Heterojunctions, Interfacial Band Bending, and 2DEG ...bnikolic/.../lectures/band_bending_2deg.pdf · PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG

PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG

Heterojunctions, Interfacial Band Bending, and 2DEG Formation

Heterojunctions, Interfacial Band Bending, and 2DEG Formation

Branislav K. NikolićDepartment of Physics and Astronomy, University of Delaware,

Newark, DE 19716, U.S.A.http://wiki.physics.udel.edu/phys824


Formation of 2DEG at the Interface of Semiconductor Heterostructures


Molecular Beam Epitaxy (MBE) Growth of Semiconductor Heterostructures

�MBE deposits the constituent elements of a semiconductor in the form of ‘molecular beams’ onto a heated crystalline substrate to form thin epitaxial layers. �The ‘molecular beams’ are typically from thermally evaporated elemental sources,�To obtain high-purity layers, it is critical that the material sources be extremely pure and that the entire process be done in an ultra-high vacuum environment. �Another important feature is that growth rates are typically on the order of a few Å/s and the beams can be shuttered in a fraction of a second, allowing for nearly atomically abrupt transitions from one material to another.

in-situ monitoring of the growth is reflection high-energy electron diffraction (RHEED)


Fundamentals of Semiconductors

�SM Hall coefficient: (i) positive in several cases, which can be interpreted by assuming that the principal charge carriers in these materials are not electrons but holes; (ii) the number of carriers depends strongly on temperature.

�SM resistivity: (i) falls in between that of metals and insulators; (ii) in contrast to metals and semimetals, resistivity of pure SM increases exponentially with decreasing temperature

Probability to generate carriers by thermal excitations:

SM resistivity is very sensitive to impurities →SM are useful because they can be doped (+ for devices materials compatibility, such as Si-SiO2, is also important)


Band Structure of Elemental and Compound Bulk Semiconductors


Undoped SM: Simplified Band Structure, DOS, and Filling Factors at Finite Temperature


Doped SM: Simplified Band Structure, DOS, and Filling Factors at Finite Temperature


Temperature Dependence of Chemical Potential in Doped (or Extrinsic) SM

DONORS

ACEPTORS


Metal-Metal Heterojunctions

vac

0

1

FE

2

FE

1

mΦ2

mΦ

z

⇒vac

FE FE1

mΦ

2

mΦ

d

z

1 2

m mΦ − Φ = ∆


p-n Junction


Metal-Semiconductor Heterjunction: Schottky Barrier Contact

Schottky barrier (SB)


Metal-Semiconductor Heterjunction: Ohmic Contact or Inversion Layer

inversion layer

accumulation layer


2DEG in Metal-Oxide-Semiconductor (MOS) Heterojunctions

Met

al

Oxid

e (=

Insu

lato

r)

Sem

iconduct

or

vac

m

FE mΦ

z

The donor atoms are far away from the quantum-well region:

→disorder felt by electrons is reduced

→conductivity through the quantum well depends on the number of carriers which can be tuned by the gate voltage instead of being fixed by the doping density

sm

vE

sm

cE

o

cE

o

vE

sm

dE

z

cE

FE


2DEG in GaAlAs-GaAs Heterostructures

EBasic idea: separate spatially the dopants and the carriers induced

stability of 2DEG:

Nazarov& Blanter: Q

uantum

Transport(CUP, 2009)


2DEG in Semiconductors Heterostructureswith Structural Inversion Asymmetry

Inversion symmetry preserved ⇒⇒⇒⇒spin degeneracy and no Rashba SO

Broken inversion symmetry ⇒⇒⇒⇒spin-splitting and Rashba SO

behavior under time reversal

conclusion

behavior under spatial inversion


What is Spin-Orbit Coupling?

SO deflection force:x

y

z


Vacuum vs. Crystalline SO Coupling Strength

Nonrelativistic expansion of the Dirac equation can be

seen as a method of systematically including the effects of the negative

energy solutions on the states of positive energy starting

from their nonrelativistic limit

VACUUM SEMICONDUCTORS

electron

hole


Energy Spectrum of the Rashba SO Hamiltonian of 2DEG

1D:

2D:

Spin configura

tion at

the Ferm

i ene

rgy

J. Nitta et al., PRL 78, 1335 (1997)


Applications: Datta-Das Spin-FET

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

M=30

M=20

Curr

ent

spin

pola

riza

tion <

|P|>

Length of M-channel wire

Pinject

=(1,0,0)

Pinject

=(0,1,0)

Pinject

=(0,0,1)

M=10

Obstacles:1. Spin injection – mismatch of SM and metallic FM properties

2. Spin dephasing

0 50 100 150 200 250 300-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0(a)

Pinject

=(1,0,0)

Cu

rren

t sp

in p

ola

riza

tio

n v

ecto

r

Length of M=30 channel wire

<|P|>

<Px>

<Py>

<Pz>

Nikolić

and Soum

a, PRB 71, 195328 (2005)

Documents

Heterojunctions, Interfacial Band Bending, and 2DEG ...bnikolic/.../lectures/band_bending_2deg.pdf · PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG