Corso FS02: Materiali e Dispositivi per optoelettronica, spintronica e nanofotonica Modulo 1: Crescita epitassiale di materiali semiconduttori (Giorgio Biasiol) Program: 1. General concepts in epitaxy 2. Epitaxial techniques: Molecular Beam Epitaxy (MBE) 3. Epitaxial techniques: Metal Organic Chemical Vapor Deposition (MOCVD) 4. Fabrication of semiconductor nanostructures

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

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

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.

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

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

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).

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.

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.

Material choices for device applications  Optoelectronics applications (e.g., optical communications, displays, sensors)  wavelength ranges within which materials emit and absorb light efficiently:  GaN-related materials: µm  GaP-related materials: µm  GaAs-related materials: µm  InP-related materials: µm (major fiber- communications wavelengths: 1550nm In 0.58 Ga 0.42 As 0.9 P 0.1; 1310nm In 0.73 Ga 0.27 As 0.58 P 0.42 )  InSb-related materials: 2-10 µm  Electronic applications (e.g., 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.

Compound semiconductors market share

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.

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.

Si MOSFET: single bulk material, doping by diffusion or implantation typical sizes ~  m InGaAs/AlGaAs p-HEMT: abrupt heterostructures, planar (  -) doping typical sizes < 10 nm 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 Bulk vs. Quantum-confined devices

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.

Introduction to Epitaxial Techniques

Crystallization and film growth  Amorphous: no ordered structures  Polycrystalline: randomly oriented grains, oriented grains, highly oriented grains epitaxy  Single crystal: bulk growth, epitaxy:  (upon) +  (ordering)

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

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

Comparison of MBE and MOCVD FeatureMBEMOCVD Source materialsElementalGas-liquid compounds EvaporationThermal, e-beamVapor pressure, Carrier gas Flux controlCell temperatureMass flow controllers SwitchingMechanical shuttersValves EnvironmentUHVH 2 -N 2 ( mbar) Molecular transportBallistic (mol. beams) Diffusive Surface reactionsPhysi-chemisorbtionChemical reactions

Advantages-disadvantages of MBE and MOCVD FeatureMBEMOCVD 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)- (H 2, Highly toxic gases) Growth rates (GaAs) ~1  m/hUp to ~4  m/h Wafer capacity7X6”, 4X8”10X8”, 5X10” EnvironmentUHV(sub)atmospheric pressure Graded composition layers- (thermal evaporation)+ (mass flow control) Defect density- (oval defects)+ Downtime-+

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.

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”,

Supersaturation  Growth rate is thermodynamically limited by chemical potential difference between fluid phase and fluid-surface equilibrium:   =  –  eq ≡ supersaturation ≡ driving force for film growth   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)

Molecular flux Molecular flux: # of molecules hitting a cross-sectional area in a time unit: J [molecules/(m 2 sec)] Maxwell-Boltzmann distribution 

Deposition rate The flux of molecules of the surface leads to deposition, with the rate of film growth depending on J Example: Silane (SiH 4 ) in VPE:  P ~ Torr (1 Torr = 133 Pa)  M: Si: 28 g/ mol and H: 1 g/ mol   film = 2.33 g/mol r ~ 50nm/sec  T ~ 400C = 673K  N A = 6.02X10 23

Mean free path d = molecular diameter ~ 0.5nm, R = 8.31 J/(mol * K) T ~ RT (300K) 1 Torr = 133 Pa ~10 -5 Torr  ~ 3m (e.g. As 4 in MBE) P >10 Torr  < 30  m (MOCVD)

Flow regimes The magnitude of 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, 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.

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. 1. Absorption/desorption of gas molecule into the film Physisorption Chemisorption 2. Surface diffusion 3. Nucleation of a critical seed for film growth 4. Development of film morphology over time All processes must overcome characteristic activation energies E i, with rates r i  exp(E i /kT), depending on atomic details of the process  Arrhenius-type exponential laws

Physi- and Chemisorption  Physisorption: precursor state, often considered as having no chemical interaction involved (van der Waals). E a ~ 100meV/atom  Chemisorption: dissociation of precursor molecule, strong chemical bond formed between the adsorbate atom or molecule and the substrate. E a ~ a few eV/atom (>~ substrate sublimation energy) Chemisorption reaction rate: R = k n s0  ; k = reaction rate constant = a exp(-E a /kT), a = characteristic atomic vibration frequency, n s0 = ML surface concentration,  = fractional surface coverage

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/cm 2 s) for surface diffusion is given as: with n s = surface concentration of reactant, d = characteristic diffusion frequency ~ s -1 E d = migration barrier energy In unit time the adatom makes d attempts to pass the barrier, with a probability of exp (-E d /kT) of surmounting it on each try. E d << E a  surface diffusion is far more likely than desorption.

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!

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

Competing processes in nucleation  Gain in bulk free energy  G v 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  G is positive).  With larger nuclei, the free energy from converting a volume of atoms to solid overcomes the added surface energy (the overall  G is negative).

Energetics of homogeneous nucleations vapor nucleus r  Bulk contribution:  G v = -  v f ;  =  v -  f = kT ln(p/p 0 ) = supersaturation, v f = V / N A = molecular volume Surface contribution:  = surface energy per unit area Total energy change on cluster formation:  G = (4  /3) r 3  G v + 4  r 2  0

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

Heterogeneous nucleation   vf  sv  fs Young’s equation:  sv =  fs +  vf cos ,  = wetting angle   sv   fs +  vf (highly reactive substrate surfaces)  cos   1;  = 0 or undefined  wetting   sv <  fs +  vf (poorly reactive substrate surfaces)  cos  < 1; 0<  <   no wetting   sv ≈  fs +  vf (metastable situation) Typical case 3: lattice-mismatched, strained heteroepitaxy Strain energy (needed to adjust to substrate lattice) depends on  fs and increases linearly with film thickness  If at 0 thickness  sv   fs +  vf, at some critical thickness  sv <  fs +  vf will be realized  2D wetting layer + 3D islands vapor nucleus substrate

Energetics of heterogeneous nucleations vapor nucleus substrate   r  vf Volume of nucleus: Surface area of nucleus:

Energetics of heterogeneous nucleations vapor nucleus substrate   r  vf same as hom. nucl., no dependence on    = 0   G * = 0; 3D droplets thermodynamically unfavored  wetting of continuous 2D film   =    G* =  G hom *; no influence of substrate

Growth modes FM: Frank-van der Merwe (2D) mode VW: Volmer- Weber (3D) mode SK: Stranski- Krastanov (2D+3D) mode 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.  sv   fs +  vf  sv   fs +  vf  sv <  fs +  vf

Examples: Frank-van der Merwe growth TEM micrograph of the active region of a lattice-matched AlInAs/GaInAs QCL grown by MBE Cho et al., J. Cryst. Growth , 1 (2001) 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., Al x Ga 1- x As/GaAs).

Examples: Stranski-Krastanov growth 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. 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

Crystallography of zinc-blende lattices 0.56 nm

{n11}A sidewall 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)  (011)  Planes with 50% Ga + 50% As  Nonpolar surfaces  Strong intra- and weak inter-plane bonding   natural cleavage planes   stable surfaces, growth difficult (01-1) cross section  {n11}  Alternating k X (100) + h X {111} with k/h = (n-1)/2  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 E F ), charge neutrality. E.g., {311}A breaks into {-233} facets

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:  = (anisotropic) specific surface free energy n = local surface orientation Construction: given  (n)  set of planes  n  (n) from origin, passing through  (n). Equilibrium shape: inner envelope of these planes.  Low-energy planes are favored and more extended (  closer to origin)   (n) has cusps for lowest-energy orientations (generally high-simmetry, low-Miller index planes)  flat facets  As T increases  (n) gets less cusped  disappearence of facets as T>T r (roughening T for each facet), until spheric shape for isotropic  (n)

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