High-energy ballistic transport in hetero- and nano-structures

High-energy ballistic transport in hetero- and nano-structures

Available online at www.sciencedirect.com Physica E 16 (2003) 129 – 136 www.elsevier.com/locate/physe High-energy ballistic transport in hetero- and...

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Available online at www.sciencedirect.com

Physica E 16 (2003) 129 – 136 www.elsevier.com/locate/physe

High-energy ballistic transport in hetero- and nano-structures D. Rakoczy, R. Heer, G. Strasser, J. Smoliner∗ Institut fur Festkorperelektronik & Mikrostrukturzentrum, TU-Wien, Floragasse 7, Wien A-1040, Austria

Abstract Ballistic electron emission microscopy (BEEM) is a three terminal extension of scanning tunneling microscopy and yields topographic and spectroscopic information on high-energy electron transport in semiconductors at nm-resolution. In BEEM on GaAs–AlGaAs double barrier resonant tunneling diodes (DBRTDs) ballistic electrons which tunnel through a resonant state inside the DBRTD result in a characteristic linear behavior in the BEEM spectrum. On DBRTDs nanostructured into narrow quantum wires, however, this tunneling is quenched for electron energies below the AlGaAs barrier heights. This quenching of the ballistic current can be explained in terms of a transfer Hamiltonian formalism applied to tunneling processes between electron systems of di5erent dimensionality. We measured BEEM spectra on InAs self-assembled quantum dots (SAQDs) for positions on the dots and for “o5-dot” regions on the so-called InAs wetting layer. From these data, we determined the local InAs–GaAs band o5sets on the dots and on the wetting layer and investigated the temperature dependence of the InAs–GaAs barrier height. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 73.23.A; 73.40; 73.63; 73.63.K Keywords: BEEM; Ballistic transport; Quantum wires; InAs self-assembled dots; Barrier heights

1. Introduction If electronic properties of arti@cial nanostructures such as quantum wires or quantum dots are studied by scanning probe techniques such as scanning tunneling microscopy (STM), one has to keep in mind that the size-quantized states are usually buried A below the sample surface. One several hundred A scanning probe technique, however, which is capable to probe sub-surface sample properties is Ballistic Electron Emission Microscopy (BEEM) [1,2], which is a three terminal extension of STM. In this method

∗ Corresponding author. Tel.: +43-1-58801-36212; fax: +43-158801-36299. E-mail address: [email protected] (J. Smoliner).

hot electrons are injected into a semiconductor via a thin metallic base layer. BEEM is a very useful tool to study various semiconductor material parameters such as Schottky barrier heights [3,4], GaAs–AlGaAs band o5sets [5], higher conduction bands in AlAs [6], size-quantized states in GaAs/AlGaAs resonant tunneling diodes [7], and minibands in superlattices [8,9]. Arti@cial nanostructures, such as quantum wires or quantum dots, are currently a topic of high interest, since they are promising candidates for a variety of optoelectronic applications. One way of producing quantum dots is provided by high strain epitaxy: Under certain growth conditions, a thin layer of material deposited on a substrate with a high lattice mismatch will form self-assembled quantum dots (SAQDs) [10,11]. A widely used heterostructure in this context is the InAs/GaAs (or InGaAs/GaAs) system, whose

1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 5 8 7 - 8

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optical properties can be exploited, for example, for quantum dot lasers [12]. InAs grows on GaAs in Stranski–Krastanow mode [10]. First the InAs “wets” the substrate and forms a highly strained epilayer. After further InAs deposition the strain is relaxed by forming dots, which are still connected by the so-called wetting layer. The surface density and the size (and therefore the intrinsic properties) of the SAQDs depend strongly on the growth conditions [13,14]. In BEEM on the self-assembled InAs quantum dots, already an indication of size-quantized states was found in the corresponding spectra [15]. Local conduction band o5sets on self-assembled GaSb dots were also studied [16]. In this work, we describe BEEM experiments on quantum wires made of nanostructured GaAs– AlGaAs double barrier resonant tunneling diodes (DBRTDs) and on InAs self-assembled dots. On quantum wires the spectral behavior on top of the wires depends on the wire width. On suNciently narrow wires (nominal width 212 nm), the BEEM current through the resonant state is suppressed, whereas on wider wires (nominal width 450 nm) the spectra are the same as on unstructured samples investigated in former experiments [17]. On InAs self-assembled dots, the barrier height at the InAs/GaAs interface both on SAQDs and on the wetting layer is studied systematically. 2. BEEM on quantum wires For BEEM on quantum wires, molecular beam epitaxy (MBE) grown GaAs–AlGaAs DBRTs were used. The samples were grown in the following way: On a semiinsulating substrate, an n-doped GaAs collector region (d = 1 m; ND = 1 × 1018 cm−3 ) layer A undoped was grown, followed by a layer of 1500 A GaAs to provide a high internal sample resistance. A thick On top of this layer, a DBRT and a 100 A protecting GaAs cap layer were grown. The AlGaAs A and an aluminum barriers had a thickness of 37 A content of 40%. The GaAs well between the barriA wide. This sample design guarantees ers was 30 A that just one resonant level exists within the AlGaAs barriers. On these samples, two types of large area, photoresist gratings with periods of 900 and 425 nm were fabricated by laser holography. After developing

tip Ef STMtip

37 Å / 30 Å / 37 Å AlGaAs/GaAs/AlGaAs

Au-base (75 Å)


GaAs collector

GaAs Ef A



Fig. 1. Sketch of the experimental setup together with a schematic conduction band pro@le of the sample. The resonant level inside the double barrier tunneling structure is also indicated.

the photoresist, the gratings were transferred into the sample using a wet chemical etchant. The resulting quantum wires had a nominal width of 450 A and 212 nm, respectively. The etch depth was 200 A so that the AlGaAs layers forming the resonant tunneling diode (RTD) were completely removed between the wires. In this way, an additional lateral size quantization was introduced in the region of the AlGaAs/GaAs/AlGaAs tunneling structure. A plot of the conduction band pro@le on a wire is shown in Fig. 1. To prepare the samples for BEEM experiments, an In/Sn collector contact was alloyed in forming gas atmosphere. Subsequently, the samples were dipped into HCl (35%) to remove the thin native oxide layer. A was evaporated as a base Finally, an Au-@lm (75 A) layer onto the grating via a shadow mask. The size of the active area was 0:2 mm×3 mm. All measurements were carried out at a temperature of T = 4:2 K and a tunneling current of 5 nA. The electrochemically etched and Au-sputtered tungsten tips which we used for our experiments had a typical tip radius of 30 nm. Fig. 2(a) shows a 3D-topographic STM picture of the nominally 450 nm wide quantum wire sample taken in liquid helium. The scan area is 1 m × 1 m.

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Fig. 3. BEEM spectra recorded in between two quantum wires (curve (1)), on top of a 450 nm wide quantum wire (curve (2)) and on top of a narrow (212 nm) quantum wire (curve (3)), respectively. All measurements were carried out at T = 4:2 K and a tunneling current of 5 nA. An o5set was added to the spectra for better clarity. Fig. 2. (a) Three-dimensional-topographic STM picture of a nominally 450 nm wide quantum wire. The scan area was 1 m×1 m. A The measurement was carried out The etch depth was 200 A. at T = 4:2 K. (b) Corresponding BEEM image measured at Vt = 1:6 V; It = 5 nA and T = 4:2 K.

Fig. 2(b) shows a 3D-picture of the corresponding BEEM current. The measurement was performed at a bias of 1:6 V, which is well above the AlGaAs barrier height of the underlying RTD. On the leftand right-hand side of the wire, where the RTD was etched away, the current is large since it is determined by the Au–GaAs Schottky barrier height. On top of the wire, the current is reduced since it is mainly determined by the larger barrier height of the underlying AlGaAs barrier. The surface corrugation of this BEEM image nicely reQects the granular structure of the Au-@lm evaporated onto the sample. In the edge areas of the wires, the BEEM signal is much weaker but clearly detectable, which we attribute to tip artifacts and ill-de@ned tunneling conditions in this regime. Fig. 3 shows three di5erent BEEM spectra recorded in between the wires (curve (1)), on top of a 425 nm wire (curve (2)) and on top of a 212 nm wide wire (curve (3)), respectively. The solid lines are a @t to the data using the same modi@ed Bell Kaiser model as in our previous work [8]. As one can see, curve (1) looks like a typical BEEM spectrum obtained on bulk GaAs. The onset bias is Vt = 0:95 V, consistent

with our earlier low-temperature BEEM experiments. Curve (2) was obtained on top of the 425 nm wide quantum wire and is identical with data obtained on unstructured RTD samples [8,17]. Here we observe a current onset around Vt = 1:06 V, which corresponds to the situation where the Fermi level in the metallic STM tip is energetically aligned with the resonant state inside the tunneling diode. As shown previously, the spectrum is linear in the regime where the Fermi energy in the tip is above the resonant level, but below the AlGaAs barrier heights [8]. When the Fermi energy is raised above the AlGaAs barriers (Vt =1:25 V), the BEEM current increases strongly. In contrast to that, the spectrum obtained on top of the nominally 212 nm wide quantum wire is strongly di5erent. Here, no current can be detected below Vt = 1:25 V, which corresponds to the situation where the Fermi energy in the tip overcomes the AlGaAs barrier height. For Vt -values above the AlGaAs barrier height the current is still reduced compared to unstructured samples. It should be pointed out that a number of reference measurements were carried out to ensure that this surprising result is not due to tip artifacts, edge e5ects or artifacts form technological processes during the fabrication process of the sample. To understand the origin of the suppressed BEEM current, we use the results of our earlier work, where we studied the physical properties of tunneling


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processes between electron systems of di5erent dimensionality, such as tunneling processes between quantum wires (or dots) and two-dimensional electron systems [18]. Similar experiments were carried out by other groups and it was found that all these experiments can be described in terms of an extended transfer Hamiltonian formalism [19,20]. Using the assumption that planar tunneling theory can be applied, the electrons in the Au-tip of the STM can be considered as a free, three-dimensional (3D) electron gas, whereas the states in the nanostructured RTDs are one-dimensional (1D) states. Then, the ballistic current tunneling from the initial (I) tip states to the @nal (F) 1D-states in the RTD is simply given by I = 2ePIF , where e is the electron charge, PIF the tunneling probability and the factor of 2 accounts for spin. Using Fermi’s Golden Rule, the tunneling probability PIF is calculated as PIF =

2   |MIF |2 [f(EI ) − f(EF )] ˝ m; n kI ; kF ×(EI − EF + eVb );


where f(E) are Fermi distribution functions, the delta function accounts for total energy conservation, n and m are the indices of all available initial and @nal states. The matrix element MIF is calculated as MIF = −

˝2 2m∗ 




d S


   9I  9F∗  : −I 9z z=z0 9z z=z0 (2)

If we take free 3D-electrons in the tip and 1D-states in the quantum wire (laterally con@ned in y-direction, z is the con@nement in growth direction), the initial and @nal wave functions I and F are written as I = eikz; I z eikx; I x eiky; I y ; F = F (z)eikx; F x n; F (y);

element for the 3D–1D tunneling process reads     ikz; I z   9 ˝2 F ∗ 9e ik z   − e z; I MIF = − ∗ F  2m 9z z=z0 9z z=z0  (4) ×(kx; I − kx; F ) eiky; I y n; F (y) dy: The @rst term is essentially the transmission coeNcient of the AlGaAs barriers, the second term containing the delta function accounts for parallel momentum conservation during tunneling and the last term is the Fourier transform of the wave functions in the @nal states. As one can see from Eq. (1), the total current is obtained by summation over all possible 1D-states. We now estimate the number of laterally con@ned @nal states between the energetic position of the resonant level and the top of the AlGaAs barriers. To estimate the number of 1D-levels we solve Poisson’s equation in two dimensions and determine the lateral con@nement at the position of the RTD. Then, we solve SchrSodinger’s equation to calculate the lateral con@nement energies inside the RTD. It is found that the potential is approximately parabolic for both wires, with con@nement energies in the order of 4:5 meV for the 212 nm wide wire and below 1 meV for the 450 nm wide wire, respectively. In other words, this means that the number of available @nal 1D-states is at least larger by a factor of four for the broad quantum wire. Since much less @nal electronic states are available inside the narrow wire, it becomes clear why in this case the ballistic current is below our detection limit. Therefore, for narrow wires a signi@cant current is only detected above the AlGaAs barrier height, where a continuum of @nal states is available. It must be pointed out, however, that the ballistic current is not a linear function of the number of @nal states. Rather it shows a complex behavior due to the inQuence of the wave function overlap integrals [18], which were not included in this simple discussion. 3. BEEM on InAs self-assembled dots


where kI and kF are the corresponding wave vectors of the initial and @nal states. The corresponding matrix

The self-assembled quantum dots (SAQDs) were grown in a Gen-II MBE system using Ga, In, Si, and As2 sources. After oxide desorption, an undoped 200 nm thick GaAs bu5er layer was deposited onto a

D. Rakoczy et al. / Physica E 16 (2003) 129 – 136


It Vt

A base contact


7 nm Au

STM tip Au

collector contact

InAs 1 µm n-GaAs collector smoothing layers 200 nm GaAs buffer S.I. GaAs substrate


Au-base layer 0





2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0



Energy (eV)

semiinsulating (1 0 0) GaAs substrate, followed by a smoothing superlattice. A 1 m thick Si-doped GaAs layer with a nominal doping concentration of 3× 1016 cm−3 grown at 600◦ C acts as a collector contact for the BEEM measurements. Before the @nal indium deposition the substrate temperature was lowered to 500◦ C. Then, eight periods of 0:07 nm InAs were deposited under a constant As2 Qux, separated by waiting loops of 25 s each. This adds up to a nominal thickness of two monolayers (ML) of InAs, forming SAQDs. The samples were then allowed to cool down below 300◦ C before being removed from the MBE chamber. To minimize the growth of a native oxide, the samples were transferred to the evaporation chamber for the Au base layer deposition immediately afterwards. Atomic force microscope (AFM) measurements show that the overall dot density is about 30 dots per m2 . The dot height varies from 8 nm to 17 nm and the dot diameter varies from 32 nm to 47 nm. Fig. 4(a) shows a sketch of the BEEM setup and the cross-sectional view of the sample. The corresponding conduction band pro@le is shown in Fig. 4(b). Note that, due to the fact that on the InAs surface the Fermi level pins above the conduction band minimum [21], the Au/InAs interface produces an ohmic contact. Further, the Fermi level in the InAs is above but close to the conduction band, so that the measured barrier height Vb is in good approximation equal to the band o5set in the InAs–GaAs system. As for the BEEM experiments on quantum wire samples, the connection to the collector layer was established by InSn pellets which were di5used into the samples at 450◦ C in forming gas atmosphere. The thickness of the deposited Au @lm for the base was A To avoid oxidation, the samples were kept in a 70 A. cryostat with a variable temperature insert, either in N2 gas or in He gas during the measurements. BEEM spectra were measured at three di5erent temperatures. More details on BEEM on InAs samples can be found in our previous publications [22,23]. Fig. 5(a) shows a topographic STM image of our sample. One small and three big dots are clearly visible. The granular structure in this image is due to the Au-@lm covering the sample. Fig. 5(b) shows the corresponding BEEM image. Here the dots are visible as brighter spots indicating areas of enhanced electron transmission. Due to the inQuence of the wetting layer, the contrast between the on-dot and o5-dot regions is rather weak.


400 800 z (Å)

EF 1200

Fig. 4. (a) Schematical view of the sample layers and the experimental setup, (b) corresponding conduction band pro@le of a sample with InAs dots on the surface. Vt is the tunneling voltage, It the tunneling current, Ic the collector current (BEEM current), EF the Fermi energy, and Vb is the barrier height at the InAs–GaAs interface.

To investigate the transmission behavior of the dots and of the InAs wetting layer, respectively, we systematically measured ballistic electron spectra on on-dot and o5-dot positions on our samples. Because the Au/InAs interface provides an ohmic contact, the onset voltage of the BEES curves is determined by the potential barrier at the InAs/GaAs interface. To extract the onset voltage, i.e. the barrier height, from the measured data we use a 52 power law @t [24]. The Bell–Kaiser model was not used because already the straightforward power law @ts our data very well and is completely suNcient for our purposes. Fig. 6 shows a typical example of two BEEM spectra at T = 300 K, one measured on a dot and the other one measured at some distance from the dot. Already from the raw data, one can see clearly that the onset voltage on the dot is strongly reduced compared to the

D. Rakoczy et al. / Physica E 16 (2003) 129 – 136


0.7 0.8 0.9 Barrier Height (eV)




T = 300 K

7 T = 300 K 6 5 4 3 2 1 0 0.6 0.7 0.8 0.9 1.0 Barrier Height (eV) (d) Count

7 6 5 4 3 2 1 0 0.6




T = 180K



Fig. 5. (a) Topographic STM image of our sample, (scan size: 500 nm × 500 nm, Vt = 1:3 V, It = 2 nA, T = 300 K). One small and three big dots are clearly visible. The granular structure in this image is due to the Au-@lm covering the sample. (b) corresponding BEEM image. The weak contrast is due to the presence of the wetting layer.


8 4 2 0 0.6




T = 10 K


0 0.6

on dot


1.0 0.5



2.0 1.5


off dot

0.0 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Tunnel Voltage Vt (V) Fig. 6. Typical BEEM spectra measured on an InAs dot and in an o5-dot region (It = 2 nA; T = 300 K).

o5-dot onset voltage, which in its turn is smaller than the value expected for an Au/GaAs Schottky contact (0:9 V). The barrier height gained from the power law @t is 0.69 and 0:80 eV for the on-dot and the o5-dot position, respectively. Further measurements at other positions on the sample show that at 300 K the barrier height on the dots is in general between 0.61 and 0:74 eV (mean value 0:69 eV), while for o5-dot locations it varies from 0.73 to 0:87 eV (mean value 0:80 eV). Histograms of the barrier height distributions for various temperatures are plotted in Figs. 7(a–c) for the on-dot positions and in Figs. 7(d–f) for the o5-dot positions. It is very instructive to compare these results with BEES measurements on an Au/InAs/GaAs system



Barrier Height (eV)

T = 10 K 10 8 6 4 2 0 0.6 0.7 0.8



Collector Current Ic (pA)

T = 300 K


Barrier Height (eV) 8



T = 180K 10 8 6 4 2 0 0.6 0.7 0.8




Barrier Height (eV)





Barrier Height (eV)

Fig. 7. (a–c) Histograms of the InAs/GaAs barrier height measured on quantum dots at temperatures of 300, 180 and 10 K, respectively. (d–f) Histograms of the barrier height between the InAs wetting layer and the GaAs measured in o5-dot regions at temperatures of 300, 180 and 10 K, respectively.

with homogeneous InAs interlayers of various thickness, carried out by Mao-Long Ke et al. [25]. They report that a single ML of InAs lowers the barrier height rapidly from 0.9 to 0:8 eV, while an increase of the nominal InAs layer thickness to 3 ML yields a further decrease to approximately 0:74 eV. For thicker layers the barrier height remains almost constant up to 27 ML, where it drops again and @nally reaches about 0:63 eV for a thickness of 33 ML (≈11 nm) and beyond. These data indicate that the average thickness of our wetting layer is about 1 ML and our dots appear to be more than 33 ML thick, which agrees very well with the dot heights gained from our AFM measurements. Of course, one must consider that the data from Mao-Long Ke et al., were obtained on homogeneous InAs layers rather than on InAs dots. The di5erent strain conditions for these two systems most probably inQuence the barrier height. To investigate the InAs/GaAs barrier height depending on the temperature, we also sampled BEES

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curves on various on-dot and o5-dot positions at 180 and 10 K, respectively. As can be seen from Fig. 7, the measurements show an increase in barrier height with decreasing temperature both for the on-dot positions and the wetting layer. On the dots (a–c), the mean value of the barrier height rises from 0:69 eV (standard deviation 34 meV) to 0:79 eV (standard deviation 13 meV) between T = 300 and 180 K. A further lowering of the temperature down to 10 K results in a just slightly higher mean barrier height of 0:82 eV (standard deviation 16 meV). Note that the distribution of the barrier height becomes signi@cantly narrower between T = 300 and 180 K, but approximately maintains its width when the temperature is reduced further. In our opinion this behavior is mainly due to the reduction of drift problems with decreasing temperature. On the wetting layer (Figs. 7(d–f)), the mean value of the barrier height rises from 0:80 eV (standard deviation 35 meV) at T = 300 K to 0:86 eV (standard deviation 12 meV) at T = 180 K and to 0:93 eV (standard deviation 13 meV) at T = 10 K. Note that the observed temperature behavior on the dots is in qualitative agreement with results obtained by Heer et al. [26] on thick and fully relaxed InAs layers on a GaAs substrate. They also found a step-like increase of the barrier height with decreasing temperature, which was attributed to a temperature-dependent Fermi level pinning at the InAs/GaAs interface.

4. Summary In summary, BEEM was used to study the electronic properties of quantum wires and the local barrier heights between InAs self-assembled quantum dots and a GaAs substrate. We have found that on 450 nm wide quantum wires, the BEEM spectrum behaves like on laterally unstructured samples, whereas on nominally 212 nm wide quantum wires, a strong suppression of the BEEM current is observed. To explain the observed e5ects, a transfer Hamiltonian formalism was adapted to tunneling processes between electron states of different dimensionality. In terms of this picture, the suppressed BEEM current on narrow quantum wires is consistently explained by the reduced number of @nal 1D-states inside the narrow wire.


On InAs self-assembled dots, we have found that our results agree quite well with those of thickness dependence studies on homogeneous InAs layers on GaAs. The mean values of the measured barrier height suggest a wetting layer of about 1 ML and a thickness of about 33 ML or greater for the dots, which is in good agreement with our results from AFM measurements. For lower temperatures a signi@cant increase of the barrier height is observed. From this behavior, we conclude that the complex inQuence of both geometry factors and temperature on the barrier height and, therefore, on the energy levels inside the dots, will make a bandstructure engineering for quantum dot applications a rather diNcult task. Acknowledgements We would like to thank G. Ploner for processing the quantum wires, B. Basnar for the AFM measurements, C. Pacher for supporting calculations, and E. Gornik for continuous support. This work was supported by FWF Austria, project No. P14604-TPH and “Gesellschaft fSur Mikroelektronik (GMe)”.

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