Download Heterojunctions, Interfacial Band Bending, and 2DEG Formation

Heterojunctions,
Heterojunctions, Interfacial
Interfacial Band
Band
Bending,
Bending, and
and 2DEG
2DEG Formation
Formation
Branislav K. Nikolić
Department 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
in-situ monitoring of the growth is reflection high-energy
electron diffraction (RHEED)
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.
PHYS824: Introduction to Nanophysics
Heterojunctions, Band Bending, and 2DEG
Fundamentals of Semiconductors
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
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 is very sensitive to impurities →
SM are useful because they can be doped (+ for devices
materials compatibility, such as Si-SiO2, is also important)
Probability to generate carriers by thermal excitations:
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
ACEPTORS
DONORS
Temperature Dependence of Chemical
Potential in Doped (or Extrinsic) SM
PHYS824: Introduction to Nanophysics
Heterojunctions, Band Bending, and 2DEG
Metal-Metal Heterojunctions
d
vac
E
1
F
1
m
Φ1m
Φ
vac
2
m
E
2
m
Φ −Φ = ∆
0
PHYS824: Introduction to Nanophysics
2
F
z
⇒E
F
Φ1m
Φ 2m
EF
z
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
Semiconductor
Oxide (=Insulator)
Metal
vac
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
PHYS824: Introduction to Nanophysics
EFm
Φm
Eco
Evo
Ecsm
Edsm
Evsm
z
Ec
EF
z
Heterojunctions, Band Bending, and 2DEG
2DEG in GaAlAs-GaAs Heterostructures
Basic idea: separate spatially the
dopants and the carriers induced
Nazarov & Blanter: Quantum
Transport (CUP, 2009)
E
PHYS824: Introduction to Nanophysics
stability of 2DEG:
Heterojunctions, Band Bending, and 2DEG
2DEG in Semiconductors Heterostructures
with Structural Inversion Asymmetry
Inversion symmetry preserved ⇒
spin degeneracy and no Rashba SO
Broken inversion symmetry ⇒
spin-splitting and Rashba SO
behavior under
time reversal
behavior under
spatial inversion
conclusion
PHYS824: Introduction to Nanophysics
Heterojunctions, Band Bending, and 2DEG
What is Spin-Orbit Coupling?
z
y
SO deflection force:
x
PHYS824: Introduction to Nanophysics
Heterojunctions, Band Bending, and 2DEG
Vacuum vs. Crystalline SO Coupling Strength
VACUUM
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
PHYS824: Introduction to Nanophysics
SEMICONDUCTORS
electron
hole
Heterojunctions, Band Bending, and 2DEG
Energy Spectrum of
the Rashba SO Hamiltonian of 2DEG
1D:
J. Nitta et al., PRL 78, 1335 (1997)
PHYS824: Introduction to Nanophysics
Spin configuration at
the Fermi energy
2D:
Heterojunctions, Band Bending, and 2DEG
Applications: Datta-Das Spin-FET
Obstacles:
1. Spin injection – mismatch of SM
and metallic FM properties
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)
<|P|>
<Px>
<Py>
<Pz>
0
50
100
150
200
250
Current spin polarization <|P|>
Length of M=30 channel wire
PHYS824: Introduction to Nanophysics
1.0
M=10
0.8
0.6
M=20
0.4
0.2
0.0
0
Pinject=(1,0,0)
Pinject=(0,1,0)
Pinject=(0,0,1)
50
100
M=30
300
Nikolić and Souma, PRB 71, 195328 (2005)
Current spin polarization vector
2. Spin dephasing
150 200 250 300
Length of M-channel wire
Heterojunctions, Band Bending, and 2DEG