Quantum Quantum HeterostructuresHeterostructures Group: Group: A Research Overview

Emilio Mendez

NTT Basic Research LaboratoriesJuly 30, 2003

A Research Overview

Goal: Discover and Elucidate Quantum Phenomena forNovel Optical and Electronic Devices

GoalGoal: Discover and Elucidate : Discover and Elucidate Quantum Phenomena forQuantum Phenomena forNovel Optical and Electronic DevicesNovel Optical and Electronic Devices

Fernando CaminoJames Dickerson (Columbia U.)Elvira Gonzalez ( U. Madrid)Vladimir KuznetsovYiping Lin (NTT BRL)A. K. NewazBent NielsenJ. K. Son (Samsung)Woon Song

External CollaboratorsF. Agullo-Rueda, CSIC, SpainA. Allerman, Sandia National Lab.B. Bennett, Naval Research Lab.R. Magno, Naval Research Lab.S. Manotas. CSIC, Spain

Recent ResearchRecent Research

•• Optical Properties of Semiconductor Microcavities(J. Dickerson and J. K. Son)

•• Electronic Vertical Transport in Type II Heterostructures(Y. Lin and E. M. Gonzalez)

•• Electronic Noise in Mesoscopic Systems(F. Camino, V. Kuznetsov, A.K. Newaz, J. K. Son, W. Song)

Semiconductor MicrocavitesSemiconductor Microcavites

IntroductionIntroduction

Physics of semiconductor multilayers has been successful in mimicking atomic systems.Analog to the Fabry-Perot, two-level atom system is the microcavity.Interaction between the electromagnetic mode and the two-level atom yields Rabi splitting, Ω.

Two LevelAtom

Fabry-Perot Cavity

Quantum Quantum --Well Well MicrocavityMicrocavity

G a A s

W e l l

λ/ 2 C a v i t y

S u b s t r a t e

p –t y p e A l A s / A l G a A sT o p M i r r o r

n –t y p e A l A s / A l G a A sB o t t o mM i r r o r

λ/ 4 L a y e r

A Quantum A Quantum WellWell in a in a MicrocavityMicrocavity

DBR

DBR

K λ/2

E1

H1

E1 + H1 = EXCITON

+ =EXCITON CAVITY POLARITON

Rabi Splitting

λ λ

Tuning Resonance ConditionTuning Resonance Condition

1 .4 8 1 .4 9 1 .5 0 1 .5 1 1 .5 2

R a b i S p lit t in g Ω

M ix e dP o la r ito n

M o d e s

R e s o n a n c e

A t R e so n a n c eE C a v ity = E E x c ito n

Q u a n tu mW e ll

M o d e

C a v ityM o d e

N o R e s o n a n c e

Ref

lect

ivity

(a.u

.)

E n e r g y (e V )

• Effective Cavity Length– Tapered cavity– Angle of incidence

• Exciton Energy– Temperature– Electric Field

0.800 0.804 0.808 0.812

Detu

ning

λ (µm)

3λ/2

1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58

Ref

lect

ivity

(a.u

.)

Energy (eV)

Reflectivity of a QuantumReflectivity of a Quantum--WellWell--MicrocavityMicrocavity

80 100 120 140 160 180 200 220 240

1.520

1.525

1.530

1.535

1.540

1.545

1.550

1.555

1.560

Cavity

Heavy HoleLight Hole

Ω2 = 4.1meV

Ω1 = 6.7meV

Ener

gy (e

V)

Temperature (K)

How to Enhance Rabi Splitting?How to Enhance Rabi Splitting?

Rabi Splitting proportional to• Exciton oscillator strength (∝binding energy)• Number of oscillators per unit length

??p-typ e AlAs / AlGaAs

M i r r o r

n-type AlAs / Al GaAs

M i r r o r

GaAs / AlGaAsS u p e r l a t t i c e

Recipe:• increase density

of quantum wells• make wells narrow

Contradictory?

λ/2 C a v i t y

Semiconductor Quantum Wells and Semiconductor Quantum Wells and SuperlatticesSuperlattices

E1

H1

EgW

CB

EgB

VB

Superlattice Regime

Coupled QW regime

Isolated QW regime

ElectricElectric--field Induced Localizationfield Induced Localization

Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity

1.46 1.48 1.50 1.52 1.54

5KStep

313K

188K

Ref

lect

ivity

(a.u

.)

Energy (eV)180 200 220 240 260 280 300 320

1.47

1.48

1.49

1.50

1.51

1.52

1.53

1.54

Ω1 = 9.5meV

Ω1

X0

C

Ene

rgy

(eV

)

Temperature (K)

E ≠ 0

Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity

1.46 1.48 1.50 1.52 1.54

5KStep

313K

188K

Ref

lect

ivity

(a.u

.)

Energy (eV)180 200 220 240 260 280 300 320

1.47

1.48

1.49

1.50

1.51

1.52

1.53

1.54

Ω1 = 9.5meV

Ω1

X0

C

Ene

rgy

(eV

)

Temperature (K)

E ≠ 0

Ω2 = 6.9meV

Ω2

X+1

Reflectivity of Reflectivity of SuperlatticeSuperlattice--MicrocavityMicrocavity

1.46 1.48 1.50 1.52 1.54

5KStep

313K

188K

Ref

lect

ivity

(a.u

.)

Energy (eV)180 200 220 240 260 280 300 320

1.47

1.48

1.49

1.50

1.51

1.52

1.53

1.54

Ω1 = 9.5meV

Ω1

X0

C

Ene

rgy

(eV

)

Temperature (K)

E ≠ 0

Ω2 = 6.9meV

Ω2

X+1

E ≈ 15 kV/cm

X-1X+1 X0 X-1X+1 X0

Photocurrent from Photocurrent from SuperlatticeSuperlattice MicrocavityMicrocavity

0 10 20 30 40 501.53

1.54

1.55

1.56

1.57

1.58

1.59

1.60

1.61

1.52 1.54 1.56 1.58 1.60 1.62

1 µA

0º

5º

10º15º

20º

25º

30º

35º40º

V = +0.25 Volts E ≈ 29 kV/cm T = 80 K

Phot

ocur

rent

(a.u

.)

Energy (eV)

50º

Heavy Hole

Light Hole

Cavity

∆ hh = 11.5 meV∆ lh = 7.2 meV

Dip

Ene

rgy

(eV

)

Angle (º)

Summary of Rabi SplittingsSummary of Rabi Splittings

2

3

4

5

6

7

8

9

10

11

12

13

0 20 40 60 80 100

2

3

4

5

6

7

8

9

10

11

12

13

T = 80 K Heavy Hole Light Hole

Rab

i Spl

ittin

g (m

eV)

Electric Field (kV/cm)

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0

Large Angle Small Angle

Flatband

StarkLadder QCSE

Applied Voltage (V)

ConclusionConclusion

• When a superlattice is immersed in a microcavity,• there is polariton coupling with individual superlattice

states;• exciton-cavity coupling can be drastically enhanced;• coupling can be tuned by an electric field.

References:Enhancement of Rabi Splitting in a Microcavity with an Embedded Superlattice,J. H. Dickerson, E. E. Mendez, A. A. Allerman, S. Manotas, F. Agulló-Rueda,

and C. Pecharromán, Phys. Rev. B 64, 155302 (2001).Electric Field Tuning of the Rabi Splitting in a Superlattice-Embedded Microcavity, J. H. Dickerson, J. K. Son, E. E. Mendez, and A. A. Allerman, Appl. Phys. Lett. 81, 803 (2002).

Vertical Transport in Type II (InAs/GaSb) Heterostructures

Vertical Transport in Type II (InAs/GaSb) Heterostructures

InAs/AlSb/GaSb SystemInAs/AlSb/GaSb System• Nearly-matched lattice constant ~ 6.1 Å• Versatile band lineups

– Straddling (AlSb/GaSb)– Staggered (InAs/AlSb)– Broken-gap (InAs/GaSb)

GaSbAlSb

InAs

0.812.300.41Eg (eV)What’s Special About this System?

• Coexistence of electron and hole gases• Advantages of InAs

– small me* (0.023 m0), larger g* (-15)– no Schottky barrier with metals

InAs/AlSb/GaSb Type II InAs/AlSb/GaSb Type II QWsQWsEn

ergy

(meV

)

InAsInAs

AlSb

GaSb

AlSb

60Å

H0

E0E0

EF

Ideally,2Ne = NhIdeally,2Ne = Nh

T = 300K

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-4

-2

0

2

4

Cur

rent

(mA

)

Voltage (V)

Is it Possible toObserve

Rashba Splitting?

??

Evidence for Two Kinds of 2D GasesEvidence for Two Kinds of 2D Gases

0 1 2

T = 4.2K

0o

15o

θ = 20o

Cond

ucta

nce

(arb

. uni

ts)

Perpendicular Magnetic Field (T)

2D Electrons2D ElectronsNe = 5 – 7 ×1011 cm-2

. . ... .

0 2 4 6 8 10 12

θ = 90o

50 %

∆σ

/σ0

Magnetic Field (T)

θH

2D Holes2D Holes

electronsholes

Vertical Vertical ShubnikovShubnikov -- de Haas Oscillationsde Haas Oscillations

0 2 4 6 8 10

20

40

60

80

ν = 4ν = 6

Cond

ucta

nce

(mS)

Magnetic Field (T)

0 2 4 6 8 10 12 14

34

36

38

40

ν = 6 ν = 4

0 2 4 6 8 10 12 140

40

80

120

160

ν = 6 ν = 4

75 Å GaSb

80 Å GaSb

GaSb

H⊥

0.25 0.50 0.75 1.00 1.25 1.50

System B60 Å GaSb

MagnetotunnelingMagnetotunneling between 2D Gasesbetween 2D Gases

E0

L4

E0’

L3 0.0 0.5 1.0 1.5 2.0

0.08

0.12

0.16

0.0 0.5 1.0 1.5 2.0

0.02

0.04

0.06Con

duct

ance

(S)

Magnetic Field (T)

0∆ ≠

0∆ =Δ

• For gases with slightly different Ns, at low fields,

tunneling between states with ∆L ≠ 0 is favored

InIn--plane Momentum Conservation?plane Momentum Conservation?

0 2 4 6 8 10

∆L=0 ∆L=1 ∆L=2 ∆L=3

Cond

. (ar

b. u

nit)

Magnetic Field (T)

Comparison Between Theory and ExperimentComparison Between Theory and Experiment

0 2 4 6 8 10

Cond

. (ar

b. u

nit)

Magnetic Field (T)

ΔL=2ΔL=1

ΔL=0

0.0 0.5 1.0 1.5 2.0

0.08

0.12

0.16

0.0 0.5 1.0 1.5 2.00.09

0.12

0.15

0.0 0.5 1.0 1.5 2.0

0.02

0.04

0.06

Cond

ucta

nce

(S)

Magnetic Field (T)

8 7 6 5 4 3 20.0

0.1

0.2

8 7 6 5 4 3 20.00

0.05

0.10

0.15

8 7 6 5 4 3 20.00

0.05

0.10

Cond

ucta

nce

(S)

Filling Factor (ν)

Effect of 2DEG Asymmetry

7.1×1011 cm-2

7.6×1011 cm-2

6.6×1011 cm-2

((ΔΔN ~ 1% NN ~ 1% Naveave))

Naverage

0.00

0.04

0.08

0 2 4 6 8 10 12 140.00

0.04

0.08

T = 4.2 K

5/28 6 3

ν = 4

T = 1.7 K

Con

duct

ance

(S)

Magnetic Field (T)

High-field Magnetotunneling

N = 2 N = 13

MagnetotunnelingMagnetotunneling at Very High Magnetic Fieldsat Very High Magnetic Fields

0 5 10 15 20 25 3020

40

60

80

100

120

140

160

180

2002 3/2 15/23468

Filling FactorT

unne

ling

Con

duct

ance

(arb

. uni

ts)

Magnetic Field (T)

V = 0

V = 12 mV

T = 0.5K

0 5 10 15 20 25 3020

40

60

80

100

120

140

160

180

2002 3/2 15/23468

Filling FactorT

unne

ling

Con

duct

ance

(arb

. uni

ts)

Magnetic Field (T)

What is the Origin of the What is the Origin of the νν = 5/2 Minimum?= 5/2 Minimum?

Facts:• Observable only when two 2D electron gases have same density• Observable at high T ( ≤5K), weakly dependent on T• Slightly enhanced by an in-plane magnetic field

Possible (“trivial”) Explanation:• Due to 2D holes with a ν = 5 filling factor, if Nh = 2Ne (ideal)• Unlikely, because:

• in practice, Nh is much less than ideal• holes not present in Shubnikov-de Haas oscillations• large m*h favors strong T dependence of H-induced features

ConclusionConclusion

• Beating effects in magneto-conductance oscillations are due to extrinsic asymmetries between 2D electron gases, not to Rashba splitting.

• In symmetric 2D-2D systems, new features are found for non-integer Landau-level occupation, whose origin is still unclear.

References:Magnetotunneling of a Two Dimensional Electron-Hole System Near Equilibrium, E. Gonzalez, Y. Lin, and E. E. Mendez, Phys. Rev. B 63, 033308 (2000).Tunneling Characteristics of an Electron-Hole Trilayer in a Parallel Magnetic

Field, Y. Lin, E.E. Mendez, and A.G. Abanov, Phys. Rev. B. 66, 195311 (2002).Magnetotunneling between Two-dimensional Electron Gases in InAs-AlSb-GaSb Heterostructures, Y. Lin, E. M. Gonzalez, E. E. Mendez, R. Magno, B. R. Bennett, and A. S. Bracker, Phys. Rev. B 68, 035311 (2003).

Shot Noise in Negative Differential Conductance Devices

Shot Noise in Negative Differential Conductance Devices

A OneA One--minute Introduction to Shot Noiseminute Introduction to Shot Noise

• Noise: temporal fluctuations of the average current through (or voltage across) a device.

• The magnitude of noise is frequently expressed in terms of thespectral density, that is, the mean of the squared currentfluctuations, δ I(f), per unit bandwidth.

• Thermal Noise: due to thermal agitation, present even if device is in equilibrium.

• Shot Noise: results from the discretenessof the electrical charge; present only when system is out of equilibrium.

ffI

fS∆

=2)(

)(δ

Shot noise measurements can unveil the nature of charge transport, beyond information provided by the electrical conductance.

Coexistence of Thermal and Shot NoiseCoexistence of Thermal and Shot Noise

H. Birk et al., Phys. Rev. Lett. 75 1610 (1995).

Shot Noise and Fano FactorShot Noise and Fano Factor

If charge transport is a random and independent process (i.e. PoissonianPoissonian), spectral density of current fluctuation is

IqS 2=

TheThe FanoFano factorfactor is defined as

IeSF

2≡

Two Examples of Shot NoiseTwo Examples of Shot Noise

Normal Metal-Superconductor Tunnel JunctionBecause current flows in terms of Cooper Pairs (Q=2e) and the process is Poissonian,

Single Barrier DiodeBecause charge flow is random and independent, S=2eI and F=1.

22

==Ie

SF

QuestionQuestion

Can we use noise to differentiate among differenttransport mechanisms in devices that have the same negative differential conductance characteristics ?

We consider three different cases:

Double Barrier Diode

Superlattice Tunnel Diode

Multiple-Quantum-Well Photodiode

Quantum-mechanical Effects on Shot Noise• Pauli exclusion principle can make shot noise sub-Poissonian• Fano factor measures deviations from Poissonian process

eISF2

)(ω≡

• In a double-barrier potential,

RΓ

eV

LΓ

2

22

ΓΓ+Γ

= RLF

21

=Γ=Γ FRLIf

1≅Γ>>Γ FRL

Fano Factor in Resonant Tunneling Diodes

100 200 300 400

0.0

0.2

0.4

0.6Actual Noise

2eI

Resonant-tunneling Diode

T = 4.2K

S I(p

A2 /H

z)

Voltage (mV)

200 250 300 350 4000.5

1.0

1.5

2.0

2.5

Fano

Fac

tor

(S/2

eI)

Voltage (mV)

0 100 200 300 4000.0

0.2

0.4

0.6

0.8

1.0

1.2

100A-40A-100A

T = 4.2K

GaAlAs-GaAs-GaAlAsC

urre

nt (µ

A)

Voltage (mV)

eV1

eV2

Explanation of Shot Noise Enhancement

Qualitatively

(Iannaccone et al., PRL 80, 1054 (1998)

Enhancement is due to “anticorrelation” effects,when the tail of the density of states isin resonance with the emitter´s band edge.

Quantitatively

Blanter and Buttiker, PRB 59, 10217 (1999)

( )

( )UQJ

Ce

eJ

F

R

∂Γ∂

≡≡Λ

Γ∆Γ−Λ

+=

hh 2

2

2

2

21

Self-consistent calculation of charging effects reveals multi-stability of current and leads to enhancement of shot noise.

Jh response of current to change in potential of the well

Superlattice Tunnel DiodeSuperlattice Tunnel Diode

Current starts to flows when small bias is applied.

Superlattices form minibands of bandwidth ∆.

When applied voltage is large enough, the minibands’energygap at the collector blocks tunneling and current drops.

Charge does not accumulate in STD.

Shot Noise in Superlattice Tunnel DiodeShot Noise in Superlattice Tunnel Diode

0 50 100 150 200 250 3000

5

10

Cur

rent

(µA

)

0 50 100 150 200 250 300

1

2

Voltage (mV)

Superlattice Tunnel Diode

Fano

fact

or

Sample: Central barrier: 102ÅGaAlAs Electrodes: 50 GaAs/GaAlAs periods, each 42 Å / 23ÅFano factor is constant (=1) throughout the applied voltage range.

Throughout positive and negative differential conductance regions, shot noise does not show either enhancement or reductionfrom Poissonian noise.

Song et al., Appl. Phys. Lett. 82, 1568 (2003)

ConclusionConclusion

Shot-noise measurements can tell whether there is significant quantum-state occupation and net charge accumulation during transport process, in which case the noise power spectrum is non-Poissonian, that is, different from S = 2eI.

References:Shot Noise Enhancement in Resonant Tunneling Structures in a Magnetic Field,

V. V. Kuznetsov, E. E. Mendez, J. D. Bruno, and J. T. Pham, Phys. Rev. B 58, R10159 (1998).Shot Noise in Negative-Differential-Conductance Devices, W. Song, E. Mendez, V. V. Kuznetsov, and B. Nielsen, Appl. Phys. Lett. 82, 1568 (2003).

Quantum Heterostructures Group: A Research OverviewIntroductionQuantum -Well MicrocavityTuning Resonance ConditionReflectivity of a Quantum-Well-MicrocavityHow to Enhance Rabi Splitting?Reflectivity of Superlattice-MicrocavityReflectivity of Superlattice-MicrocavityReflectivity of Superlattice-MicrocavityPhotocurrent from Superlattice MicrocavitySummary of Rabi SplittingsConclusionInAs/AlSb/GaSb SystemInAs/AlSb/GaSb Type II QWsVertical Shubnikov - de Haas OscillationsMagnetotunneling between 2D GasesIn-plane Momentum Conservation?Comparison Between Theory and ExperimentHigh-field Magnetotunneling