Dynamics of tunneling into charge-tunable Si quantum dots

Superlattices and Microstructures, Vol. 28, No. 5/6, 2000 doi:10.1006/spmi.2000.0938 Available online at http://www.idealibrary.com on

Dynamics of tunneling into charge-tunable Si quantum dots Y. S HI† , X. L. Y UAN , J. W U , H. M. B U , H. G. YANG , P. H AN , Y. D. Z HENG Department of Physics & National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China

T. H IRAMOTO Institute of Industrial Science, University of Tokyo, Tokyo 106-8558, Japan (Received 26 July 2000) Using frequency-dependent admittance spectroscopy, the dynamics characteristics of tunneling into charge-tunable silicon quantum dots (Si-QDs) with a SiO2 /Si-QDs/SiO2 /Sisubstrate structure are investigated. Two resonance peaks, both for capacitance and conductance in the inversion region, are observed at room temperature, being attributed to the direct tunneling between the conductance band of Si-substrate and the lowest two electronic state levels of the Si-QD. Moreover, the Coulomb charging energy of the dots is extracted from the experimental results. c 2000 Academic Press

Key words: quantum dots, direct tunneling, Coulomb charging effect, admittance.

1. Introduction Silicon quantum dots (Si-QDs) have been successfully used in single-electron transistor and memory devices [1–4]. In particular, the size of the Si-QD can be reduced down to the order of a nanometer by electronbeam patterning or self-assembled growth methods, and as a result, both quantum confinement and Coulomb charging effects become most significant and measurable at room temperature [5]. So far, the physical properties of Si-QDs have been studied mainly with optical and tunneling current spectroscopy techniques. Recently, admittance spectroscopy on suitably designed tunnel capacitors containing the large ensembles of quantum dots has been established as a powerful technique to investigate the quantum confinement and Coulomb charging effects of quantum dots in III–V semiconductor systems [6–10]. In comparison with III– V systems, however, there has been no report on the application of admittance spectroscopy to a Si-QD system. In this paper, we present the investigation of the dynamics of tunneling into charge-tunable Si-QDs embedded in a SiO2 matrix using frequency-dependent admittance spectroscopy. It is well known that both the quantum confinement and Coulomb charging energies are strongly dependent on the size of a dot. Obviously, the size uniformity is the key point to the admittance spectroscopy technique used for a large ensemble of dots [6, 8]. In order to improve effectively the size uniformity of the Si-QDs, the samples were specially oxidized under an oxygen atmosphere at 750 ◦ C taking advantage of the self-limited oxidation effect [11, 12]. Owing to the extremely small size and good uniformity of Si-QDs, the obvious resonance peaks are obtained at room temperature in both capacitance and conductance spectra, which are † E-mail: [email protected]

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c 2000 Academic Press

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Tunneling oxide Ec Efs Ev ttot

tb

Efm

B Cs

A

Rq C

Fig. 1. A, Schematic of tunnel capacitor structure containing Si-QDs. B, Sketch of the energy band along the growth direction. C, The equivalent circuit for the admittance measurement.

attributed to the direct tunneling between the conductance band of Si-substrate and the lowest two states (the s states) of the Si-QD. Furthermore, the Coulomb charging energy of the dots is discussed.

2. Experimental The schematic of the sample structure used in this work is given in Fig. 1A, all samples were fabricated on p-type (100) Si substrate with resistivity ρ ≈ 10  cm−1 . In the fabrication, firstly, Si-QDs were selfassembled at 585 ◦ C on a 3 nm thick thermally grown tunneling SiO2 layer with a LPCVD system. Combining the observations of atomic force microscopy and scanning electron microscopy as shown in Fig. 2, it was estimated that the hemispherical Si-QDs have a density of 2–4 × 1011 cm−2 with an average diameter of ∼8 nm and height ∼4 nm. Subsequently, an in situ deposition of the gate control dioxide layer with a thickness of 14 nm was carried out. In particular, the samples were oxidized at 750 ◦ C for 100 min in an oxidation furnace, and the final size of the Si-QDs was estimated to be ∼4 nm. After all thermal treatment, Al was finally evaporated onto the top and back surfaces as the gate and back contact to form the SiO2 /SiQDs/SiO2 /Si-substrate tunnel capacitor structure, where the Si-QDs were embedded in between a direct tunneling SiO2 barrier and a thick SiO2 control gate. For measurement, a HP4194A Impedance/Gain-phase Analyzer was used to obtain the frequency-dependent capacitance and conductance spectra simultaneously.

3. Results and discussion Fig. 1B and C show the energy band and equivalent circuit of the tunnel capacitor structure in the inversion region. Capacitance spectroscopy measurement allow us to study the electronic state levels of dots [6, 7]. An increased capacitance signal with respect to bias reflects the gate voltage at which electrons are exchanged between the substrate and dots. In particular, a capacitance resonance peak occurs for the gate bias voltage where the Fermi level of the substrate is close to an electronic state level of the dot. Therefore, it can well control single electrons to inject into the dots and to occupy the lowest electronic states through adjusting gate bias voltage. Due to the small physical dimensions of the dots, the electronic state levels are separated both by quantum confinement energy and Coulomb charging energy. The lowest and second state are doubly and fourfold

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Fig. 2. SEM image of as-grown Si-QDs on a SiO2 layer.

degenerate, usually being labeled the s and p shells. In the present work, the size of Si-QDs is extremely small ∼4 nm. As a result, the quantum confinement effect becomes more predominant than that in III–V quantum dots with a size of ∼20 nm. Approximating a dot as a perfect sphere of radius r , the self-capacitance Ctt is simply given by ∼4π εSi ε0r , the Coulomb charging energy E c by e2 /2Ctt , and the ground-state eigenenergy E q by h¯ 2 /2m ∗e · (π/r )2 . Assuming an effective diameter of 4 nm for the present Si-QDs, we estimate the self-capacitance of ∼0.9 aF and the corresponding E c ∼ 92 meV and E q ∼ 370 meV. The capacitance–voltage (C–V ) characteristics measured at 0.5, 1 and 5 kHz at room temperature are shown in Fig. 3. Two capacitance resonance peaks located at the gate voltages of 0.44 and 1.16 V can be clearly seen, and are labeled as E1 and E2, respectively. The amplitudes of the capacitance peaks decrease with increasing frequency, but the peak positions do not shift obviously. The two capacitance resonance peaks could be attributed to electron tunneling into the lowest states (the s states) of the dots. Here, the possibility of interfacial states can be excluded because the peaks appear in the revision region. For the gate voltages below 0 V, the capacitance curve exhibits usual behavior in the accumulation and depletion regions with a flat-band voltage V f b at −0.68 V. Neglecting band bending of the substrate in the inversion region, the nth electronic state level E n in a dot can be extracted from the gate voltage Vgn at a observed capacitance peak by using the following simple relation [7]: tb E n /e = (Vgn − VT ) (1) ttot where tb and ttot are the thickness of the tunneling layer and the total thickness of the capacitor structure, respectively, and VT is the threshold voltage. As the two capacitance resonance peaks E1 and E2 in Fig. 3 are assigned to electron tunneling successively into the s states of the dots, experimentally, the spacing 1E = E 2 − E 1 ∼ 150 meV between the two s-electrons could be mainly attributable to Coulomb charging energy. In fact, the electronic state level is very complicated, and is strongly affected not only by the size and shape of the dot, but also by the number of occupied electrons. Importantly, for a Si-QD embedded in a SiO2 layer,

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C

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v Fig. 3. Capacitance–voltage (C–V ) characteristics measured at frequencies of 0.1, 1 and 5 KHz at room temperature. The peaks appearing in the inversion region are attributed to electron direct tunneling processes.

the physics determining the electrostatic energy involves polarization and self-polarization effects besides the Coulomb charging effect, owing to the difference in the static dielectric constant of silicon (ε = 12) and that of SiO2 (ε = 4) [13–16]. Moreover, the inter-dot Coulomb interaction effect was also discussed by Metzner et al. [17]. Considering Coulomb and polarization interactions for Si-QDs embedded in a SiO2 matrix, for example, Babic et al. [14] reported one- and two-electron electrostatic energies with 434 and 1094 meV for a diameter of 4 nm, respectively. Therefore, there are many evaluated values for the Coulomb charging energy in a Si-QD, for example, the difference between the energies of the two s-electrons in the dot of diameter 4 nm is in the range 90–660 meV. For the charging process in the charge-tunable Si-DQs based on the equivalent circuit proposed in Fig. 1, the capacitance and conductance can be respectively described by the following equations [5, 18]: C0 Cs [1 + (ωτ )2 ] , C0 + Cs (ωτ )2 p (Cs − C0 )ωτ G(ω)/ω = 2 C0 Cs C0 + Cs (ωτ )2 C(ω) =

(2)

where C0 is a series combination of Cs and Cq the time constant τ = Rq Cq . It can be seen from Fig. 3 that the amplitudes of the capacitance peaks decrease with increasing frequency. At higher frequencies we do not have a tunneling event within once cycle of the ac signal. The area under each peak gives the amount of electron that has tunneled into the dots. For the measurement at the frequency 0.5 kHz, the area under the two peaks is almost equal. Upon increasing the frequency, the area of the peak E2 decreases faster than that the peak E1. Moreover, the normalized conductance (G/ω–V ) characteristics at three frequencies are shown in Fig. 4. Two conductance peaks appear also in the inversion region. However, the conductance peaks are located at 0.26 and 1.0 V, respectively, for the curve taken at 0.5 kHz, which are just at the positions of half the amplitude of the corresponding capacitance peaks in Fig. 3. The observed relationship between the capacitance and conductance spectroscopy techniques is in good agreement with the expectation of eqn (2). In the investigation on the InAs dots, the capacitance resonance peaks corresponding to the first and second electron states (the s and p states), and even to the third one (the d state), have been observed [8]. In the present work, however, only the first state has been detected. The reasons could be due to a higher electronic state level for the extremely small size of Si-QDs. Symmetrically, one should expect holes to be injected from the

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v Fig. 4. Normalized conductance–voltage (G/ω–V ) characteristics measured at three frequencies.

substrate into the dots in the accumulation region, but this is very difficult to observe because of the strong background capacitance.

4. Conclusions We have investigated the dynamics of electron tunneling into charge-tunable Si-QDs with a SiO2 /SiQDs/SiO2 /Si-substrate structure using frequency-dependent admittance spectroscopy. Owing to the extremely small size and good uniformity of Si-QDs, the direct tunneling processes of electrons from the substrate into the lowest two electronic state levels have been observed at room temperature. The first two resonance peaks are assigned corresponding to sequential loading of two electrons in one dot, and yield a difference of Coulomb charging energy. Acknowledgements—This work is partly supported by the National Natural Science Foundation of China (Grant No. 19774033) and Huo Ying-dong Education Foundation.

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