Surfaces and Interfaces of III-V

Semiconductor Sys tems :

from g row t h i s s ues t o e lect ronic

proper t ies

Rita Magri CNR-Nano Istituto di Nanoscienze and

Department of Physics, University of

Modena and Reggio Emilia, Modena,

ITALY

TMCSIII: Jan 2012, Leeds

Acknowledgements

Conor Hogan

Rodolfo Del Sole

CNR-Istituto di Struttura della Materia,

Rome,European Theoretical Spectroscopy

Facility (ETSF) and Department of Physics,

University of Rome “Tor Vergata”, Rome,

ITALY

Alex Zunger NREL, USA

FUNDING: Assegno della Fondazione CRM, PRIN-2005, PRIN-2007,

CINECA Supercomputing Grants

Aim of research

• Understand the link between structural motifs and electronic properties

(structure carrier states comparison with experiment)

• To optimize device design

• To interpret spectroscopic features when spectroscopy is used to characterize the materials

Outline

2D growth

Electronic properties of Abrupt vs Segregated

Interfaces

The dilemma of the c(2x6) surface reconstruction

lattice-matched GaSb/InAs interface

GaSb(001) surface

Empirical Pseudopotential Method

Scalar and Relativistic Plane-Wave Pseudopotential

Method

InAs/GaSb (lattice-matched

system)

Broken-Gap Lineup

• Semiconductor because of

the e1 and h1 confinement

• Possibility of tuning the band

gap between <0 ↔ 400 meV

• Type II: short periods to increase

the radiative ricombination

efficiency

Structure Determination

Atomistic Semiempirical Pseudopotential

Method

• Vext(r) is determined by a superposition of

screened atomic potentials located at the atom

equilibrium positions

We choose an appropriate functional form depending

from a number of parameters

Non self-consistent method

Spherical screened local

potential

)()(,,

R

ion RrVrV

)()( GVeerVGi

G

rGi

ion

q

n

rqivqverv 1|)(|)(

)(

One possible choice

• 5 Parameters fit to reproduce:

1)(

23

2

1

2

0

qaea

aqaqv

• v(q) continous function of q

1. Gaps Eg and effective masses m*

2. Hydrostatic ag and biaxial b deformation potentials

3. Band offsets and spin-orbit splitting so

4. LDA-predicted single band edge deformation potentials av, ac

)()( 4

Travn

indicates atom type

Fit: results

Atom equilibrium positions from elastic

energy minimization

• Valence force field method

),( iirE is minimized with respect to the positions of all atoms (also

subjected to constraints) starting from a chosen

atomic configuration

The minimum provides the elastic (strain) energy and

the relaxed atomic positions

Elastic constants

Atomistic Empirical Pseudopotential

Electronic Structure

)()(2

2

rrRrvm n

n

• Solve the Schrödinger equation:

each atom

individually

described

strain minimizing

atomic positions

plane wave

expansion of

ψ(r)

• no LDA errors

• not self-consistent Folded

spectrum

method

The spectrum at the left is the original spectrum

of H. The spectrum at the right is the folded

spectrum of (H-E_ref)^2

• correct symmetry: band and valley

couplings given correctly

Results for the (InAs)6/(GaSb)m and

(InAs)8/(GaSb)n superlattices

with increasing n we expect a

reduction of Eg

Eg

InAs Gap

e1

hh1

GaSb Gap

m = 8 n = 8, 12, 16, …, 40

Kaspi et al., APL

76, 409 (2000)

Expt.

• Atomistic Empirical Pseudopotential Method

including spin-orbit coupling

Blue-shift of gap with increasing n

Superlattices with abrupt interfaces

The reason for this behavior

Electron states overlap for small values of n (thin GaSb layers)

The interaction pushes down the level energy

PHYSICAL REVIEW B

68, 155329 (2003)

R. Magri and A. Zunger

So the trend is predicted but the gap values

are not ……..

The calculated gaps are too

small expecially for the thin GaSb

barriers

n

Why?

The interfaces are never abrupt

Interfacial broadening

As and In within GaInSb

Sb within InAs

Normal (InAs-on-GaSb) IF

rougher

Steinshnider et al. PRL

85,4562 (2000)

The kinetic model of MBE growth

ESb/As (subsurf Sb surf As) s-->b

Segregation Energies:

In/Ga = EIn/Ga - EIn/Ga b-->s s-->b

b-->s ESb/As (subsurf As surf Sb)

EIn/Ga (subsurf Ga surf In) b-->s

EIn/Ga (subsurf In surf Ga) s-->b

Cations:

Anions:

The rate equations • The rate of change of the concentration xA(t) of surface A atoms is:

• The rates of the exchange reactions depend on the growth

temperature Tg

• Under the conditions of the conservation of A atoms, of the total number of atoms and:

)()()()()()(

// txtxPtxtxPtdt

tdx b

B

s

A

bs

BA

s

B

b

A

sb

BAA

s

A

gB

bsBA

Tk

E

bs

BA eP

/

/

1)()( txtx b

B

b

A

b-->s s-->b For cations: EIn/Ga = 1.8 eV , EIn/Ga = 2.0 eV

(Dehaese et al. APL 66, 52 (95)) No values in the literature for the anions!

Tg = 440 °C

Tg

=380°C

r = 0.25 ML/s

b s ESb/As = 1.68 eV

s b ESb/As = 1.75 eV

Anion energy barriers for subsurface ↔ surface exchange

Interface shift

R. Magri and A. Zunger, Phys. Rev. B

64, R081305 (2001)

Segregated profiles

Electronic consequences of interfacial

segregation

M. J. Yang, W. J. Moore, B. R. Bennett, and

B. V. Shanabrook, Electron. Lett. 34, 270

(1998)

R. Magri and A. Zunger, Phys. Rev. B

64, R081305 (2001)

(InAs)5.5/(In0.28Ga0.72Sb)10/(InAs)5.5/(AlSb)14

THEORY EXPT

Surprisingly, PL peak (energy gap)

increases significantly with Tgrowth

above 450 C!

Interface shift

Interface shift

ONE REASON FOR GAP INCREASING

R. Magri and A. Zunger, Phys. Rev. B

64, R081305 (2001)

So, one reason for the

increasing gap with Tg is the

narrowing of the InAs well the

electron state goes up

• Another feature of

InAs/GaSb is the

presence of different

bonds at the

interfaces even in

superlattices with

abrupt interfaces

SECOND REASON: INTRODUCTION OF MORE Ga-As and In-

Sb BONDS

But InAs/GaSb is a true quaternary system

In a ternary system like GaAsxSb(1-x) the number of nearest

neighbor bonds is determined uniquely by x

Given composition x and size of system

(N total numebr of n.n. bonds): Nx Ga-As and N(1-x) Ga-Sb

N total number of n. n.bonds

Alloy InyGa1-yAsxSb1-x

Nyx number of nInAs

N(1-y)x number of nGaAs

Ny(1-x) number of nInSb

N(1-y)(1-x) number of nGaSb

Only in a perfectly random alloy But if we change Ni bonds

of kind Ga-As and In-Sb in

bonds of kind Ga-Sb and In-As

the total composition (x,y)

does not change

Thus there are different bonding configurations corresponding to composition (x,y)

To specify a given bonding configuration I need a further parameter ξ

ξ = 0 random alloy

ξ > 0 more Ga-Sb (In-As) bonds than Ga-As (In-Sb)

ξ < 0 more Ga-As (In-Sb) bonds than Ga-Sb (In-As)

As

Ga

Sb

In

As

In

Sb

Ga

- + + -

Segregation introduces more bonding disorder at the interfaces

From the study of random InyGa1-yAsxSb1-x alloys

• At the usual growth temperatures the alloy is not random:

what bonding configurations have (InGa)/(AsSb)?

})({})({})({ istrainichemitot SESESE

Minimization of energy functional

Monte Carlo simulation at finite Temperature

Results for : at T = 600°C we find = 0.025 > 0

enrichment of Ga-Sb and In-As bonds

= 0 (random)

Eg = 0.70

= 0.025 (real T = 600°C)

Eg = 0.67

SRO reduces gap of

30 meV

What we learn from the study on the

quaternary alloys

• The introduction of disorder at the

interfaces due to segregation (introducing

more Ga-As and In-Sb bonds) tends to

increase the band gap

J. OF APPL: PHYS. 98, 043701 (2005)

R. Magri, A. Zunger, and H. Kroemer

Final Comparison with Expt.

Tg = 380°C

0.5 ML/s

Tg = 380°C

Growth Temperature

Deposition Rate

PHYS.

REV. B 68,

155329

(2003)

R. Magri and

A. Zunger

Outline

2D growth

Electronic properties of Abrupt vs Segregated

Interfaces

The dilemma of the c(2x6) surface reconstruction

lattice-matched GaSb/InAs interface

GaSb(001) surface

Empirical Pseudopotential Method

Scalar and Relativistic Plane-Wave Pseudopotential

Method

Sb-stabilized GaSb(001) surface

(1) GaSb(001) is the only one among the III-V(001) surfaces

that in the V-rich regime does not form the c(4x4)

reconstruction but a seemingly metallic long dimer chain

reconstruction ….. Why?

c(2x6)

1x3

c(2x10)

RHEED

(2) The structure of the

c(2x6) reconstruction is

unknown

Known reconstructions of Sb-rich

GaSb(001)

The (1x3) phase

The c(2x6) phase?

Proposed models

Long

single-chains

Observed by STM

One lattice unit shifting of the (4x3) cells

along the x4 axis

Moderately Sb-rich reconstructions

High Sb-rich coverage regime of GaSb(001)

The surface reconstructions

Shown by all III-V (001) surfaces

BUT GaSb (001) Shown only by

GaSb (001) Satisfies the electron counting rule Violates the electron counting rule

Surface Energy Calculations

• Total energy calculations using the Quantum-Espresso Package

• DFT-LDA

• Plane-wave Pseudopotential Approach – 15 Ry. cutoff

• Norm-Conserving Scalar and Relativistic Pseudopotentials

• Structure minimized with respect to the electronic degrees of freedom and the ionic degrees of freedom (using forces calculated using the Hellmann-Feynman theorem)

RAS Calculations

Reflectance anisotropy

spectroscopy (RAS)

R

RRRAS

110101

Surface Model:

Supercells (11 layer slab, 10A vacuum)

Back surface passivated with pseudo-H

Optical properties:

Independent particle level (DFT-RPA)

Scissors shift +0.4eV

Spin-orbit coupling included

Many body effects tested but neglected

Fact: long Sb dimer chains are unstable

• The c(4x4) reconstruction is

relatively stable, satisfies the

Electron Counting Rule

(ECR) and is semiconducting

(like the more stable (4x3)

reconstructions)

• Long chain c(2x10) and

c(2x6) structures are

unstable, do not satisfy the

ECR and are metallic

Ab-initio calculation of the surface energy g

Surface phase diagram

M. C. Righi, R. Magri ,and C. M. Bertoni,

PHYS. REV. B 71, 075323 (2005)

Fact: The Reflectance Anisotropy Spectra of c(2x6) • RAS were taken on

GaSb(001) surfaces with a

clear c(2x6) LEED

No known reconstruction model

agrees with experiment!!!

THEORY EXPT

C. Hogan, R. Magri and R. Del Sole,

Phys.Rev B 83, 155421 (2011)

Spin-orbit effects on RAS

Spin-orbit

coupling can

influence optics:

● lifting of degeneracies of

energy levels

● hybridization of states of

different spin

● spin-flip processes

We found no improvement

GaSb(001): a new structural motif?

• To satisfy the ECR the Sb chains have to be

interrupted by missing dimers [like in c(4x4) or

displaced dimers [like in (4x3)]

• However, also the substitution of a group V atom

with a group III atom in the layer below the dimer

chains can lower the surface metallicity.

Excess electron

= 0 if ECR is satisfied

Ga

substituting Sb dimer motifs

Ga surface antisite defects TOO FEW

TOO MANY

Metallic

EF in conduction

Metallic

EF in valence

RIGHT NUMBER

Semiconducting

• Thus the ECR can be satisfied in different ways

by changing the different structural motifs

First question: if we insert Ga substitutional defects in the right number to satisfy

the ECR in the long chain reconstructions, what happens to the surface energy?

We obtain stable structures?

The surface energy lowers considerably but these structures are still less stable than

(4x3)

C. Hogan, R. Magri, and R. Del Sole

PRL 104, 157402 (2010)

Then, why long chain reconstructions are

observed instead of c(4x4) or (4x3)?

• Metastable phases are stabilized by the particular

environmental conditions.

• Hypothesis: V-rich conditions stabilize Ga defects in

GaSb(001) and not in other III-V(001)

All the surfaces experimentally studied with RAS were

prepared under very rich Sb conditions

Surface energy versus excess electrons

Sbf

bulk

Ga

bulk

SbphaseGaphaseSb HEEDFE 2),(

We insert

Ga antisite

defects in

these

structures

Results

• Only in the case of GaSb(001) the Ga defect becomes stable

when the electron excess is higher of = 0.14 the defect

occurs spontaneously

C. Hogan, R. Magri, and R. Del Sole

PRL 104, 157402 (2010)

Two strategies: missing dimers or Ga

defects, what GaSb(001) prefers?

In GaSb(001)

Ga defects are

always

favored over

dimer

removal

both ways satisfy

the ECR

C. Hogan, R. Magri, and R. Del Sole

PRL 104, 157402 (2010)

Why GaSb(001) is so unique?

• First, we note GaSb(001) and metallic Sb are well

matched. Dimer formation does not strain too much the

surface

• Thus, it is possible to have

electronic excess charge

fluctuations at the surface.

Sb-dimer enrichment

does not increase the surface

strain

Also ……

Ga- Sb Bond softness

Another possible case:

Bi stabilized InSb(001)

surface

Also in that case a

c(2x6) reconstruction is

observed

C. Hogan, R. Magri and R. Del

Sole, Phys.Rev B 83, 155421

(2011)

Surface structure

at minimun energy

without Ga

Surface structure

at minimum

energy with Ga

BUT without Ga

Strain energy

Sb Ga

Bonding energy

Coming back to c(2x6)

The presence of

the defects

decreases the

positive peak

between 2-3 eV

and leads to a

good agreement

with the

experimental RAS

for the long chain

reconstructions

Thank you for your attention

Folded spectrum method

[ℏ2/2m ∇2 + Vps(r) + Vnl – ref]2 i(r, ) = (i - ref)

2 i(r, )

The spectrum at the left is the original

spectrum of H. The spectrum at the

right is the folded spectrum of (H-

E_ref)^2

ref