1-Mesoscopic phenomena in semiconductor nanostructures by quantum design.pdf
Introduction to semiconductor nanostructures - · PDF fileIntroduction to semiconductor...
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Introduction to semiconductor nanostructures
Peter KratzerModern Concepts in Theoretical Physics: Part II
Lecture Notes
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• The Fermi level (chemical potential of the electrons) falls in a gap of the band structure.
• Doping allows us to control the position of EF in the gap.
• Either electrons (n-type) or holes (p-type) act as carriers of charge.
• Long-lived optical excitations.
What is a semiconductor ?
Under which conditions does the quantum nature of the carriers show up ?
intrinsic p-type n-type
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… a different answer
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k
ε(k)
• σ(T) = e n(T) µ (T)• n(T) depends both on doping
and temperature
• Boltzmann statistics often sufficient to describe temp. dependence
• sometimes k ~ 0.01 alat
Basics of Transport
• conductivity σ(T) = enµ(T)• Fermi statistics,
εF~10 eV, kT << εF , kF~ alat• mobility µ: similar physics in
metals and semiconductors Drude: µ(T)=eτ(T)/m
• replace electron mass by effective mass
Is this ALL that quantum mechanics has to tell us ?
12 )(
−
∂∂∂
=ji kk
m kε
metal semiconductor
10-2 .. 105~10−2µ (cm2/Vs)
<1091021 .. 10−10>1022n (cm–3)
<10−10103 .. 10−9>104σ (Ω−1 cm−1)
insulatorsemiconductormetal
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k
ε(k)
• σ(T) = e n(T) µ (T)• n(T) depends both on doping
and temperature
• Boltzmann statistics often sufficient to describe temp. dependence
• sometimes k ~ 0.01 alat―1
Basics of Transport
• conductivity σ(T) = enµ(T)• Fermi statistics,
εF~10 eV, kT << εF , kF~ alat―1
• mobility µ: similar physics in metals and semiconductors Drude: µ(T)=eτ(T)/m
• replace electron mass by effective mass
Is this ALL that quantum mechanics has to tell us ?
12 )(
−
∂∂∂
=ji kk
m kε
metal semiconductor
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Excitons
• Bound system of electron and hole, cf. hydrogen atom
• Exciton radius re = a0 ε/m*1/m* = 1/me + 1/mhGaAs: re ~ 112 a0
• For structures of lateral dimensions < re, quantum confinement effects can be expected.
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Nobel Prize in Physics 2000
Herbert Kroemer Zhores I. Alferov Jack S. Kilby..for developing semiconductor heterostructures ..for his part in the
in high-speed and optoelectronics integrated circuit
25 % 25 % 50 %
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What is a heterostructure ?
A device build from different semiconductor materials, thus exploiting the differences in band structure.
original drawing by Herbert Kroemer, 1957
AlGaAs AlGaAsGaAs
collector base emitter
bipolar transistor
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Molecular Beam Epitaxy
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thermodynamics of heteroepitaxy: growth modes
• Frank-van der Merwe: ∆γ ≤ 0wetting of the substrate,layer-by-layer growth
• Volmer-Weber: ∆γ > 0no wetting, three-dimensional island growth
• Stranski-Krastanow : ∆γ ≤ 0 for the first layer(s), later ∆γ > 0 (e.g. due to lattice mismatch)island growth on the wetting layer
∆γ = γf + γi −γs
f: films: substratei: interface
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Heterostructures: Band gaps/Misfits
lattice constant [Å]
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Heterostructures: electrostatic potential
∆−
∆=
kTE
kTE
nekTw cc
I 2exp
2 020εε
∆EV
∆Ec EF
inversion depletion
DD Ne
kTw 202εε
=
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Heterostructures: sub-bands
• Quantization of electron motion in z-direction → sub-bands
• “remote” doping → µ > 105 cm2/Vs– Ballistic motion of the electrons for d < vF τ– Fractional Quantum Hall Effect
ε2―εF > kT )(*2
)( 222
yxii kkm
++=h
εε k
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From 2D to 0D: Density of States
3D
2D
1D
0D
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From 2D to 1D and 0D: Practical ways
• By engineering– Lithography + etching– Cleaved-edge overgrowth– Confinement induced by
• electrostatics (gate)• STM tip, ..• strain
• By self-assembly– Colloidal quantum dots– Epitaxial quantum dots
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Cleaved-edge overgrowthWidening of the potential well→ quantum wire
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Colloidal CdSe Quantum dots
application: fluorescence markers in cellsnanocrystals of different sizes(different growth conditions)
wet chemical synthesis
tri-n-octyl phosphine oxide +di-methyl-cadmium
tri-n-octyl phosphine + bis-(trimethyl-silyl) selenide
1 sec
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Self-Assembled Quantum Dots
Transmission electron micrograph (D. Gerthsen, TU Karlsruhe)
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Epitaxial Quantum Dots: discrete DOS
cathodoluminescence temperature-independent line width
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Applications
• 2D heterostructures:– high-electron-mobility transistor (HEMT) → high-
frequency electronics (cell phone, satellite TV)– solar cells with high efficiency
• Quantum dots:– light-emitting diodes, lasers – optical and IR detectors
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mean free path of carriers in 2 DEG can be larger than gate length → ballistic transport
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What is a laser ?
Light Amplification by stimulated emission of radiation
Requirements:• lasing medium with many objects (atoms, molecules, quantum dots, …)
capable of resonant electronic transitions• population inversion
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Heterostructures in Non-Equilibriumdouble-heterostructure diode in forward bias
n-AlGaAs p-AlGaAsi-GaAs
quasi-Fermi level for electrons
quasi-Fermi level for holes
DOS ?e–
h+
strong inversion in i-GaAs !
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Quantum Dot Laser
• lower threshold current than Quantum Well Laser• threshold current less temperature-dependent• varying the size and shape of the dot allows to tune emission
wavelength (without need to introduce different chemical elements)
1 ps
20-40ps
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p-GaAs
p-AlGaAsp-GaAsn-GaAs
n-AlGaAs
n-GaAs
Ti-Pt-Au
Ni-Ge-Au
light-emitting layer
Semiconductor Lasers: graded-index waveguide
(110) Cleavage plane →(semi-)transparent mirrors
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Semiconductor Lasers: VCSELVertical-Cavity Surface-Emitting Laser
electrical contact
upper mirror
blindlaser medium
lower mirror
electrical contactGalliumarsenide semicond. substrate
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Summary
• molecular beam epitaxy → semiconductor heterostructures → band structure engineering → many novel devices
• semiconductors are an ideal playground to see quantum confinement effects, due to small electron wavevectors / large exciton radii
• self-assembled structures advantageous over “engineered” structures (small size, high density,..)
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Literature
• textbooks– P. Y. Yu and M. Cardona, Fundamentals of Semiconductors,
Springer, 1996– R. Enderlin and A. Schenk, Grundlagen der Halbleiterphysik,
Akademie-Verlag, 1992 – D. Bimberg, M. Grundmann, and N.N. Ledentsov, Quantum
Dot Heterostructures, Wiley, 1999• articles
– Zh. I. Alferov, V. M. Andreev, and N. N. Ledentsov , http://link.edu.ioffe.ru/pti80en/alfer_en
– Zh. Alferov, Semiconductors 32 (1998), 1