Conductance fluctuations and noise in barely conducting N+ wires

Superlattices and Microstructures, Vol. 9, No. 1, 1991

35

CONDUCTANCE FLUCTUATIONS AND NOISE IN BARELY CONDUCTING N+ WIRES A R Long*, M Rahman+, M Kinsler#, C D W Wilkinson+, S P Beaumont+ and C R Stanley+ *Department of Physics and Astronomy, +Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8QQ, Scotland, UK. (Received 13 August

1990)

Conduction in narrow n+-GaAs wires prepared by reactive ion etching of epitaxial layers has been studied at low temperatures. Applications of high electric fields for short periods or exposure to low intensity visible light enables the number of carriers in the samples to be decreased or increased. Photocurrent noise is found to be anomalously large for samples with closely spaced voltage probes. When samples are allowed to relax after the introduction of a non-equilibrium carrier concentration, steps are observed in the conductance which we ascribe to single electrons interacting with traps• From the magnitude of these steps, we estimate the coherence length in these samples to be of the order of the wire width, and postulate that the electron coherence is limited by trapping events occurring at the wire edges.

In this paper we describe measurements made on degenerate n-type GaAs wires at low temperatures (typically 12K). Such wires are fabricated from 50nm epitaxial layers grown on semi-insulating substrates by molecular beam epitaxy. The wire patterns are defined by electron beam lithography producing resist or metallic masks. The remaining n material is then etched away using a reactive ion etch, based on SiC14. Using this procedure, wires may be prepared with widths down to 50nm. An important feature of the preparation method is that during removal of the excess GaAs, the sidewalls of the wires suffer damage. As a result traps are generated which remove carriers from the wire and hence enhance the effective depletion width at each side. The wires then do not conduct until they are made rather wider than would be predicted from simple l-D depletlon calculatlons . For devlce purposes, such damage is undesirable, but for investigations of transport in quasi l-D systems, it is extremely useful. This is because the number of free carriers in the wires can be changed during the course of an experiment by exchange with the traps. If a high field (= 3.105Vm -I) is applied to a wire for a period of typically tens of seconds then carriers will be promoted to occupy traps in the edge regions and the wire conductance will fall. The process can be reversed by exposing the wire to weak super- band-gap light which generates electron-hole pairs. These are swept apart by the field at the wire edges and the damage centres are emptied by hole trapping leaving the electrons to contribute an enhanced photoconductance. This photoconductance is

0 7 4 9 4 0 3 6 / 9 1 / 0 1 0 0 3 5 + 04 S02.00/0

persistent, decaying slowly and approximately logarithmically with time after the light source is removed. It is straightforward to show, by examinin E the isolation of neighbouring wires that, at the low excitation intensities used, the photocurrents are restricted to the wires. The two excitation processes are reciprocal; any wire can be converted successively to high and low conductance states. Wires with widths (w), close to the cut-off value (wc) at which they are fully depleted when first prepared, can be switched between states in which the conductance of the wires is large and immeasurably small. Full details of these physical processes will be given in a future publication. In fig. I we show an example of the behaviour of a wire with dimensions close to w after the c application of a high field pulse. This wire was lO~m long and was studied by measuring the conductance between the end contacts (a 2-terminal (2-T) measurement) at a field low enough not to drive carriers into the traps. Two points should be noticed about this figure. Firstly the magnitude of the conductance in this recovery phase is very much less than that of fully conducting wires of the same length. Under illumination of intensity around ImWm -2 the same wire had a conductance of about 2~S. Secondly the recovery is characterised by steps in which the conductance changes discontinuously. The exact pattern of these steps varies between different excitation cycles on the same wire and for different wires similarly excited, but their magnitudes remain similar, typically lOnS for 10~m wires. In certain

© 1991 Academic Press Limited

Superlattices and Microstructures, Vol. 9, No. 1, 1991

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circumstances we observe multiple transitions between different conductance states (telegraph noise) with similar magnitudes of conductance difference. We interpret the step structure as resulting from a change in carrier number by unity somewhere within the length of the wire, or in the case of the rather rarer telegraph noise from the movement of a trapped charge in a multiply connected defect. This is a similar conclusion to that of Mailly et. al. 2 who performed high field excitation and recovery experiments on etched modulation doped wires. The low overall conductances of the wires in the recovery state suggest that in the early stages the wires may be inhomogeneous along their lengths, and that their resistances are then dominated by regions where the conducting channel is cut. This inhomogeneous behaviour has been confirmed by studying the 4-terminal (4-T) conductances of the wires using potential probes attached down their length. To analyse the magnitude of the step changes in conductance in such a non-uniform configuration is not straightforward. To d o s o we h a v e e x a m i n e d s a m p l e s w h i c h h a v e p o t e n t i a l probes attached very short distances apart. Earlier studies of "universal" conductance fluctuations i n simL a r n + - G a A s w i r e s i n h i g h e r conductance states 3 suggest that the coherence length at low temperatures is of the order of the wire width. The sample geometry we have recently been using (fig. 2) has probes at separations of only a few wire widths and is therefore expected to cover only a small number of coherence lengths. In fig 3 we present data for a wire having this geometry and with w just below w . Both 2-T and 4-T data are presented, c for a cycle in which the wire starts from a configuration in which it is switched hard off (by the previous application of a high field). The sample is then illuminated at 50s using a

Figure 2 A plan of the lithographic pattern used for measurements of wires using closely spaced potential probes (V ÷ a n d V-) and broader current l e a d s (I ÷ a n d I - ) .

HeNe laser and a significant photoconductance is observed. After about 600s, the light is removed and the conductance allowed to decay freely in the dark.

We start first by discussing the photoconductance and the noise in the photoconductive state which is apparent from the diagram. Photoconductance noise has been studied in wider GaAs wires similarly prepared by Bykov et. al. 8. In analysing this data it is necessary to appreciate that, as well as the sample between the voltage probes, the current leads were also prepared by etching and show edge damage. It is therefore necessary to allow for this in comparing 2-terminal and 4-terminal data. To do this we assume that the edges ave the same on all wire segments and therefore that the total conductance of the segment i under illumination of intensity I can be written in the f o r m Gi(I] where

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ll.(Gi(I) - dol) = 12.(G2(I] - Go2] (2] Data for a range of intensities spanning four orders is plotted in fig. 4. Note that the

Superlattices and Microstructures, Vol. 9, No. 1, 1991 ,

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Figure 3 a) 2-T and b) 4-T conductance measurements taken at 12K on a sample made using the pattern of fig. 2 from an ~ i ~ a y e r with a carrier concentration of 9xl0-Vm -. The wire width was 145nm. The photoconductance was measure~ between 50 and 450s with approximately ImWm -= falling on the sample.

sample photoconductance increases by less than a factor of 2 over this range, typical of persistent photoconductivity. The linear relationship revealed by this graph justifies our assumption of the equivalence of all etched edges in the sample. The gradient of the graph 12/11 is consistent with the known geometry of the device. The intercept on the horizontal axis is essentially the core conductance of the current leads, as the wire itself is switched off in the initial dark state, but the current leads, being rather wider, are not. We can now use this series model to analyse the noise in the photoconductance signal. This we believe arises predominantly from shot noise in the trapping process; the measured noise in the source is not expected to have any influence on the measurements. Observations of the decay of the photocurrent show that the trapping time distribution is logarithmic, with

a low cut-off at about lOms. This is reflected in the frequency spectrum of the noise which is observed to be I/f-like between O.l and lOHz. In fig. 3, the noise was sampled by making conductance measurements every 2s. From the raw data, the series model is used to derive the normalised r.m.s, fluctuations AG./G. in both i i

the wire and the leads. To analyse these values we first have to make allowance for the changes in number of carriers in the different cases. Following a common result 4 found in systems showing flicker noise, we assume that the overall mean square fluctuations in carrier number are given by AN 2 = ~ N

(3)

where ~ is only weakly dependent on N. Assuming constant carrier mobility ~, the number of carriers in a given sample is related to the conductance by (4) N i = Gili2/e~ Hence as AG over any bandwidth will reflect AN, we predict AG./G. i i

~ I/~/N.

1

~ 1/1.VG. i i

(5)

When plotted in this form (fig. 5), the data for different illumination intensities follow a good straight line for large N, both for the wire and for the leads. The gradient of the line is consistent with ~ ~ i, assuming the hulk mobility and a reasonable distribution of trapping times. However at small N, the noise greatly increases. We ascribe this to mesoscopic fluctuations in the scattering configuration due to the continually changing occupation pattern of the traps. Such fluctuations invalidate our assumption of

38

Super/attices and Microstructures, Vol. 9, No. 1, 1991 1

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made in calculations note however

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found ]f data on long wires are analysed. From the |OnS steps in fig. ], we estimate l,#

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Figure 5 Normalised RMS Rhotoconductance noise against a measure of N -t/2 where N is the number of carriers in the sample.x - data taken from the leads, • - data for wire segment.

constant mobility. A more complete analysis of this phenomenon is in course of preparation. We now turn to the decays observed after removal of the light (fig. 3). The 2-T decay is essentially smooth and monotonic. Some step structure is observed but on the scale of 40nS and hence almost undetectable in the diagram as drawn. On the other hand the 4-T curve shows much stronger fluctuations, with steps of typical magnitude I-2~S and excursions in both directions. Repetitions of this measurement from different starting conditions give statistically similar but not identical results. Analysing firstly the magnitude of the 4-T step structure, we assume that it results from quantum interference effectsS'6and that therefore in one cell of length L~, the phase

]60nm for I = lO~m and w = qOnm. Finally, we discuss the correlation between the 2-T and 4-T data. Comparing the curves of fig. 3, it will be seen that not all the steps and the drift observed in the 4-T data are reflected in the 2-T result, This is not unexpected however as the former is particularly susceptible to fluctuations of scattering configuration in the throats of the voltage probes. These will not be seen in the overall conductance of the device between the current pads. To summarise, we have some evidence that when these wires are close to cut-off, they become inhomogeneous. However this does not appear greatly to affect estimates of the coherence length made by assuming conductance steps result from single electrons interacting with traps. Studying the photoconductance noise is a promising new technique for examining mesoscopic effects in these systems. Acknowledgment - we should like to acknowledge helpful discussions with J.H.Davies. This work was supported by the Science and Engineering Research Council of the U.K. under Grants GR/F 31472 and GR/F 80890.

References. I

2 3

breaking length, the steps associated with changes of scattering configuration or of charge number will be = ea/h. For a I-D array of N. cells, this conductance fluctuation will be reduced 7'a by a factor

of N# 2. Hence

use

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=

I]/N ~

the conductance fluctuation is valid, it ]s interesting tc that similar values of k~ are

we can

for

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sample, obtaining a result of 120nm. This value is much less than estimates of the coherence length assuming the dominance of electronelectron scattering 9. It is also of the same order as the wire width (145nm), as was observed in "universal" conductance fluctuation studies of similar wires with w > w 3. It is c likely that coherence is limited in these samples by inelastic processes involving shallow traps at the wire edges. The value of L# should be treated with some caution as it is by no means clear that in wires of such low conductance the assumption of weak scattering

5.

6. 7.

8.

9.

S Thoms, S P Beaumont, C D W Wilkinson, J Frost and C R Stanley, Proceedings of International Conference on Microcircuit Engineering, Interlaken (1986). D Mailly, M Sanquer, J-L Pichard and P Pari, Europhysics Letters 8, 471 (1989). R P Taylor, L Eaves, P C Main, G P Whittington, S Thoms, S P Beaumont and C D W Wilkinson, Proceedings of International Conference on the Application of High Magnetic Fields in Semiconductor Physics, Wurtzburg (1986); Surface Science 196, 52 (1988). See for example in A van den Zie], Noise in Measurements, Wiley (New York - 1976). B L Al'tshuler and B Z Spivak, Journal of Experimental and Theoretical Physics Letters, 42, 447 (1985). 5 Feng, P A Lee and A D Stone, Physical Review Letters 56, 1960 (1986). D E Beutler, T L Meisenheimer and N Giordano, Physical Review Letters 58, 1240 (1987). A A Bykov, G M Gusev, Z D Kvon, D I Lubyshev and V P Migal', Journal of Experimental and Theoretical Physics Letters 49, 135 (1989). G Rickayzen, Green's Functions and Condensed Matter, Academic Press, London (1980), p. 139.