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PART II: MOLECULAR BEAM EPITAXY

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1 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

2 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.

3 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).

4 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

5 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

6 Schematics of an MBE system
Pumping system Effusion cells Liquid N2 cryopanels around main walls and source flange thermal isolation among cells prevent re-evaporation from parts other than the cells additional pumping Substrate manipulator Analysis tools: RHEED RGA Optical (ellipsometry, RDS...) Cell shutters

7 Pumping system Minimization of impurities: R ~ 1ML/sec, n ~ 1022at cm-3, p ~ 10-6Torr for nimp < 1015 cm-3  p < Torr In practice: p ~ – Torr, mostly H2 Used pumps: ion, cryo, Ti-sublimation.

8 Effusion cells Temperature regulation by high-precision PID regulators
Crucible Filament Heat Shielding Thermocouple Head Assembly Mounting Flange and Supports Power Connector 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. Features of an effusion cell 6 – 10 cell in a source flange Co-focused onto substrate  flux uniformity Flux stability <1% / day  DT < T ~ 1000 ºC Temperature regulation by high-precision PID regulators Minimization of flux drift as material is depleted  choice of geometry

9 Crucibles Cylindrical Crucible Conical Crucible SUMO® 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 SUMO® Crucible + Excellent charge capacity + Minimal shutter-related flux transients

10 Valved cracker For elements which sublime as molecules (As, P, Sb …)
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., As2) or uncracked material (e.g., As4).

11 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

12 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 cm2

13 Vapor pressure chart As4 Ga Al
TAs4 < Tsubstr < TGa,Al  As re-evaporation  growth in As4 overpressure

14 Numerical Application:
Estimation of the GaAs growth rate r Typical values: T (Ga cell) =1000oC=1273oK  P ~ 10-3 Torr

15 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

16 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

17 Bonding: In (Ga), or In-free (clamped)
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

18 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

19 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).

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

21 Surface sensitivity of RHEED
Ek = 5-40KeV l = Å Q = 1-3o d(penetration) = lesin q le  10ML  d = 0.5ML  Surface sensitivity

22 2D (1st layer of perfectly flat surface)
Diffraction: 3D vs 2D 2D (1st layer of perfectly flat surface) 3D G  // ∞ rods a=5.65Å  G=2p/a=1.1 Å-1 Ek=5KeV  k1/l=36.5Å-1  k >> G DK = G

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

24 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

25 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

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

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

28 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

29 GaAs (2x4) Reconstruction
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)-b2(2X4) V. P. LaBella et al., Phys. Rev. Lett. 83, 2989 (1999)

30 GaAs surface phase diagram
As-stable (2X4): 4 phases with As coverage 0.25 → 0.75 Lower T, higher As4/Ga: As-rich c(4X4) with additional As dimers Higher T, lower As4/Ga: Ga-stable (4X2), Ga dimers along [110] Even higher T, lower As4/Ga: Ga droplets Other reconstructions exist, maybe as interference between domains

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

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

33 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).

34 Three-phases model substrate heating block vapor elements mixing zone substrate crystallization zone molecular beam generation zone Gas phase (molecular beam generation + vapor mixing zones): complete lack of order, no homogeneous reactions (ballistic transport). Crystalline phase (substrate, epilayer): complete short- and long-range order. 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.

35 Atomic-scale mechanisms of epitaxial growth
Adsorption (physi-chemisorbtion) of the costituent atoms or molecules impinging on the substrate surface Surface diffusion Thermal desorption Formation of two-dimensional clusters Incorporation at steps Step diffusion Incorporation at kinks It is evident from that figure that the molecule adsorbed in the precursor state has to overcome a lower barrier when it is subsequently chemisorbed at the surface, then in the case when it re-evaporates into the vacuum, because Ea<Edp. The illustrated situation is a special example; a variety of other potential configurations can also exist. All steps (a-f) strongly dependent on kinetics (T, r, V/III ratio, crystal orientation...)

36 Surface diffusion in MBE

37 2D nucleation–surface diffusion: RHEED analysis
High T  l > l0 step-flow growth Critical T: Tc ≈ 590C  l ≈ l0 l0 Low T  l < l0 Layer-by-layer growth is characterized by two limiting cases. One limit is where surface migration lengths are much smaller than substrate surface features, i.e. terraces separated by step edges, where growth occurs by the nucleation of two-dimensional islands. The other limit is where migration lengths are much greater than surface terraces, where growth occurs by attachment of adatoms to the step edges. The step edges then propagate at a velocity depending on the step density and growth rate; this limit is called step-flow growth. nucleation of 2D islands l0 Neave et al, APL 47 (1985) 100

38 Growth modes: GaAs homoepitaxy
Transition from 2D island nucleation to step flow growth (MOCVD). 5X5mm2 post-growth AFM scans, heigth scale 2-5nm

39 Growth modes: Si homoepitaxy
In-vivo STM of Si (001) homoepitaxy; 0.3X0.3 mm2 scans B. Voigtländer et al., Phys Rev. Lett. 78, 2164 (1997) T = 450C island nucleation growth T = 550C Step-flow growth

40 Determination of diffusion coefficient
Exactly: t = tnuc Assumption: t = 1/r (upper limit) l = l(T, r, V/III) Einstein relation: l2 = 2Dt D = diffusion coefficient, t = characteristic time for diffusion  D = l2 / (2t), D = D0 exp (-ED / kT) ED = activation energy for Ga surface diffusion Experiment: measurement of Tc(r) at fixed misorientation (l(Tc) = l) Arrhenius plot  ED = 1.3±0.1eV D0 = 0.85 X 10-5 cm2 s-1 Neave et al, APL 47 (1985) 100

41 Surface diffusion: a more rigorous approach
Assumptions: Vicinal surface with uniform step separation l0 Rough step edge  negligible step diffusion  1D problem JAs >> JGa  As disregarded except for reaction at step edge Basic diffusion equation (steady-state) ns = adatom surface concentration Ds = surface diffusion coefficient J = flux from Knudsen cell ts = re-evaporation (residence) time ls = sqrt (Dsts) = 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.

42 Solution of diffusion equation
 Surface concentration : (for ls >> l0 (typical for MBE) Close to step edges, adatoms reach the step and incorporate before re-evaporation  lower density

43 Boundary condition at step edge
nstep given by balance of incorporation flow at the step and surface diffusion flow Incorporation flow ( step supersaturation): Nernst-Einstein relation Js = surface lateral flux nstep = concentration at step edge ne = equilibrium concentration Dstep = a2/ tstep = step diff. coeff. a = lattice constant tstep = adatom relaxation time to enter the step tstep depends on activation energy to enter the step and on kink density

44 Boundary condition at step edge
nstep given by balance of incorporation flow at the step and surface diffusion flow Surface diffusion flow (for ls >> l0)

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

46 Step edge activity J, l0 decreased (small Ga flux to the step)
Temperature increased (tstep decreased) J, l0 increased (high Ga flux to the step) Temperature decreased (tstep increased) Step edge very active to accept Ga atoms, nstep → ne Negligible incorporation of Ga atoms at steps, nstep → n∞

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

48 2D nucleation vs. step flow
At the middle of the terrace amax > ac  2D nucleation amax < ac  step flow

49 2D nucleation vs. step flow
At the middle of the terrace Applications: GaAs (001): larger flux, smaller miscut larger amax Higher Tc for 2D nucleation

50 MBE growth of III-V binary compounds and alloys

51 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

52 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.

53 As2 growth kinetics Supplied by GaAs or As cracker source
Adsorbed as mobile precursor (physisorption) No Ga: Fast desorption as As2 or As4 (low T) With Ga: Dissociative chemisorption (1st order reaction) Sticking coefficient  Ga flux (max = 1) Desorption of excess As  stoichiometry

54 As4 growth kinetics No Ga: fast desorption With Ga:
2nd order reaction between pairs of As4 on Ga sites  4 incorporated As atoms + 1 desorbed As4 Max. sticking coefficient = 0.5 Second-order dependence of As4 desorption rate on adsorption rate Similar behavior for other III-V compounds or alloys

55 Simulation of GaAs (001)-(2X4) growth P. Kratzer and M. Scheffler, Phys. Rev. Lett. 88, 036102
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 As2; topmost As dimerized along [-110] unless Ga atom in between > 30 processes with rate laws Gi=G0exp (-Ei/kT); activation energies Ei by DFT Surface mobility: Ga, As2 (no As) Ga flux: 0.1ML/s Ga diffusion: anisotropic, 10 hopping processes Ga incorporation for strongly bound configurations  stop diffusion As2 incorporated as dimer (no dissociation) on sites with 3-4 bonds to Ga As2 desorption: 3 events with different rates depending on environment Simulation results

56 Surface segregation of more volatile group-III element
AxB1-x-V alloys Standard temperatures: sticking coefficient = 1  growth rate r = rA + rB, composition x = rA/(rA+rB) 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

57 Difference in adsorption efficiency
III-AxB1-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

58 MBE growth of lattice-matched and lattice-mismatched heterostructures

59 GaAs/AlxGa1-xAs heterostructures
Lattice-matched system for 0 < x < 1 Interface atomic structure influences optical and electronic properties of HS, QW and 2DEG-based devices lGa >> lAl  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

60 Growth interruptions: effects on the optical properties of GaAs/AlGaAs QWs M. Tanaka, H. Sakaki, J. Cryst. Growth 81, 153 (1987) Growth interruption x = 0.33 x = 1 A above-below B above C below D none 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. l(roughness) << l(exciton); l(roughness) >> l(exciton)  sharp PL l(roughness) ≈ l(exciton)  broad PL

61 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 AlxGa1-xAs multilayer, where O concentration is higher for higher x. O segregates at interfaces where lower x material is grown on higher x one. S.Naritsuka et al., J. Cryst. Growth 254, 310 (2003)

62 Lattice-mismatched heterostructures
Needed to expand flexibility in materials choice (e.g., InxGa1-xAs/GaAs) Misfit: fi = (asi-aoi)/aoi i = x,y (growth plane) a = lattice constant s = substrate o = overlayer fx,y (InAs/GaAs) ≈ 7%

63 Growth mode for small lattice mismatch
Energy Layer thickness Ee > ED Relaxation through dislocations Ee = ED Ee < ED Pseudomorphic growth ED Ee 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 Ee (increasing) < ED (constant), dislocations for Ee > ED.

64 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.

65 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 f0 the adjustement of the two lattices by dislocations is energetically more favorable than by strain for thicknesses exceeding the critical thickness h0 dislocations are energetically more favorable than strain H. Luth, “Surfaces and Interfaces of Solid Materials”, 3° ed., Springer, Berlin, 1995

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

67 Strained epitaxy: experiment
GaAs Existence of kinetic barriers  critical thicknesses much larger than predicted by energetic balance. Methods to increase t0: 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 In0.75Ga0.25As/ In0.75Al0.25As QW grown dislocation-free on a GaAs (001) substrate (f ~ 5%) by insertion of a ~1mm-thick InxAl1-xAs step-graded BL (F. Capotondi et al., Thin Solid Films 484, 400 (2005).))

68 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 InxGa1-xAs/In.53Ga.47As for the onset of 3D growth (t3D) and misfit dislocations (tc), at T = 525C. Transition from dislocations to 3D occurs (TRM) at x ~ .75, i.e., f = 1.7% (M. Gendry et al., Appl. Phys. Lett. 60, 2249 (1992)) tc TRM t3D 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).

69 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).

70 Doping in III-V materials
Top: free-carrier densities in Si-doped {311}A and (100) GaAs at 300 K as a function of the V4 /III ratio. Dotted line: NSi. Bottom: Phase diagram (V4 /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) K.Kohler et al., JCG 127, 720 (1993). Compositional dependence of Si donor activation energy in AlxGa1-xAs (N. Chand et al., PRB 30, 4481 (1984) SIMS profiles of Si-d doped GaAs grown at different T (A. P. Mills et al., JAP 88, 4056 (2000) 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 ~1019 cm-3 before compensation (substitution on As sites, Si-vacancy complexes, Si clusters…) Diffusivity towards the surface at doping levels higher than about 2X1018 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 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)

71 Modulation doping and the two-dimensional electron gas
Electrical conduction (otherwise semi-insulating) BUT Introduction of impurities  source of scattering, limitation of mobility at low temperatures Bulk doping 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).

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


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