Giant temperature resonances of noise in submicron quantum well structures

~

Solid-State Electronics Vol. 37, Nos 4-6. pp. 1011-1014, 1994

Pergamon

Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00 + 0.00

GIANT TEMPERATURE RESONANCES OF NOISE IN SUBMICRON QUANTUM WELL STRUCTURES S. T. STODDART I, A. K. GEIMI#, S. J. BENDING 1, J. J. HARRIS2, A. J. PECK3 and K. PLOOG4 ~School of Physics, University of Bath, Claverton Down, Bath BA2 7AY, "Interdisciplinary Research Centre, Imperial College, Prince Consort Road, London SW7 2BT, England, 3Max-Planck-lnstitute ffir Festkrrperforschung, Heisenbergstr. 1, D-70569 Stuttgart and 4Paul-Drude-Institute fiir Festkfrperelectronik, Hausvogteiplatz 5-7, O-1086 Berlin, Germany Abstract--We show that excess noise in micron-sized samples fabricated from Si-doped GaAs/GaAIAs quantum wells and heterostructures is a strong non-monotonic function of temperature with several sharp peaks below room temperature. The noise power at the peaks exceeds the background noise by several orders of magnitude. The observed behaviour represents a classical noise source where only a single type of switching defect with a well-definedactivation energy is present. We attribute the resonances to deep metastable donors and provisionally identify one of the donors as the known DX-centre in GaAs and GaA1As.

Low-frequency noise in solids has received considerable attention in recent years. It has been shown that almost any resistor demonstrates excess noise with an approximately 1/f-shaped power spectrum and it is well established that this noise can be described as arising from the thermally activated switching of defect states[I,2]. Each defect gives rise to a Lorentzian power spectrum whose superposition leads to l/f-noise if the distribution of relaxation rates is fairly fiat. Recently, using sufficiently smalllength-scale devices random telegraph noise due to single defect switchings has been observed[3-5]. If the sample size is increased, the number of the elementary noise sources increases and it is possible to follow the transformation of the telegraph noise into l/fnoise[2-4]. New noise sources can also be activated by raising the temperature which changes the spectrum into 1/f-form and leads to a monotonic increase of the noise power. In this paper we report noise with a resonant-like temperature dependence. Sharp peaks in the noise have been seen against a negligibly small background in micron and submicron devices fabricated from 6-doped GaAs quantum wells and GaAIAs/GaAs heterostructures containing a high-mobility two-dimensional electron gas (2DEG). The temperature resonances in the noise are in striking contrast with one's common experience that noise is a monotonic or, at least, smooth function of temperature[I,2]. Despite the fact that this type of noise behaviour has never been observed before, we show that it corresponds to the simplest model of random telegraph noise[l,2,6]. The observed noise arises when the switching defects are exactly the same and differences fPresent address: Physics Department, University of Nottingham, Nottingham NG7 2RD, England.

in their thermally activated relaxation times r are minimal. This condition appears to be fulfilled in Si-doped GaAs and GaAIAs where the dominant defect (Si) becomes metastable at high concentrations[7]. A Si atom can only occupy a few strictly determined sites in the crystal lattice of GaAs and its energy is not affected by lattice imperfections as in the case of polycrystallineand amorphous materials which have previously been studied. We show that the dominant contribution to the observed noise arises from the thermally activated switching of DX-like centres[7]. The noise can be persistently quenched by infra-red illumination which also leads to persistent photoconductivity (PPC) in our structures. The switching defects influence the electrical conduction due to the sensitivity of the resistance of a small sample to the state of every single impurity within it. Two types of structures have been investigated in our experiment. The f-doped GaAs quantum wells were grown by molecular-beam epitaxy on semi-insulating GaAs substrates and consisted of 500 nm of undoped Ga07Al03As followed by a GaAs quantum well of width in the range 10-20 nm and terminated with 250nm of undoped Ga07Al03As and a 20nm GaAs capping layer. A Si 6-doped plane of nominal concentration in the range (2.5-5)x 10~2cm-: was placed in the centre of the quantum well. The quantum confinement of the Si doping layer increases the separation between the two-dimensional (2D) electron subbands and allows one to work in the simplest situation when only one 2D subband is occupied. Further information about the structures and their characterisation can be found elsewhere[8]. The second type of structure we have studied is the standard modulation-doped GaAIAs heterostructure with 2D electron concentration ---2.7 x 10J~cm-2 and mobility ~ 750,000 cm2/Vs at 4.2 K.

1011

S.T. STODDARTet al.

1012

Hall bar structures with several voltage probes were fabricated using photolithography and wet chemical etching. Samples with different conducting widths b between 0.5 and 8/am have been investigated and the separation between the centres of adjacent voltage probes is twice the characteristic sample width, d.c. currents between 1 and 100/~A//am are passed through the sam,_mp~and signal fluctuations at the voltage probes ( x / ( A V 2)) are measured using the noise option of a E G & G 5210 Lock-in amplifier at a chosen frequency f i n the range 1-104 Hz. Bandwidths A f i n the range 0.1-1 Hz around the centre frequency were selected. Figure 1 shows typical examples of the temperature dependence of the noise a t f = 30 Hz for both types of structure studied. Three peaks near 50, 80 and 170 K are clearly seen for the case of the I 0 nm wide 6-doped quantum well (nsi = 5 x 10 ~2cm -2) and only one peak near 180 K has been observed for the modulation doped sample. We find that the noise signal changes linearly with the current ( x / ( A V 2) oc I ) indicating that these are fluctuations in the resistance R. Consequently, experimental data are presented using the normalized noise power S ( f ) = (A V2)/V: = ( A R 2)/R 2. The power S is found to be inversely proportional to the distance between voltage probes and the sample width b (i.e. S oc I/A where A is the sample area). In the plots, S is multiplied accordingly by the active area (S, = S x A ) and is given in units m2Hz-L The positions and the amplitudes of the noise peaks as a function of temperature depend on the

15

30Hz

I I I

"E 10

25 0 .A, 2 50 100 150 200 250 T (K) ,

,

,

,

,

Fig. 2. Noise peaks in the ~-doped GaAs quantum well of Fig. 1 at two different measurement frequencies. measurement frequencyf. Figure 2 shows an example of this dependence for the top trace in Fig. I. In Fig. 3(a,b) the positions, Tm~x, and heights, S~aX, of two of the noise maxima observed in the quantum well sample are plotted as a function of frequency. We note that Snma*decreases with frequency as l / f and l/Tmax decreases as In(f). At a fixed temperature, Sn(f) has exactly the Lorentzian form S , ( f ) 0 c [1 + ~ f 2 ] - 1 as also shown in Fig. 3(a) for the peak near 170 K. All our results follow directly from the standard theory of excess noise[l,2]. A switching defect can be characterised by its relaxation time r and the magnitude fir of changes in the sample resistance: AR (t)_~ 5rexp(-t/r). The noise power spectrum

1.0

10

20 a

7-?- 15 ~E e,l

N

7x

10

1

0

/

a

E

E

~

0.5 o E

-.-110 x

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O

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10

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5

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0.0 14

b

6

12

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2

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..... 50

g

100 150 200 250 ,300 T (K)

Fig. 1. (a) Noise power as a function of temperature in a 2/am wide sample fabricated from a I0 nm wide fi-doped GaAs quantum well and (b) in a 0.5/am modulation-doped heterostructure sample. The low temperature section of (a) is magnified by a factor of 10 and shifted for clarity.

1

10

102 10 3 f (Hz)

104

8

Fig. 3. Frequency dependence of the magnitude and position of noise maxima in the &-doped quantum well structure of Fig. I. Open and solid circles are for the peaks near 80 K and 170 K respectively. Also shown is the noise power spectrum for a fixed temperature of 170 K (rhombic symbols). Solid lines are the best fits to eqn (I).

Excess noise in submicron quantum wells 40

due to N identical but uncorrelated defects is given then by:

S (f) = N(fir/R )23/[1 + (2rrf3)2].

SSE]?I~6--FF

f= IOOHz~

"I-N 3 0

(1)

At moderate temperatures the switches are usually thermally activated and can generally be described by 3-1 =~o~exp(_EA/kT). If there are many defects present with a wide spread in their activation energies EA, the integration of eqn (1) leads to a l/f dependence and the noise is a smooth function of temperature[l,2]. However, in the case where E A and 30 have well-defined values, a noise peak will occur. A characteristic frequency of the random resistance switches (v ~ 3 - ' ) changes exponentially rapidly with temperature, resulting in a resonance when v matches the measurement frequency. Due to this exponential behaviour the resonance can survive over a very wide frequency band and for the maximum bandwidth A f = 10+4Hz available in our experimental set-up (the integral noise power in the range f = 1-104 Hz) the peak widths in Fig. 1 would only increase by a factor of 3. We note that more detailed models of two-state random telegraph noise[9,10] which take into account the balance between generation and recombination processes cannot explain resonances in the noise. The appearance of peaks requires that the recombination process is a background process and its relaxation rate not be coupled to the generation frequency via a balance equation. Equation (1) implies that SF* oc l/f and EA/Tm~, = -in(2nfi0). Solid lines in Fig. 3 show the best fits to the experimental dependencies for the quantum well structure. We obtain E 1 ~_ 0.1 eV, E~ = 0.145 eV, E3A= 0.37 eV, where the upper index denotes different switching defects in the order of appearance with increasing temperature, and z0 is found to lie in the range 10-H--10-L3s. When the values of E A and 30 are known, eqn (1) allows us to compare directly the experimental temperature dependences of S, with theory without using any fitting parameters. An example of such a comparison is shown in Fig. 4 where the theoretical curve follows the observed temperature dependence perfectly. The agreement is excellent for peaks 1 and 2 although peak 3 is 30% wider than expected from eqn (1) probably indicating that there is some small spread in the value of the activation energy for this type of defect. The same analysis for GaAIAs/GaAs heterostructure samples gives EA = 0.42(+0.02)eV and 302 10 -11 s. Both studied types of structure demonstrate strong low temperature persistent photoconductivity (PPC) indicating that deep metastable donors are present in a concentration comparable with the Si doping level. Figure 4 shows a direct connection between the noise and PPC in the quantum well structure. As the electron concentration increases upon infra-red illumination the noise decreases rapidly indicating that deep donors (probably DX-like centres whose concentration decreases under illumination) are respon-

1013

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O

20

dlO

0 60

L

S

100

80

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T (K) 1.0 ~ ~"

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0 E 0.5 0

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\

•

\

o\Q

•

\

\,o o

o.o 3.3

b

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3.'7 4.'1 n (1012cm -2)

,

o

r~ ~ 4.5

Fig. 4. Persistent suppression of the noise peak by infra-red illumination in the 6-doped quantum well structure of Fig. 1 (a) Noise in the dark (upper curve; n = 3.3 x 1012crn-2) and after partial illumination (lower curve; n-~ 3.8 x 1012crn-2). The solid line in (a) shows temperature dependence of noise calculated directly from eqn (1). (b) Variation of the height of the noise peaks with total electron concentration.

sible for the observed noise. All the peaks are significantly suppressed by illumination. Note that neither the position or the shape of the peaks alters while the Fermi energy of the 2DEG increases substantially. This implies that conduction electrons at the Fermi level do not directly participate in the noise and we observe switches between the deep-donor state and some intermediate state rather than the shallow-donor state. It is very probable that the dominant peaks near 170 K in the noise spectra of both our structures are due to the known DX-centre. The activation energy for this peak in the GaAIAs/GaAs heterostructure is in good agreement with the known value of 0.43 eV for the DX-centre in GaAIAs[7]. However, the dominant peak in the quantum well has E 3 = 0 . 3 7 e V which is only in fair agreement with _---0.33eV measured by DLTS for the DX-centre in n + - GaAs[7]. This is probably due to considerable changes in the band structure arising from 6-doping in a quantum well[8]. Another deep donor in the quantum well device with an activation energy of 0.145 eV can possibly be attributed to a donor which was found in AlxGaj_xAs for x < 0.15 and has a thermal emission energy in the range

1014

S.T. STODDARTet al.

0.13--0.16 eV[l 0]. The donor responsible for the small peak near 50 K remains unidentified. Note that different types of donor are present in the f-doped GaAs quantum well rather than a single donor with different energy levels. This is evident from Fig. 4(b) which shows the dependences of S max on electron concentration after illumination for the two major peaks in the quantum well sample. The very different behaviour of the peaks under illumination implies that different defects are responsible for these resonances. It is clear from Fig. 4(b) that illumination removes the captured electrons much easier from defects of type 2 and only then starts to depopulate type-3 deep donors. This difference in sensitivity to illumination for the two states has been directly confirmed by measuring the time variation of the total concentration under continuous illumination which shows two distinct levels of saturation, one with a short and another with a long time constant. Finally, we discuss the scaling of the noise and its absolute magnitude. A switching DX-like centre changes the scattering cross-section for conduction electrons (a) by a value 6a. First order corrections to the Boltzman equation due to the switching of a single impurity lead to resistance changes 3r/R = (1/Ni)3a/a where N~ is the total number of impurities in a sample which differs from the number of switching defects N[ll]. The noise power in the peak [see eqn (1)] is given by N ( f r / R 2) oc N / N .2, oc 1/A as observed in the experiment. Assuming that the impurity concentration n~/A is equal to the doping level, data in Figs 3(a) and 4(b) can be used to show that 6a/a ~- 0.1 and 0.3 for peaks 2 and 3 in the quantum well structure, respectively. The fact that the inferred values of 3a/a are of the order of unity confirms that coupling between the switching defects and the conductance occurs via a change in the scattering cross-section of the DX-like centres. This simple consideration is not directly applicable to the modulation-doped heterostructure since donors are remote from the carriers, phonon

scattering is dominant for the 2DEG at these temperatures and a parallel conductance in the Si-doped GaAIAs layer is probably present. In conclusion, micron-sized samples of 6-doped GaAs quantum wells and modulation-doped beterostructures show giant peaks in the temperature dependence of the excess noise power. This noise is caused by the temperature activated switching of many Si donors with a single well-defined relaxation rate. The defect leading to the strongest resonance near 170 K is tentatively identified as the known DX-centre. Noise measurements of the type described here represent a powerful tool for the identification and characterisation of deep metastable defects and have clear implications for practical limits on the operation of submicron quantum well devices. Acknow&dgement--This work was supported by SERC grant no. GR/H23573.

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