Microelectronic Engineering 30 (1996) 479-482
Nanofabrication with a full control of the electrodes and quantum well dimensionalities: 3D-0D resonant tunnelling through quantum boxes G. Faini a t , C. Vieu a, F. Laruelle a, H. Launois a, P. Krauz b, E. Bedel c, C. Fontaine c, A. Munoz-Yague c aL2M-CNRS, 196 Avenue H. R a v r r a , B.P. 107, 92225 Bagneux Cedex - France ~'tel: (33 1) 42 31 74 30; fax: (33 1) 42 31 73 78; e-mail: [email protected]
bCNET - Lab. de Bagneux, 196 Avenue H. RavEra, B.P. 107, 92225 Bagneux Cedex - France CLAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex - France
Abstract A novel nanofabrication technique for the realization of nanometer resonant tunnelling diodes with independent control of the electrodes and quantum well dimensionalities is presented. Liquid helium temperature current-voltage (I-V) characteristics exhibit a set of resonance lines due to the tunnelling of the 3D electrode electrons through the 0D states of the quantum box. Preliminary results on the line shape and on the relative intensity dependence of the lines with the radius of the box and the principal quantum number are also discussed.
Introduction S e m i c o n d u c t o r m a t e r i a l s have now well established their capability not only for device applications but also as a tool for basic research studies. Advances in Molecular Beam Epitaxy (MBE), and in processing techniques such as Electron Beam Lithography (EBL) and transfer associated methods, have allowed the fabrication and study of macroscopic systems in which the electron wavelike behaviour, and in particular quantum interferences, is the relevant mechanism of the carrier transport. Among all these studies, evidence of the transport through the discrete states of quantum boxes has been addressed by several groups in the last past y e a r s [ I ] . In particular, double barrier resonant tunnelling structures (DBRTS) have revealed their good capability as a tool to probe the quantum boxes spectra by means of transport measurements [2,3,4]. In such structures, the current flows through the hetero-interfaces and senses the effects of the additional fabrication imposed lateral confinement. Previous technological approaches to fabricate such quantum boxes [2,3,4], induce the reduction of the dimensionality not only in the quantum well but also in the electrodes. For the smallest structures, the system consists in a quantum box coupled to two quantum wire electrodes so that the measured current is due to 1D-0D tunnelling. As the radius varies, the 1.
quantum box level and the quantum wire subband splitting change leading to the analysis of complex spectra [4,5,6]. In this work we report on the experimental study of the tunnelling of 3D emitter electrons through the 0D states of the quantum box based on a new fabrication technique allowing us to separate the dimensionality of the quantum well from that of the electrodes. In a first step we d e s c r i b e the technological approach we have used to reach this goal: EBL coupled to ion beam implantation and MBE regrowth are thus detailed. In a last section we show that with this approach, we can really investigate the radius dependence of quantum boxes without varying the nature of the electrodes, in order to perform a real spectroscopy of the discrete states of the three dimensionally confined quantum well.
2. Nanofabrication process This new fabrication process involves two MBE growth steps, separated by a set of technological runs. The MBE sample was conventionally grown on a n ÷ Si doped GaAs substrate. The DBRTS was chosen similar to our standard structure . It consists on a 480nm l x l 0 TM cm 3 Si doped GaAs buffer layer followed by a 480nm 2x1017 cm -3 Si doped GaAs electrode. The active layer region is the following: an undoped 20nm GaAs spacer grown in
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G. Faini et al. / Microelectronic Engineering 30 (1996) 479-482
order to prevent Si segregation in the DBRTS with consequent degradation on the I-V characteristics ; then an undoped 5.1nm GaAs quantum well cladded in between two undoped A1.33Ga.67As 8.7nm thick barriers and, finally, a last layer composed by a 30nm undoped GaAs spacer. EBL is used in order to define a Ni layer pattern by conventional lift-off. This layer acts as a mask for the implantation at 200°C of 5x1014 cm "2 Ga ions, with an energy of 50keV. Areas ranging from 50nm to 50[xm in width are thus protected from the effects induced by the implantation process. After the removal of the mask in an aqueous solution of H N O 3, the sample is prepared for the epitaxial regrowth of the top electrode. The regrown layer consists in a 500nm 2x1017 cm -3 Si doped GaAs top electrode followed by a 500nm lxl018 cm -3 Si doped GaAs cap layer. Details on the cleaning of the surface for the regrowth and on the structural and electrical characteristics of the epitaxial heterointerface are given on reference . EBL is then used to define a new Ni mask for a deep SiCI 4 reactive ion etching for devices isolation or localized TEM investigations . Finally a last EBL level is used for conventional ohmic contacts deposition.
lO0~m top ohmic contact
sample used for the transport measurements in order to be sure that geometry and the nominal physical dimensions of the quantum boxes are those defined by EBL and ion implantation (8). Electrons in the electrodes can freely move in the three space directions due to the bulk-like nature of the contacts. When a voltage bias is applied between the two contact electrodes, the electronic current is constraint to flow through the constriction fabricated in the central buried double barrier region: the electron plane waves of the emitter are thus coupled with the eigenfunctions of the quantum box and the transport properties are dominated by the 3D-0D tunnelling transitions. With this unique process, we are able to measure I-V spectra of diodes having identical 3D electrodes but effective physical quantum well radius varying from 50nm to 50ktm.
3. 3D-0D resonant tunnelling: experimental results and discussion In figure 2 we plot the liquid helium temperature I-V characteristic of a nominal 400nm physical radius quantum box. Superimposed on the main broad resonant peak, we observe multiple peaks clearly resolved. The magnitude of these features is surprisingly high as compared to our previous measurements carried out on the deep etched structures [3,4]. Their amplitude is more than 100 times greater than the magnitude of the noisy current (500fA) for voltage biases less than the threshold voltage. In the following, we mainly focus on the shape and relative intensity of the resonance lines.
J Ga implanted region
back ohmic contact Figure 1: Scheme of the final devices fabrication
Figure 1 summarizes the whole process, the top contact electrode is 1001.tmxl00l.tm wide, whereas the quantum boxes dimensions are defined by the first EBL on the buried hetero-interface. Localized TEM investigations are performed on the same
i1~=~" 0.51'5 00nm~ T=4K,R=4 0.4 0.Vol 5 tage 0.6 Bias(V)
Figure 2: I-V spectrum of a nominal 400nm radius quantum box, at 4K
G. Faini et al. /MicroelectronicEngineering 30 (1996) 479-482
A very different line shape is expected in the 3D0D tunnelling case as compared to the 1D-0D one. In 1D-0D tunnelling, as previously observed [3,4], the spectra show a steplike structure in the I-V characteristics. The alignment of the quantum box energy level EQB with the emitter Fermi energy E F as the voltage bias is increased induces the opening o f a c o n d u c t i n g channel. This channel will participate to the total current as long as EQB falls into the range of the Fermi sea, i.e. in the 1D case, until the voltage bias aligns EQB with the bottom of the 1D emitter subband. The (E) -1/2 dependence of the 1D emitter density of states cancels with the (E) 1/2 dependence of the electrons velocity so that the contribution of each conducting channel to the total current is constant, giving rise to the steplike observed behaviour (3, 4). A downward staircase due to the closing of the conducting channels is also observed [3, 4], if Coulomb repulsion inside the quantum box is relevant . Let us consider now a 3D electrode. The qualitative behaviour of the I-V spectra can be quite easily described considering energy and momentum conservation in the different cases of the quantum box dimensionality . In the quantum box case all the directions are quantized so that only the total energy is conserved: the current is thus maximal when EQB is aligned with E F and decreases with the increase of the voltage bias . The behaviour of the 1D-0D and the 3D-0D tunnelling cases are thus strongly different. The shape of the resonance lines we observe in our experiments is appreciably different than that we measured in the deep etched structures [3,4] as clearly shown in figure 2. The three successive more pronounced lines above 0.54V exhibit a sharp current increase as the resonance sets in, followed b y a quite slow rounded decrease as the voltage bias increases. Our voltage resolution of 500~tV in these runs is good enough to characterize the shape of the line without any ambiguity. The lines width is about 6mV, the sharp increases of the current occurring in about 1.5mV, whereas the rounded slow decrease being about 5mV in width. The rounded shape for the resonance line as the voltage bias increases is also predicted by more realistic calculations of the IV spectra taking into account the temperature effects and quantum box levels width . This behaviour is observed in almost all the lines measured i n our spectra, as shown e.g. in figure 2: the rounded shape of the features in the differential negative resistance region (0.6
closing of the higher energy quantum box levels conducting channels. In figure 3 we plot the relative intensity of the lines as a function of the quantum box radius for the first four quantum box energy levels. The relative intensity has been deduced from the experimental spectra as following. From each spectra we have extrapolate an average curve fitting the data without taking into account the resonance lines due to the tunnelling through the 0D states of the quantum box. This give a baseline which fits the main resonant broad peak described above for the figure 2. We subtract this baseline to the experimental data in order to get only the contribution of each resonance line to the current. Due to the quite low voltage step resolution for the s m a l l e s t m e a s u r e d device (R=50nm), some lines seems split in several sublines due in fact to some digital error. Thus, an average value of the current is taken to account for each level contribution. These values are reported in figure 3 for the first four lines.
& 120 ..~ 100
~ 4o 20
i. 0 
. .I -
200 300 Nominal Radius (nm)
n=2 n=I n=0
Figure 3: Relative line intensity vs quantum boxes radius and principal quantum number n
We consider as usually that the electron motion of the electrons in the longitudinal and transverse directions can be separated and we assume a parabolic approximation for the lateral confining potential [4,6]. This assumption turns out to be realistic for an implantation induced lateral confinement. Thus the eigenfunctions of the quantum box are those of the harmonic oscillator. The current driven by each resonance channel can be evaluated by the estimation of the coupling between the emitter electron plane waves and the eigenfunctionS of the quantum box [11,12]: the current is in fact proportional to the overlap between the considered eigenfunction of the
G. Faini et al. / Microelectronic Engineenng 30 (1996) 479-482
quantum box level and a particular plane wave of the emitter electrons conserving the energy during the tunnelling . Calculations of the relative intensity AI of the tunnelling current through the quantum box levels have been carded out as a function of the box radius R and the level index n . For the first few levels the AI=f(R) curve displays an almost linear increasing behaviour until a critical radius value R0 is reached. Above R 0 the relative intensity AI slightly decreases with R. The calculation shows that the Value of R 0 is level dependent. This result implies that if one considers the first 4 levels (as those plotted in figure 3), for large enough radius (say R>300nm) the magnitude of the intensities increases with n, whereas in the other limit (R<100nm) the magnitude of the ground state of the quantum box (n=0) is the larger one, the contribution of the higher excited states of the quantum box being negligible as n increases. The calculation exhibits a crossover region for 100nm
4. Conclusion A novel processing technique allowing the fabrication of nanometer resonant tunnelling diodes with a full control of the electrodes and quantum well dimensionalities have been realized. The I-V spectra exhibit resonance lines attributed to the 3D-0D electron tunnelling. The preliminary results described
here are in good agreement with theoretical expectations for the line shape and for the relative intensity dependence of the lines with the radius and with the level index of the quantum box.
Acknowledgments We wish to thank C. Mayeux and D. Arquey for technical help. We gratefully acknowledge fruitful discussions with M. Boero and J. Inkson. This work was in part supported by ESPRIT Basic Research Action 6536, LATMIC II.
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