Doping dependence of self-diffusion in germanium ...

Doping dependence of self-diffusion in germanium and the charge states of vacancies T. Südkamp, H. Bracht, G. Impellizzeri, J. Lundsgaard Hansen, A. Nylandsted Larsen, and E. E. Haller Citation: Applied Physics Letters 102, 242103 (2013); doi: 10.1063/1.4811442 View online: http://dx.doi.org/10.1063/1.4811442 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/102/24?ver=pdfcov Published by the AIP Publishing

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APPLIED PHYSICS LETTERS 102, 242103 (2013)

Doping dependence of self-diffusion in germanium and the charge states of vacancies €dkamp,1 H. Bracht,1,a) G. Impellizzeri,2 J. Lundsgaard Hansen,3 T. Su A. Nylandsted Larsen,3 and E. E. Haller4 1

Institute of Materials Physics, Westf€ alische Wilhelms-Universit€ at M€ unster, 48149 M€ unster, Germany CNR-IMM MATIS, University of Catania, I-95123 Catania, Italy 3 Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus, Denmark 4 Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 2

(Received 23 April 2013; accepted 2 June 2013; published online 18 June 2013) Self-diffusion in boron-doped germanium has been studied at temperatures between 526 and 749 C with secondary ion mass spectrometry. Self-diffusion under acceptor doping is retarded compared to intrinsic conditions. This demonstrates the contribution of charged vacancies in selfdiffusion. Taking into account the dominance of doubly negatively charged vacancies under donor doping, the doping dependence of self-diffusion is best described with an inverse level ordering for singly and doubly negatively charged vacancies for all doping conditions. The level ordering explains the dominance of doubly charged vacancies under donor doping and their decreasing contribution with increasing acceptor doping until neutral vacancies mediate selfC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4811442] diffusion. V Intrinsic point defects in semiconductors such as vacancies (V) and self-interstitials are known to mediate the diffusion of self- and substitutional foreign-atoms. These intrinsic defects can exist in various charge states that become important in self- and foreign-atom diffusion when the position of the Fermi level is altered by doping.1–3 The acceptor nature of V in germanium (Ge) was first proposed by Valenta and Ramasastry in 1957.4 Subsequent analyses of Werner et al.5 on the doping dependence of self-diffusion confirmed the acceptor state of V and suggest the dominance of neutral V0 and singly negatively charged V under p- and n-type doping conditions. Recently, self-diffusion in Ge under n-type doping was revisited utilizing isotopically controlled Ge multilayer structures.2,3 Diffusion of n-type dopants such as phosphorous, arsenic, and antimony in these isotope structures directly reveal the impact of doping on self-diffusion and clearly demonstrate the dominance of doubly negatively charged V 2 under intrinsic and n-type doping conditions.2,3 This indicates that the energy level related to the double acceptor state of V 2 must be located below the center of the Ge band gap. In order to determine the preferred charge states of V under p-type doping, simultaneous experiments on self- and p-type dopant diffusion would be highly favorable but, unfortunately, are not feasible due to the slow diffusion of p-type dopants such as boron (B),6,7 aluminium,8 gallium,9–11 and indium12,13 in Ge. Therefore, in this work, Ge self-diffusion under p-type doping is investigated by means of Ge isotope heterostructures homogeneously doped with B during molecular beam epitaxy (MBE). An isotope heterostructure consisting of nat Geð130 nmÞ= 70 Geð300 nmÞ=nat Geð300 nmÞ and homogeneously doped with B was grown by means of MBE at 600 C within 2 h on a 530 lm thick (100)-oriented nat Ge substrate wafer. The p-type substrate with a resistivity of 1.3 X cm is doped with gallium to a concentration of about 3 1015 cm3 . The enrichment of a)

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the 70Ge layer amounts to about 96%. Samples with lateral dimensions of 4 4 mm2 were cut from the deposited wafers, cleaned in organic solvents, etched in 5% diluted HF, and purged in distilled and deionized water. Subsequently, the samples were sealed in quartz ampoules under pure argon (99.999%), which were evacuated to a pressure of 1 or n=ni < 1 holds. Equation (7) is used to describe the temperature dependence of DGe ðnÞ=DGe ðni Þ. As demonstrated by Fig. 3, this ratio decreases with decreasing temperature. Data reported by Vanhellemont and Simoen22 for ni and the Fermi level Eif under intrinsic conditions approximated by half of the energy band gap, i.e., Eif 1=2Eg , are considered. With these settings, only the energy level positions EV =0 and EV 2= of V and V 2 remain as unknown parameters. Recently, Mesli et al.20 investigated by means of deep level transient spectroscopy the defects introduced in Ge by low-temperature electron irradiation. They assigned an electronic energy level located at 0.14 eV above the VBM to V 2 . Considering this energy level to be fixed to the valence band, i.e., EV 2= ¼ 0:14 þ VBM, the energy level EV =0 remains as single parameter. The best fit to the temperature dependence of self-diffusion yields EV 1=0 ¼ VBM þ ð0:2860:01Þ eV and is illustrated by the solid line in Fig. 3. The energy level positions within the Ge band gap are illustrated in the inset of Fig. 3. An inverse level ordering for the V-related defects is suggested, i.e., the single acceptor state lies above the double acceptor state. This negative-U behavior of the two energy levels cannot be excluded according to theoretical calculations of Coutinho et al.19 The ordering of the energy levels leads to a dominance of V 2 under n-type doping and of V0 under p-type doping, i.e., V are not expected to control self-diffusion under any doping conditions. This is highlighted by Fig. 4 for 700 C that shows the individual contributions of V 0 ; V , and V 2 to the total Ge self-diffusion coefficient as a function of n=ni . For doping levels n=ni > 2; V 2 mainly mediates self-diffusion. This is consistent with results reported by Brotzmann et al.2 on Ge self-diffusion at 700 C under n-type doping. On the other hand, Werner et al.5 deduced from the doping dependence of self-diffusion at 700 C that V0 and V control self-diffusion. Figure 4 explains the origin of this misleading interpretation.


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Appl. Phys. Lett. 102, 242103 (2013)

vacancies do not prevail self-diffusion under any doping level. The charge states determined for vacancies in Ge provide an overall consistent interpretation of the doping dependence of Ge self-diffusion investigated in this and works reported in the literature.2–5

r

FIG. 4. Individual contributions DVGe of neutral (r ¼ 0: thin solid line), singly (r ¼ 1: short-dashed line), and doubly (r ¼ 2: dashed line) negatively charged V r to Ge self-diffusion at 700 C. The total Ge self-diffusion coefr ficient DGe is given by the sum of the individual contributions DVGe and shown by the thick solid line. The inset shows the corresponding thermal equilibrium concentrations Ceq V r normalized to the total thermal equilibrium 0 2 under pconcentration Ceq V and demonstrates the dominance of V and V and n-type doping, respectively. Note, V do not prevail at any doping level.

For the doping conditions considered by Werner et al.,5 which range from 0:25 < n=ni < 1:3, a slope less than or equal to 1.0 is suggested for DGe ðnÞ (see Fig. 3, upper thick solid line). This shows that the dominance of V 2 becomes first apparent at higher n-type doping levels. Accordingly, the doping dependence of Ge self-diffusion calculated on the basis of the inverse level ordering is fully consistent with present experimental results on self-diffusion in Ge under various doping levels. The inset of Fig. 4 illustrates the thermal equilibrium concentrations Ceq V r as function of the doping level. The respective concentrations of V 0 ; V , and V 2 are normalized to the total thermal equilibrium concentration Ceq V at the particular doping level. This total V concentration depends on the doping level and is given by the sum of Ceq V r with r 2 f0; 1; 2g. Accordingly the normalized total V concentration equals one for all doping conditions. The insetted figure clearly shows the dominance of V 2 under n-type doping and of V0 under p-type doping. V does not control selfdiffusion under any doping conditions. In conclusion, experiments on Ge self-diffusion under homogeneous boron doping reveal an increasingly reduced self-diffusion with decreasing temperature compared to electronic intrinsic conditions. The doping dependence of selfdiffusion is accurately described by an inverse ordering of the electronic energy levels introduced by the single and double acceptor states of the vacancy. This negative-U behavior of the acceptor levels describes the dominance of doubly negatively charged and neutral vacancies under nand p-type doping conditions, respectively. Singly charged

The authors thank TASCON GmbH in M€unster for the SIMS measurements. This work was funded by the Deutsche Forschungsgemeinschaft under Grant No. BR 1520/6-2 as well as an individual grant within the Heisenberg program for H.B. The isotopically enriched Ge was developed with funding by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the U.S. DOE under Contract No. DE-AC0205CH11231. 1

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