Microelectronic Engineering 47 (1999) 35-37

Quantum Hall effect breakdown of two dimensional hole gases

S. T. Stoddart, R. Wirtz, L. Eaves, B. L. Gallagher, P. C. Main and M. Henini

School of Physics & Astronomy, University of Nottingham, NG7 2RD, UK

The breakdown of dissipationless current flow of the quantum Hall effect is studied for a two-dimensional hole gas at filling factors v = 1 and 2. Voltage steps and hysteresis are observed and compared with previously published work on electron systems.

The integer quantum Hall effect (IQHE) is characterised by almost dissipationless electron transport in a two-dimensional electron gas (2DEG) at low temperatures and high magnetic fields, B [ 11. The effect occurs when the Landau level filling factor v = hnJeB is close to an integer (ns is the electron sheet density). Under these conditions the current- carrying electrons are transported between current probes along equipotentials. The Hall conductance IN, is then quantised in integral units of e2/h. Soon after the discovery of the QHE, it was found that dissipation sets in and the precise quantisation breaks down when the current exceeds a certain critical value I, [2-51. Dissipation is measured as the voltage drop V, between longitudinal voltage probes. Around breakdown, V, is frequently observed to increase in a step-like way as a function of I or B [3,6-81. Despite the importance of the QHE in metrology and a wealth of experimental data [9], the origin of the breakdown remains controversial. Possible mechanisms include generation of hot electrons [lo], percolation due to an increased number of delocalised states [l 11, inter-Landau level transitions [ 12,13,5,14], emission of acoustic phonons [ 151 and the formation of compressible metallic filaments at high Hall fields [ 161. Recently, a phenomenological similarity between QHE breakdown and the breakdown of streamline flow in classical fluids has been proposed, suggesting that breakdown occurs when the Hall field is large enough to push conducting electrons to the hard wall potential at the physical edge of the Hall bar, where extended states have a large velocity gradient (“oC, the cyclotron frequency) [9].

To our knowledge, there has been no detailed study of breakdown in high-quality, 2D hole gases (2DHG) [ 171. This is surprising since the hole system has properties which differ significantly from the 2DEG. In particular, the 2D subband of heavy hole character has a large effective mass [ 181 and hence a cyclotron splitting fro, several times smaller than for electrons. Also, the hole coupling to phonons differs markedly from that of electrons.

In this paper we investigate the breakdown of the dissipationless IQHE for a 2DHG heterostructure. The Hall bar structure (width 200 pm) was an MBE-grown GaAs/(AlGa)As heterostructure on a (3 1 l)A GaAs substrate with Si (acceptor do It had a mobility of 13.4 m2 V-’ s-l at 300 mK and a sheet density of 1 .O x 10’ 3 !?

ing. rn- .

Figure 1 shows a typical magnetoresistance curve for the 2DHG plotted as V,(B) when a large current is passed in the region of the v = 1 QH plateau. Hysteresis is observed on 0167-9317/99/S - see front matter 0 1999 Elsevier Science B.V. All rights reserved. PII: SOl67-9317(99)00142-2

36 S.T. Stoddart et al. I Microelectronic Engineering 47 (1999) 35-37

sweeping the magnetic field (or current) into and out of the dissipationless state, together with clearly defined step-like structure in V,(B) on the low magnetic field side of the v = 1 minimum in V,(B). On the high B side of v = 1 there is a smooth increase of V, with B.

Figure 2 shows the breakdown curves near v = 2. Hysteresis is again observed, but in this case the steps occur on the high magnetic field side of the minimum. Note that the steps and hysteresis become more pronounced at higher currents and the height AV, of the first step increases slightly with increasing I between 7 and 8.5 pA. At 9 pA, dissipation occurs at all B around v = 2.

The values of the Hall voltage at breakdown are V, = 0.24 V (v = 1) and V, = 0.11 V (v = 2). The breakd own curve for holes at v = 1 shows a qualitative resemblance to previously published data for 2DEG systems at v = 2 (see Figure 3) where the measured voltage height AV, of the breakdown steps is typically 5-20 meV, or equivalently (0.2- l.l)fiio,,/e where fiace is the electron cyclotron energy. For our hole gas the step height is smaller, typically 1 mV. However, given the large effective mass (-0.3 m,) for holes and the low sheet density (lower B-values at v = 1 and 2) of our sample, the step heights in units of Ao,,/e are -1 and comparable with those for electrons [9]. Also, our data suggest a common physical process is responsible for breakdown in both electron and hole gases.

However, it is interesting to note that for the 2DHG steps occur on the low B side of v = 1 and the high B side of v = 2. This may be related to the admixing of spin and orbital terms for 2D valence states. Assuming a hole cyclotron mass of 0.30 m, we find that the critical value of eV&?io, at breakdown is 148 on v = 1 and 135 on v = 2, similar to the large values typically found for 2DEG Hall bars [9].

This work and LE were supported by the EPSRC (UK).

REFERENCES

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Phys. 17 (1984) 6177-90. 13. 0. Heinonen, P.L. Taylor and S.M. Girvin, Phys. Rev. 30 (1984) 3016-3019. 14. L. Eaves and F.W. Sheard, Semicond. Sci. Tcchnol. 1 (1986) 346-349. 15. P. Stieda and K. von Klitzing, J. Phys. C: Solid State Phys. 17 (1986) L483-L486. 16. V. Tsemekhman et al., Phys. Rev. B 55 (1997) R10201-R10204. 17. M. Henini et al., Appl. Phys. Lett. 65 (1994) 2054-2056. 18. S. Hill et al., Physica B 211 (1995) 440-443.

XT. Stoddart et al. I Microelectronic Engineering 47 (1999) 35-37 37

20

qw

10

0 4.15 4.20

B m

Figure 1 Breakdown of the dissipa- tionless QH state at v = 1 for holes showing hysteresis (I= 9.2 lr.A, T = 300 mK). Arrows indicate the direction of the field sweep and the numbers refer to chronological order.

vx

11 .o 11.5 12.0

Figure 3 Breakdown of the dissipa- tionless QH state for electrons :

(a) Hysteresis effect at v = 2 and B = 11.5 T, adapted from Figure 1 of Mokerov et al. [6]. (b) Hysteresis effect at v = 2 and I = 210 fl, adapted from Figure 1 of Cage et al. [7].

Figure 2 Hysteretic breakdown of the dissipationless QH state at v = 2 for holes at various constant currents. Solid (dotted) lines are sweep up (down).