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
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Formation of 2DEG at the Interface of Semiconductor Heterostructures
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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)
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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)
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Band Structure of Elemental and Compound Bulk Semiconductors
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Undoped SM: Simplified Band Structure, DOS, and Filling Factors at Finite Temperature
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Doped SM: Simplified Band Structure, DOS, and Filling Factors at Finite Temperature
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Temperature Dependence of Chemical Potential in Doped (or Extrinsic) SM
DONORS
ACEPTORS
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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 = ∆
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
p-n Junction
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Metal-Semiconductor Heterjunction: Schottky Barrier Contact
Schottky barrier (SB)
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
Metal-Semiconductor Heterjunction: Ohmic Contact or Inversion Layer
inversion layer
accumulation layer
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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)
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
What is Spin-Orbit Coupling?
SO deflection force:x
y
z
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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)
PHYS824: Introduction to Nanophysics Heterojunctions, Band Bending, and 2DEG
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)