Multiphoton-assisted tunneling, dynamic localization and absolute negative conductance

surface science ELSEVIER

Surface Science 361/362 (1996) 176-180

Multiphoton-assisted tunneling, dynamic localization and absolute negative conductance B.J. K e a y " * , S.J. Allen, Jr. a, K . D . M a r a n o w s k i b, A.C. G o s s a r d b, U. B h a t t a c h a r y a c, M.J.W. R o d w e l l c • Center for Free-electron Laser Studies, University of Cal~orrda, Santa Barbara, CA 93106, USA b Materials Department, University of Cal~ornia, Santa Barbara, CA 93106, USA * Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, USA Received 21 June 1995; acx:epted for publication 7 August 1995

We report the observation of Absolute Negative Conductance (ANC), multiphoton stimulated emission and dynamical localiTation in sequential resonant tunneling semiconductor superlattices driven by intense terahertz electric fields. With increasing terahertz field strength the conductance near zero dc bias decreases towards zero and then becomes negative. This is accompanied by new steps and plateaus that axe attributed to multiphoton-assisted resonant tunneling between ground states of neighboring quantum wells accompanied by the stimulated emission of a photon.

Keywords: Photon emission; Quantum effects; Superlattices; Tunneling

1. Introduction We report the observation of dynamic localization, absolute negative conductance (ANC) and electric field domains driven by photon-assisted tunneling (PAT) in multi-quantum well superlattices. Theories predicting dynamic localization and absolute negative conductance in semiconductor superlattices subjected to ac electric fields have existed for twenty years [1], but have not been verified experimentally. These theories are based upon semiclassieal models of electron motion in superlattices in the miniband or coherent tunneling * Corresponding author. Quantum Institute, Broida Hall, UCSB, Santa Barbara, CA 93106, USA. Fax: + 1 805 685 4495; e-mail" keay~qi.ucsb.edu.

regime. An essential feature of these models is Bloch oscillation in the presence of intense high frequency electric fields, high frequency fields sufficient to drive carriers beyond the miniband zone boundary, into a region of k-space with negative velocity [1]. However, in this report we are concerned with sequential resonant tunneling, distinguished from the former by incoherent tunneling and a loss of phase memory after tunneling into a neighboring well. There has been little discussion about this case, discouraged perhaps by the notion that a ladder of levels, the ground states of superlattice quantum wells in an applied electric field, are all equally populated and therefore offer no net coupling to the photon field [2]. At the outset we wish to distingaish the observation of ANC from rectification in asymmetric

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R Z Keay et aL/Surface Science 361/362 (1996) 176-180

structures like solar cells, p-n junctions and Schottky diodes. In the work reported here, we have an essentially symmetric structure and no current flows at zero applied dc bias with or without intense tera~ertz electric fields. The phenomenon is more closely related to absolute negative conductance in resonant tunneling diodes [3] and in bulk GaAs driven with strong microwave fields at GHz frequencies [4]. Here, in a combined dc and ac electric field the average current can be negative at a positive dc bias because the current on negative swings of the microwave field can be greater than the current on positive swings of the oscillating field. This is a purely classical, circuit effect but analogous to the aforementioned theoretical predictions of absolute negative conductance caused by large k-space excursions in the strongly driven Bloch oscillator [1]. We believe the observations made here are beyond simple rectification in asymmetric structures or the classical absolute negative resistance produced by driving a symmetric device into its differential negative resistance r e , m e with a strong ac field. PAT is a well established phenomenon describing quasi-particle t-nneling in superconducting electronics in the presence of high frequency radiation [5]. Only recently has it become apparent in high frequency transport in semiconductor multiquantum well supeflattices [ 6 - 9 ] and nanostructures [10,11]. The recent development of an intersubband laser is thought to rely, under some conditions, on photon-assisted tunneling [ 12].

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The devices were then glued onto a high resistivity hemispherical silicon lens and gold wires were bonded to the two gold bows. The experiments were performed over a temperature range of 8-15 K with the sample mounted in a temperature controlled flow-type cryostat with Z-cut quartz windows. The radiation was incident on the curved surface of the silicon lens with the polarization parallel to the axis connecting the two gold lobes of the bow-tie.

3. Dynamic localization, multiphoton emission and NAC In Fig. 1 we show the dc current-voltage (I-V) characteristics measured without radiation and with terahertz radiation at three different laser powers. The I-Vwithout laser radiation (Exc =0) shows an ohmic region characteristic of miniband transport followed by saw tooth oscillations associated with sequential resonant tunneling and electric field domains [13]. At low bias, the current through the sample occurs via ground state to ground state tunneling. As the bias is increased, the current approaches a "critical current", the maximum current that the ground state to ground tunneling can support, and a quantum well breaks off forming a high field domain. The high field domain is characterized by the alignment of the ground state in one well with the excited state in

0

.

6

~

2. Exl~rim~t The sequential resonant tunneling supeflattice used in these experiments consisted of 300 nm of GaAs doped at n + = 2 x l 0 1 S c m -3, followed by a 50nm GaAs spacer layer and ten 15nm GaAs quantum wells and eleven 5 nm GaAs/ Alo.3oGao.voAs barriers and capped by another 50urn GaAs spacer layer and 300nm of n + = 2 x 1018 cm -3 Si doped GaAs. The substrate is semi-insulating and the superlattice and spacer layers were n doped to 3 x 1015 era-3 with Si. These experiments were facilitated by integrating the superlattice into broad band bow-tie antennas.

0.4 W'~THz1~1~ ~ 1 0.2 -0.2 -0.4 -0.6

-0.2

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Volts Fig. 1. Current-voltage charactoristics measured without radiation and with 1.30 THz radiation at three different laser field

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the. "down hill" well. As the bias is increased still further one well after another breaks off into the high field domain, indicated by the saw tooth NDR structure, until the entire sample is encompassed by the high field domain. In this work we are concerned only with the behavior near zero bias, where the transport occurs via ground state to ground state tunneling. In the presence of a terahertz electric field the conductance at zero bias is at first suppressed. That is to say, the terahertz electric field tends to localize the electrons, a manifestation of dynamic localization. However, as the dc bias is. increased the one-photon emission channel is brought into resonance with the ground state in the neighboring well and the current increases, resulting in the formation of a step in the I-Vcharacteristic. (Note that the voltage where this occurs is approximately Nf~,o/e, where N is the number of quantum wells. N = 10 here. The relation is not exact due to a voltage drop in the set back regions between the n + contacts and the superlattice). At the next higher power shown in Fig. 1, the conductance near the origin actually becomes negative. When this happens the electrons use the absorbed energy from the laser field to tunnel against the applied dc bias. While localization and near zero conductance is predicted absolute negative conductance is not. At this level of terahertz excitation, as the dc bias voltage is increased beyond the absolute negative conductance region, the one-photon emission step is encountered in the I - V characteristic (Fig. 1). The current becomes positive and the electrons are driven down the superlattice accompanied by the stimulated emission of a photon [14]. Remarkably, a two-photon emission step is also seen at the appropriate voltage. Finally, at the highest power shown in Fig. 1, the one-photon emission step is substantially diminished, the current at the two photon step has decreased by a factor of two and the formation of the threephoton emission step is clearly seen at the appropriate bias voltage. It is clear (Fig. 1) that the transport through the various emission channels, as well as the zero bias conductance, is strongly dependent on the laser field strength. In Fig. 2 we show the step height

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~ ', ' -5 . . . . . . . . . . 2 4 6 8 10 Laser Field S~'~gfla (kV/em)

12

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Fig. 2. The step height versus laser field strength for one-, two-, and thro~photon ~sisted tunneling and the zero bias differentia/conductance, zero-photon process, at 1.30 ~ The three arrows indicate the location of the maximums of J~ and respectively and the minimnm of Jo2. The lines are t o aid the eye.

for the one-, two- and three-photon emission steps and zero bias conductance as a function of terahertz field strength. For the one-, two- and threephoton processes these steps are defined as the height along the current axis from the base of the step to the upper edge of the step. For each, the step at negative and positive bias has been averaged. The zero bias conductance has been defined as the difference in current measured from the be~nning of the ohmic region at negative bias through the origin to the end of the ohmic region, measured at positive bias, divided by the voltage difference. We can project these results on the model of Tien and Gordon in the following way. We assume that the basic transport mechanism is the sequential tunneling from one quantum well to its neighbor. Then, following Tien and Gordon [5] we expect that in the presence of a laser field the transition probability to virtual states separated from the ground state by + nhto is proportional to J~(edE,~/tico). In particular, J2o(edE,o/hro) describes the suppression of the conductance at zero bias, i.e. dynamic localization, and we expect the conductance to be driven to zero when the argument, edE,~/tito, equals the zero of the Bessel function. Likewise, we expect the new channels, that appear as steps at the appropriate bias voltage,

R J. Keay et aL/Surface Science 361/362 (1996) 176-180

to

develop

in

a

non-monotonic

way

as

J~(edEac/~io~). This is essentially what is observed in Fig. 2. In fact, we can sca.le the horizontal axis so that the minimum in the zero bias conductance, and the maxima in the photon-assisted channels align with the appropriate minimum and maxima of the Bessel functions. The arrows are shown in Fig. 2 and can be simultaneously brought into agreement with a single scaling which then defines the field strength inside the superlattice. The agreement with Tien and Gordon's approach is quite good. While the d y n a m i c localization is expected, the absolute negative conductivity does not arise in a straightforward way from this model and requires some consideration of level width, temperature and electron distribution. In Fig. 3a and Fig. 3b we schematically show a broadened level in one well coupled to the neighboring well by the laser field. For the purposes of this discussion we assume that the electrons in these wells are distributed thermally with more at the bottom of the broadened levels than at the top. It is important to realize that near the first minimum of 2~(edE~o/~ico)transport will be dominated by the photon-assisted channels. In Fig. 3a the applied dc field is less than hco/ed and the one-photon emission channel is blocked by filled final states, but the absorption channel can proceed and the current will flow to the left or against the applied dc bias. As soon as the dc bias exceeds t~co/ed, Fig. 3b, the picture is reversed and current will flow from left to right, in the direction of the applied dc bias. In this picture the range of dc voltages over

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which this scenario takes place is intimately related to the level broadening. For very narrow well defined levels, this dispersive behavior of the current flow, first against the applied bias, then with it, wili occur over a very narrow voltage range. The strength of this discontinuity while obviously related to the strength of the terahertz electric field will may also depend on temperature in an interesring way. At high temperature, where kT>>AE (ztE is a measure of level broadening) there will be little strength in this discontinuity r14]. Furthermore, it would appear that the occurrence of a negative current flow for a small positive bias requires a level broadening that is su~cient to cause the tails of the energy levels to extend to within reach of the photon-assisted channel but not so broad that it will completely "wash out" the effect. It seems likely that the photon-assisted channels which correspond to stimulated emission of as many as three terahertz photons are critically related to level broadening as well. Under dc bias the ladder of q,,~ntum well ground states will all be equally occupied and, at first glance, net stimulated absorption or emission of a photon should be absent. But it is apparent that net gain (stimulated emission) can appear on the low frequency side of the Stark ladder splittings and net loss (stimulated absorption) can occur on the high frequency side. This view relieves the apparent contradiction with Bastard et aL [2]. In conclusion, we have observed dynamic localization and negative absolute conductance in a multi-quantum well superlattice in the sequential tunneling limit. The dynamic localization and NAC are accompanied by the appearance of photonassisted channels that correspond to the stimulated emission of as many as three terahertz photons.

Acknowledgements Fig. 3. (a) Broadened levels in the presence of radiation at low bias; emission channels are inhibited while the absorption channels are enhanced. (b) At higher bias the absorption channels are inhibited while the emission channels are not. The arrows represent fixed photon energy and represent the inhibited pro-

cess (dashedarrow) and enhancedprocess (solidarrow).

We would like to thank the staff at the Center for Free-electron Laser Studies for their help: J.R. Allen, D. Enyeart, G. Ram/an and D. White. Funding for the Center for Free-electron Laser Studies is provided by the Ofl~ce of Naval Research. Additional funding was provided by the

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Army Research Office, the NSF and the Air Force Office of Scientific Research.

[7] [8]

References ["1] V.V. Pavlovich and E.M. Epshtein, Sov. Phys. Semicond. 10 (1976) 1196. [2] G. Bastard, J ~ Brown and R. F ~ l ~ a , in: Solid State Physics: Semiconductor Heterostructures and Nanostructmes, VoL44, Eds. tL Elxten~ch and D. Turnbull (Academic Press, San Diego, 1994) p. 325. [3] Sollner et aL, in: Physics of Quantum Electron Devices, Ed. Federico Capasso (Springer, Berlin, New York, 1990). [4] Juras Pozhela, Plasma and Current Instabilities in Semiconductors (Pergamon, Oxford, New York, 1981). [5] P,K. Tien and J.P. Gordon, Phys. Rev. 129 (1963) 647. [6] P.S.S. Gnimaraes, B.J. Keay, J.P. K~min~ki~SJ. Allen, Jr,

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