1. Corso FS02: Materiali e Dispositivi per optoelettronica, spintronica e nanofotonica Modulo 1: Crescita epitassiale di materiali semiconduttori (Giorgio Biasiol)
Program:
General concepts in epitaxy
Epitaxial techniques: Molecular Beam Epitaxy (MBE)
Epitaxial techniques: Metal Organic Chemical Vapor Deposition (MOCVD)
Low-dimensional semiconductor nanostructures

2. PART I: GENERAL CONCEPTS IN EPITAXY
Applications of compound semiconductors
Introduction to epitaxial techniques
Basic concepts in epitaxy
Crystallography of zinc-blende lattices

3. Applications of compound semiconductors
H. S. Bennett, "Technology Roadmaps for Compound Semiconductors”,
International Technology Roadmap for Compound Semiconductors (ITRCS) Bulletin Board,

4. Inorganic semiconductor materials
Inorganic semiconductors can be roughly divided into two categories:
Elemental semiconductors, belonging to the group IV of the periodic table (Si, Ge)
Compound semiconductors, synthetic materials not existing in nature, composed of elements from groups III (Al, Ga, In) and V (N, P, As, Sb), or from groups II and VI.

5. Crystal form of semiconductors
Most semiconductors crystallize in a form identical to diamond.
In compound semiconductors, group-III and group-V atoms alternate within the unit cell (zincblende). As Ga
Unit cell of GaAs. The side is about 0.56nm

6. From silicon to compound semiconductors
Traditional devices (electronics, computing): silicon-based.
New advanced devices: based on synthetic compound semiconductors.

7. New possibilities provided by compound semiconductors
These materials allow to overcome some limits intrinsic to Si technology:
In many cases, differing from Si, they have direct band gaps  light emitters,  both electronic and optoelectronics applications;
They generally have a larger electron mobility  devices are faster and less power-consuming;
They allow a great flexibility in the fabrication of materials with the desired features, and in the combination of two or more materials in a device (heterostructures).

8. Semiconductor Heteroepitaxy “Road-map”
Richness and variety of III-V’s  high-performance "band-gap engineered" heterostructures and devices with optical and electronic properties difficult to achieve in other materials.

9. Trends of compound semiconductors vs. Si
Communications products to replace computers as key driver of volume manufacturing.
Present and future volume products include:
cell phones and video phones
Bluetooth appliances
Optoelectronics (lasers, diodes, sensors…)
automotive electronics that add functionality of home and office to cars and trucks.

10. Some applications of compound semiconductors
Optoelectronic devices (LED, LASER) for the production and sensing of light, and for telecommunications
High-speed transistors (HEMT), used, e.g., in mobile telephony and satellite systems.

11. Compound semiconductors market share

12. Material choices for device applications: Optoelectronics
major fiber-communications l’s: 1550nm - In0.58Ga0.42As0.9P nm - In0.73Ga0.27As0.58P0.42
Application examples: optical communications, displays, sensors)  wavelength ranges within which materials emit and absorb light efficiently:
GaN-related: µm
GaP-related: µm
GaAs-related: µm
InP-related: µm
InSb-related : 2-10 µm

13. Material choices for device applications: Electronics
Applications examples: wireless communications based on high-frequency RF or microwave carriers, radars, and magnetic-field sensors) 
trade-offs between performance and material robustness during device manufacture and operation. In practice, GaAs-related materials are the most common, but InP-related materials and InSb-related materials also have important applications.

14. Electron confinement
Many of these devices involve structures based on electron confinement. This effect limits electronic motion to two, one or zero dimensions.
Such structures are composed of layers of a material where electrons are confined, sandwiched in layers acting as an energy barrier. They are called quantum wells, wires or dots, depending on dimensionality.
Section of a LASER structure based on a GaAs QW embedded in AlGaAs barriers.

15. Typical sizes to observe quantum confinement
Conduction electrons in semiconductors have wavelengths of the order of 10nm.
 To observe quantum confinement effects, quantum wells (wires, dots) must have sizes around 10nm.
Next-generation devices (e.g., quantum cascade lasers) may include layers <1nm thick.
Energy profile of a GaAs/AlGaAs quantum well and electronic wave functions of two confined levels.

16. Bulk vs. Quantum-confined devices
Si MOSFET: single bulk material, doping by diffusion or implantation typical sizes ~ mm
InGaAs/AlGaAs p-HEMT: abrupt heterostructures, planar (d-) doping
VCSEL (left: upper and lower DBRs and active region; right: blow-up of active region): 100s of layers of different materials with sub-ML precision
typical sizes < 10 nm

17. Why Epitaxy? Sizes < 10nm
 structure and composition control with accuracy better than the single atomic monolayer (~0.3nm)
Semiconductor growth techniques that allow this control are called epitaxial techniques.
Growth takes place on planar, single-crystal substrates, atomic layer – by – atomic layer.

18. Introduction to Epitaxial Techniques

19. Crystallization and film growth
Amorphous: no ordered structures
Polycrystalline: randomly oriented grains, oriented grains, highly oriented grains
Single crystal: bulk growth, epitaxy: e p i (upon) + t a x i  (ordering)

20. Growth Processes
Bulk techniques (massive semiconductors, wafers): Si, compounds semiconductors.
Epitaxy (higher cost of the growth process): high control of interfaces  thin films, quantum confined systems.
Epitaxy : film growth phenomenon where a relation between the structure of the film and the substrate exists  single crystalline layer grown on a single crystal surface. Film and substrate of the same material: homoepitaxy. Film and substrate are of different materials: heteroepitaxy

21. Growth techniques for bulk semiconductors 1 Crystal pulling (Czochralski method)
The CZ technique consists of dipping an oriented seed into the molten charge.
Solid-liquid equilibrium is established and the seed is pulled out to obtain a large crystal.
The melt will freeze following the crystallographic orientation of the seed.
The monocrystalline seed is suspended to a pulling rod and rotated during the growth.
The pulling rod is then lifted and the melt crystallizes at the interface of the seed by forming a new crystal portion.
Dislocation-free conditions.
GaAs crystals have been grown since 20 years

22. Growth techniques for bulk semiconductors 2 Horizontal/Vertical Bridgman and Vertical Gradient Freeze
The method consists of a boat which is translated across a temperature gradient in order to allow the molten charge contained in the boat to solidify starting from an oriented seed.
The solidification can be achieved by moving either the boat or the furnace.
An excess of Group V (As, P) is necessary to control the melt composition.
Horizontal method used for polycrystals (D-shaped wafers).
Vertical method more popular: wafer uniformity, minimized thermal gradients (reduced dislocation density).

23. Epitaxial techniques:
LPE: near-equilibrium technique; fast, inexpensive, poor thickness/interface control (OK only for bulk growth)
MBE, MOCVD: slower, monolayer control on thickness and composition  heterostructures, quantum confined systems, band-gap engineering
Interest for both studies of fundamental physics/materials science and for commercial applications of advanced devices

24. Comparison of MBE and MOCVD
Feature
MBE
MOCVD
Source materials
Elemental
Gas-liquid compounds
Evaporation
Thermal, e-beam
Vapor pressure, Carrier gas
Flux control
Cell temperature
Mass flow controllers
Switching
Mechanical shutters
Valves
Environment
UHV
H2-N2 ( mbar)
Molecular transport
Ballistic (mol. beams)
Diffusive
Surface reactions
Physi-chemisorbtion
Chemical reactions

25. Advantages-disadvantages of MBE and MOCVD
Feature
MBE
MOCVD
Thickness/composition control + -
Process simplicity
+ (ballistic transport, physisorption)
- (hydrodynamics, chemical reactions)
Abrupt junctions
<1ML (Shutters)
~3ML (Valves)
In-situ characterization
+ (RHEED)
Uncommon (RAS)
Purity
+ (UHV)
- (C incorporation)
Health, safety
+ (solid sources)
- (H2, Highly toxic gases)
Growth rates (GaAs)
~1mm/h
Up to ~4mm/h
Wafer capacity
7X6”, 4X8”
10X8”, 5X10”
Environment
UHV
(sub)atmospheric pressure
Graded composition layers
- (thermal evaporation)
+ (mass flow control)
Defect density
- (oval defects)
Downtime

26. Hybrid techniques
Gas source MBE, Metal Organic Molecular Beam Epitaxy (MOMBE), Chemical Beam Epitaxy (CBE).
Principle: using group V or/and group III gas sources in a UHV MBE environment.
Developed in order to combine advantages (but also disadvantages!) of MBE and MOCVD.

27. Device applications and epitaxy
Products range from a commercial epiwafer supplier
Source:
MATERIAL SYSTEMS
DEVICES
APPLICATIONS
  GaAs   AlGaAs   InGaP   InGaAs   InSb
  • MESFETs   • HEMTs   • PHEMTs   • HBTs   • Lasers
  • Mobile Telephony   • Global Positioning Systems (GPS)   • Satellite Systems   • Direct Broadcast Satellite (DBS)   • Paging   • Wireless LAN / Wireless Cable   • Automotive Radar
  InP   InGaAs   InAlAs   InGaAlAs   InGaAsP   InGaAsN
  • DH, QW, DFB Lasers   • LEDs   • VCSELs   • Detectors   • HBTs
  • Optical Fiber Communications   • Sensors   • Infra-Red Cameras   • Wireless Communications
  GaAs   AlGaAs   InGaAs   Pseudomorphic   InGaAlAs   InGaAsP
  • DH, QW,     Pseudomorphic Lasers   • VCSELs   • HEMTs   • FETs   • Solar Cells   • Detectors
  • Fiber Amplifiers, Gigabit Ethernet   • Medical Systems   • Solid State Laser Pumps   • CD, Minidisc   • GPS   • Automotive   • Satellite Systems
  InGaP   InAlP   GaN   InGaN   InGaAlN
  • Visible Lasers   • UHB LEDs   • Visible VCSELs   • HBTs   • DJ Solar Cells
  • Displays   • DVD / CD   • Illumination   • Pointers / Bar Code   • Wireless Communications   • Satellite Systems   • Medical Applications
High-speed electronics
Optoelectronics

28. Basic concepts in epitaxy
J. B. Hudson, “Surface Science – An Introduction”, Butterworth-Heinemann, Boston, 1992
I. V. Markov, “Crystal Growth for Beginners”, World Scientific, Singapore, 1995
A. Pimpinelli and J. Villain, “Physics of Crystal Growth”, Cambridge University Press, 1998
T. F. Gilbert, “Methods of Thin Film Deposition”,

29. Supersaturation
Growth rate is thermodynamically limited by chemical potential difference between fluid phase and fluid-surface equilibrium:
Dm = m – meq ≡ supersaturation ≡ driving force for film growth
Dm must be positive for growth to take place (  energy gain by adding atoms to the solid phase)
Real growth rates are limited by other factors (mass transport, reaction kinetics)

30. Molecular flux
Molecular flux: # of molecules hitting a cross-sectional area in a time unit: J [molecules/(m2sec)]
Maxwell-Boltzmann distribution 

31. Deposition rate
The flux of molecules of the surface leads to deposition, with the rate of film growth depending on J
Example: Silane (SiH4) in VPE:
P ~ Torr (1 Torr = 133 Pa)
M: Si: 28 g/ mol and H: 1 g/ mol
rfilm = 2.33 g/mol r ~ 50nm/sec
T ~ 400C = 673K
NA = 6.02X1023

32. d = molecular diameter ~ 0.5nm,
Mean free path
d = molecular diameter ~ 0.5nm,
R = 8.31 J/(mol * K)
T ~ RT (300K)
1 Torr = 133 Pa
~10-5 Torr  l ~ 3m (e.g. As4 in MBE) P
>10 Torr  l < 30mm (MOCVD)

33. Flow regimes
The magnitude of l is very important in deposition. This determines how the gas molecules interact with each other and the deposition surface. It ultimately influences film deposition properties.
The flow of the gas is characterized by the Knudsen number: Kn= l / L, where L is a characteristic dimension of the chamber (given).
Kn > 1: the process is in high vacuum (molecular flow regime).
Kn < 0.01 the process is in fluid flow regime.
In between there is a transition region where neither property is necessarily valid.

34. Steps for Deposition to Occur
Every film regardless of deposition technique (PVD, CVD, sputtering, thermally grown…) follows the same basic steps to incorporate molecules into the film.
Absorption/desorption of gas molecule into the film Physisorption Chemisorption
Surface diffusion
Nucleation of a critical seed for film growth
Development of film morphology over time
All processes must overcome characteristic activation energies Ei, with rates ri  exp(Ei/kT), depending on atomic details of the process  Arrhenius-type exponential laws

35. Physi- and Chemisorption
Physisorption: precursor state, often considered as having no chemical interaction involved (van der Waals). Ea ~ 100meV/atom
Chemisorption: dissociation of precursor molecule, strong chemical bond formed between the adsorbate atom or molecule and the substrate. Ea ~ a few eV/atom (>~ substrate sublimation energy)
Chemisorption reaction rate:
R = k ns0 Q; k = reaction rate constant = naexp(-Ea/kT), na = characteristic atomic vibration frequency, ns0 = ML surface concentration, Q = fractional surface coverage

36. Surface Diffusion
Overall surface energy can be minimized if the atom has enough energy & time to diffuse to a low energy add site (i.e., step or kink).
The reaction rate (in molecules/cm2s) for surface diffusion is given as:
with ns = surface concentration of reactant, nd = characteristic diffusion frequency ~ 1014s-1 Ed = migration barrier energy
In unit time the adatom makes nd attempts to pass the barrier, with a probability of exp (-Ed/kT) of surmounting it on each try.
Ed << Ea  surface diffusion is far more likely than desorption.

37. Diffusion coefficient, diffusion length
Diffusion coefficient (mean square displacement of the random walker per unit time):
with a = lattice constant
Adatom lifetime before desorption:
Diffusion length (characteristic length within which the adatom can move):
Measurable quantity!

38. Nucleation
Homogeneous nucleation: takes place in the gas phase (only in MOCVD), parasitic reactions
Heterogeneous nucleation: takes place on the film surface

39. Competing processes in nucleation
Gain in bulk free energy DGv with respect to individual atoms
Loss of surface free energy with respect to individual atoms 
For a stable film, a critical size nuclei is needed.
With embryos smaller than that, the surface energy is to large and the overall reaction is thermodynamically unfavorable (the overall DG is positive).
With larger nuclei, the free energy from converting a volume of atoms to solid overcomes the added surface energy (the overall DG is negative).

40. Energetics of homogeneous nucleations
vapor r
nucleus
Bulk contribution: DGv = -Dm / vf; Dm = mv-mf = kT ln(p/p0) = supersaturation, vf = V / NA = molecular volume
Surface contribution: g = surface energy per unit area
Total energy change on cluster formation: DG = (4p/3) r3 DGv + 4p r2 g < >0

41. Critical nucleus
unstable equilibrium!
Critical radius for stable nucleation (only for positive supersaturation):
d(DG)/dr = 0 
(a few atoms) – Thomson-Gibbs equation
universal results (liquid and crystal phases)

42. Heterogeneous nucleationq
gvf
gsv
gfs
vapor
nucleus
substrate
Young’s equation: gsv = gfs + gvf cos q, q = wetting angle
gsv  gfs + gvf (highly reactive substrate surfaces)  cos q  1; q = 0 or undefined  wetting
gsv < gfs + gvf (poorly reactive substrate surfaces)  cos q < 1; 0<q<  no wetting
gsv ≈ gfs + gvf (metastable situation)
Typical case 3: lattice-mismatched, strained heteroepitaxy
Strain energy (needed to adjust to substrate lattice) depends on gfs and increases linearly with film thickness
 If at 0 thickness gsv  gfs + gvf , at some critical thickness gsv < gfs + gvf will be realized  2D wetting layer + 3D islands

43. Energetics of heterogeneous nucleations
gvf
nucleus
vapor q
substrate r q
Volume of nucleus:
Surface area of nucleus:

44. Energetics of heterogeneous nucleations
gvf
nucleus
vapor q
substrate r q
same as hom. nucl., no dependence on q
q = 0  DG* = 0; 3D droplets thermodynamically unfavored  wetting of continuous 2D film
q = p  DG* = DGhom*; no influence of substrate

45. Growth modes gsv  gfs + gvf gsv  gfs + gvf gsv < gfs + gvf
FM: Frank-van der Merwe (2D) mode
VW: Volmer-Weber (3D) mode
SK: Stranski-Krastanov (2D+3D) mode
gsv  gfs + gvf
gsv  gfs + gvf
gsv < gfs + gvf
FM growth: The interatomic interactions between substrate and film materials are stronger and more attractive than those between the different atomic species within the film material. VW growth: opposite situation. SK growth occurs for interaction strengths somewhere in the middle.

46. Examples: Frank-van der Merwe growth
Layer-by-layer growth (Frank - van der Merwe) is the most used epitaxial process in semiconductor device production. It is most often realized for lattice matched combinations of semiconductor materials with high interfacial bond energies (i.e., AlxGa1-xAs/GaAs).
TEM micrograph of the active region of a lattice-matched AlInAs/GaInAs QCL grown by MBE Cho et al., J. Cryst. Growth , 1 (2001)

47. Examples: Stranski-Krastanov growth
Stranski-Krastanov - grown islands can be overgrown by the same barrier material as the substrate, to form buried quantum dots, completely surrounded by a larger band gap barrier material.
These dots are optically active due to their damage-free interfaces and are very well suited for studies of quantum phenomena. They are very promising systems for laser production, once high enough uniformity is achieved
AFM image of uncapped InAs/GaAs quantum dots formed just afted the critical thickness on a wetting layer showing monolayer-high 2D islands. The sample is MBE-grown at TASC.

48. Crystallography of zinc-blende lattices
0.56 nm

49. Technologically important surfaces
(100)
Alternating equidistant Ga-As planes
2 dangling bonds/atom
Monoatomic steps  Similar As-Ga concentrations (depending on reconstruction)
The most important orientation for epitaxy
{111}
Alternating Ga + As planes with alternating dangling bonds and 1/3 + 2/3 interplane distances
Surfaces can be formed only by breaking the weakly bond planes
 Intrinsically polar surfaces on opposite sides of wafer: {111}A (Ga-terminated), {111}B (As-terminated)
Real surfaces: surface relaxation, reconstruction, faceting
Examples:
(100): reconstruction linked to As/Ga ratio on surface, depends on supersaturation
{n11}: needed to satisfy electron counting criterion (electrons from dangling bonds must be on states below EF), charge neutrality. E.g., {311}A breaks into {-233} facets
(011)
Planes with 50% Ga + 50% As
Nonpolar surfaces
Strong intra- and weak inter-plane bonding
 natural cleavage planes
 stable surfaces, growth difficult
{n11}
Alternating k X (100) + h X {111} with k/h = (n-1)/2
{n11}A sidewall
(01-1) cross section

50. Equilibrium shape of crystals J. Y
Equilibrium shape of crystals J. Y. Tsao, Material Fundamentals of Molecular Beam Epitaxy (Academic Press, Boston, 1993)
Wulff theorem: equilibrium crystal shape minimizes total surface free energy:
g = (anisotropic) specific surface free energy
n = local surface orientation
Construction: given g(n)  set of planes  ng(n) from origin, passing through g(n). Equilibrium shape: inner envelope of these planes.
Low-energy planes are favored and more extended (g closer to origin)
g(n) has cusps for lowest-energy orientations (generally high-simmetry, low-Miller index planes)  flat facets
As T increases g(n) gets less cusped  disappearence of facets as T>Tr (roughening T for each facet), until spheric shape for isotropic g(n)

51. Equilibrium shape of GaAs N. Moll et al., Phys. Rev. B 54, 8844 (1996)
{100}, {011}, {111}A and {111}B considered (lowest-energy from experience)
Calculation of absolute surface energies as a function of chemical potentials and related surface reconstructions
As-rich environments (usual for MBE, MOCVD): all four orientation coexist in equilibrium, with small (~10%) differences in surface energy
Applicable to InAs and other III-Vs with similar surface reconstructions