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Tight-binding design of intersubband transitions in InGaAs/AlAs quantum heterostructures grown pseudomorphically on InP J EAN -M ARC J ANCU , FABIO B ELTRAM Scuola Normale Superiore and Istituto Nazionale per la Fisica della Materia, Piazza dei Cavalieri 7, I-56126 Pisa, Italy R EINHARD S CHOLZ Institut f¨ur Physik, Technische Universit¨at Chemnitz, D-09107 Chemnitz, Germany A LDO DI C ARLO Universit`a di Roma “Tor Vergata” and Istituto Nazionale per la Fisica della Materia, I-00133 Roma, Italy (Received 26 October 1998) Intersubband optical properties of InGaAs/AlAs quantum heterostructures grown on InP are analysed. Our calculations based on a recently developed empirical tight-binding model show that the system is ideally suited for the tailoring of optical properties in a wide range. In particular, structures matching the frequency requirements of ultra-fast fibre optics communications are presented and discussed. c 1999 Academic Press

Key words: InGaAs/AlAs quantum wells, intersubband transitions, tight-binding method.

1. Introduction Semiconductor heterostructures have attracted a great deal of interest because of the unprecedented flexibility in tailoring their optical and transport properties offered by modern epitaxial growth techniques. The tuning of intersubband (ISB) transition energies between quantized subbands of semiconductor quantum wells (QWs) or minibands in superlattices, for instance, is of crucial importance for the realization of infrared detectors [1] and mid-infrared semiconductor lasers [2]. In n-type GaAs/AlGaAs QWs, ISB resonances are limited to the far- and mid-infrared spectral regions [3, 4]. Recently, the use of narrow Inx Ga1−x As/AlAs strained QW structures grown on GaAs [5–7], has led to the wavelength lowering of the IR threshold down to 1.75 µm, owing to the large Inx Ga1−x As/AlAs conduction band offset, which provides a large tunability of the ISB transition energies [6]. In these systems, the lowest conduction band state derives mainly from the bulk InGaAs 0 valley and strong ISB absorption was observed, corresponding to the broad range of available 0-like ISB transitions within the QW Brillouin zone. However, quantum-size effects in the InGaAs layers, associated with well thickness and indium mole fraction, can push the lowest 0 conduction-band state near or above the X conduction-band extremum localized in the AlAs barrier layers [8]. This leads to carrier transfer from the 0 subband to the X subbands [9]. This fact clearly prevents the efficient exploitation of this material system for device implementations because of the resulting strong modification of the ISB absorption 0749–6036/99/010351 + 05

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In0.52Al0.48As

AlAs

In0.4Ga0.6As

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In0.52Al0.48As 0

0.40 eV

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Fig. 1. Band alignment of the In0.52 Al0.48 As/AlAs/In0.4 Ga0.6 As/AlAs/In0.52 Al0.48 As heterostructure, grown pseudomorphically on InP. The calculated 0 electron confinement barrier is 1.33 eV in the In0.4 Ga0.6 As layers whereas the X electrons are confined in the AlAs layers. The potential offset between the 0 band-edge of the central strained In0.4 Ga0.6 As well and the X z band-edge of the strained AlAs barrier is 0.48 eV.

characteristics, i.e. dipole moment and electron density of the ground subband. A larger ISB level spacing, without carrier transfer into the barrier, can only be achieved by controlling the X -level position in the barrier. To this end, Inx Ga1−x As/AlAs/In y Al1−y As short-period superlattices are of particular interest since quantum confinement increases the energy of the X -level in the AlAs barrier, so that true, type-I structures can be realized. Consequently, ISB resonances up to 0.8 eV have been observed [6].

2. Empirical tight-binding model In this work, such device tailoring is investigated within the tight-binding (TB) approximation using an empirical sp3 d5 s∗ nearest-neighbour model including spin–orbit coupling. This 40-band TB model adequately reproduces measured effective masses, interband transition energies and deformation potentials of III-V semiconductors [10]. The usefulness of this TB model was recently demonstrated in the calculation of the electronic properties of short-period superlattices [11] and quantum wells [8, 12].

3. InGaAs/AlAs heterostructures grown pseudomorphically on InP Figure 1 shows the energy level diagram of an In0.52 Al0.48 As/AlAs/In0.4 Ga0.6 As/AlAs/In0.52 Al0.48 As heterostructure, grown pseudomorphically on InP (001). This material combination is characterized by tensile strain effects that lower the 0 and X z band minima, both in the In0.4 Ga0.6 As and in the AlAs layers. The band profile was calculated assuming a conduction to valence-band offset ratio of 67:33 between bulks. This value gives a discontinuity of the 0 edge between In0.52 Al0.48 As and In0.4 Ga0.6 As of 0.40 eV, in agreement with experimental results [13]. The resulting 0 electron potential barrier is 1.33 eV for the central In0.4 Ga0.6 As QW, whereas the AlAs X 6c band edge is 0.48 eV above the In0.4 Ga0.6 As 06c level. In order to ensure that the resulting heterostructure is of type I, while maximizing the ISB transition energy, we focused on 7 ML-wide In0.4 Ga0.6 As QWs. The thickness of the confining AlAs barriers was chosen in order to achieve large ISB transition energies together with a strong optical dipole moment, and to suppress carrier transfer from the 0 to the X subband. Figure 2A shows the two lowest 0-like and the first X -like conduction subband minima as a function of barrier thickness, and in Figure 2B, the optical coupling strength between the two lowest 0-like conduction states are presented. Both the energy difference between the two lowest 0 states and the difference between the lowest 0 and X z states increase with decreasing barrier thickness, suggesting the choice of thin barriers. On the other hand, the strength of the intersubband absorption is suppressed in this

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1.6

1.4

B 6

4

2

0 0

2

4 6 8 10 Barrier thickness (ML)

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Fig. 2. A, Subband energies for the structure of Fig. 1 at k = 0, for 7 ML In0.4 Ga0.6 As wells, as a function of AlAs barrier thickness. The energy is measured from the In0.52 Al0.48 As valence-band maximum. The lowest two 0-like quantum-well states are shown as solid lines with squares, the X z -like barrier states as dashed lines with crosses. B, Squared dipole matrix element for the intersubband transition between the two lowest 0 conduction states, as a function of AlAs barrier thickness.

case. From the transition strength in Fig. 2B we conclude the best choice is a barrier thickness of 7 ML. In this case, the energy spacing between the lowest 0 and X states is 120 meV. Therefore, any electron spill over to the X (barrier) states should be suppressed, and a large electron density in the first 0 subband becomes possible. The smaller barriers have a further advantage: they favour tunnelling processes populating the lowest 0-like QW state.

4. Comparison with infinite AlAs barrier In order to evaluate the quality of the In0.4 Ga0.6 As/AlAs 7 ML/7 ML structure, it is useful to consider the infinite AlAs barrier thickness limit for samples grown pseudomorphically on GaAs. For this case, Fig. 3A shows the in-plane energy dispersion as a function of wavevector k and Fig. 3B, the optical matrix element between the conduction ground state C1 and the higher levels up to C17, the strongest transition being to the second-lowest 0-like state, C16. It should be noted that the maximum optical dipole moment is comparable to that of the QW heterostructure chosen in Fig. 1. However, Fig. 1 corresponds to a much larger 0–X separation: 120 meV (Fig. 2A) instead of 76 meV (Fig. 3A). As a direct consequence, in Fig. 3A the crossing between the lowest 0 subband in the well and the lowest X subband in the AlAs barrier occurs at small k and has a drastic impact on the optical properties. This prevents the use of large 0-like electron densities in the ISB process for similar configurations. This behaviour is supported by experimental results, where the ISB absorption of the 7 ML-wide In0.4 Ga0.6 As/AlAs QW was found to be strongly inhibited [9]. Figure 4 shows the calculated ISB absorption spectrum for the optimum barrier thickness of 7 ML. The rapid fluctuation in the spectrum is due to the discretization of the Brillouin zone integration and should not be given a physical value. A strong absorption is found within a wide energy range of 140 meV, corresponding to the available 0-like ISB transitions. It should be noted that this system provides strong optical activity in the transparency window of optical fibres, λ = 1.55 ± 0.02 µm, and is fully compatible with good crystalline quality.

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0.05 0.10 [k00]

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4

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0 –0.10

–0.05 [kk0]

0.00 (2π/a)

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Fig. 3. A, Energy dispersion for the conduction subbands of an In0.4 Ga0.6 As/AlAs quantum-well with 7 monolayers well width and infinite barriers, grown pseudomorphically on GaAs. Energies are measured from the AlAs valence band maximum. The two lowest 0-like conduction subbands C1 and C16 are shown as continuous lines, dashed lines display X -like conduction subbands. B, Squared dipole matrix element for z-polarized light, for the intersubband transition between the conduction ground state and all conduction subbands C j up to j = 17. The transition between the two lowest 0-like states, C1 → C16, is shown by a continuous line, the other transitions C1 → C j by dashed lines.

Intersubband absorption strength (a.u.)

1000

800

600

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700 Energy (meV)

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Fig. 4. Intersubband absorption spectrum of the In0.52 Al0.48 As/AlAs/In0.4 Ga0.6 As/AlAs/In0.52 Al0.48 As quantum-well heterostructure grown on InP with 7 ML wells and optimum AlAs barrier thickness of 7 ML. The polarization is along the growth direction z.

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5. Conclusion In conclusion, we have analysed the potential of InGaAs/AlAs/InAlAs grown pseudomorphically on InP (001) for the implementation of ISB-based optoelectronic devices. It has been shown that it is possible to tailor such structures in the range of interest for fibre communications. Acknowledgement—Work at Scuola Normale Superiore was supported, in part, by the European Commission under contract BPRRCT97-0557. RS acknowledges the Deutsche Forschungsgemeinschaft for financial support.

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