Si heterostructures probed with capacitance spectroscopy

Thin Solid Films 336 (1998) 332±335

Formation of zero-dimensional hole states in Ge/Si heterostructures probed with capacitance spectroscopy A.I. Yakimov*, A.V. Dvurechenskii, A.I. Nikiforov, O.P. Pchelyakov Institute of Semiconductor Physics, 630090 Novosibirsk, Russia

Abstract Hole energy spectrum in Ge/Si(001) heterostructures grown by molecular-beam epitaxy are studied using capacitance spectroscopy at a temperature range of 4.2±300 K. We ®nd that the formation of Ge islands as the effective ®lm thickness exceeds six monolayers leads to the appearance of the zero-dimensional hole states associated with Ge quantum dots. Analysis of the capacitance±voltage characteristics of structures containing the quantum-dot `atoms' and the quantum-dot `molecules' reveals the Coulomb charging effect. q 1998 Elsevier Science S.A. All rights reserved. Keywords: Capacitance spectroscopy; Quantum dots; Silicon; Germanium

1. Introduction Zero-dimensional systems or quantum dots (QD) exhibit con®nement in all three directions in space. Electronic and optoelectronic QD devices, operating at room temperature, require the application of regular arrays of small (#10 nm) nanocrystallites which must be very uniform in size to produce the well-de®ned discrete energy levels and can be viewed as `arti®cial atoms'. One approach to the creation of such structures is based on the phenomenon of coherent with the substrate (i.e. dislocation-free) island formation during strained layer epitaxy, where the strained energy in the ®lm is partially reduced at the cost of increased extra surface area. The very promising system which shows the wellde®ned nanocrystal growth in the form of `hut' clusters and can be easily built into the existing paradigm of silicon integrated electronics is the Ge-on-Si (001) heterostructure [1±4]. Under proper growth conditions, Ge islands have nanometer dimensions with a uniform size distribution, thus in principle lending themselves to use as QD. Usually, the formation of the islands is monitored by re¯ecting high-energy electron diffraction (RHEED) [5], atomic force microscopy [4], scanning tunneling microscopy (STM) [1] and transmission electron microscopy [6]. Recently, optical methods, such as Raman spectroscopy [7] and photoluminescence measurements [8], have been used to observe some quantum size-dependent effects in pseudomorphic Ge ®lms. In the present work, the electronic * Corresponding author. fax:1007 3832 333502; e-mail: [email protected].

spectrum in Ge/Si heterostructures with different effective thicknesses deff of Ge ®lm embedded in Si(001) barriers is investigated with capacitance spectroscopy. We have established that when deff reaches the critical value of about six monolayers (ML), the discrete hole states with d -like density were born as a result of the formation of the layer of Ge QD. Our experiments also reveal the doublet structure in the hole spectrum which is attributed to the Coulomb charging effects. 2. Experimental details and sample preparation Germanium on silicon ®lms were grown using a MBE installation `Katun-C' equipped with two e-beam evaporaÊ /s for Si and tors for Ge and Si, with a deposition rate of 1 A Ê /s for Ge. The growth process was controlled in of 0.35 A situ using the RHEED technique (20 kV). Silicon (001) wafers with boron concentration of about 10 19 cm 23 were used as substrates. After preliminary chemical processing, the substrates were placed in the growth chamber where they were cleaned by low Si ¯ux at 8008C for 15 min. As a result of cleaning, an atomically pure surface with a sharp (2 £ 1) diffraction pattern is formed. Next, a 10-nm thick SiGe buffer layer with Ge composition of 20% was grown at 5008C. To study the capacitance±voltage (C±V) characteristics, three types of structures were grown. Structure A consists of the following layers in order of growth from the SiGe buffer layer: a 7-nm Si layer which in series with the buffer alloy acts as a barrier for hole tunneling from the back contact into

0040-6090/98/$ - see front matter q 1998 Elsevier Science S.A. All rights reserved. PII S0040-609 0(98)01250-4

A.I. Yakimov et al. / Thin Solid Films 336 (1998) 332±335

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Fig. 3. Free-hole pro®les for deff ˆ 0 and 2 ML Ge. Inset shows the valence band pro®le under reverse bias.

Fig. 1. Scanning tunneling microscopy (STM) image of Ge/Si (001) ®lm with Ge thickness of 10 ML.

the dots; a Ge ®lm with deff ˆ 0 2 20 ML deposited at 3008C; a 50-nm Si blocking layer. All the structures were capped with 50 nm Al to obtain the Schottky barrier (see inset of Fig. 1). The Si layers doped with boron to a concentration of about 7 £ 1016 cm23 were fabricated at 5008C. In structure B, the thickness of Si layer separating the SiGe alloy from the dots (deff ˆ 10 ML) was increased up to 12 nm to impede the hole tunneling. Sample C contains two Ge layers, both with deff ˆ 10 ML; the ®rst one (layer A) was placed at the same position as that in the sample A, the

second Ge layer (B) was embedded inside the blocking barrier above the ®rst layer by 5 nm. A fascinating feature of the self-assembled QD superlattices is that the dots in successive layers are spatially correlated [4]. The new islands tend to nucleate directly above buried islands. Thus, samples A and B represent an array of `arti®cial atoms' and sample C ± an array of `arti®cial molecules'. Samples were analyzed ex situ using STM at room temperature. Fig. 2 depicts the ®nal surface morphology of 10 ML thick Ge ®lm. The surface shows a high density (nQD < 3 £ 1011 cm 23) of three-dimensional islands (height 2 nm, diameter 13±15 nm). The hole occupation of the dots is controlled by applying a voltage Vg between a gate electrode and substrate and monitored with the device's capacitance [9]. Capacitance measurements were performed at a temperature range of 4.2±300 K with an excitation amplitude of 5 mV and a frequency 0.04±5 kHz using the lock-in technique.

3. Results and discussion 3.1. Quantized energy states of QD `atoms'

Fig. 2. Capacitance±voltage characteristics for sample A at T ˆ 300 K. The effective thickness of Ge ®lm is varied from 0 to 20 ML.

Fig. 3 depicts the C±V traces at T ˆ 300 K of seven Atype samples with different effective thicknesses of the Ge layer. The sample, which does not contain germanium in silicon (0 ML), shows the usual decrease of the capacitance due to the increase of the depletion region width. At reverse bias, the edge of depletion region enters the degenerated substrate and capacitance starts to change more slowly with Vg. In the framework of the depletion approximation, the free-hole pro®le p… x† can be determined from the experimental CV curve by p… x† ˆ 2C3 =‰e110 S2 …dC=dCdVg †Š, with x being given by x ˆ 110 S110 =C…Vg †, where 110 is the dielectric constant, S is the gate area. The pro®le is shown in Fig. 1. At deff ˆ 2 ML, the continuous ¯at Ge wetting layer is grown. It absorbs holes from Si and forms the two-

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A.I. Yakimov et al. / Thin Solid Films 336 (1998) 332±335

Fig. 4. Capacitance±voltage characteristics of sample A at: (a) T ˆ 300 K, background hole concentration p ˆ 7 £ 1016 cm 23; (b) T ˆ 4:2 K, p ˆ 7 £ 1016 cm 23; (c) T ˆ 4:2 K, p ˆ 2 £ 1017 cm 23.

dimensional (2D) carrier gas. The latter is responsible for the capacitance plateau observed between 0.1 and 0.3 V (Fig. 3) and for the peak of free-hole concentration in Fig. 1. As it has been established by the RHEED studies [5] and the Raman scattering of light [7], the coherent 3D islands appear when deff . 4±6 ML. At the ®rst stage, they are not suf®ciently uniform in size. Therefore, the energy levels of the carriers con®ned in an array of islands are not well de®ned and the spectrum bears a resemblance to the case of 2D gas. In a range of deff from 8 to 13 ML two capacitance peaks are observed, being evidence of the appearance of two discrete hole states. The doublet structure is more clearly seen at 4.2 K (Fig. 4) in sample A and is not observed in sample B (Fig. 5). By integrating the capacitance over two peaks we estimate the correspondent charge density to be …5:7 ^ 0:3† £ 1011 cm 22 which is quite close to the doubled

Fig. 5. Capacitance±voltage characteristics of samples A, B and C at T ˆ 4:2 K. Each structure A and B contains only one layer of Ge nanocrystals buried in Si. The distance between the substrate and QD layer is 17 nm in A and 22 nm in B. In sample C both of these layers are embedded inside the Si ®lm forming an array of QD `molecules'.

value of the dot density, 2nQD < 6 £ 1011 cm 22. Thus, we conclude that the discrete spectrum is associated with the formation of the uniform ensemble of Ge islands. In sample B, the thick bottom Si layer prevents hole tunneling to the dots, making the loading and unloading of the dots dif®cult within one period of the a.c. frequency. This is why the capacitance does not show any features. With increasing of the background hole concentration from 7 £ 1016 cm 23 to 2 £ 1017 cm 23, the hole occupation per dot, Nh, at a reverse bias increases as well (Fig. 4). This con®rms our interpretation of the capacitance peaks. Fitting the doublet to the sum of the linear background and the two Gaussian peaks and taking into account a leverarm coef®cient h ˆ bT =bT L < 0:25 (L is the distance between the front and back gates, bT is the distance between dots and the back gate) which sets a reduction factor from the applied voltage into energy scale, we ®nd that the gap between the split peaks is reduced from DE ˆ 87 meV at deff ˆ 8 ML to DE ˆ 32 meV at deff ˆ 13 ML (T ˆ 300 K). The hole level splitting of about 30 meV at T . 100 K in the ground state has been observed in similar self-assembled QD layers by admittance spectroscopy [10] and attributed to the Coulomb charging effect. This assumption will be con®rmed in the next section. 3.2. Coulomb interaction in QD `molecules' Fig. 5 shows the C±V curves of samples A, B and C for comparison. The structure with two QD layers (C) also exhibits only two capacitance peaks as well as sample A. But the distance between peak maxima is larger then that in A by a factor of about 1.7. This difference can be easily explained if we assume the Coulomb interaction is the origin of the single-particle state splitting. The coherent coupling between the counterpart dots in two layers (between dot A and dot B),  DT < …"v=p†exp 2R=aB , is ,2.6 meV, where "v < 100 meV [10] is the distance between single-particle energy levels, R ˆ 5 nm is the interdot distance, aB < 2 nm is the Bohr radius for heavy holes in Ge. The potential distribution due toÿ depletion region formed in Si is given by
w… x† ˆ fB 2 eNA =eNA 110 ‰W…Vg †x 2 x2 =2Š, where f B is the Schottky barrier height, W the depletion width, NA the background acceptor concentration. In the range of Vg < 20:05±0:35 where the capacitance peaks are observed, the calculated energy difference between two quantum wells A and B is 9±25 meV. This value is smaller than DE and exceeds DT. Under such conditions, the states are mainly localized in either well A or B. At Vg ˆ 0:35 V, the dot A is charged by the ®rst hole and we observe the capacitance peak. The calculations shows that dot B should be loaded by the ®rst hole at Vg < 0:2 V but the corresponding capacitance maximum is not seen because of the same reason as for sample B. The second peak at Vg < 20:05 V arises from the second hole which enters the dot A. In order to load a hole into a dot now, one has to overcome the Coulomb

A.I. Yakimov et al. / Thin Solid Films 336 (1998) 332±335

repulsion of all charges already on the dots A and B. Thus, the presence of the occupied dots in layer B shifts the position of the second capacitance peaks to higher forward biases in comparison with sample A. 4. Conclusions In summary, the capacitance spectroscopy has been used to study the electronic spectrum in Ge/Si heterostructures containing quantum dots. We have shown that the formation of the uniform in size Ge nanocrystals as a result of the morphological transformation of germanium layers during their MBE growth on Si(001) is accompanied by the appearance of the discrete d -like hole states. The observed energy level splitting has been attributed to the Coulombic charging effect in quantum-dot `atoms' and quantum-dot `molecules'. Acknowledgements The authors wish to thank Dr. B.Z. Olshanetskii, Dr. S.A. Tiis and I.G. Kozhemyako for STM measurements. Finan-

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cial support from the Russian State Scienti®c and Engineering Program on Physics of Solid State Nanostructures (grant 98-1100) is greatly appreciated.

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