Surface Science 361/362 (1996) 656-659
Conductance instabilities in quantum point contacts J.C. S m i t h a, C. B e r v e n a, M . N . W y b o u r n e ~'*, S.M. G o o d n i c k b • Department of Physics, University of Oregon, Eugene, OR 97403, USA b Department of Electrical and Computer Engineering, Oregon State University, Corvallis, OR 97331, USA Received 14 June 1995; accepted for publication 30 August 1995
Al~tract We present low-temperature electron transport measurements on quantum point contacts defined by electrostatic constrictions in the two-dimensional electron gas of a GaAs/AIGaAs heterostructure. Infrared illumination and annealing reverm'oly changes the nature of the electron transport through the point contact, from ideal point contact behavior to transport that shows two-level conductance fluctuations. In the ideal case, the dependL-nce of the differential conductance on the bias across the contact is used to determine the shape of the transverse confining potential In the non-ideal case, current-controlled negative differential conductance in the device chaxacteristic is observed, and is shown to be the average of a two-level random telegraph s i ~ a l The random telegraph signal consists of fluctuations between two welI-defined differential conductance states. We suggest the fluctuations are due to changes in the tl's.nsverse conflnin S potential caused by the dynamics of D X centers in the A1GaAs near the point contact.
Keywords: Electrical transport; Superconductor-semiconductor heterostructures
1. Imroductiou Over the past few years, much work has been devoted to near-equilibrium transport through quantum waveguides and point contacts . In this case, the energy eVa associated with an applied bias V.d iS less than the one-dimensional sub-band separation. The current-voltage (I-V) characteristic is linear. There have also been reports of non-linear transport in these systems E2,3]. This occurs when eV.d becomes comparable to the sub-band separation, so that a different number of sub-bands are available for transport in the forward and reverse directions. We refer to these linear and non-linear transport re#rues as ideal since they show no * Corresponding author. Fax: + 1 541 3465861; o-mAih wybourne~oregon.uoregon.odu
regions of instability. In certain circ-m~tances, under high source-drain bias conditions and when the channel is pinched-off~ current-controlled s-shaped negative differential conductance (SNDC) has been observed. SNDC has previously been explained by the heating and thermal runaway of a confined region of carriers E4]. We refer to this transport r e , me as non-ideal. In this paper we discuss the changeover from ideal to non-ideal behavior. and present random telegraph switching data in the non-ideal r e , m e which indicates that the origin of the SNDC is possibly associated with the dynamics of impurities close to the point contact.
Quantum point contact devices of physical width 0.2/an were fabricated on a molecular-beam epi-
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3".C Smith et aL/Surface Science 361/362 (1996) 656-659
taxy grown, uniform modulation-doped GaAs/Alo.27Gao.vsAs heterostructure, shown schematically in Fig. la. The GaAs cap and the doped AIG-aAs layer both had an Si donor concentration of 1 x 10is cm -3. Electron-beam lithography was used to define the Schottky gate electrodes, which were made from 25 um Au thermally deposited on 7.5 nm Ti. The point contact is formed by applying a negative gate bias V~ to both gate electrodes. At V~=0.0 V and 4.2 K, the material has an electron density and mobility of 3 x 10Ix cm-2 and 1 × 106 cm2fV.s, respectively. The corresponding Fermi wavevector and energy are 46 um and 10.7 meV, respectively. The devices were mounted in a pumped 4He cryostat fitted with an infrared fight-emitting diode (A= 830 rim) for device illumination. Typically, the devices were cooled in the dark from 200 to 1.2 K at a rate of 2 K rain -1, and the I-Vcharacteristic was measured before and after illnmlnation. During illnmination the " lattice temperature increased by less than 1 K, and after returning to thermal equilibrium the conductance had increased by up to 5%, showing that Si donor ionization had taken place. Equilibrium conductance measurements were made on many devices using a 70/~V amplitude, 23 Hz source-drain bias and lock-in amplifier detection of the current Constant current measurements were used to study the non-equilibrium I-Vcharacteristics. The two-level fluctuations were investigated by applying a constant voltage across a load resistor RL, in series with the device, and measuring the current through the device as a function of time.
3. Results and discussion
Fig. 2 shows the differential conductance (G) as a function of V,d for a point contact that has ideal transport behavior. The equilibrium conductance of this device shows eight high-quality plateaus. The shape of the confining potential in the constriction was determined by fitting G(V,d), following the analysis of Martin-Moreno et al. . Below pinch-off, the ratio of the sub-band energy differences (Fig. lb) Z=(E3 - E 2 ) / ( E 2 - E 1 ) ~ 1.43, which is inconsistent with a parabolic potential, for which Z = 1. We obtain the best fit using a potential of the form e(x)=a(V,,)x 6. Above pinch-off, as V, becomes less negative, the prefactor a becomes smaller, increasing the slope of the potential at the Fermi level This is similar to the results found for confining potentials in waveguides . We attribute the high power of the potential to the unusual geometry of the point contact used. As illustrated 6
Fig. 2. Diff~m'ntial conductance as a function of voltage across a point contact. The measurements were made at 1.2 K. The inset shows the nhan.el width and Oo as a function of gate bia&
30\ 20 \ I
Fig 1. (a) ~ h e m s t i c diagram of the point contact device. (b) The potential energy profile of the point contact.
£ C. ~nlth et aL/Surface Science 361/362 (1996) 6~6-6~9
in Fig. lb, the confining potential is offset above the conduction band edge by an energy ~o that depends on Vs . From the data we have also determined the dependence of ~o and the cb~nnel width on Vv as shown in the inset of Fig. 2. As seen from the inset, at pinch-off ( V g = - 1.45 V) the values of the channel width and ~bo approach the Fermi wavelength and energy, respectively. Furthermore, at the gate voltage corresponding to channel formation, the predicted width is close to the 0.2/an lithographic width. After cooling, ideal transport characteristics were obtained; however, infrared illumination or rapid quenching from room temperature produced nonideal behavior, as shown in Fig. 3. Ideal behavior can be restored by annealing at or above 120 K for 12 h. The annealing time and temperature are consistent with those required to deionize D X centers in Alo.27Gao.TsAs  and provide strong evidence that ionized D X centers near the point contact are associated with the SNDC . Instabilities associated with the SNDC were studied by measuring fluctuations in the device current and voltage at different DC operating points determined by the load resistor. When the bias conditions are such that the load line crosses the SNDC, the current (voltage) fluctuates between a high (low) and low (high) value. The fluctuations correspond to switching between the low conductivity state, found below the SNDC region, and the high conductivity state, found above the SNDC region. Fig. 4 shows a typical device characteristic at a single gate voltage with the high and low states for various values of RL. Interestingly, the .
.......... ............... "
~"//" .... ~.:iii~
Vtd(mV) Fig. 3. The eta'rent-voltagerdatiombip of a point contact showing ideal (dotted curves)and non-ideal(solid curves) behavior. The change was caused by infra_redill-mln~tionat 1.2 K.
5 6 7 8 9 10 11 12 13' 14 15 16 V,a (mY) Fig. 4, The I - V ~ e r i s f i c for one gate voltage (-2.3 V) indicafin$ three bias conditionsOven by the load resistors: (a) 1, (b) 15, and (c) 100 kO. Switching occurs between a high conductance~atte(squmzs)and a low conductance~ate (triangles). The inset shows the time dependencefor bias conditions (a), (b) and (c).
two states do not necessarily lie on the characteristic, but instead lie on projections of the characteristic above and below the SNDC region. Hence, the SNDC region appears to be a region of bistability between the two differential conductance states, and the. steady-state I - V characteristic represents a time average of many individual switching events. The transitions between the high and low states have an exponential behavior that can be explained by the transient response of the load resistor is series with the device, which is in parallel with an 830 pF capacitor. The capacitor represents device a n d p a r a s i t i c capacitance in the experimental arrangement. The transient is caused by the device switching between the two conductance states and, as a consequence of the circuitry, the present experiment does not measure the time taken to switch between states. The times spent in either state have an exponential distribution, characteristic of the Lorentzian spectrum of random telegraph noise. The time in each state is characterized by an average lifetime ~. For different values of Vs and different bias voltages, the lifetime of the high conductance state takes the form ~hocexp(I/Io) . The lifetime in the low conductance state appears to be independent of current. Random telegraph signals associated with discrete resistance switching have been reported in several small devices, including silicon MOSFETs
~C. 5-~nithetal./SurfaceScience361/362 (1996) 656-659
, and tunnel diodes , and in equilibrium measurements of point contacts l9 ]. Such behavior has been attributedto potentialfluctuationscaused by the trapping and detrapping of electrons from a single localized state,or by the interaction of a collectionof localiTedstates l 10]. That the switching observed in our devices is a random telegraph process suggests that a dynamic process involving D X centers may be the origin of the conductance instability. According to the multi-channel LandauerBtRtiker formalism, the current through a quasiadiabatic point contact is determined in part by the barrier height (¢o)and profile,which is characterized by a parameter g [-4].If a D X center, or collection of centers, near the point contact is fluctuating between two charge states, this may cause ~bo, or 0g or both, to fluctuate between two values. These changes will be seen as telegraph noise in the transport through the point contact. The region of SNDC could then be the time average of the bistable current associated with each value of ~o and/or u.
Acknowledgement This work was supported in part by the Office of Naval Research N00014-93-1-0618.
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