Weak localization of holes in acceptor-doped SiGe quantum wells

Weak localization of holes in acceptor-doped SiGe quantum wells

ARTICLE IN PRESS Physica B 340–342 (2003) 827–830 Weak localization of holes in acceptor-doped SiGe quantum wells M.S. Kagana,*, G.M. Min’kovb, N.G...

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ARTICLE IN PRESS

Physica B 340–342 (2003) 827–830

Weak localization of holes in acceptor-doped SiGe quantum wells M.S. Kagana,*, G.M. Min’kovb, N.G. Zhdanovaa, E.G. Landsberga, I.V. Altukhova, K.A. Koroleva, R. Zoblc, E. Gornikc a

Institute of Radioengineering and Electronics, Russian Academy of Sciences, 11-7, Mokhovaya, GSP-9, K-9 101999 Moscow, Russia b Ural State University, 620083 Ekaterinburg, Russia c Institute for Solid State Electronics, Technical University of Vienna, Vienna, Austria

Abstract Negative magnetoresistance is observed in boron-doped SiGe/Si quantum-well structures. The effect of a random potential caused by charged boron d-layers in barriers on quantum corrections to the conductivity is observed and explained. Elastic and inelastic scattering times of holes as well as the magnitude of the random potential are determined. r 2003 Elsevier B.V. All rights reserved. Keywords: SiGe structures; Quantum well; Negative magnetoresistance

1. Introduction

2. Experimental

Negative magnetoresistance (NMR) discovered many years ago has been explained at the beginning of 1980s by magnetic field destroying constructive interference of electron wave functions on closed paths of successive scattering events (weak localization, see e.g. Ref. [1] and references therein). A long-scale random potential should hinder the interference and reduce quantum corrections to conductivity [1,2]. In this report, we present the observation of NMR in acceptor-doped SiGe quantum-well (QW) structures and discuss the influence of the random potential on its magnetic-field dependence.

The p-type Si/Si1xGex/Si QW structures MBEgrown pseudomorphically on the n-type Si substrates were studied at temperatures from 2 to 4.2 K. The Ge content in SiGe alloy was 0.15. The SiGe layer of 20 nm thickness was d-doped in the QW middle with boron, the B concentration was 6  1011 cm2. The QW was sandwiched between Si buffer (130 nm wide) and cap (60 nm) layers both doped with one B d-layer with B concentration of 4  1011 cm2–1012 cm2. The barrier dlayers were positioned at a distance of 30 nm from each QW interface (Fig. 1). Bias was applied to the SiGe layer via thermal diffusion made Au contacts. The distance between contacts was 0.7 cm. DC voltage upto 10 V and 1 ms voltage pulses from 10 to 300 V were applied along the QW to the contacts. The pulsed voltage was used to avoid

*Corresponding author. Tel.: +7-095-2034-812; fax: +7095-2038-414. E-mail address: [email protected] (M.S. Kagan).

0921-4526/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2003.09.226

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90 V 75 60

σ , Ohm-1

10

10

45 30

-6

0.05

p-SiGe layer

20

n-Si substrate

10

0.1

0.15

1/T, K

0.2

0.25

-1

Fig. 2. Temperature dependence of conductivity at different electric fields. Inset: equivalent scheme of structure. Fig. 1. Schematic view of structure.

the sample heating. The current through the SiGe layer parallel to the interfaces was measured as a function of magnetic field H up to 5 T directed perpendicular to the SiGe layer. The calculations of a potential profile for our structures performed in Ref. [3] taking into account the pinning of the Fermi energy at the surface show that the Fermi level is close to the first level of size quantization in the QW. The boron level in the QW is filled and the conductivity along the QW is due to free holes supplied from B d-layers in barriers. Some part of the holes accumulates on the surface creating a built-in transverse electric field. One can change the Fermi level position and free-hole concentration in the QW by means of a transverse electric field effect [4]. The temperature dependence of conductivity of SiGe layer, sðTÞ; is shown in Fig. 2 for different voltages. One can see that the activation energy decreases with electric field approaching zero above 60 V. The activation energy is due to thermal excitation of holes from the Fermi energy to a mobility edge. The sðTÞ dependences in Fig. 2 at different lateral electric fields are quite similar to those observed in Ref. [4] at different transverse voltages. This means that it is possible to shift the Fermi energy also by lateral electric fields (parallel to the interfaces). It is

due to p–n junctions between the contacts and n-Si substrate (see the inset in Fig. 2). A potential drop on one of the p–n junctions between p-contacts and n-Si substrate, which acts as a barrier, creates a rather large transverse electric field between SiGe layer and the substrate. Fig. 3(a) shows the magnetic-field dependence of relative conductivity at different bias. For all voltages, besides 300 V, the NMR is observed in the range of H upto 5 T. At low H, sðHÞ obeys the H2 law. Above B2 T, the classical dependence Ds=s ¼ ðmH=cÞ2 ðDs ¼ sðHÞ  sð0Þ; m is the hole mobility, c is the light velocity) becomes essential showing that NMR saturates. The hole mobility at 4.2 K determined from the slope of high magnetic field region is about 500 cm2/V s, and corresponding mean free time t ¼ mm =e ¼ 9  1014 s: Note that the condition mH=c51 is fulfilled at the magnetic fields used. The magnetic field dependence of sðHÞ=s at 10 mV for different T is shown in Fig. 3(b). The interval of magnetic fields where the NMR is observed decreases with lowering of T. The temperature dependence of hole mobility shown in the inset in Fig. 3(b) points out the acoustic scattering of holes. However, the mobility values are too low. For estimating the mobility, we used the hole effective mass m determined from the binding energy of boron in QW for Si/Si0.85Ge0.15/ Si (27 meV [3]). It turns out that m=0.3 m (m is the free electron mass).

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wave function due to inelastic scattering, lH ¼ ðc_=eHÞ1=2 is the magnetic length. At low H, when lH blj ; expression (1) gives ðDs=sÞpt2j t2 H 2 ;

Fig. 3. Magnetic field dependence of relative conductivity: a) at different voltages, T=4.2 K; (b) at different T, U=10 mV.

3. Discussion We believe that the NMR which appeared in the SiGe QWs is a result of magnetic-field suppression of quantum interference corrections to the conductivity. This is confirmed by the dependences of NMR on H at different electric fields E, applied to the SiGe layer parallel to the interfaces, presented in Fig. 3. Here, the classical H2 dependence of Ds=s is subtracted from experimental MR curves. Note the H2 dependence of relative NMR at low magnetic fields and the saturation at high H. The saturation disappears with increasing electric field. For calculating of the NMR, we used the expression derived for two-dimensional Fermi gas [1] 2 Ds=s ¼ ðl2 =lbÞf2 ðlj2 =lH Þ:

ð2Þ

that coincides with the experimental observation (Fig. 4). The dependence of DsðHÞ=s calculated by means of expression (1) is shown by the dotted line in Fig. 4. The best fit is obtained for tj B1012 s and characteristic hole energy ec E5:5 meV (We take tj and t to be energy independent.) Thus, the necessary condition for weak localization to observe, tj =tb1; is fulfilled in our samples. At low electric fields, the experimental curves deviate essentially from theoretical predictions (see Fig. 4). The saturation begins at the magnetic fields when lH Blj (similar to that observed in bulk Ge with the random potential of charged impurities [2]) while it should be at lH El [1]. The saturated value of DsðHÞ=s should coincide with the value of the quantum correction to the conductivity which for the two-dimensional case should be of the order of (l2 =lb). This ratio is near 0.2 for the energy ec found here. The saturated value of DsðHÞ=s is approximately one order of magnitude less (see Fig. 4). We attribute these facts to the existence of random potential in our system, too. The random potential should exist due to charged d-layers of boron in the barriers. The magnitude g of the random potential induced in the QW plane by these d-layers can be estimated by means of formulae (11) of Ref. [5]; in doing so, we obtained gE6 meV: This is consistent with the hole energy ec obtained from fitting the experimental and

ð1Þ

1=2

Here l ¼ ð_=2 meÞ is the wavelength of hole with an energy e, l ¼ vt is mean free path, v is the hole velocity, b is the QW layer thickness, f2 is a function determined in Ref. [1], f2 ¼ ln x þ Cð0:5 þ 1=xÞ; C is digamma function, lj ¼ ðDtj Þ1=2 is the dephasing length, D is the diffusion coefficient, tj is the dephasing time of the hole

Fig. 4. Dependence of relative magnetoconductivity on magnetic field at different voltages. Dotted line presents the calculation with expression (1).

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calculated DsðHÞ=s curves. Thus, the reason for the small values of saturated DsðHÞ=s and the low magnetic fields for the saturation is a suppression of the quantum corrections to the conductivity as a result of the random potential [1,2]. The increase of the free hole concentration with increasing voltage (see Fig. 2) reduces the random potential owing to the free-carrier screening and increases the quantum corrections. That is why the better fit of the NMR curves with theory occurs at higher electric fields.

Acknowledgements This work was supported by the Russian Foundation for Basic Research (Grants 02-0216373, 03-02-16419), Russian Academy of Sciences (LDQS Program), Russian Ministry of Science

and Technology and European Office of Aerospace Research and Development (Grant ISTC #2206).

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