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Microelectronic Engineering 17 (1992) 5 17-520

Elsevier

5 7

Resonant tunnelling in O-D and 1-D double barrier systems

G. Faini, A. Ramdane+, D. Mailly, F. Mollot and H. Launois

Laboratoire de Microstructures et de MicroClectronique - CNRS

196, avenue H. RavCra 92220 Bagneux - France

+ present address: CNET, 196, avenue H. RavCra 92220 Bagneux - France

Abstract

We present an experimental study consisting of O-D and 1-D energy spectroscopy by means

of transport and magnetwtransport measurements carried out in nanometric double barrier reso-

nant tunnelling heterostructures. Coulomb blockade effects in our structures are discussed.

1. Introduction

The study of low dimensional semiconductor systems has attracted a great deal of interest in

the past few years. Advances in nanofabrication technology have allowed the fabrication of qua-

si one- and zero- dimensional quantum wires and dots.

Quantum confinement along the epitaxial growth direction is controlled to thicknesses down

to atomic layers. Additional lateral confinement is further obtained by either a fabrication im-

posed depletion layer [ 1,2] or an electrostatic field induced by a gate at the surface of the heteros-

tructure [3,4].

Modelling of these systems is non-trivial. As lateral dimensions are reduced, fewer and fewer

electrons are present and may no longer behave as a part of continuum [.5]. In particular correla-

tion effects should be important if the number of electrons and their spatial extent are reduced,

and then Coulomb interactions may become dominant: in small enough systems, the addition

of a single electron significantly changes the Coulomb energy of the system, so that the tunnel-

ling of an electron is inhibited for biases V < Vc = e / 2C, where e is the elementary charge and

C the capacitance of the junction[6]. Charge and spatial quantization effects may become inex-

tricably linked and the question which then arises is how to distinguish between the two.

In this work we report the observation of resonant tunnelling in quantum -dot and -wire

double barrier heterostructures. The constricting lateral potential arises from fabrication im-

posed lateral depletion layers. The effect of an applied magnetic field, which should help sepa-

rate between charge and spatial quantization, has been investigated.

2.

Samples and fabrication process

The MBE double barrier structure consists of a 5.1-nm undoped GaAs quantum well, sand-

wiched between two 8%nm undoped A1.33Ga.&s tunnel barriers, separated from the

heavil

doped electrodes by a 10.2-nm undoped spacer layer. The electrodes consist of a 750-nm

4;

2x10

-3m S&doped GaAs layer, followed by a 250-nm 1018 cmm3 S&doped GaAs cap layer.

The fabrication process has already been described elsewhere [2], only a brief summary of

it will be given here. Electron beam lithography at 50kV using a JEOL 5DII e-beam system is

used to define a selective mask for SIC4 reactive ion etching. After the removal of the mask, a

polyimide is spun on the sample and cured to planarize and isolate the devices. 02-plasma etch-

0167-9317/92/ 05.00 0 1992 - Elsevier Science Publishers B.V. All rights reserved.

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Faini et al. I Double barrier resonant tunnell ing

ing of the polyimide is then carried out to unveil the top of the pillars and walls. Final etch depth

is controlled by laser interferometry and viewing in an optical microscope. This last step could

also be controlled in a SEM as shown in figure 1. The final step consists in the Au-Ge-Ni ohmic

contact formation, allowing to connect either groups of diodes in parallel or isolateddevices. The

height of all the structures is about 2 pm, pillar diameters ranged from 200 nm to 2 pm and wall

widths ranged from 100 nm to 1 pm with a length of 10 j.tm.

6.00

0.00

.640 .960

1.26 1.60 1.92

Voltage Bias V

Fig1 : Plasma unveiling of top of a 400nm

Fig.2: I-V characteristics of 200nm and 400nm

diameter pillar diameter pillar diodes

3. Resonant tunnelling in O-D and 1-D double barrier structures: experimental results

Previous reports have already been made where evidence of resonant tunnelling through both

discrete quasi-levels in quantum boxes [2,7] and quantum wires [7] has been presented.

Figure 2 gives the I-V characteristics at liquid helium temperature for pillar diodes of 200

nm and 400 nm nominal diameters. Multiple peaks are clearly resolved on both curves and prac-

tically equally split by about 70 mV and 35 mV respectively. The lines splitting increases with

decreasing the pillar size and the smearing out of the peaks with increasing temperature is more

pronounced for the wider pillars [2]: this is consistent with the interpretation that these lines are

related to discrete electronic states in the system.

The question of whether resonant tunnelling through small double barrier diodes is dominated

by spatial quantization, single electron charging or both effects, has recently been discussed [8].

Further measurements at lower temperatures (250 mK) and in magnetic fields up to 6T have

been performed to test the hypothesis of coexistence of the two phenomena in our structures.

The second derivative of the current versus the applied voltage d21 / f12 for a group of nine

400 nm-nominal diameter pillars connected in parallel, in zero applied magnetic field and in a

field of 6 teslas, is plotted in figure 3, allowing a more accurate determination of resonance bias

positions. The applied magnetic field is directed parallel to the current flow. More attention has

been paid to the data at threshold bias, which show the presence of several lines not discussed

previously [2,7]. The effect of the magnetic field appears as a change of the relative strength of

the resonance lines as well as a shift in voltage positions of some of them.

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519

Quantum wire diodes of nominal length 1Opm and widths ranging from 1OOnm to lpm were

also investigated. Figure 4 shows a typical spectrum for a single lOO-nm lateral width wall. The

peaks resolved in the voltage range 1.51.7V are broader than in the previous case of 3D-con-

finement with a splitting of about 40mV for the better resolved fiit two. A similar analysis to

the O-D previous case, with a particular attention paid to the data at threshold bias showing the

occurrence of more better resolved resonant lines, is in progress.

.400 600 .800 1 oo

Voltage Bias V

1.20

Fig. 3: dzI / dV* for B=OT and 6T,

Fig. 4: I-V spectrum of a 1OOnm wide

for 400nm diameter pillar wire diode at 4.2K

4. Discussion

A simple picture for the structures fabricated with our process consists of a quantum box em-

bedded in between two quantum wire electrodes [7]. In the absence of charge quantization ef-

fects, the I-V spectrum would then consist of resonances arising from tunnelling between 1-D

emitter subbands and O-D levels in the well as the bias is increased [9]. The resonant tunnelling

sets in when the ground state in the well becomes aligned with the first populated subband in the

emitter. A rounded-step-like I-V curve then results until the ground state passes the bottom of

the emitter conduction band.

A full self-consistent formalism is needed to accurately account for the observed features

[lo]. We nevertheless can make a rough estimate of the cormsponding energy splittings if we

assume a linear AE =f AV) relationship with a proportionality factor determined at threshold

voltage. Two models for the fabrication imposed lateral confining potential have been consid-

ered to account for the data [ 111: the zero magnetic field calculated voltage positions are reported

in figure 3 in the upper and lower row of arrows for a parabolic and a hard-wall type confining

potential respectively. The calculated energy splittings are broadly consistent with the measured

ones in the framework of the two models, but the inverse pillar radius variation of the spacing

between lines seems to favour a parabolic confining potential model [ 111.

Magnetc+tunnelling data at 6T are also shown in figure 3. It is now well established that appli-

cation of a magnetic field to a confined electronic system has a pronounced effect on spatial

quantization [ 121. At low magnetic fields such as the magnetic length 1, = ,@ is larger or

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Faini et al. I Double barrier resonant tunnell ing

comparable to the lateral size resulting from the confining potential, a complex spectrum results.

In figure 3, the appearance of extra peaks, especially at the highest bias voltages, seems then to

imply a spatial quantization dominated energy level scheme, consistent with the value of the

magnetic length at 6T estimated at about 1Onm which is comparable to the undepleted core pillar

radius of about 30nm

[

111.

Coulomb blockade effect could also be responsible for the observed data [ 111: modelling the

double barrier structure as two capacitors in series, we estimate an elementary charging energy

e2/2C of about 3meV, comparable to the energy splittings induced by lateral confining potential.

One might assume the possible coexistence of charge and spatial quantization [ 131 but, neverthe-

less, our structure is symmetrical, so that the necessary condition to observe charging effects,

collector tunnelling rate