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, 1997, 39, 4 Luminescence of Excitons in Slightly Asymmetric Double Quantum Wells A.V. Akimov, E.S. Moskalenko, A.L. Zhmodikov, D.A. Mazurenko, A.A. Kaplyanskii, L.J. Challis, T.S. Cheng, C.T. Foxon A.F.Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St.-Petersburg, Russia Physics Department, Nottingham University, University Park NG7 2RD, Nottingham, UK ( 26 1996 .) We report the first studies of exciton luminescence spectra from asymmetric double quantum wells (DQWs) of very similar width. The DQWs were of GaAs/AlGaAs and the differences in widths of the coupled wells were one or two monolayers. The coupled direct and indirect exciton states anticross with a resonance splitting of 1.33 meV.

An additional luminescence line appearing at low temperatures is identified as a localized indirect exciton.

An asymmetric double quantum well (DQW) in which GaAs substrates. Fig. 1 shows the growth scheme for wafer the two QWs are separated by a narrow barrier gives rise NU1117. The barriers are all of Al0.33Ga0.67As and the QWs to a minimum of four luminescence lines. Two of these are of GaAs. The thickness b of the narrow barriers between due to recombination of so-called direct exciton (DX) states two QWs is 38.2 and that of the thicker barriers between in which the electron and hole are in the same quantum DQWs is 203.5. The widths aw, an of the QWs differed well and two to indirect exciton (IX) states in which the by 1ML in NU1116 (aw - an = 2.85 ) and 2MLs in electron and hole are in different wells [16]. A number NU1117 (aw - an = 5.7 ) with layer widths (aw/b/an of optical studies have been made of these systems and of in ) of 101.8/38.2/99.0, 90.5/38.2/87.6 and 82.0/38.2/79.1 the changes in line positions when the relative positions in NU1116 and 200.7/38.2/195.0, 101.8/38.2/96.1 and of the energy levels in the two QWs are shifted by an 82.0/38.2/76.3 in NU1117. All the DQWs showed similar applied electric field F. The energies of the indirect excitons results and in the present paper we concentrate on those vary approximately linearly with F while those of the direct obtained with the 101.8/38.2/96.1 DQW.

excitons are approximately fixed. As a result, the DX and IX lines cross or rather anticross since the electrons involved in both emission processes can tunnel through the barrier Indium Applied voltage, V separating the wells. (In principle this can also happen for contact holes but in this case the tunnelling rate is too small to Semitransparent Constantan contact produce measurable effects.) In previous studies of such systems [117], the widths of 50 GaAs the coupled quantum wells differed by several monolayers 203.5 AlGaAs Barrier leading to differences in the DX energies of 10 meV or 76.3 GaAs QW(narrow) more. In the present work however, the DQWs are only DQW 38.2 AlGaAs Barrier slightly asymmetric, the widths of the coupled QWs differing 82.0 GaAs QW(wide) by only 1 or 2 monolayers (MLs). The main purpose of working with such systems is that they have the potential to 203.5 AlGaAs Barrier operate as tunable spectrometers of non-equilibrium acoustic 96.1 GaAs QW(narrow) phonons in the important range below 1000 GHz in which DQW 38.2 AlGaAs Barrier phonons propagate ballistically through material such as 101.8 GaAs QW(wide) GaAs allowing the possibility of detailed study of relaxation 203.5 AlGaAs Barrier and other processes. This work will be discussed in a later paper. In the course of investigating these systems 195.0 GaAs QW(narrow) however we have found that the spectroscopic properties of DQW 38.2 AlGaAs Barrier the devices used are very well defined and, of particular note, 200.7 GaAs QW(wide) provide the first observation of indirect exciton localization.

203.5 AlGaAs Barrier It is that aspect of the work that is reported here.

1 mGaAs Buffer Layer 0.4 mm Semiinsulating GaAs 1. Samples and experimental details Substrate Samples were taken from two wafers, NU1116 and Indium contact NU1117, each consisting of a 1 m GaAs buffer layer followed by three DQWs. The structures were grown by Figure 1. The layer structure of wafer NU1117.

MBE at T = 630C on 0.4 mm thick (001) semi-insulating 736 A.V. Akimov, E.S. Moskalenko, A.L. Zhmodikov, D.A. Mazurenko, A.A. Kaplyanskii, L.J. Challis, T.S. Cheng,...

contacts and, by adjusting V to a particular value V = Vf, the internal electric field can be compensated and flat band conditions obtained: F + F0 = 0 (Fig. 2, b). The corresponding band diagram for V > Vf for the DQW used in our experiments is shown schematically in Fig. 2, c.

To analyse the experimental results it is necessary to know how F depends on the voltage V applied to the contacts.

Fortunately, as is shown in Sec. 2.A, there is a wide range of V where a linear dependence F(V ) =kV is observed with k = 7 103 cm-1 for T = 10-20 Kand V >1 V although this is not the case over the whole experimental range. k decreases with temperature below 10 K and, for example, at T = 5 K, k = 3 103 cm-1. The sign of the internal Figure 2. The band diagram of a DQW. a for zero applied field is such that a positive voltage of the Schottky contact is field (internal field F0 only), b under flat band conditions needed to compensate F0 and from the size of k we conclude (F + F0 = 0), c for positive net field (F + F0 > 0).

that one DQW has a resistance comparable with 0.4 mm of semi-insulating GaAs, a somewhat surprising result.

2. Experimental results and discussion The experiments were carried out in a continuous flow helium cryostat with temperature control of 0.01 K.

A. Ant i cr os s i ng of Di r ect and I ndi r ect The luminescence was excited by a HeNe laser beam E x c i t o n S t a t e s. The luminescence spectrum of DQW ( = 730 nm) focussed down to 100 m diameter. The power density at the surface of the sample was < 1W/cm2 101.8/38.2/96.1 consists of several narrow ( 1 meV) lines whose width and energy correspond to exciton recombinaand underbarrier optical excitation was used to avoid lumition. The luminescence spectrum depends strongly with V nescence from excitons bound to impurities in the barriers.

and T in both line position and intensity and measurements The luminescence was analysed by a double monochromator at T = 20 K are shown in Fig. 3, a for several values of with 0.2 meV spectral resolution and detected by a photoV. Four excitonic lines are observed of which line 1 is multiplier followed by a photon counting system.

dominant and, for V < 2 V, has energy, h1 = 1.5551 eV, As already noted, the relative energy positions of the in good agreement with that calculated for a direct heavyelectron levels in a DQW are strongly affected by electric hole exciton in the wider (101.8 ) QW. The line shifts to fields [117] and we have used this to make a detailed lower energy as V increases (Fig. 3, a) and for V > 2 V, a examination of the luminescence as a function of energy second line 2, appears from the high energy side, increases in level separation. DQWs in fact invariably contain an internal intensity and approaches an energy equal to the initial energy electric field F0 (Fig. 2, a) whose magnitude and direction of line 1. The energy, 1.5589 eV, of line 4 corresponds to depend mainly on the doping of the GaAs/AlGaAs layers. In that of a direct heavy-hole exciton in the narrower (96.1 ) the arrangement normally used for electric field experiments QW at low voltages but shifts to higher energies and weaker an undoped DQW is located between p- and n-layers and F0 intensities as V is increased and another line, 3, appears is determined by space charge effects. However the doping whose energy approaches the initial energy of line 4.

of the p and n layers leads to exciton luminescence lines Only two lines, 1 and 3, are detectable at lower temtoo broad (up to 10 meV) for the resolution required here peratures and this is illustrated by the data in Fig. 3, b for and so, in the present work, nominally undoped material T = 5 K. However for V > 3 V another line, L, appears was used with residual impurity concentration in the GaAs 1 meV lower in energy than line 1 which it accompanies of n 1014 cm-3. A semitransparent constantan film was as it shifts to lower energies with increasing V. Line evaporated above the DQWs to form a Schottky contact disappears for V > 3.7 V but line L continues to follow (Fig. 1) and an indium film was deposited on the back side of line 1s high temperature position always being 1 meV the substrate. No change in luminescence spectrum could lower in energy. Its possible origin is discussed later.

be detected after the contact deposition and the spectral The origin and behaviour of lines 14 seem readily width of the exciton lines at helium temperatures remained explained in terms of DX and IX recombination as shown 1 meV.

in Fig. 4, a. The DX lines are referred to as DXW The internal electric field in these structures changes (wide QW) and DXN (narrow QW) and their excitonic with optical excitation by an amount which varies with energies (-point) are given respectively by both intensity and lattice temperature T and it seems likely D D D D that the field is associated with space charge in the buffer Exw = Eew - Ehw - EB, Exn = Een - Ehn - EB, (1) layer/GaAs substrate interface and Fermi level pinning at the surface although this has not been established. The total where Eew, Een, Ehw, Ehn are the electron and hole energies in D field can be modified by applying a voltage V between the the wide and narrow QWs respectively and EB is the binding , 1997, 39, Luminescence of Excitons in Slightly Asymmetric Double Quantum Wells D I levels should cross, Exw(n) = Exw(n), (Fig. 4, b) when the applied field Frw(n) equals 0 D I Frw = Ee + EB - EB - F0, ez 0 D I Frn = Ee - EB + EB - F0, (4) ez 0 0 where Ee = Een - Eew. However the coherent electron tunnelling that can take place at or near resonance leads to anticrossing and so to splitting into symmetric and antisymmetric combinations of the DXN and IXN and of DXW and IXW eigenstates as shown in Fig. 4, c for DXN and IXN states. The energy splitting h/e, where e is the electron tunnelling time, and in these combined states the electron is shared between the two QWs while remaining bound to a localized hole in one of the QWs.

Frw(n) differs somewhat from the field Fre at which the electron levels in the wide and narrow QWs are in resonance 1 (Fre + F0 = Ee ) because of excitonic effects; this ez difference appears to have been overlooked in some of the earlier papers [3,4,6,16,17]. When anticrossing is included, the expressions for the energy levels [6] become 1/ D I D I E1,2 = Exw + Exw Exw - Exw 2 + 2, 1 D I D I 1/E3,4 = Exn + Exn Exn - Exn 2 + 2 (5) and we note that the anticrossing has previously been observed in photoconductivity [16], optical absorption [6] and photoluminescence [18] experiments.

Figure 3. Luminescence spectrum of DQW measured at 20 (a) and 5 K (b) for different applied voltages V. The dotted lines are drawn for the eye to follow the peak position of the exciton luminescence lines.

energy of DX. The quadratic Stark effect is negligible for D F + F0 < 10 kV/cm so that, as noted, the energies Exw, D Exn are essentially independent of V and only depend on the widths, an and aw.

The energies of the indirect excitons equal I I I I Exw = Een - Ehw - EB, Exn = Eew - Ehn - EB, (2) I where EB equals their binding energy and the subscript in each expression, (xw) or (xn), indicates the location of the hole (w = wide QW, n = narrow QW). Previous measurements [3,4,16,17] have shown that a pure IX state has a linear Stark effect so that I 0 0 I Exw = Een - Ehw - e(F + F0)z - EB, I 0 0 I Figure 4. a) The band diagram and exciton transitions of the Exn = Eew - Ehn + e(F + F0)z - EB, (3) DQW. b) The dependence (schematic) of the exciton energies on 0 where Een(w) and Ehn(w) are the energies of the electrons applied field F; the circles show the DX/IX anticrossing regions.

and holes under flat band conditions (F + F0 = 0). From c) A diagram showing the level splitting between the symmetric S| and antisymmetric AS| eigenstates at the anticrossing.

Eqs.(1) and (3) it is seen that the DXW(N) and IXW(N) 10 , 1997, 39, 738 A.V. Akimov, E.S. Moskalenko, A.L. Zhmodikov, D.A. Mazurenko, A.A. Kaplyanskii, L.J. Challis, T.S. Cheng,...

which has not previously been reported. As V increases, line L remains red-shifted from 1, IXW, by an approximately constant energy, 1 meV, but grows in size while line 1 falls.

We attribute line L to a localized indirect exciton (LIX):

the indirect exciton 1 bound to an impurity or interface defect. Support for this comes from the size of the redshift which is close to the binding energy of bound excitons in GaAs QWs [20]. Line L disappears for T > 10 Kwhile line 1 remains and this is consistent with the dissociation of localized excitons (which have only a small density of states) into free excitons with increasing temperature.

The reason why line L only appears for V > 3 V and increases in intensity at the expense of line 1 as V increases seems explicable in terms of the lifetime of the IXW state.

At high voltages this is a pure IX state and since this has the lowest exciton energy it has a long lifetime [1] and so a good chance of being captured by a defect before annihilation. However, as V decreases, IXW moves towards the anticrossing so there is an increasing admixture of DXW into the IXW state. This leads to a steady decrease in the radiative lifetime and hence in the chance of capture before annihilation. It seems likely that the IXN exciton should also become localized at low voltages where it has the lowes Figure 5. The measured (symbols) and calculated (solid curves) energy and this should lead to a line approximately 1 meV energies of the exciton lines as a function of applied voltage at below 3. No evidence of this can be seen in Fig. 3 but this 20 K. The circles show the DX/IX anticrossing regions.

may be because of difficulties in resolving it from line 3 in the region where lines 1 and 3 cross.

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