Henini M. Handbook of Self Assembled Semiconductor Nanostructures for Novel devices in Photonics and Electronics
Подождите немного. Документ загружается.
Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 469
2100
QD1
X
X
(a) (b)
QD2
X X
X
X
X2
X2
2076
2074
2072
2070
2068
2066
2064
2062
2098
V
A1
CdTe
i-ZnTe
p-ZnTe
E
F
D
SS
2096
2094
2092
2090
2088
8 4 4 20246 810
Bias voltage (V)
QD3
PL intensity. (arb. units)
Energy (meV)
E
ex
2147 meV & 2412 meV
E
ex
2147 meV
E
ex
2412 meV
X
2
x 10
2074
2076 2078 2080 2082
Ener
g
y (meV)
2084 2086
2088
X
X
X
048
Bias voltage (V)
(c)
Figure 14.15 Colour-scale plot of the photoluminescence intensity of a non-magnetic QD (a) and a single
Mn-doped QD (b) in a Schottky structure as a function of emission energy and bias voltage. The series of emission
lines can be assigned to QD s-shell transitions, namely the recombination of the neutral exciton ( X ), biexciton ( X
2
),
positively charged exciton ( X
) and negatively charged exciton ( X
). (c) Details of the PL of a single Mn-doped QD
under resonant excitation (E
ex
2147 meV), non-resonant excitation ( E
ex
2412 meV) and both resonant and
non-resonant excitation.
CH014-I046325.indd 469CH014-I046325.indd 469 6/27/2008 4:30:05 PM6/27/2008 4:30:05 PM
470 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
At zero bias, excess electrons can also be injected in the QD using resonant optical excitation
into the QD levels. Under resonant excitation (energy below the band gap of the barriers), opti-
cal transitions from delocalized valence band states to the confi ned electron levels will preferen-
tially create electrons in the QD [64] : the probability of fi nding an excess electron in the QD is
increased. As presented in Fig. 14.15c , the negatively charged exciton emission is then seen for
some discrete excitation energies. After the recombination of the charged exciton X
, a single
hole is likely to be captured to neutralize the QD and create a neutral exciton. This neutraliza-
tion process is responsible for the simultaneous observation of charged and neutral species under
resonant excitation ( Fig. 14.15c ).
The charge state of the dot can also be optically tuned ( Fig. 14.15c ). By combining a weak
non-resonant excitation with the resonant one, a few carriers are created in the ZnTe barrier.
They do not signifi cantly contribute to the luminescence (lower PL spectra in Fig. 14.15c ) but
reduce the PL contribution of X
in favour of the neutral species. This evolution is character-
istic of a photo-depletion mechanism in modulation-doped QDs [54] . High-energy photoexcited
e–h pairs are dissociated in the space charge region surrounding the negatively charged QDs and
neutralize the QDs.
These two charge control mechanisms (bias voltage and resonant excitation combined with
photo-depletion) allow the interaction between individual carriers (electron or hole) and an indi-
vidual magnetic atom to be independently probed. Let us fi rst consider the negatively charged
exciton. Figure 14.16a presents detail of the recombination spectrum for X
coupled with a sin-
gle Mn atom obtained at zero bias under resonant excitation. Eleven emission lines are clearly
observed with intensity decreasing from the outer to the inner part of the emission structure.
PL intensity (arb. units)
2079207820772076
Energy (meV)
(a)
(b)
E
PL
(c)
j
z
3/2
σ
z
1/2
S
z
5/2
5/2
J 2
J 3
3
3
3
3
3
3
2
2
2
2
2
2
Figure 14.16 (a) Detail of the unpolarized emission spectrum of a negatively charged exciton ( X
) coupled with an
Mn atom. (b) Scheme of the σ optical transitions of ( X
, Mn) and their respective PL intensity distribution (c).
A simple effective spin Hamiltonian quantitatively accounts for the emission spectrum shown
in Fig. 14.16a . The emitting state in the X
transition has two conduction band (CB) electrons
and one hole coupled to the Mn. The effect of the two spin-paired electrons on the Mn is strictly
zero. Thereby, the spin structure of the X
state is governed by the interaction of the hole with
the Mn. Based upon the results presented in section 14.3, we propose the following Hamiltonian:
H
ε
hMn h zz
ISj jS jS
2
()
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
(14.9)
CH014-I046325.indd 470CH014-I046325.indd 470 6/27/2008 4:30:07 PM6/27/2008 4:30:07 PM
Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 471
where S
is the Mn spin operator and j
acts on the hole’s lowest energy doublet. The fi rst term
is the spin conserving or Ising exchange whereas the second is only possible if there are some
heavy–light hole mixing [49, 65] . From our measurements we fi nd that ε is small and, in a fi rst
stage, we neglect it. Later we will show its infl uence. The 12 eigenstates of H
h
Mn
with ε 0 are
organized as six doublets ( Fig. 14.16b ) with well-defi ned S
z
and j
z
(Mn and hole spin along the
z -axis). We label these states as S
z
, j
z
. Recombination of one of the CB electrons with the hole of
the X
state leaves a fi nal state with a single CB electron coupled to the Mn. The spin Hamiltonian
of this system is the ferromagnetic Heisenberg model,
H
eMn e
e
IS
σ
. The 12 eigenstates of
the Mn–electron complex are split into a ground state septuplet (total spin J 3) and a fi ve-fold
degenerate manifold with J 2. We label them all as J , J
z
.
Thereby, for each of the six doublets of X
there are two possible fi nal states after annihila-
tion of an e–h pair, with either J 2 or J 3. From this consideration alone, we would expect
12 spectrally resolved lines. Their weight is given by both optical and spin conservation rules.
Since electrons and holes reside in s and p bands, respectively, the Δ L 1 optical selection rule
is immediately satisfi ed. The polarization of the photon imposes an additional selection rule on
Δ M which is accounted for by the spin of the electron and hole. The Mn spin is not affected by
the transition.
The weight of optical transitions between the initial state i
( ↑ , ↓ )
e
S
z
, j
z
and the fi nal
state f
J , J
z
is proportional to
|| ||〈∑ 〉fPjcdi
zj
z
σσ
σ(, )
2
, where c
σ
annihilates a CB electron
with spin σ , and d
jz
annihilates a VB hole with angular momentum j
z
. Here P ( σ , j
z
) is given by the
polarization selection rule.
Let us consider, for instance, σ recombination transitions where the
( ↓
e
, ⇑
h
)
e–h pair is anni-
hilated. Each of the six doublets, characterized by their Mn spin projection S
z
, can be an initial
state. After the electron–hole annihilation, the resulting state is S
z
, ↑
e
which, in general, is not
an eigenstate of H
e,Mn
. The intensity of the optical transition to a given fi nal state J , Jz
is propor-
tional to the overlap J , J
z
S
z
, ↑
e
, which is nothing but a Clebsh–Gordan coeffi cient. The highest
energy transition, with σ polarization, would correspond to the initial state
(, ) | ,↑↓ ⇑
eh
52/
and a low energy fi nal state J 3 , J
z
. After the photon emission, the state of the system is
S
z
5/2, ↑
e
which is identical to J 3 , J
Z
3
and thereby gives the highest optical weight
( Fig. 14.16b ). In contrast, emission from that initial state to J 2 , J
z
is forbidden. The other fi ve
doublets have optical weights lying between 1/6 and 5/6 with both J 2 , J
z
and J 3 , J
z
fi nal
states. Thereby, the number of spectrally resolved lines in this model is 11.
The relative weight of the emission lines is accounted for by the model. According to the fi nal
state, the transitions belong to either the J 2 or the J 3 series. As the initial S
z
decreases, the
overlap of ↑
e
S
z
to the J 3 ( J 2) states decreases (increases). As presented in Fig. 14.16c , the
PL of X
can be seen as a superposition of two substructures: six lines with intensities increasing
with their energy position (transitions to J 3 states) and fi ve lines with intensities decreasing
with increasing their energy position (transitions to J 2 states).
Reversing the role of the initial and fi nal states, and neglecting the small coupling of two holes
to the Mn spin [74] , this model should account for the emission from X
states. Actually, differ-
ent energy splittings are observed for the different excitonic species in the same QD. For instance,
in QD3 ( Fig. 14.15c ) one measured Δ E
X
1 . 2 3 m e V, Δ E
X
1.36 meV and Δ E
X
0 . 9 5 m e V.
The energy splitting is mostly due to the Mn–hole exchange coupling, which in turn is inversely
proportional to the volume of the hole wave function. The difference between Δ E
X
and Δ E
X
indicates that a signifi cant fraction of the confi nement of the hole comes from the Coulomb
attraction of the two electrons in the initial state of the X
emission. In contrast, in the fi nal state
of the X
emission, there is no electron to attract the hole, resulting in a spread of the hole wave
function and a smaller exchange energy. This difference appears directly in the emission struc-
ture shown in Fig. 14.15 , where the peak structure of X
is not well resolved.
In Fig. 14.17a we show the intensity of X
emission as a function of the direction of a linear
analyser. It is apparent that the central lines are linearly polarized. This polarization can only be
understood if we allow for some spin–fl ip interaction between the Mn and the hole (second term
in Eq. 14.9 ). Provided that ε 1, the effect of this interaction is small both on the wave function
and on the degeneracy of all the doublets except the third, which is split, as illustrated in the inset
of Fig. 14.17 . The split states are the bonding and antibonding combinations of S
z
1/2, ⇑
h
CH014-I046325.indd 471CH014-I046325.indd 471 6/27/2008 4:30:08 PM6/27/2008 4:30:08 PM
472 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
and S
z
1/2, ⇓
h
. These states are coupled, via linearly polarized photons, to the 2 , 0
and
3 , 0
e–Mn complex and four linearly polarized lines should be observed on the emission spectra
as shown in the insets of Fig. 14.17c and d . Polarization directions are controlled by the distribu-
tion of strains through the Bir–Pikus Hamiltonian [65, 76] .
We can obtain numerical values of I
h
, I
e
and ε for the charged excitons comparing the tran-
sition probabilities calculated with model (14.9) ( Fig. 14.17c ) to the experimental data. The
electron–Mn exchange integral I
e
is deduced from magneto-optics measurements on the neutral
exciton [4] . I
h
, the hole–Mn exchange integral, is then chosen to reproduce the overall splitting of
the two charged species ’ emission structure. There is a good agreement between the experimental
150
(a) (b)
Linearly Polarized angle (°)
100
50
0
2077
2078
Energy (meV) Energy (meV)
2079 2080 2081
PL intensity (arb. units)
1.0 0.5 0.5
0.0 0.00.5 0.5 1.0
h–Mn
h–Mn
h–Mn
No VBM
E
e–Mn
(c)
(d)
e–Mn
Ener
g
y (meV) Ener
g
y (meV)
With VBM
π
x
π
x
π
y
π
y
Figure 14.17 Colour scale plot of the dependence of the PL of ( X
, Mn) (a) and ( X
, Mn) (b) on the direction of a
linear analyser, in the same QD. Three lines in the centre of the structure are linearly polarized. (c) and (d) Calculated
linearly polarized PL spectra of ( X
, Mn) and ( X
, Mn) with exchange integrals I
e
and I
h
chosen to reproduce the
overall splitting for X
and X
presented in (a) and (b). Transitions are arbitrarily broadened by 10 μ eV. The schemes
in (c) and (d) show energy levels involved in ( X
, Mn) and ( X
, Mn) recombination with valence band mixing. The
central inset presents the energy level scheme of the h–Mn system without and with valence band mixing (VBM).
CH014-I046325.indd 472CH014-I046325.indd 472 6/27/2008 4:30:09 PM6/27/2008 4:30:09 PM
Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 473
data (QD3 in Fig. 14.15c ) and our model with I
e
4 0 μ eV, I
h
( X ) 1 5 0 μ eV, I
h
( X
) 9 5 μ eV and
I
h
( X
) 1 7 0 μ eV. The different values of I
h
directly refl ect the expected variation of the confi ne-
ment of the hole. The main characteristics of the emission spectra are well reproduced, namely
the number of emission lines, their intensity distribution and the linear polarization structure,
with a slight valence band mixing coeffi cient ε 0.05. This small value of the valence band mix-
ing coeffi cient shows that hole–Mn exchange interaction remains highly anisotropic.
14.6 Conclusion
Let’s recall that the precise control of electronic spins in semiconductors is a very active fi eld
nowadays, the so-called spintronics, which needs, besides the potential applications, to have a
deep insight of the effects which combine manipulation of charges and manipulation of spins.
Among this large activity, the development of techniques for optical control of single spins in the
solid state is motivated by the possibility of using single spins embedded in nanostructures for
the implementation of quantum information processing devices. These devices will require the
detection and manipulation of individual spins and ensure their interaction with the semicon-
ductor carriers. However, in such a nanometre-size system, it is important to tune independently
the quantum dot charge states and the magnetic doping in order to elucidate the interactions
with the different charge carriers.
Quantum dots made of a II–VI semiconductor (such as CdTe) in which manganese atoms
randomly substitute cadmium (Mn in II–VIs is an isoelectronic impurity, i.e. it is not electrically
active) allow the various confi gurations to be properly tuned. In particular we can study the case
of a single Mn atom interacting with an excess of one hole, which is the expected confi guration
in worldwide developed III–V semiconductor quantum dots.
We have shown that the injection of a controlled number of carriers in an individual II–VI QD
permits spin splitting of a single magnetic ion to be controlled. The exchange interaction with a
single carrier acts as an effective local magnetic fi eld that splits the Mn levels in a zero-applied
magnetic fi eld. We have fabricated a device with electrically tunable magnetic properties, in anal-
ogy with two-dimensional DMS-based electrically active heterostructures [7–9] , but scaling the
number of controlled magnetic atoms down to one and the size of the active region down to a
few nanometres. Micro-photoluminescence experiments permit the identifi cation of three mag-
netically different ground states corresponding to three charge states ( 1e and 0) and meas-
urement of the exchange interaction of both a single electron and a single hole with a single
magnetic atom. The fi nal state of ( X
, Mn) transition (1h,1Mn) is non-degenerate in the absence
of an external magnetic fi eld. This splitting of the different spin confi gurations should effi ciently
increase the spin relaxation time of both Mn and holes.
The observation of an individual spin in a quantum dot opens new possibilities in informa-
tion storage. The spin of an isolated Mn atom should present a relaxation time in the millisecond
range. This property could be exploited to store digital information on a single atom. The device
presented here is a fi rst step towards the development of new memories in which an information
digit would be stored on the spin state of an individual atom.
Acknowledgements
The authors like to acknowledge Prof. Joaquim Fernandez–Rossier (Univ. Alicante) for his theo-
retical support in the interpretation of the electrical control data.
References
1. H.C. Manoharan , C.P. Lutz , and D.M. Eigler , Nature 403 , 512 ( 2000 ) .
2. P. Gambardella , S. Rusponi , M. Veronese , S.S. Dhesi , C. Grazioli , A. Dallmeyer , I. Cabria , R. Zeller ,
P.H. Dederichs , K. Kern , C. Carbone , and H. Brune , Science 300 , 1130 ( 2003 ) .
3. A.M. Yakunin , A.Yu. Silov , P.M. Koenraad , J.-M. Tang , M.E. Flatte , W.V. Roy , J.D. Boeck , and
J.H. Wolter , Phys. Rev. Lett. 92 , 216806 ( 2004 ) .
CH014-I046325.indd 473CH014-I046325.indd 473 6/27/2008 4:30:10 PM6/27/2008 4:30:10 PM
474 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
4. L. Besombes , Y. Leger , L. Maingault , D. Ferrand , H. Mariette , and J. Cibert , Phys. Rev. Lett. 9 3 ,
207403 ( 2004 ) .
5. A.J. Heinrich , A. Gupta , C.P. Lutz , and D.M. Eigler , Science 306 , 466 – 469 , ( 2004 ) .
6. F. Jelezko , T. Gaebel , I. Popa , A. Gruber , and J. Wrachtrup , Phys. Rev. Lett. 92 , 076401 ( 2004 ) .
7. H. Ohno , D. Chiba , F. Matsukura , T. Omiya , E. Abe , T. Dietl , Y. Ohno , and K. Ohtani , Nature 408 ,
944 ( 2000 ) .
8. H. Boukari , P. Kossacki , M. Bertolini , D. Ferrand , J. Cibert , S. Tatarenko , A. Wasiela , J.A. Gaj , and
T. Dietl , Phys. Rev. Lett. 88 , 207204 ( 2002 ) .
9. D. Chiba , M. Yamanouchi , F. Matsukura , and H. Ohno , Science 301 , 943 ( 2003 ) .
10. Al.L. Efros , E.I. Rashba , and M. Rosen , Phys. Rev. Lett. 87 , 206601 ( 2001 ) .
11. A.O. Govorov and A.V. Kalameitsev, Phys. Rev. B 71 , 035338 (2005). A.O. Govorov, ibid. 72 ,
075359 (2005).
12. J.I. Climente, M. Korkusinski, P. Hawrylak, and J. Planelles, Phys. Rev. B 71 , 125321 (2005);
F. Qu and P. Hawrylak, Phys. Rev. Lett. 95 , 217206 (2005); F. Qu and P. Hawrylak, ibid. 96 ,
157201 (2006).
13. J. Fernandez-Rossier and L. Brey , Phys. Rev. Lett. 9 3 , 117201 ( 2004 ) .
14. A.O. Govorov , Phys. Rev. B 72 , 075358 ( 2005 ) .
15. F. Qu and P. Hawrylak , Phys. Rev. Lett. 96 , 157201 ( 2006 ) .
16. A.V. Chernenko , P.S. Dorozhkin , V.D. Kulakovskii , A.S. Brichkin , S.V. Ivanov , and A.A. Toropov ,
Phys. Rev. B 7 2 , 045302 ( 2005 ) .
17. A.A. Maksimov , G. Bacher , A. McDonald , V.D. Kulakovskii , A. Forchel , C.R. Becker , G. Landwehr ,
and L.W. Molenkamp , Phys. Rev. B 6 2 , R7767 ( 2000 ) .
18. J. Seufert , G. Bacher , M. Scheibner , A. Forchel , S. Lee , M. Dobrowolska , and J.K. Furdyna , Phys.
Rev. Lett. 88 , 027402 ( 2002 ) .
19. G. Mackh , W. Ossau , D.R. Yakovlev , A. Waag , G. Landwehr , R. Hellmann , and E.O. Gobel , Phys.
Rev. B 4 9 , 10248 ( 1994 ) .
20. D.R. Yakovlev , K.V. Kavokin , I.A. Merkulov , G. Mackh , W. Ossau , R. Hellmann , E.O. Gobel ,
A. Waag , and G. Landwehr , Phys. Rev. B 5 6 , 9782 ( 1997 ) .
21. P.S. Dorozhkin , A.V. Chernenko , V.D. Kulakovskii , A.S. Brichkin , A.A. Maksimov , H. Schoemig ,
G. Bacher , A. Forchel , S. Lee , M. Dobrowolska , and J.K. Furdyna ,
Phys. Rev. B 6 8 , 195313 ( 2003 ) .
22. A. Hundt , J. Puls , and H. Henneberger , Phys. Rev. B 6 9 , 121309 ( 2004 ) .
23. G. Bacher , A.A. Maksimov , H. Schomig , V.D. Kulakovskii , M.K. Welsh , A. Forchel , P.S. Dorozhkin ,
A.V. Chernenko , S. Lee , M. Dobrowolska , and J.K. Furdyna , Phys. Rev. Lett. 89 , 127201 ( 2002 ) .
24. D.J. Norris , Nan Yao , F.T. Charnock , and T.A. Kennedy , Nanolett. 1 , 3 ( 2001 ) .
25. S.C. Erwin , L. Zu , M.I. Haftel , A.L. Efros , T.A. Kennedy , and D.J. Norris , Nature 436 , 91 ( 2005 ) .
26. A.K. Bhattacharjee and J. Perez-Conde , Phys. Rev. B 6 8 , 045303 ( 2003 ) .
27. P.I. Archer , S.A. Santangelo , and D.R. Gamelin , Nanolett. 7 , 1037 ( 2007 ) .
28. S. Mackowski , T. Gurung , H.E. Jackson , L.M. Smith , G. Karczewski , and J. Kossut , Appl. Phys. Lett.
87 , 072502 ( 2005 ) .
29. J.K. Furdyna , J. Appl. Phys. 64 , R29 ( 1998 ) .
30. Semiconductors and Semimetals , vol. 25 , ed. by J.K. Furdyna and J. Kossut ( Academic , Boston ,
1988 ) .
31. J. Schneider , U. Kaufmann , W. Wilkening , M. Baeumler , and F. Kohl , Phys. Rev. Lett. 59 , 240 ( 1987 ) .
32. M. Linnarsson , E. Janzn , B. Monemar , M. Kleverman , and A. Thilderkvist , Phys. Rev. B 5 5 , 6938
( 1997 ) .
33. J.A. Gaj , W. Grieshaber , C. Bodin , J. Cibert , G. Feuillet , Y. Merle d’Aubigne , and A. Wasiela , Phys.
Rev. B 50 , 5512 ( 1994 ) .
34. Y. Shapira , S. Foner , D.H. Ridgley , K. Dwight , and A. Wold , Phys. Rev. B 30 , 4021 ( 1984 ) .
35. J.M. Fatah , T. Piorek , P. Harrison , T. Stirner , and W.E. Hagston , Phys. Rev. B 49 , 10341 ( 1994 ) .
36. W. Grieshaber , A. Haury , J. Cibert , Y. Merle d’Aubigne , A. Wasiela , and J.A. Gaj , Phys. Rev. B 5 3 ,
4891 ( 1996 ) .
37. J.A. Gaj , R. Planel , and G. Fishman , Solid-State Commun. 29 , 435 ( 1979 ) .
38. A. Twardowski , P. Swiderski , M. von Ortenberg , and R. Pauthenet , Solid-State Commun. 5 0 , 509
( 1984 ) .
39. W. Pacuski , D. Ferrand , J. Cibert , C. Deparis , J.A. Gaj , P. Kossacki , and C. Morhain , Phys. Rev.
B 73 , 035214 ( 2006 ) .
CH014-I046325.indd 474CH014-I046325.indd 474 6/27/2008 4:30:10 PM6/27/2008 4:30:10 PM
Probing and Controlling the Spin State of Single Magnetic Atoms in an Individual Quantum Dot 475
40. J.M. Hartmann , J. Cibert , F. Kany , H. Mariette , M. Charleux , P. Alleyson , R. Langer , and G. Feuillet ,
J. Appl. Phys. 80 , 6257 ( 1996 ) .
41. J. Cibert , Y. Gobil , Le Si Dang , S. Tatarenko , G. Feuillet , P.H. Jouneau , and K. Saminadayar , Appl.
Phys. Lett. 56 , 292 ( 1990 ) .
42. S.H. Xin , P.D. Wang , A. Yin , C. Kim , M. Dobrowolska , J.L. Merz , and J.K. Furdyna , Appl. Phys. Lett.
69 , 3884 ( 1996 ) .
43. Y. Terai , S. Kuroda , K. Takita , T. Okuno , and Y. Masumoto , Appl. Phys. Lett. 73 , 3757 ( 1998 ) .
44. F. Tinjod , I.C. Robin , R. Andre , K. Kheng , and H. Mariette , J. Alloys Comp. 371 , 63 ( 2004 ) .
45. F. Tinjod , B. Gilles , S. Moehl , K. Kheng , and H. Mariette , Appl. Phys. Lett. 82 , 4340 ( 2003 ) .
46. I.C. Robin , R. Andr , C. Bougerol , T. Aichele , and S. Tatarenko , Appl. Phys. Lett. 88 , 233103 ( 2006 ) .
47. F. Tinjod and H. Mariette , Phys. Status Solidi. B 241 , 550 ( 2004 ) .
48. R. Brazis and J. Kossut , Solid-State Commun. 122 , 73 ( 2002 ) .
49. J. Fernandez-Rossier , Phys. Rev. B 73 , 045301 ( 2006 ) .
50. G. Lentz , A. Ponchet , N. Magnea , and H. Mariette , Appl. Phys. Lett. 55 , 2733 ( 1989 ) .
51. J.M. Moison , C. Guille , F. Houzay , F. Barthe , and M. Van Rompay , Phys. Rev. B 40 , 6149 ( 1989 ) .
52. A.O. Govorov , Phys. Rev. B 70 , 035321 ( 2004 ) .
53. J. Seufert , M. Rambach , G. Bacher , A. Forchel , T. Passow , and D. Hommel , Appl. Phys. Lett. 8 2 ,
3946 ( 2003 ) .
54. A. Hartmann , Y. Ducommun , E. Kapon , U. Hohenester , and E. Molinari , Phys. Rev. Lett. 8 4 , 5648
( 2000 ) .
55. L. Maingault , L. Besombes , Y. Leger , C. Bougerol , and H. Mariette , Appl. Phys. Lett. 8 9 , 193109
( 2006 ) .
56. L. Besombes, K. Kheng, and D. Martrou, Phys. Rev. Lett. 85 , 425 (2000); id. J. Cryst. Growth 214
742 (2000).
57. I.A. Merkulov , D.R. Yakovlev , A. Keller , W. Ossau , J. Geurts , A. Waag , G. Landwehr , G. Karczewski ,
T. Wojtowicz , and J. Kossut , Phys. Rev. Lett. 83 , 1431 ( 1999 ) .
58. D. Keller , D.R. Yakovlev , B. Knig , W. Ossau , Th. Gruber , A. Waag , L.W. Molenkamp , and
A.V. Scherbakov , Phys. Rev. B 65 , 035313 ( 2001 ) .
59. D. Scalbert , J. Cernogora , and C. Benoit la Guillaume , Solid-State Commun.
66 , 571 ( 1988 ) .
60. W. Maslana , P. Kossacki , M. Bertolini , H. Boukari , D. Ferrand , S. Tatarenko , J. Cibert , and J.A. Gaj ,
Appl. Phys. Lett. 82 , 1875 ( 2003 ) .
61. S. Bhunia and D.N. Bose , J. Appl. Phys. 87 , 2931 ( 2000 ) .
62. L. Besombes , K. Kheng , L. Marsal , and H. Mariette , Phys. Rev. B 65 , 121314 ( 2002 ) .
63. K. Brunner , G. Abstreiter , G. Bohm , G. Trankle , and G. Weimann , Phys. Rev. Lett. 73 , 1138 ( 1994 ) .
64. A. Vasanelly , R. Ferreira , and G. Bastard , Phys. Rev. Lett. 89 , 216804 ( 2002 ) .
65. A.V. Koudinov , I.A. Akimov , Yu.G. Kusrayev , and F. Henneberger , Phys. Rev. B 7 0 , 241305
( 2004 ) .
66. F.V. Kyrychenko and J. Kossut , Phys. Rev. B 70 , 205317 ( 2004 ) .
67. Y. Léger , L. Besombes , L. Maingault , D. Ferrand , and H. Mariette , Phys. Rev. B 7 2 , 241309 ( 2005 ) .
68. Y. Léger , L. Besombes , J. Fernández-Rossier , L. Maingault , and H. Mariett e , Phys. Rev. Lett. 9 7 ,
107401 ( 2006 ) .
69. Y. Léger , L. Besombes , L. Maingault , and H. Mariette , Phys. Rev. B 76 , 045331 ( 2007 ) .
70. Y. Léger , L. Besombes , L. Maingault , D. Ferrand , and H. Mariette , Phys. Rev. Lett. 95 , 047403 ( 2005 ) .
71. V.D. Kulakovskii, G. Bacher, R. Weigand, T. Kummell, and A. Forchel, Phys. Rev. Lett. 82 , 1780
(1999); L. Besombes, K. Kheng, and D. Martrou, Phys. Rev. Lett. 85 , 425 (2000).
72. A. Kuther , M. Bayer , and A. Forchel , Phys. Rev. B 58 , R7508 ( 1998 ) .
73. J. Allègre , B. Gil , J. Calatayud , and H. Mathieu , J. Cryst. Growth 101 , 603 ( 1990 ) .
74. L. Besombes , Y. Leger , L. Maingault , D. Ferrand , H. Mariette , and J. Cibert , Phys. Rev. B 7 1 ,
161307 ( 2005 ) .
75. M.M. Glazov , E.L. Ivchenko , L. Besombes , Y. leger , L. Maingault , and H. Mariette , Phys. Rev. B 7 5 ,
205313 ( 2007 ) .
76. M. Tadic , F.M. Peeters , and K.L. Janssens , Phys. Rev. B 65 , 165333 ( 2002 ) .
77. U. Bockelmann and G. Bastard , Phys. Rev. B 45 , 1688 ( 1992 ) .
78. T. Tanaka , J. Singh , Y. Arakawa , and P. Bhattacharya , Appl. Phys. Lett. 62 , 756 ( 1993 ) .
79. S. Cortez , O. Krebs , and P. Voisin , J. Vac. Sci. Technol. B 18 , 2232 ( 2000 ) .
CH014-I046325.indd 475CH014-I046325.indd 475 6/27/2008 4:30:10 PM6/27/2008 4:30:10 PM
Quantum Dot Charge and Spin Memory Devices
Jonathan Finley
Walter Schottky Institut and Physik Department, Technische Universität München,
D-85748, Garching, Germany
15.1 Introduction
Conventional non-volatile semiconductor memories represent binary information by switching
the charge stored on a capacitor via a transistor. Each silicon-based capacitor–transistor subunit
constitutes one memory cell within a large and independently addressable array. These funda-
mental concepts for dynamic random access memories (DRAM) were patented in 1967 [1] and
introduced to the market a few years later by the Intel Corporation [2] . Over the 35 years since
the fi rst DRAM chips appeared, we have witnessed a seemingly relentless increase of the maxi-
mum integration density of Si-based memory and logic chips with minimum feature sizes reduc-
ing exponentially, from over 10 μ m in 1972 to less than 50 nm in the latest prototype memory
cells. This relentless trend towards miniaturization, and the seemingly self-fulfi lling prophecy
that has become known as Moore’s law [3] , shows little sign of abating despite minimum feature
sizes rapidly approaching lengthscales where quantum mechanical effects begin to dominate the
properties of the system. However, downscaling comes at the price of ever more stringent tol-
erances as lengthscales approach the limits of nanofabrication technologies. The ultimate non-
volatile memory cell would represent one bit of information by storing a single charge carrier on
a nanoscale capacitor [4] . Since conventional nanofabrication technologies are not yet able to
manufacture conventional DRAM cells with suffi ciently small dimensions, semiconductor quan-
tum dots (QDs) may offer an elegant and direct method to create huge ensembles of electronic
traps for single or very few carriers [5] .
Quantum dots are quasi zero-dimensional nanostructures that can localize charge carriers in
all three spatial directions to lengthscales comparable to their de Broglie wavelength. The effec-
tive three-dimensional confi nement potential can be created using one of many approaches. Two
of the most widely studied QD systems are formed either by modulating the chemical composi-
tion of the dot relative to its environment [6] or by electrostatically defi ning a potential minimum
within a two-dimensional quantum fi lm using metallic gates on the sample surface [7] . These
two types of QDs differ fundamentally in their ability to confi ne carriers: chemically defi ned dots
can simultaneously trap both electrons and holes and are, thus, optically active , while electro-
statically defi ned dots tend to trap only one charge polarity (usually electrons) and are optically
inactive . In this chapter we focus exclusively on optically active quantum dot nanostructures
and investigate their suitability as optically addressable charge and spin memory structures.
An inhomogeneously broadened ensemble of such QD-like absorbing centres has strong potential
for application as a wavelength domain optical data storage medium [8, 9] . Optical data storage
offers many advantages including the robustness associated with “ non-contact ” data access via a
CHAPTER 15
CH015-I046325.indd 476CH015-I046325.indd 476 6/24/2008 5:06:23 PM6/24/2008 5:06:23 PM
Quantum Dot Charge and Spin Memory Devices 477
laser, high data storage densities, non-volatility and fast read and write access [10] . Like memory
and logic chips, the technologies for optical data storage have downscaled rapidly from the fi rst
compact discs in the early 1980s to DVD discs, DVD-RW technologies that rely on phase change
media and now Blu-Ray discs operating at shorter wavelengths (405 nm, cf. 640 nm for DVD-
RW) [11] . However, the data storage densities of these conventional optical technologies are
defi ned by the diffraction limited size of the laser focal volume, which sets the area occupied by a
single bit of information. Moving to bit sizes below the diffraction limit will call for new concepts
such as wavelength domain [8] or holographic optical data storage concepts [12] .
In this chapter we review the use of self-assembled QD nanostructures for optical charge and
spin storage devices. After discussing the major physical, electronic and optical properties we
describe how single charges can be optically generated in QDs and illustrate some of the progress
over the past ten years. As we will see, while other materials may eventually emerge to be more
suitable for optical data storage, the methods developed provide a valuable tool to study funda-
mental properties of semiconductor QDs. We then continue to describe how the spin of optically
generated charges can be orientated by controlling the polarization of the light used to gener-
ate them. This approach provides a direct method to probe electron and hole spin relaxation in
self-assembled QDs – a topic with strong relevance for future spin-based quantum information
processing [13] .
15.1.1 Self-assembled quantum dots
Of the many types of QD materials for optical applications , nanoscale self-assembled islands
formed by a strain-driven self-assembly are among the most widely investigated. This epitaxial
growth mode is driven by the trade-off between strain and surface energies during heteroepitax-
ial growth of materials that have different lattice constants [14, 15] . Goldstein et al. were the fi rst
to report the observation of such island formation in a semiconductor system during the growth
of InAs–GaAs superlattices [16] . While initially being considered to be an undesirable side effect
of strained layer epitaxy, it was quickly realized that such nanoscale islands could be grown with-
out defects and, thus, could exhibit excellent optical properties. From the earliest studies of self-
assembled quantum dots, InAs grown on GaAs has remained one of the most important systems
for optical applications.
Due to the 7% lattice mismatch, InAs initially grows on GaAs as a highly strained two-dimen-
sional (2D) layer termed the wetting layer. This 2D growth mode continues until a thickness of
approximately one atomic layer whereupon the growth transforms from 2D–3D clustering of
islands, due to the reduction of the strain energy arising from island formation, which outweighs
the additional surface energy of the multifaceted crystal surface. The process gives rise to a series
of nano-sized islands that form on top of the underlying wetting layer as discussed in other chap-
ters in this volume. Figure 15.1a compares a typical atomic force microscopy image recorded from
uncapped self-assembled InAs QDs formed on GaAs with an atomic illustration of a single dot. For
In
x
Ga
(1
x
)
As self-assembled QDs grown on GaAs ( x ), typical heights are 2–8 nm with base
widths of the order of ~5–25 nm. A real densities of the nanostructures can be tuned in the range
10
9
–10
11
c m
2
(see Fig. 15.1a ) by controlling the growth conditions. After formation the islands
are overgrown by GaAs to form fully encapsulated QDs that are optically active.
15.1.2 Fundamental optical properties and single particle non-linearities
The confi nement lengthscales of self-assembled QDs is such that the electron and hole single par-
ticle states are fully quantized with a discrete density of states. Since the vertical ( z ) height of the
dots tends to be much larger than their lateral ( x, y ) dimensions as discussed above, the motion
along the vertical and lateral directions is largely decoupled: the strong vertical confi nement
tends to determine the effective band gap of the dots together with the strain, while the spectrum
of lowest lying single particle quantum states are representative of the effective lateral confi ne-
ment potential [17] . Within the QD research community these orbital states are often denoted
by the labels s, p, d, , , etc. in analogy to the orbital states of atoms, as depicted schematically
CH015-I046325.indd 477CH015-I046325.indd 477 6/24/2008 5:06:24 PM6/24/2008 5:06:24 PM
478 Handbook of Self Assembled Semiconductor Nanostructures for Novel Devices in Photonics and Electronics
Quantum dot
E
CB
VB
s-s p-p
d
(a)
(b)
Wetting layer
z
y
x
(X,Y)
s
s
p
p
d
200 nm
Figure 15.1 (a) Atomistic illustration and atomic force microscopy image of an uncapped ensemble of self-assembled
InGaAs quantum dots. In the illustration, the Ga and As atoms are green and yellow, respectively, while In atoms are
coded red. This image illustrates the typical random alloy composition of a self-assembled quantum dot – image repro-
duced with permission of M. Migliorato, University of Manchester, UK. (b) Schematic representation of the discrete
orbital electronic structure in the conduction and valence bands of a self-assembled QD. Only the lateral confi nement
potential is depicted since the vertical confi nement tends to be much stronger due to the smaller spatial extent of the
QDs and the principal quantum number associated with vertical motion is identical for the lowest lying orbital states.
in Fig. 15.1b . However, one should appreciate that the real symmetry of the envelope wavefunc-
tions is lower than real atoms due to the effects of inhomogeneous composition and shape of
the dots and piezoelectric potentials. The energy separation of the orbital states lies in the range
ω
sp
e
10 −meV
for electrons and
ω
sp
h
5 −meV
for holes, depending on the microscopic
details of the effective confi nement potential. For electrons, these energy scales are up to 3 k
B
T
or greater at room temperature, as required for most device applications. The fundamental inter-
band absorption energy of the QDs can be tuned over the range 0.9eV to 1.8eV either by
varying the growth conditions (and hence size of the QDs), the dot composition or by growing
the dots in a matrix other than GaAs. Many material combinations have been studied in the III–
V semiconductor family including AlGaAs for increased emission energies [18] and InGaAs for
reduced emission energies [19] . For an in-depth recent review of the fundamental optical proper-
ties of QDs and their numerous applications in optoelectronics the reader is referred to [20] and a
number of other chapters in the present volume.
All types of semiconductor QDs have the common property that their interband optical
response is highly sensitive to the charges they already contain. Thus, if one measures some
property, such as the frequency of emitted photons, the result will depend on the number, orbital
confi guration and spin of charges already within the dot. In this respect, one can consider
the optical response of a single QD to be non-linear even at the level of a single charge carrier.
This extraordinary sensitivity to charge occupation already forms the basis of the operation of
many QD devices within nanoelectronics and nanophotonics. Examples include the single elec-
tron transistor [7] and the deterministic generation of single photons for quantum cryptogra-
phy [21] or entangled photon pairs generated by the cascaded biexciton–exciton decay [22] .
Fundamentally, all these applications are enabled by strong Coulomb interactions between the
charges trapped by the dots which are strongly enhanced by the complete spatial confi nement.
These ideas are illustrated in Fig. 15.2a which provides a schematic illustration of the interband
optical emission spectrum of a single QD in the absence of Coulomb interactions (lower panel),
and compares it with the situation with the strong Coulomb interactions switched on (upper
panel) [23] . Without Coulomb interactions, the interband transitions in the dot mostly take place
between single particle orbital states with the same quantum number ( s , p , etc. – see Fig. 15.1b ).
The emission spectrum would then consist of a series of discrete transitions as depicted sche-
matically in Fig. 15.2a . In reality, band mixing effects and reduction of the symmetry of the dot,
due to an inhomogeneous composition profi le and piezoelectric charges, would still give rise to
weakly allowed transitions between other orbital states ( s , s , etc.), although the spectrum would
CH015-I046325.indd 478CH015-I046325.indd 478 6/24/2008 5:06:24 PM6/24/2008 5:06:24 PM