Density tuning of one-dimensional Density tuning of one-dimensional electron gaselectron gas

in a doped T-shaped quantum wirein a doped T-shaped quantum wire( ( studied by photoluminescence-studied by photoluminescence-

excitation spectraexcitation spectra ) )Toshiyuki IharaToshiyuki Ihara, Masahiro Yoshita, Hidefumi Akiyama, Masahiro Yoshita, Hidefumi AkiyamaLoren N. Pfeiffer, Ken W. WestLoren N. Pfeiffer, Ken W. West

Institute for Solid State Physics, University of Tokyo, and CREST, JST, JapanInstitute for Solid State Physics, University of Tokyo, and CREST, JST, JapanBell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 0797Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 0797

44

’’07 5/807 5/8 　　 QTuL4QTuL4 　　 @ Q@ QELSELS

OutlineⅠ 　 Introduction / Sample / Optical setup

Ⅱ 　 Results for high-density 1D electron gasⅢ 　 Results for electron-density dependencesⅣ 　 Summary

Introduction : Low-dimensional electron systems in Introduction : Low-dimensional electron systems in semiconductorsemiconductor

VkCk

kk ffEI 1

Vk

Ck

kk ffEA 1

1986 Asada et. al., IEEE J. Quantum Electron.

Sharp density of states (DOS)Quantum (Fermi / Bose) statistics

Many-body effect (Exciton, Trion, FES, BGR)

Interests in Fundamental physics and Applications in Low-dimensional system

Quantum wire Laser diodeM. Okano et al., App. Phys. Lett. 90, 091108 (2007).S. Liu et al., Jpn. J. Appl. Phys. 46, L330 (2007).

Early works of experiments on Low-dimentional electron systemsEarly works of experiments on Low-dimentional electron systems2D electron system

Density-tuning of 2DEG by gate Absorption measurements Interesting physics

1D electron system

’91 J. M. Calleja, SSC

’01 D. Y. Oberli, Physica E

’02 H. Akiyama, SSC

1D FES effect

1D BGR effect

’87 M. S. Skolnick, PRL

’93 K. Kheng, PRL

’99 V. Huard, PRL

’00 R. Kaur, PSS(b) [1]

’02 T. Ogawa, Nonlinear Opt.

Fermi edge singularity (FES)

Trions (Charged excitons)

evolution from trions to FES

calculations (FES theory)

sample growthoptical measurement

High-quality single quantum wire Density-tuning of 1DEG by gate Absorption measurements

< Targets of our investigation >

Experimental Difficulties in

Small number ofexperimental works

[1]

FES

Excitons (X)

Trions (X-)

Band-to-Band

recombination

Ele

ctro

n d

ensi

ty

high

low

T-wire fabricated by Cleaved edge overgrowth T-wire fabricated by Cleaved edge overgrowth methodmethod

＜ wire size ＞

14 x 6nm x 4mm (single)

＜ doping [2] ＞

①Si modulation doping②gate electrode　　　→ tunable density

Epitaxy was done by Dr. L. N. Pfeiffer in Lucent-Bell lab in U.S.

① ② ③ ④

[1] M. Yoshita, H. Akiyama, L. N. Pfeiffer, and K. W. West, Jpn. J. Appl. Phys. 40, L252 (2001).[2] H. Akiyama, L. N. Pfeiffer, A. Pinczuk, K. W. West, and M. Yoshita, Solid State Commun. 122, 169 (2002).

[1]

Optical setupOptical setup

Point 1 keep excitation power stablePoint 2 set excitation and detection　　　　　 perpendicular to each other

PLE measurement on a ground state of a single T-wire

Point 3 　 set the sample angle tilted and cut laser scattering by iris Point 4 　 set polarization of excitation and detection perpendicular to each other

PL (photoluminescence)PLE (PL-excitation)

- emission- absorption

We succeeded

Results for high-density 1D electron gasResults for high-density 1D electron gas

5K

We observed PL peak at Band edge and PLE onset at Fermi edge

Exc.

Pex = 40W

Small hole density

Estimation of carrier temperature from PL/PLE Estimation of carrier temperature from PL/PLE ratioratio

We observed PL peak at Band edge and PLE onset at Fermi edge

Estimated temperature : 9.8±0.5K （ kBT

～ 1meV ）

Sawicki et al., Phys. Rev. A54, 4837 (1996).

Chatterjee et al., Phys. Rev. Lett. 92, 067402 (2004).

TkA

I

B

exp

We observed PL peak at Band edge and PLE onset at Fermi edge

Estimation of electron density by free-particle model Estimation of electron density by free-particle model calculationcalculation

Estimated density : 6x105 cm-1 　（ Ef

～ 5meV ）

VkCk

kk ffEI 1

Vk

Ck

kk ffEA 1

Pronounced FES effect was NOT observed

Ef/kBT ～５Estimated temperature : 9.8±0.5K （ kBT

～ 1meV ）

Asada et. al., IEEE J. Quantum Electron.

(1986)

0067.0 mme 0105.0 mmh

Temperature dependence of Temperature dependence of ＰＬ ＰＬ and and ＰＬＥ ＰＬＥ at 0.7Vat 0.7V

tem

pera

ture

high

low

We observed Signature of 1D DOS singularity at Band-edge absorption peak

T=5K (Ef/kBT ～ ５ )

PLE onset at Fermi edge (FE)

T=50K (Ef/kBT ～ 1)

sharp PLE peak at Band edge (BE)

Good agreement with calculations.Characteristic of 1D systems.

Gate-voltage dependences at 5KGate-voltage dependences at 5K

Gate

volt

age

high

low

Estimated density : 6x105 cm-1 　（ Ef

～ 5meV ）

Non-doped limit at Zero 　 density （ Ef

～ 0meV ）

Gate-voltage dependences at 5K (0.7 - 0.5 Gate-voltage dependences at 5K (0.7 - 0.5 V)V) Red shifting PLE onset at Fermi

edge

Red shift of Fermi edge Decrease of Electron density

Gate-voltage dependences at 5K (0.4 - 0.35 Gate-voltage dependences at 5K (0.4 - 0.35 V)V)Characteristic double peak

structure

We observed Characteristic double peak PLE structure with Band edge and Fermi edge

Gate-voltage dependences at 5K (0.3 – 0 V)Gate-voltage dependences at 5K (0.3 – 0 V) Crossover to excitonic regime (Vg < 0.2V) from band-to-band recombination regime (Vg > 0.3V) Analogous to the results for 2D electron systems [’99 V. Huard, PRL, '00 R. Kaur, PSS(b), '02 T. Ogawa, Nonlinear Opt. ]

Gate-voltage dependences at 5K (0.3 – 0 V)Gate-voltage dependences at 5K (0.3 – 0 V)

PLE at 0V is consistent with that of non-doped quantum wire [ Itoh et al., APL 83, 2043 (2003). ] 0V corresponds to Limit of non dope (zero density)

Splitting of X should be due toML fluctuations of stem well

Crossover to excitonic regime (Vg < 0.2V) from band-to-band recombination regime (Vg > 0.3V) Analogous to the results for 2D electron systems [’99 V. Huard, PRL, '00 R. Kaur, PSS(b), '02 T. Ogawa, Nonlinear Opt. ]

Comparison whole experimental results with Comparison whole experimental results with calculationscalculations

ne=3x105cm-1 ～ 2.5x105cm-1

Non-degenerated 1D electron gas (Ef/kBT < 2)Double peak induced by 1D DOS

ne < 1.5x105cm-1

Limit of non dope (zero density)

Signature of 1D DOS singularity also appears in the characteristic double peak structure at 0.35-0.4V !!

Ele

ctro

n d

ensi

ty

high

low

Vg = 0.7 - 0.4 V

ne=6x105cm-1 ～ 3x105cm-1

Degenerated 1D electron gas (Ef/kBT > 2)Vg = 0.4 - 0.35

V

Vg < 0.2 V

Differences between 2D and 1D systemsDifferences between 2D and 1D systems2D electron system

Density-tuning of 2DEG by gate PL and PLE measurements Interesting physics

1D electron system’87 M. S. Skolnick, PRL

’93 K. Kheng, PRL

’99 V. Huard, PRL

’00 R. Kaur, PSS(b) [1]

’01 G. Yusa, PRL

strong FES

charged exciton (Trions)

evolution from trions to FES

Trions with Fractional QHE

[1]

FES

Excitons (X)

Trions (X-)

Band-to-Band

recombination

Ele

ctro

n d

ensi

ty

high

low

Signature of 1D DOS singularity

Unique feature of High-quality1D electron systems

Characteristic double peak structure with

band edge and Fermi edge

SummarySummary

Variable-density 1D electron gas was realized

in a T-shaped quantum wire with a gate structure.

PLE measurements on a 1D ground states

were achieved on an isolated single quantum wire.

We observed a signature of 1D DOSrepresented by an absorption peak at the band

edge,which indicates a high uniformity of our sample.

The tunable density range covers from 0 to 6x105cm-1

Future investigation

Remove ML fluctuations in the stem well ( ～ 0.2meV) Measurements at much lower temperature (T ＜ 5K) Measurements under magnetic field (B ～ 10T)

PLE measurement on ground states absorption PLE measurement on ground states absorption peakpeak

The amount of laser scattering is smaller than that of PL

We can set the PLE window for the ground state emission !!

M. S. Skolnick et al., Phys. Rev. Lett. 58, 2130 (1987).M. S. Skolnick et al., Phys. Rev. Lett. 58, 2130 (1987). PL of doped InGaAs quantum wells at various Temperature

Observation of strong FES effects

K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993).K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993). Absorption of dilute-doped CdTe quantum wells

under magnetic field

Observation of negatively charged excitons

V. Huard et al., Phys. Rev. Lett. 84, 187 (1999).V. Huard et al., Phys. Rev. Lett. 84, 187 (1999). Absorption of doped CdTe wells at various density

under magnetic field

Observation of crossover from X- to FES

R. Kaur et al., Phys. Status Solidi B 178, 465 (20R. Kaur et al., Phys. Status Solidi B 178, 465 (2000).00).

PLE spectra on doped GaAs quantum wells with a gate

Density-tuning of 2DEG by gate PLE measurements

J. M. Calleja et al., Solid State Commun. 79, 911 (199J. M. Calleja et al., Solid State Commun. 79, 911 (1991).1).

PL and PLE spectra on doped GaAs quantum wires

Investigation of 1D FES effects

D. Y. Oberli et al., Physica E 11, 224 (2001).D. Y. Oberli et al., Physica E 11, 224 (2001). PL and PLE spectra on doped V-groove quantum

wires

FES effect can be strong due to extrinsic origin such as higher subband, hole localization.

H. Akiyama et al., Solid State Commun. 122, 169 (200H. Akiyama et al., Solid State Commun. 122, 169 (2002).2).

PL spectra on single doped T-wire at various density

Investigation of 1D BGR effects

M. Yoshita et al., Jpn. J. Appl. Phys. 40, L252 (20M. Yoshita et al., Jpn. J. Appl. Phys. 40, L252 (2001).01).

Succeeded to improve the uniformity of the second QW (Arm well)

S. Chatterjee et al., Phys. Rev. Lett. 92, 067402 (2004).S. Chatterjee et al., Phys. Rev. Lett. 92, 067402 (2004). time-resolved PL spectra in conjunction with absorption spectra

multi (20) quantum wells non-doped system pulse excitation non-resonant excitation (13.6meV higher energy)

H. Itoh et al., App. Phys. Lett. 83, 2043 (2003).H. Itoh et al., App. Phys. Lett. 83, 2043 (2003).

X

0V is consistent with the results for non-doped quantum wire

Abstract figure 2 : results for the 1D wireAbstract figure 2 : results for the 1D wire

PL and PLE spectra for doped T-wire at 0.7V and 0V

Abstract figure 3 : results for the 2D Arm wellAbstract figure 3 : results for the 2D Arm well

PL and PLE spectra for Arm well at 0.8V and 0.2V

Characterization Characterization ～ ～ PL and PLE spectra PL and PLE spectra overviewoverview

A clear PLE peak of wire ground state

stokes shift ＜ 0.2meV

We assigned the peaks by PL and PLE measurement at various position

Free particle model calculation (C-V Free particle model calculation (C-V expression)expression)

VkCk

kk ffEI 1

Vk

Ck

kk ffEA 1

0067.0 mme

0105.0 mmh

/11 D

''1'0 1 dBffI VC

D

''1'0 1 dBffA VC

D

VC

e

CC m

k

2

22

h

VV m

k

2

22

1/exp1 Tkf BCCCC

1/exp1 Tkf BVVVV

2

2'exp'

B

VC kk

1D DOS, Effective mass approximation, k-conservation

Fermi distribution functions, Carrier densities

Broadening functions

0 1 dfn i

Di VCi ,

Free particle model calculation (e-h expression)Free particle model calculation (e-h expression) VkC

kk

k ffEI 1

Vk

Ck

kk ffEA 1

0067.0 mme

0105.0 mmh

/11 D

'''0 1 dBffI he

D

''11'0 1 dBffA he

D

he

e

ee m

k

2

22

h

hh m

k

2

22

1/exp1 Tkf Beeee

1/exp1 Tkf Bhhhh

2

2'exp'

B

he kk

1D DOS, Effective mass approximation, k-conservation

Fermi distribution functions, Carrier densities

Broadening functions

0 1 dfn i

Di VCi ,

Processing on T-shaped quantum wireProcessing on T-shaped quantum wire