Resonant tunneling through coupled InAs quantum dots

Resonant tunneling through coupled InAs quantum dots

Physica B 249—251 (1998) 243—246 Resonant tunneling through coupled InAs quantum dots Kanji Yoh*, Hironobu Kazama, Takaya Nakano Research Center for ...

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Physica B 249—251 (1998) 243—246

Resonant tunneling through coupled InAs quantum dots Kanji Yoh*, Hironobu Kazama, Takaya Nakano Research Center for Interface Quantum Electronics, Hokkaido University, North 13, West 8, Sapporo 060, Japan

Abstract We report the observation of electron tunneling through coupled quantized states in stacked InAs quantum dots embedded in AlAs single barrier for the first time. We speculate that the series of observed dips in the second derivative of the current corresponds to four current peaks with relative coupling energy separation of 5—8 meV. Comparison of these results with calculational results based on the device structure revealed that the data fit reasonably well if we assume the effective mass of electrons in the dots to be (0.085$0.005)m . This result of energy dependent effective mass of electrons is consistent with the 0 previous experiments on infrared spectroscopy and quasi-1D transport. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Resonant tunneling; Coupled quantum dots; InAs

1. Introduction Recent progress of molecular beam epitaxy has made it possible not only to fabricate self-assembled InAs quantum dots and bury them in a single AlAs barrier [1,2], but also to stack them on top of previous dots separated by a thin barrier using self-assembled growth technique and the Stranski— Krastanow mode [3]. We have fabricated a stack of InAs quantum dots buried in AlAs single barrier and investigated the electron tunneling through coupled quantized states at 4.2 K. 2. Fabrication and the structure of the device The heterostructure was grown by MBE on an n`-GaAs substrate as shown in Fig. 1. The hetero* Corresponding author. Fax: #81 11 716 6004; e-mail: [email protected]

structure consists of 6000 A_ of n`-GaAs layer grown on n`-GaAs substrate, 2000 A_ of GaAs, 100 A_ of AlAs barrier, five sequential layers of InAs quantum dots separated by each of 30 A_ of AlAs layer, 130 A_ of AlAs barrier, 50 A_ of GaAs layer and 6000 A_ of n`-GaAs layer. The thick (2000 A_ ) undoped GaAs layer below the tunneling barriers is intended to increase the measurement resolution in detecting the peak positions by imposing high leverage factor on the anode side. Gross lateral device size is 50 lm]50 lm. Average dot density was estimated to be 1.5]109 cm~2 by atomic force microscope (AFM) observation. InAs coverage was 2.2 ML with arsenic pressure of 2.3]10~6 Torr, substrate temperature of 500°C and growth rate of 0.05 ML/s was used. Cross-sectional TEM photograph of the present structure is shown in Fig. 2. From this picture, dot size is estimated to be between 80 and 100 A_ in diameter and 15 A_ in height. We have calculated the coupled eigenenergies and

0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 0 7 - 0

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Fig. 1. The heterostructure of the device. Four InAs quantum dots are stacked on top of each other in an AlAs single barrier.

Fig. 3. Schematic energy band diagram along the axis, normal to the interface, which penetrates a stack of InAs dots. Two bunches of energy states are expected. The wave function shape in the lower bunch of four states are shown.

the lateral confinement effect is negligible. The expected energyband separation due to the coupling turned out to range between 5—20 meV depending on the effective mass used in the calculation of the energy eigenvalues as we will see later in the next section.

3. Results and discussion

Fig. 2. The cross-sectional TEM micrograph of the device. Four InAs quantum dots are seen to be stacked in an AlAs single barrier with the lateral and vertical dimension of 80 and 15 A_ , respectively.

wave functions of the coupled states based on the structural parameters obtained by growth conditions and the cross-sectional TEM observation. Fig. 3 depicts the shape of the wave functions in each eigenstate in the coupled dots assuming that

The I—» characteristics and its differential curve of the device exhibits four peaks measured at 4.2 K as shown in Fig. 4. In the figure, the forward (reverse) bias corresponds to electron tunneling from surface (substrate). In this figure, data from three consecutive measurements are plotted on top of each other. Reasonably reproducible results are obtained although direct current peaks are difficult to see because of the pronounced background current. However, in the differential plots, a structure is seen. In order to clarify the current peak positions, the second derivative of the current is plotted

K. Yoh et al. / Physica B 249–251 (1998) 243–246

Fig. 4. The I—» characteristics and the differential curve of the device exhibits four peaks measured at 4.2 K. In the differential curve, structures are seen as shown by the arrows.

Fig. 5. The second derivative of the current is plotted against bias voltage measured at 4.2 K. Four dips, which presumably correspond to the four current peaks, are indicated by arrows.

against bias voltage in Fig. 5. We attribute these dips as current peaks of resonant tunneling through coupled quantum dot states. We have neglected the smaller dips as secondary effects. This might be impurity effects or it might be caused by a chaotic movement caused by non-idealistic shape of the stacked dots. The relative peak positions were estimated from the measured peak voltage and energy band shape at each resonant conditions with the leverage factor of nearly ten. These results are compared with the calculational results of relative

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Fig. 6. Measured relative peak positions are compared with the calculational result of relative quasi-bound state energies taking the effective mass in InAs dots as a parameter. Data fit reasonably well if we assume a relatively large effective mass of electrons in an InAs stack.

quasi-bound state energies taking the effective mass in InAs dots as a parameter as shown in Fig. 6. In the calculation, a multiple quantum well structure is assumed, but the estimated energy difference of the coupled states turned out to be small enough to justify the assumption. Due to the energy dependent effective mass [4] in a quantum dot, the calculational result with the relatively heavy InAs effective mass of (0.085$0.005)m agrees reason0 ably well with the experiment. This result is consistent with the unexpectedly high effective mass reported in infrared spectroscopy experiment [5,6] and single electron charging experiment of InAs dots buried in GaAs near the quasi-one-dimensional (1D) modulation doped field effect transistor (MODFET) structure [7]. In the present experiment, the charging effect is not expected to overlap with the energy separation by coupling because the asymmetric barrier structure does not allow electron accumulation in the coupled wells. We will be able to investigate the competition between the dot charging and coupled energy separation by making the anode side of the barrier thicker than the cathode side in the future experiment.

4. Conclusions We have reported the observation of electron tunneling through coupled quantized states in

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stacked InAs quantum dots embedded in AlAs single barrier for the first time. We speculate that the series of observed dips in the second derivative of the current corresponds to four current peaks with relative coupling energy separation of 5—8 meV. Comparison of these results with calculational results based on the structure revealed that the data fit reasonably well if we assume the effective mass of electrons in the dots to be (0.085$0.005)m . This result 0 of relatively large effective mass of electrons in InAs dots is consistent with the previous experiments on infrared spectroscopy and quasi-1D transport.

References [1] A. Thornton et al., 9th Int. Conf. on Superlattices, Microstructures and Microdevices, Lie`ge, Belgium, 14—19 July 1996. [2] M. Narihiro et al., 12th Int. Conf. on Physics and Application of High Magnetic Fields in Semiconductors, Wurzburg, Germany, July 1996. [3] M. Grundmann et al., Int. Conf. on InP and Related Materials, 1996. [4] N. Nishiguchi, K. Yoh, Jpn. J. Appl. Phys. 36 (1997) 3928. [5] M. Fricke, A. Lorke, J.P. Kotthaus, G. Medeiros-Ribeiro, P.M. Petroff, Europhys. Lett. 36 (1996) 197. [6] B.T. Miller, W. Hansen, S. Manus, R.J. Luyken, A. Lorke, J.P. Kotthaus, S. Huant, G. Mederios-Ribeiro, P.M. Petroff, Phys. Rev. Lett. 56 (1997) 6764. [7] K. Yoh, J. Konda, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134.