Materials Science and Engineering/Derivations/Models of Micro and Nanoscale Processing/Surfaces and Interfaces

Pseudomorphic Growth

Occurs with similar lattice constant and structure

Growth types depend on processing conditions

Lattice typically needs to be less than 0.5%

Grow diamond tin and zincblende possible because interface energy is low enough to stabilize phase

Metastable growth - thickness beyond which the phase transforms to stable phase

Interface energy effect becomes smaller

Misfit Accomodation

Coherently strained - becomes energetically favorable to form misfits

Glide and leave a misfit dislocation

Dislocations can multiply

Nucleate a dislocation at surface

Glide and remove strain at film

Critical Thickness

Thermodynamic quantity

Kinetics determine whether dislocations form

Depend on temperature - grow metastable film to higher thickness

Kinetic Phenomena

Treatment of kinetics

Mathews

Dislocation motion

Assume Boltzman like jump

Strain energy relief rate is proportional to v

Tendency to overestimate extent to which it is possible to grow strained film

Dodson and Tsao

Improved understanding

Dislocation motion also dependent on stress

Revisit with atomistic models

Nucleation of a Dislocation Loop

Treat nucleation similar to nucleation of phase transition

Energy per unit length of dislocation and step at the surface

Closed 1D defect loop

Shear over area distance equal to the Burger's vector

Calculate the critical energy to create a stable loop

Nucleation loops very unlikely

Comparison with growth on mesas

Most patches remain dislocation free

Estimate concentration by looking at how density depends on size of patches

Types of Defects

• Stacking faults
• Interfacial misfit dislocations
• Threading screw dislocations
• Growth spiral
• Stacking fault in film
• Stacking fault in substrate
• Hillock
• Precipitate or void

Stacking Fault

Two-dimensional feature

Use substrates with ledges on surface

Ensure that the surface is free of patches of oxide

Propagate existing ledges - choice of stacking determined

Modes of Heteroepitaxy

Transition depends on temperature

Rough film evolves into islands

Frank-Van der Merwe Growth

Pseudomorphic growth

Add Ge and achieve pseudomorphic growth

Volmer-Weber Growth

Island, "3D"

Stranski-Krastanov Growth

Starts 2D, becomes 3D

Highly strained surface

Reduce strain by developing roughness

Hydrogen induced embrittlement

Rediscover analysis

Strain relief process results in islanding

Pertubation in strained surface

Square wave with amplitude c

Strain energy times volume per unit area

Increase surface area by creating wave

Critical stress

With a critical stress, there is a wavelength above which the pertubation is stable

Longer wavelength corresponds to smaller rate of growth

Surface energy cost too high with high k number

Instability possible through evaporation

Islanding is a method of strain relief

Kinetic mechanism is surface diffusivity

Relieve stress through islanding or misfit dislocation

Activation energy of glide : 0.1 ev

Activation energy of surface diffusion : 0.5 eV

Islanding at high temperature

SiGe greater than critical thickness

Want islanding: high temperature

Volmer-Weber Growth

Occurs with wide range of materials

Single crystal film

Crystallographic orientation templated by substrate

Film can be single crystal and still contain many defects

Growth by any mechanism other than Frank-Van der Merwe is not epitaxy

Nucleation of islands

Island growth

Growth of GaAs on Si

Always grow with islands

Islands start pseudomorphic

Growth errors lead to dislocations

Slight island rotations

PbTe on CaF2 - Volmer-Weber Growth

Ag on NaCl - with stacking faults

Epitaxial alignment

Interface energy that is strongly dependent on orientation of substrate to island

Growth of islands with particular energies

Interface energy minimization leads to epitaxial alignment

Iron on gallium arsenide

Match every other atom

Matching forms a deep cusp

CdTe on GaAs

Many metal-metal combinations

Same relationship to FCC

Grow epitaxial films by Volmer-Weber

Avoid defects if possible

To avoid SK and VW growth:

• Work with lattice matched systems
• Live with strain
• Manage strain relief

Pseudobinary solution

Lattice matched substrate

GaAs and GaSb form pseudobinary solution

Plot relationship by plotting lattice constant as function of mole fraction

Strained Layer Superlattices

Grow a layer with small critical thickness

Grow another layer with low critical thickness with misfit in opposite direction

Cancel effects of distortion

Grow strained layer superlattice

Graded Layer

Learn how to engineer dislocations

Threading dislocation

Not enough strain to produce islanding

Enough strain to cause dislocation to glide

Threading dislocation concentration low in substrate

Begin with graded layer and create GaAs layer

Compound semiconductor with direct band gap on silicon