 - 0. 1 ≈ 140 – 170 ºC, 0. 02 nm s-1 For multi-quantum well structures there are in situ anneals at 550 ºC for 30 min for each quantum well Low growth temperature results in many vacencies, thermal cycling results also in vacencies, vacencies condense into equlibrium shape and size voids ---------- Si buffer layer 550 ºC (001) Si substrate, 550 ºC K. S. Min and H. A. Atwater, Appl. Phys. Lett. 72 (1998) 1884 Snx. Si 1 -x/Si (multi-)quantum well structures additional ex situ anneals 550 - 900 ºC, 30 minutes, the crucial endotaxy process that lead to high Sn contents

3. 2. Void filling and phase separation 100 nm left: increase of QD size with ex-situ annealing time, nonlinearities due to diffusion shortcuts (dislocations, …) middle: CTEM overview, note QDs within the Si spacer layers right: HRTEM, perfectly pseudomorph growth, so there must be other diffusion shortcuts

50 nm 2 nm Z-contrast STEM images of Sn 0. 1 Si 0. 9/Si multi-quantum wells left: Sn precipitates inside the spacer/capping layers right: void that is at its interface with Si matrix lined by Sn

calculated “empty” void experiment calculated “fully Sn filled” void experiment left: tetrakaidecahedron with shape parameter A = t / a, equilibrium shape of voids - also shape of prospective -Sn precipitates, consistent with Neumann’s symmetry principle, anisotropy of interface energy density right: quantitative EELS, calculations for “empty” and “fully Sn filled” voids superimposed

5 nm left: [110] cross section, voids partially filled with Sn right: same voids significantly more filled with Sn as result of in-situ anneal at 300 ºC for 3 hours (under the microscope)

[001] [010] 5 nm [100] [110] cross section, early stage of phase separation mechanism phase separation seem to start with formation of {111} Sn-Si interfaces and preferential substitutional Sn-Si replacements in areas around intersecting {111} planes

3. 3. Shape transition with -Sn precipitate size 5 nm 25 nm left: from tetrakaidecahedron, as dominated by the anisotropy of interface energy density (Neumann’s principle), to right: essentially an octahedron, as possibly dominated by anisotropy of the elastic mismatch energy – volume (elastic lattice mismatch energy) increases faster than surface (interface energy)

3. 4. β-Sn and its orientation relationship 002 Si & 011 Sn 111 Si 200 Sn 2 nm 100 Sn 111 Si [011]Sn projection 111 Si 002 Si & 011 Sn left: bright field STEM, right: power spectrum, strain minimizing orientation relationship (011)β-Sn║(002)Si, (600)β-Sn║(440)Si, and [077]β-Sn║[660]Si assuming Si and β-Sn lattice constants: 2. 8 %, 1. 2 %, 0. 9 % linear mismatch, nothing like the 19. 5 % -Sn would have ! shape rhombic dipyramidal polyhedron, Neumann’s principle:

3. 5. Thermodynamics -Sn β-Sn Comparing Gibbs free energies: G = E – TS + p. V = Bα-Sn Vα-Sn, ≈ 9. 6 ke. V for 10 nm diameter model QD, 21739 atoms, 0. 44 e. V per atom, 18. 6 GPa, (Sn 0. 5 Si 0. 5, 0. 27 e. V per atom, 12. 1 GPa) Eβ-Sn – T Sβ-Sn + Bβ-Sn ΔVβ-Sn + Iβ-Sn/Si + Iinc < Eα-Sn – T Sα-Sn + Bα-Sn ΔVα-Sn + Iα-Sn/Si bulk α-Sn β-Sn, 286 K, E – TS will be about same for both phases at room temperature

homogenous contributions to interface energies (ISn/Si) also about equal due to mismatch strain minimizing orientation relationships Bβ-Sn ΔVβ-Sn ≈ 0 incoherent contribution to interface energy β-Sn/Si: Iinc ≈ 0. 1 ke. V (from dislocation theory) Eβ-Sn – T Sβ-Sn + Bβ-Sn ΔVβ-Sn + Iβ-Sn/Si + Iinc < Eα-Sn – T Sα-Sn + Bα-Sn ΔVα-Sn + Iα-Sn/Si reduces to 0. 1 ke. V < 9. 6 ke. V, structural transition to β-Sn type energetically favorable! kinetics may be slow but TEM several years after growth show both - and β-Sn precipitates (also β-Sn 26 % higher density than α-Sn)

4. Summary and Conclusions - atomic order does definitively exist in III-V and II-VI QD structures, - this reduces band gap, understanding and controlling is needed, such AO-QDs possess their own PL, have smaller band gaps, and are structurally more stable than ordinarily strained (random alloy) QDs, better quantum dots - void mediated formation mechanism for α-Sn QDs may allow growth of exotic quantum dots, e. g. (In, Si, As) in Si by endotaxy, N. D. Zakharov et al. Appl. Phys. Lett. 76, 2677 (2000) - structural transformation α-Sn into β-Sn, may render devices useless over time ---------------------------------------- emerges as a research topic in its own right - TEM/STEM and complementary structural methods (such as synchrotron based GI-XRD) as well as spectroscopic method (such as PL) are to be combined - structural and spectroscopic analyses are to be combined with (in situ and ex situ) heat treatments of specimen