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PART II: MOLECULAR BEAM EPITAXY Description of the MBE equipment Reflection High Energy Electron Diffraction (RHEED) Analysis of the MBE growth process Surface diffusion in MBE MBE growth of III-V binary compounds and alloys MBE growth of lattice-matched and lattice- mismatched heterostructures Doping in III-V materials

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Molecular Beam Epitaxy (MBE) Ultra-High-Vacuum (UHV)-based technique for producing high quality epitaxial structures with monolayer (ML) control. Introduced in the early 1970s as a tool for growing high-purity semiconductor films. One of the most widely used techniques for producing epitaxial layers of metals, insulators and superconductors. Research and industrial production applications (Al-containing, high speed devices). Simple principle: atoms or clusters of atoms, produced by heating up a solid source, migrating in UHV onto a hot substrate surface, where they can diffuse and eventually incorporate. Despite the conceptual simplicity, a great technological effort is required to produce systems that yield the desired quality in terms of material purity, uniformity and interface control.

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Description of the MBE equipment M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current status”, Springer (1996) G. Biasiol and L. Sorba, in “Crystal growth of materials for energy production and energy-saving applications”, R. Fornari, L. Sorba, Eds. (Edizioni ETS, Pisa, 2001) pp (http://www.tasc- infm.it/research/amd/file/school.pdf).

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MBE Facility Growth, preparation and introduction chambers Stainless steel, bake-out up to 200C for extended periods of time Image: Veeco Gen-II High-mobility MBE system at TASC

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Research and production MBE systems R & D Riber Compact21 system: Vertical reactor Up to 1X3” wafer 6 to 11 source ports Production Riber MBE6000 system: Up to 4X8” wafers (MBE7000 model) 10 large capacity source ports Fully motorized wafer handling and transfer

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Schematics of an MBE system Liquid N 2 cryopanels around main walls and source flange thermal isolation among cells prevent re-evaporation from parts other than the cells additional pumping Effusion cells Pumping system Cell shutters Substrate manipulator Analysis tools: RHEED RHEED RGA RGA Optical (ellipsometry, RDS...) Optical (ellipsometry, RDS...)

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Pumping system Minimization of impurities: R ~ 1ML/sec, n ~ at cm -3, p ~ Torr for n imp < cm -3 p < Torr In practice: p ~ – Torr, mostly H 2 Used pumps: ion, cryo, Ti-sublimation.

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Effusion cells Principle of operation of the Knudsen cell. The most common type of MBE source is the effusion cell. Sources of this type are sometimes called Knudsen cells, or K-cells, in reference to the evaporation sources used by Knudsen in his studies of molecular effusion. However, a “true” Knudsen cell has a small diameter orifice (<1mm) to maintain high pressure within the crucible. With certain exceptions, this practice is undesirable in MBE because it limits deposition rates. Conventional MBE effusion cells are usually fit with a removable, open-faced crucible having a large exit aperture. The crucible and source material are heated by radiation from a resistively heated filament. A thermocouple is used to allow closed loop feedback control. Crucible Filament Heat Shielding Thermocouple Head Assembly Mounting Flange and Supports Power Connector Thermocouple Connector Features of an effusion cell 6 – 10 cell in a source flange Co-focused onto substrate flux uniformity Flux stability <1% / day T < T ~ 1000 ºC Temperature regulation by high-precision PID regulators Minimization of flux drift as material is depleted choice of geometry

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Crucibles Cylindrical Crucible + Good charge capacity + Excellent long term flux stability - Uniformity decreases as charge depletes - Large shutter flux transients possible Conical Crucible - Reduced charge capacity - Poor long term flux stability + Excellent uniformity - Large shutter flux transients possible SUMO® Crucible + Excellent charge capacity + Excellent long term flux stability + Excellent uniformity + Minimal shutter-related flux transients

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Valved cracker 1. Cracking zone 2. Conductance tube 3. Mounting flange 4. Power and thermocouple connectors 5. Bulk evaporator zone 6. Crucible 7. Back flange 8. Valve positioner Principle of operation for the Valved Cracker. The source material is loaded into the large capacity crucible and heated. A needle valve in the conductance tube regulates the amount of evaporant that enters the growth chamber. Cracking zone temperature is controlled so as to produce beams of either cracked (e.g., As 2 ) or uncracked material (e.g., As 4 ). For elements which sublime as molecules (As, P, Sb …)

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Dopant sublimation sources “SUSI” Si sublimation source from Omicron Sublimation from a Si wafer Suitable for doping and thin Si layers High crystal quality and purity Low growth rates

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Evaporation flux The flux J at the substrate a distance d (cm) from the tip of the cell and on its axis can be calculated, assuming that the evaporant is in equilibrium with its vapor at pressure p (Torr) (cosine law of effusion, see lecture 1): M: molecular weight in amu T: source temperature in K A: source area in cm 2

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Vapor pressure chart Ga Al As 4 T As4 < T substr < T Ga,Al As re-evaporation growth in As 4 overpressure

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Numerical Application: Estimation of the GaAs growth rate r Typical values: T (Ga cell) =1000 o C=1273 o K P ~ Torr

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Cell shutters Function: flux triggering Materials: Ta – Mo Mechanical or pneumatic actuators Operation (~50ms) much faster than ML deposition time (~1s) Designed for more than 1 million cycles Not outgassing from cell heating Minimization of heat shield no flux transients Computer control for reproducibility

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Substrate manipulator Continuous azimuthal rotation uniformity Heater behind sample (Ta, W, C): temperature uniformity, small outgassing Beam flux monitor (BFM) opposite to sample for flux calibration Temperatures up to >1000C

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Wafer holders Mo- or Ta- made holders Bonding: In (Ga), or In-free (clamped) Quick and easy transfer Image: In-free, 3-inch sample holder fitting a quarter of a 2-inch wafer

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Residual Gas Analyzer Filament: Atoms and molecules are ionized in a signal ion source following electron impact. Electrons are emitted from the hot filaments. Quadrupole: Ions with a specific mass-to-charge ratio are filtered by applying a combination of DC and RF voltages to each quadrupole. Faraday Cup: Mass filtered ions are collected by the Faraday cup detectors. Functions: leak detection, measure of the system cleanliness (quality of bake and pumping, impurities from outgassing...), studies of growth mechanisms

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Reflection High Energy Electron Diffraction (RHEED) M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current status”, Springer (1996) G. Biasiol and L. Sorba, in “Crystal growth of materials for energy production and energy-saving applications”, R. Fornari, L. Sorba, Eds. (Edizioni ETS, Pisa, 2001) pp (http://www.tasc- infm.it/research/amd/file/school.pdf).

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Reflection High Energy Electron Diffraction Cells substrate RHEED // substrate Control of the crystallographic structure of the growing epitaxial surface Pattern for 2D surface: series of // lines Si(001) RHEED patterns sputter-cleaned surface rough surface high density of steps perfect surface

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Surface sensitivity of RHEED E k = 5-40KeV = Å = 1-3 o d(penetration) = e sin e 10ML d = 0.5ML Surface sensitivity

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Diffraction: 3D vs 2D G // ∞ rods a=5.65Å G=2 /a=1.1 Å -1 E k =5KeV k 1/ =36.5Å -1 k >> G 2D (1st layer of perfectly flat surface) 3D K = G

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Ideal RHEED Pattern Ewald sphere Projected image on screen Sample Perfect 2D crystalline surface Perfectly monochromatic, collimated beam Ideal pattern: series of points on a half circle (for each nth-order Laue zone) Intersection of Ewald sphere with G vectors

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Diffraction in real case Thermal vibrations, lattice imperfections finite thickness of reciprocal lattice rods Divergence and dispersion of e-beam finite thickness of Ewald sphere Diffraction spots streaks with modulated intensity even for 2D surfaces

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Non-ideal Surfaces Ideal surface circular arrays of (elongated) spots Amorphous layers no diffraction pattern, diffuse background Polycrystallyne – textured surface diffuse rings (Debye-Sherrer construction) 3D surface electrons transmitted through surface asperities and scattered in different directions spotty RHEED pattern Ideal surface Polycrystal Rough surface

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Non-ideal Surfaces: Example RHEED SEM De-oxidized GaAs substrate + 15nm epitaxial GaAs + 1 m epitaxial GaAs A. Y. Cho, J. Cryst. Growth 201/202 (1999), 1 Lateral, periodic intensity modulation!

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GaAs (001): (2x4) RHEED Pattern 2x ([110] direction ) 4x ([-110] direction) Reciprocal space

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GaAs (2x4) Reconstruction Original model: GaAs(001) (2x4) unit cell: 3 As dimers along [-110] + 1 dimer vacancy surface energy reduction Top As layer Top Ga layer 2nd As layer Direct space

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Top As layer Top Ga layer 2nd As layer Further studies (total energy calculation, STM: 4 phases with As coverage 0.25 → 0.75 and different dimer distribution. Right: STM of GaAs(001)- 2(2X4) V. P. LaBella et al., Phys. Rev. Lett. 83, 2989 (1999) GaAs (2x4) Reconstruction

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GaAs surface phase diagram As-stable (2X4): 4 phases with As coverage 0.25 → 0.75 Lower T, higher As 4 /Ga: As-rich c(4X4) with additional As dimers Higher T, lower As 4 /Ga: Ga-stable (4X2), Ga dimers along [110] Even higher T, lower As 4 /Ga: Ga droplets Other reconstructions exist, maybe as interference between domains

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Growth dynamics: RHEED Oscillations RHEED maximum spot intensity indicate completion of growing layers layer-by-layer control of the growing crystal surface # of deposited atomic layers = # of maxima growth rate = 1ML /

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GaAs Growth Oscillation dumping: statistical distribution of growth front → constant surface roughness. Persistence of RHEED oscillations layer-by-layer epitaxial quality Shutter closed: GaAs: 2D rearrangement of mobile Ga adatoms intensity recovery AlAs: low surface mobility of Al adatoms no recovery

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Analysis of the MBE growth process M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current status”, Springer (1996). G. Biasiol and L. Sorba, in “Crystal growth of materials for energy production and energy-saving applications”, R. Fornari, L. Sorba, Eds. (Edizioni ETS, Pisa, 2001) pp (http://www.tasc- infm.it/research/amd/file/school.pdf).

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Three-phases model 1.Gas phase (molecular beam generation + vapor mixing zones): complete lack of order, no homogeneous reactions (ballistic transport). 2.Crystalline phase (substrate, epilayer): complete short- and long-range order. 3.Near-surface transition layer (substrate crystallization zone): area where all processes leading to epitaxy occur (heterogeneous reactions on hot surface). Layer geometry and processes strongly dependent on growth conditions. substrate heating block vapor elements mixing zone substrate crystallization zone molecular beam generation zone

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Atomic-scale mechanisms of epitaxial growth Adsorption (physi-chemisorbtion) of the costituent atoms or molecules impinging on the substrate surface a.Surface diffusion b.Thermal desorption c.Formation of two-dimensional clusters d.Incorporation at steps e.Step diffusion f.Incorporation at kinks All steps (a-f) strongly dependent on kinetics (T, r, V/III ratio, crystal orientation...)

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Surface diffusion in MBE

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2D nucleation–surface diffusion: RHEED analysis nucleation of 2D islands step-flow growth High T > 0 Low T < 0 Neave et al, APL 47 (1985) 100 Critical T: T c ≈ 590C ≈ 0 0 0

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Growth modes: GaAs homoepitaxy Transition from 2D island nucleation to step flow growth (MOCVD). 5X5 m 2 post-growth AFM scans, heigth scale 2-5nm

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Growth modes: Si homoepitaxy In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 m2 scans B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997) T = 450C island nucleation growth T = 550C Step-flow growth

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Determination of diffusion coefficient = (T, r, V/III) Einstein relation: 2 = 2D D = diffusion coefficient, = characteristic time for diffusion D = 2 / (2 ), D = D 0 exp (-E D / kT) E D = activation energy for Ga surface diffusion Experiment: measurement of T c (r) at fixed misorientation ( (T c ) = l) Arrhenius plot E D = 1.3±0.1eV D 0 = 0.85 X cm 2 s -1 Neave et al, APL 47 (1985) 100 Exactly: = nuc Assumption: = 1/r (upper limit)

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Surface diffusion: a more rigorous approach Assumptions: Vicinal surface with uniform step separation 0 Rough step edge negligible step diffusion 1D problem J As >> J Ga As disregarded except for reaction at step edge Basic diffusion equation (steady-state) n s = adatom surface concentration D s = surface diffusion coefficient J = flux from Knudsen cell s = re-evaporation (residence) time s = sqrt (D s s ) = re-evaporation diffusion length T. Nishinaga, in “Handbook of crystal growth”, vol.3, p.666, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V.

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Solution of diffusion equation Surface concentration : (for s >> 0 (typical for MBE) Close to step edges, adatoms reach the step and incorporate before re- evaporation lower density

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Boundary condition at step edge J s =surface lateral flux n step =concentration at step edge n e = equilibrium concentration D step = a 2 / step = step diff. coeff. a =lattice constant step =adatom relaxation time to enter the step n step given by balance of incorporation flow at the step and surface diffusion flow Incorporation flow ( step supersaturation): step depends on activation energy to enter the step and on kink density Nernst-Einstein relation

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Boundary condition at step edge n step given by balance of incorporation flow at the step and surface diffusion flow Surface diffusion flow (for s >> 0 )

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Supersaturation ratio at step edge p e = equilibrium pressure of growth atom with the surface m = mass of growth atom

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Step edge activity J, 0 decreased (small Ga flux to the step) Temperature increased ( step decreased) Step edge very active to accept Ga atoms, n step → n e J, 0 increased (high Ga flux to the step) Temperature decreased ( step increased) Negligible incorporation of Ga atoms at steps, n step → n ∞

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Critical supersaturation for 2D nucleation Nucleation theory: Where = atomic (cell) volume h = step height = free energy of 2D nucleus side surface I c = nucleation rate

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2D nucleation vs. step flow At the middle of the terrace max > c 2D nucleation max < c step flow

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2D nucleation vs. step flow At the middle of the terrace Applications: GaAs (001): larger flux, smaller miscut larger max Higher T c for 2D nucleation

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MBE growth of III-V binary compounds and alloys

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Modulated molecular beam techniques Experimental technique: Modulated-Beam Mass Spectrometry (MBMS) Applications: studies of growth process chemistry in GaAs MBE on (001) surfaces Basic method: evaporation of neutral atoms beam onto substrate; detection of desorbing flux with RGA mass spectrometer Problem: discrimination beteen background and desorbing species Solution: modulation of incident beam or desorbing flux. C. T. Foxon and B. A. Joice, Surf. Sci. 50 (1975) 434, Surf. Sci. 64 (1977) 293 C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V

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Binary III-V compounds Group III (Al, Ga, In): monomers, low vapor pressure at typical substrate growth temperatures sticking coefficient = 1 (no desorption or re-evaportation) group-III flux determines growth rate. Group V (P, As, Sb): dimers-tetramers, high vapor pressure sticking coefficient < 1 need for overpressure to maintain stoichiometry.

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As 2 growth kinetics Supplied by GaAs or As cracker source Adsorbed as mobile precursor (physisorption) No Ga: Fast desorption as As 2 or As 4 (low T) With Ga: Dissociative chemisorption (1st order reaction) Sticking coefficient Ga flux (max = 1) Desorption of excess As stoichiometry

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As 4 growth kinetics No Ga: fast desorption With Ga: 2nd order reaction between pairs of As 4 on Ga sites 4 incorporated As atoms + 1 desorbed As 4 Max. sticking coefficient = 0.5 Second-order dependence of As 4 desorption rate on adsorption rate Similar behavior for other III-V compounds or alloys

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Simulation of GaAs (001)-(2X4) growth P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, Kinetic Monte Carlo (kMC) simulations, rates derived from density-functional theory (DFT) chemical bonding on atomic level and surface morphology at the large length and time scales characteristic for growth. GaAs (001)-(2X4) growth from Ga and As 2 ; topmost As dimerized along [- 110] unless Ga atom in between > 30 processes with rate laws i = 0 exp (-E i /kT); activation energies E i by DFT Surface mobility: Ga, As 2 (no As) Ga flux: 0.1ML/s Ga diffusion: anisotropic, 10 hopping processes Ga incorporation for strongly bound configurations stop diffusion As 2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga As 2 desorption: 3 events with different rates depending on environment Simulation results Simulation results

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A x B 1-x -V alloys Standard temperatures: sticking coefficient = 1 growth rate r = r A + r B, composition x = r A /(r A +r B ) High temperatures: Transition from group-V stable surface (i.e. (2X4) in GaAs) to metal-rich surface high group-V flux to keep surface stoichiometry. Desorption of more volatile group-III element (In > Ga > Al) deviations from ideal r and x Surface segregation of more volatile group-III element C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V

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III-A x B 1-x alloys More complicated situation, no easy relation between x (vapor) and x (solid): Difference in adsorption efficiency Difference in vapor pressure (P > As > Sb) (at low T preferential incorporation of low vapor pressure dimer or tetramer) Mutual interference of the sticking coefficients C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V

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MBE growth of lattice-matched and lattice-mismatched heterostructures

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GaAs/Al x Ga 1-x As heterostructures Lattice-matched system for 0 < x < 1 Interface atomic structure influences optical and electronic properties of HS, QW and 2DEG-based devices Ga >> Al intrinsic asymmetry between morphology of “normal” (AlGaAs-on-GaAs) and “inverted” (GaAs-on- AlGaAs) interfaces High reactivity of Al segregation of impurities towards the inverted interface

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Growth interruptions: effects on the optical properties of GaAs/AlGaAs QWs M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987) Growth interruption x = 0.33x = 1 A above-below B above C below D none (roughness) > (exciton) sharp PL (roughness) ≈ (exciton) broad PL An exciton is a bound state of an electron and a hole in an insulator (or semiconductor), or in other words, a Coulomb correlated electron/hole pair. It is an elementary excitation, or a quasiparticle of a solid. A vivid picture of exciton formation is as follows: a photon enters a semiconductor, exciting an electron from the valence band into the conduction band, leaving a hole behind, to which it is attracted by the Coulomb force. The exciton results from the binding of the electron with its hole the exciton has slightly less energy than the unbound electron and hole. The wavefunction of the bound state is hydrogenic. However, the binding energy is much smaller and the size much bigger than a hydrogen atom because of the effects of screening and the effective mass of the constituents in the material.

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Impurity segregation in AlGaAs High reactivity of Al atoms (with respect to Ga). higher incorporation of impurities, with segregation to the surface. inverted interface is more contaminated than normal one. Left: SIMS profiles of O impurities in an Al x Ga 1-x As multilayer, where 1. O concentration is higher for higher x. 2. O segregates at interfaces where lower x material is grown on higher x one. S.Naritsuka et al., J. Cryst. Growth 254, 310 (2003)

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Lattice-mismatched heterostructures Needed to expand flexibility in materials choice (e.g., In x Ga 1- x As/GaAs) Misfit: f i = (a si -a oi )/a oi i = x,y (growth plane) a = lattice constant s = substrate o = overlayer f x,y (InAs/GaAs) ≈ 7%

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Energy Layer thickness Growth mode for small lattice mismatch Separate bulk layers of materials A and B, with a(B) > a(A) Epitaxy of thin layer of B on substrate A: pseudomorphic (strained) growth for E (increasing) E D. E > E D Relaxation through dislocations E = E D E < E D Pseudomorphic growth EE EDED

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Dislocations Edge dislocation: line defect that occurs when there is a missing row of atoms. The crystal arrangement is perfect on the top and on the bottom. The defect is the row of atoms missing from region b. This mistake runs in a line that is perpendicular to the page and places a strain on region a.

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Critical thickness and dislocations Thin epilayer grown on substrate with different lattice parameter Energetics: Strain: increases with thickness Dislocations: thickness independent Energetic trade-off between pseudomorphic and dislocated epilayers: beyond a critical lattice misfit f 0 the adjustement of the two lattices by dislocations is energetically more favorable than by strain for thicknesses exceeding the critical thickness h 0 dislocations are energetically more favorable than strain H. Luth, “Surfaces and Interfaces of Solid Materials”, 3° ed., Springer, Berlin, 1995

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Critical thickness: energetic calculations Minimization of energy for the epitaxial system Critical thickness in units of a s as a function of f, for the introduction of 60 o misfit dislocations on (111) glide planes in a (001) interface M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current status”, Springer (1996)

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Strained epitaxy: experiment Existence of kinetic barriers critical thicknesses much larger than predicted by energetic balance. Methods to increase t 0 : Reduction of surface diffusion (Low T, Ga-stabilized surfaces (InGaAs on GaAs), surfactants) Gradual lattice accommodation (graded buffer layers (BL)) Image: TEM cross section of a metamorphic In 0.75 Ga 0.25 As/ In 0.75 Al 0.25 As QW grown dislocation-free on a GaAs (001) substrate (f ~ 5%) by insertion of a ~1 m-thick In x Al 1-x As step-graded BL (F. Capotondi et al., Thin Solid Films 484, 400 (2005).)) GaAs

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Strained growth: Onset of 3D growth (S-K) Very large mismatch: strain relaxation energetically more favorable by 3D islanding, rather than dislocations. Right: critical thicknesses as a function of x in In x Ga 1- x As/In.53 Ga.47 As for the onset of 3D growth (t 3D ) and misfit dislocations (t c ), at T = 525C. Transition from dislocations to 3D occurs (T RM ) at x ~.75, i.e., f = 1.7% (M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992)) t 3D tctc T RM M. A. Herman, H. Sitter, “Molecular Beam Epitaxy, Fundamental and Current status”, Springer (1996); original data from M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992).

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Doping in III-V materials C. T. Foxon, in “Handbook of crystal growth”, vol.3, p.156, ed. By D.T.J. Hurle, 1994 Elsevier Science B.V G. Biasiol and L. Sorba, in “Crystal growth of materials for energy production and energy-saving applications”, R. Fornari, L. Sorba, Eds. (Edizioni ETS, Pisa, 2001) pp (http://www.tasc- infm.it/research/amd/file/school.pdf).

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Doping necessary for carrier transport in electronic or optoelectronic devices Doping by group II (p-type), IV (p- or n- type) and VI atoms (n-type) Group II II-b atoms (Zn, Cd): too high vapour pressure at usual growth temperatures not used in MBE II-a atoms (Be in particular): the universal choice Group-VI atoms uncommon (surface segregation, re-evaporation) Group-IV atoms amphoteric: donors (if incorporated on group-III sites) or acceptors (on group-V sites) C: acceptor, but very low vapour pressure, very high T (> 2000C) Ge: amphoteric behavior difficult to control Sn: too high surface segregation Si: universal n-type dopant in (Ga,In,Al)As (001) –n up to ~10 19 cm -3 before compensation (substitution on As sites, Si-vacancy complexes, Si clusters…) –Diffusivity towards the surface at doping levels higher than about 2X10 18 cm -3 problem in sharp doping profiles –Donor ionization energy increases in AlGaAs reduced doping efficiency –GaAs(311)A surfaces : n- to p-type transition depending on T and III/V ratio can be used as p-type dopant SIMS profiles of Si- doped GaAs grown at different T (A. P. Mills et al., JAP 88, 4056 (2000) Compositional dependence of Si donor activation energy in Al x Ga 1-x As (N. Chand et al., PRB 30, 4481 (1984) Top: free-carrier densities in Si- doped {311}A and (100) GaAs at 300 K as a function of the V 4 /III ratio. Dotted line: N Si. Bottom: Phase diagram (V 4 /III ratio – T) for the conduction type of Si doped {311}A GaAs. Dot size activation efficiency. (N. Sakamoto et al., APL 67, 1444 (1995) Doping in III-V materials K.Kohler et al., JCG 127, 720 (1993).

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Modulation doping and the two-dimensional electron gas Bulk doping Electrical conduction (otherwise semi-insulating) BUT Introduction of impurities source of scattering, limitation of mobility at low temperatures Temperature dependence of mobility in n-type GaAs. The dashed curves are the corresponding calculated contributions from various mechanisms. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, Berlin, 1996).

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Modulation doping and the two-dimensional electron gas H. Störmer, Surf. Sci.132 (1983) 519 Increase of mobility Solution: spatial separation between doping layer and conducting channel projects/correlated/pop-up2-1.html

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