Recent results on superlattice transport and optoelectronics applications

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999 Article No. spmi.1998.0606 Available online at http://www.idealibrary.com on

Recent results on superlattice transport and optoelectronics applications J. F. PALMIER OPTO+, G. I. E., route de Nozay, 91460 Marcoussis, France C. M INOT, J. C. H ARMAND France Telecom CNET/DTD, 196 Avenue H. Ravera, 92220 Bagneux, France A. S IBILLE ENSTA, Bd Victor, 75739 Paris cedex 15, France D. TANGUY, E. P ENARD France Telecom CNET/DTD, 2 Avenue P. Marzin, 22301 Lannion, France

(Received 26 October 1998) Recent results involving miniband transport in superlattices at millimetre (mm) wave frequencies are reviewed. The miniband negative differential conductance up to very high frequencies allows for a new kind of device, the superlattice photo-oscillator. A practical application for optical to mm-wave conversion is demonstrated. An analysis of the intrinsic limitations in the transport processes led to recent progress in the understanding of superlattices physics involving Zener inter-miniband tunneling. c 1999 Academic Press

Key words: superlattice, transport, optoelectrics, tunneling.

1. Introduction In recent years, semiconductor superlattices (SLs) have proved a remarkable testbed for different band structure phenomena which are difficult to observe in bulk materials. Wannier–Stark localization, Bloch oscillations and Esaki–Tsu negative differential conductance have thus been unambiguously demonstrated. In addition, SLs now appear a promising alternative to other devices for very high frequency applications, in the millimetre (mm) or sub-mm wavelength range, for which conventional techniques are not yet operable. This is the case for oscillators based on the negative miniband effective mass, in which practical interest has been renewed by the possibility of efficient optical injection locking. This leads to particularly simple device principles, which have actually been tested in wireless links between 15 and 40 GHz, and should be usable at higher frequencies. In the first part of this paper we present SLs as mm-wave oscillators, and show recent results on GaInAs/ AlInAs devices, which are photosensitive at optical telecommunication wavelengths (between 1.3 and 1.6 µm). The difficulties linked to the achievement of the long-wavelength device will be discussed in the context of 0749–6036/99/010013 + 07

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c 1999 Academic Press

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SL multi-miniband transport. In Section 2 we give a more comprehensive analysis of the transport results presented in the first. In Section 3 system experiments involving SL oscillators are presented, and the reasonable potential for such applications is discussed. Transport in SLs beyond semiclassical theory is finally investigated in specially designed GaAs/AlAs SLs. We report on samples in which inter-miniband Zener tunneling has been purposefully favored. The physical interpretation of the observed effects are particularly useful in explaining the different features of the long-wavelength SL oscillators.

2. Miniband transport The semiclassical model (SCM) describes the electron transport in a single miniband according to simple models [1]. This hides the stratified nature of the SL in an effective medium description, according to the application of Bloch’s theorem for the electron transport in the growth direction (z). Resulting from a competition between Bloch oscillations which suppress any charge transport, and the collisions which tend to restore it, a maximum in the velocity–field law (V –F) appears for a critical field Fc . This model and its quantum mechanical hopping approach has been extensively discussed in the literature. In recent efforts to exploit the negative branch of the velocity–field law, some advantages of the SL over bulk materials have been emphasized: • the frequency limit is very high (close to the Bloch frequency); • the flexibility of the superlattice structure is of great help in tailoring defined (V –F) characteristics. Experimental evidence for nonlinear miniband transport has been published [2]. Two main parameters are considered: the critical field and the peak velocity. According to the SCM, the critical field Fc is limited by the collision time τ which is just the inverse Bloch pulsation as ed Fc = ~/τ (d is the SL period). In agreement with the discussion above, if the collision frequency increases, transport reduces to the ohmic limit, i.e. a dc current which increases with the applied field; in the opposite limit (vanishing collisions), it leads to the Bloch oscillation regime resulting in a zero dc current. Values for Fc between a few hundred V cm−1 and 30 kV cm−1 have been reported. The peak velocity v p which scales with 1 or 12 depending on the temperature, spans over several orders of magnitude. Extensive use of the Boltzmann transport equation solutions allows for a better insight into both v p and Fc variations with SL parameters [3]. Time-resolved photocurrent experiments have provided direct observation of negative differential conductance in the time domain, and an analysis of heating effects as a balance between elastic and inelastic interactions [4]. This approach has also demonstrated optical control of high-frequency oscillations, paving the way for optoelectronic applications [5]. Complementary evidence for miniband transport has been given by high-frequency noise measurements [6]. In the latter work, the SL diffusion coefficient in the growth direction has been measured and successfully compared with SCM calculations, demonstrating, in particular, a strong decrease in the diffusion coefficient with the applied electric field due to miniband nonparabolicity. This low noise figure also encourages the use of SL in device applications, in comparison with hot electron results in bulk materials. The SCM limit is reached as soon as the Bloch wavefunction coherence in the growth direction is destroyed. At zero electric field, defects and phonons are at the origin of the coherence destruction. A very approximate estimate of such effects gives a lower limit for 1 ≈ ~/τin , τin being the inelastic collision time, resulting in a limit of a few meV only. For nonzero electric fields, according to Wannier, the electron wavefunction is the product of the Bloch wavefunction and a localized envelope. In fact, the shape of the wavefunction postulated by Wannier continuously evolves between the Bloch expression and a single cell localized state at extremely high electric fields. It is therefore not surprising that in suitably designed SL samples, both miniband nonlinear transport and Wannier–Stark localization are observed. In Ref. [7] those two effects co-exist, and a localization field about twice Fc was reported. In the following we address results and applications in the miniband regime and, more particularly, slightly above Fc to take benefit from the negative differential conductance for high-frequency device applications. In the Wannier–Stark limit for which the SCM no longer applies, a general model was proposed by Laikthmann and Miller [8], building a bridge between the SCM and hopping models.

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Table 1: Main design parameters and reference energies for the two SL structures A and B.

A B

Well (Å) 45 60

Barrier (Å) 20 20

%Ga–%Al 48/0 24/24

Miniband (meV) 56 84

Gap (meV) 903 820

Nd (cm−3 ) 1016 1016

L (µm) 1.0 0.71

3. Superlattices as mm-wave oscillators This paper concerns quite recent results focused on SL photo-oscillators, for applications above 30 GHz and at optical telecommunication wavelengths (1.3–1.6 µm). Two different SL structures have been designed, here noted as A and B, their characteristics being described in Table 1. Structure A is designed for an absorption wavelength of 1.35 µm. Although the latter is not suited to long distance optical communications, it allows for a GaInAs/AlInAs SL design with optimal microwave efficiency, a moderately small period of the order of 60 Å, and a fair separation between the first and second miniband. Structure B is designed for longer wavelengths (1.48 µm); it is characterized by wider wells and barriers, and a lower barrier energy (using a quaternary GaAlInAs alloy instead of lattice-matched AlInAs). Experimental details for the preparation of such SL devices can be found in Ref. [9]. The difference in the design and one of the main difficulties is illustrated by the DC characteristics, which is quite different for both structures, as shown in Fig. 1. It is clear from the figure that the B structure shows only a narrow voltage range for microwave generation due to a positive conductance occurring beyond 0.8 V. In contrast, structure A is more robust and the parasitic positive conductance only appears beyond 3 V. Inter-miniband transitions may be responsible for such an unexpected positive differential conductance, which will be discussed later on. Both A and B structures have been processed for microwave measurements up to 65 GHz, ensuring very low parasitic capacitance and inductance to measure the intrinsic SL conductance. In Fig. 2 reflexion coefficient S11 measurements are reported. Using the direct relation between the intrinsic conductance and S11 , i.e. S11 = (Z − Z 0 )/(Z + Z 0 ), we directly see the negative differential conductance band which corresponds to |S11 | > 1. For structure A a resonant behaviour is observed in good agreement with the space charge amplification, very similar to Gunn device behaviour. For electric fields just above Fc , the gain bandwidth is broad; however, at higher applied voltages the reflexion peak sharpens and shifts to lower frequencies. Although the field in the structure becomes inhomogeneous, the frequency shift may be interpreted in terms of the reduction of the mean drift velocity under increasing field, a feature characteristic of negative differential velocity. For that sample, a maximum of the absolute value of the conductance is obtained near 40 GHz. In contrast, structure B significantly deviates from the classical theory. In this case the parasitic positive conductance contributes to a shrinkage of the resonant behaviour. The fabrication of mm-wave sources from structure B nevertheless leads to multi-mode cavity oscillations of up to 74 GHz [10]. Other groups have reported similar results in GaAs/AlAs SLs [11].

4. Superlattice devices as optical signal converters One of the most interesting applications of SL in mm-wave frequencies and beyond is the possibility of achieving simple optical injection locking oscillators, as first reported by Cadiou et al. [12]. The basic experiment is described in Fig. 3. A 1.3 µm laser source is modulated at 38 GHz. The resulting signal enters the window of a SL device. In this experiment, the A structure is particularly well suited. When the light modulation frequency is close to the free-running SL oscillator, locking to the injected signal frequency occurs. Compared with the phase-locked loop, this approach is certainly less versatile, but it is much more economical in that it needs only one component and potentially can also be extended to higher frequencies. The locking bandwidth (frequency range within which the oscillator locks on to the optical signal frequency)

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Current (mA)

20

15

10 Sample A Sample B 5

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Applied voltage (V) Fig. 1. The dc characteristics for samples A and B measured at T = 300 K.

7

2.4

Sample A

Sample B

2.2

6

0.8 V

2.0

–1.8 V 4 –1.4 V

–2.4 V

3

–1 V 2

–2.8 V

Reflection gain |S11|

Reflection gain |S11|

5

1.8

0.6 V

1.6

1.1 V

1.4

1.2 V

1.2 1.0

1.4 V

0.8

0V

0.6 0.4

1

0.4 V

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0 0

10

20

30

40

Frequency (GHz)

50

60

0

10

20

30

40

50

60

Frequency (GHz)

Fig. 2. Millimetre-wave reflection gain obtained with the two samples A and B. For sample A the SCM model (dotted lines) is in a fair agreement with experimental results.

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Polarization Control

Laser

17

Mach–Zener Modulator

Lensed fibre

Attenuation

Superlattice Oscillator 38 GHz Synthetizer

Spectrum Analyser

140

Locking bandwidth (MHz)

120

100

80

60

40

20

0 –10

–9

–8

–7

–6

Average optical power (dBm) Fig. 3. Direct optical injection locking in a SL oscillator at 38 GHz: experimental scheme and locking bandwidth versus average optical power.

has been measured versus the optical signal injected power. In Fig. 4 we recall a recent result from Ref. [13], showing a locking band of the order of 100 MHz for a total optical power of less than 6 dBm. A system experiment using A devices has also been performed, with QPSK random data bit transmission. A bit error rate of less than 109 at 60 MB s1 has been obtained, with only 40 dBm of injected electrical signal.

5. Zener inter-miniband resonant breakdown These phenomena and device applications involve SL transport in a single electron miniband. However, we may expect the presence of high-laying minibands to affect transport in a qualitatively new manner. For instance the application of sufficiently high electric fields opens the way to inter-miniband transfer, an effect suspected to play a detrimental role in the smearing of Bloch oscillations or in the efficiency reduction of SL microwave oscillators [10]. Here we experimentally explore inter-miniband conduction in a GaAs/GaAlAs

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Conductance (mS) Velocity (106 cm s–1)

6

‘Experimental’ 1

4

1 1

1 4

1 1

2(1)

2(1) 3(3)

2(2)

3

3(3)

1

2(2)

‘Ladder’ model

2

2(3)

2

1 1

0 0

2(3)

50 100 Electric field (kV cm–1)

0.045 – 20 GHz 0 0

1

2 3 Bias (V)

4

5

Fig. 4. V –F relation (‘experimental’, left) accounting for the dc and microwave SL conductance. Each peak is due to an inter-miniband resonant tunneling transition.

SL, so designed that the inter-miniband spacing allowed transfer under moderate fields. The SL was undoped (n = 1014 electron cm−3 ), in order to prevent the formation of high field domains localized on the SL period scale [14]. Nevertheless, the quasi-continuous miniband states under the electric field are broken into so-called Wannier–Stark ladders of localized states. When several minibands are involved in the processes understudy, resonance conditions are possible between levels centered on nonidentical SL periods. Whenever these conditions are fulfilled, they lead to de-localization of the states, thereby strongly enhancing transport along the SL axis. In the effective medium approach allowed by the homogeneity of the field over several periods, a velocity–field relationship may still be defined, which is expected to show peaks at resonant values of the electric field. The peak velocities may roughly be estimated as the tunneling distance, divided by the half Rabi oscillation period between the two tunnel coupled interacting levels (ladder model). In Fig. 4 we show the conductance–voltage characteristics at 300 K of a GaAs/Ga0.75 Al0.25 As SL with 35 and 11 monolayers for the well and the barrier, measured at microwave frequencies ranging from 0.045 to 20 GHz. Because of the coupling between the charge densities and drift velocities in the Poisson equation the conductance of n+ -n-n+ structures exhibits complex frequency dependences, when the V –F relation is nonuniform. This leads to peaks at inter-miniband resonant voltages, of increasing magnitude as the frequency is raised, in quite good agreement with simulations [15]. The extraction of peak velocities from data compares favorably with those estimated as quoted above, for various inter-miniband transitions between the first, second and third minibands, and up to 3 SL periods for the tunneling distance.

6. Conclusions In this paper we have summarized some recent results obtained in SL miniband transport, and report on practical applications in the context of optical access for communication networks. The intrinsic microwave properties of the SL material are indeed attractive, and the ability to mix them with telecommunications light signals in GaInAs/AlInAs SLs has been demonstrated up to 40 GHz. The intrinsic frequency limit of such devices is very high and, in the future, research attempts should probably be pushed beyond 100 GHz. On the

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other hand, multi-miniband transport has also been investigated in this work, and shown to be at the origin of Zener breakdown, present in certain structures even under moderate voltages. The latter effect implies severe limitations to the operation of long-wavelength photo-oscillators, unless a specific design effort is carried out to remove it. Fortunately although up to now only two material systems, GaAs/AlAs and GaInAs/AlInAs and one layer combination (ABABAB. . .) have been explored, other compositions and combinations are still possible in order to solve this fundamental physics difficulty.

References [1] }L. Esaki and R. Tsu, IBM J. Res. Dev. 14, 61 (1970); V. A. Yakovlev, Sov. Phys. Solid State 3, 1442 (1962). [2] }A. Sibille, J. F. Palmier, H. Wang, and F. Mollot, Phys. Rev. Lett. 64, 52 (1990). [3] }G. Etemadi and J. F. Palmier, Solid State Commun. 86, 11, 739 (1993). [4] }C. Minot, H. Le Person, J. F. Palmier, and F. Mollot, Phys. Rev. B47, 10 024 (1993). [5] }H. Le Person, C. Minot, L. Boni, J. F. Palmier, and F. Mollot, Appl. Phys. Lett. 60, 2397 (1992). [6] }E. Dutisseuil, A. Sibille, J. F. Palmier, V. Thierry-Mieg, M. De Murcia, and E. Richard, J. Appl. Phys. 80, 12, 7160 (1996). [7] }A. Sibille, J. F. Palmier, and F. Mollot, Appl. Phys. Lett. 60, 457 (1992). [8] }B. Laikhtmann and D. Miller, Phys. Rev. B48, 5395 (1993). [9] }J. F. Palmier, C. Minot, H. Le Person, J. C. Harmand, N. Bouadma, J. C. Esnault, D. Arquey, F. Heliot, and J. P. Medus, Electron. Lett. 32, 1506 (1996). [10] }C. Minot, N. Sahri, H. Le Person, J. F. Palmier, J. C. Harmand, J. P. Medus, and J. C. Esnault, Superlatt. Microstruct. 23, 1323 (1998). [11] }E. Schomburg et al., MSS8 Proceedings, Physica E2, 295 (1998). [12] }J. F. Cadiou, J. Guena, E. Penard, P. Legaud, C. Minot, J. F. Palmier, H. Le Person, and J. C. Harmand, Electron. Lett. 30, 1690 (1994). [13] }D. Tanguy, E. Penard, P. Legaud, and C. Minot, Proceedings Microwave Photonics, Duisburg, 1997, edited by G. Mercator (Universit¨at Optoelektronik). [14] }H. Grahn, K. Von Klitzing, K. Ploog, and G. D¨ohler, Phys. Rev. B43, 12094 (1986). [15] }A. Sibille, J. F. Palmier, and F. Laruelle, Phys. Rev. Lett. 80, 4506 (1998).