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 (

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 (

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 (

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 (

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
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