Vacancy-impurity complexes and diffusion of Ga and Sn in intrinsic and p -dopedgermaniumI. Riihimäki, A. Virtanen, S. Rinta-Anttila, P. Pusa, J. Räisänen, and The ISOLDE Collaboration

Citation: Applied Physics Letters 91, 091922 (2007); doi: 10.1063/1.2778540 View online: http://dx.doi.org/10.1063/1.2778540 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Enhanced oxygen diffusion in highly doped p -type Czochralski silicon J. Appl. Phys. 100, 103531 (2006); 10.1063/1.2369536 Germanium n + p junction formation by laser thermal process Appl. Phys. Lett. 87, 173507 (2005); 10.1063/1.2115078 The antimony-vacancy defect in p -type germanium Appl. Phys. Lett. 87, 172103 (2005); 10.1063/1.2112168 Improvement of properties of dynamic random access memories capacitors by PH 3 plasma doping processafter the formation of hemispherical-grained silicon J. Vac. Sci. Technol. B 17, 1017 (1999); 10.1116/1.590686 Atomistic analysis of the vacancy mechanism of impurity diffusion in silicon J. Appl. Phys. 83, 7585 (1998); 10.1063/1.367874

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Vacancy-impurity complexes and diffusion of Ga and Sn in intrinsicand p-doped germanium

I. Riihimäki, A. Virtanen, and S. Rinta-AnttilaDepartment of Physics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland

P. Pusa, J. Räisänen,a� and The ISOLDE CollaborationAccelerator Laboratory, University of Helsinki, P.O. Box 43, FIN-00014 Helsinki, Finland

�Received 21 June 2007; accepted 10 August 2007; published online 30 August 2007�

The charge state of mobile vacancy-impurity complexes in germanium was studied via the effect ofp-type �Ga� doping on Ga and Sn diffusions. Tin diffusion retards significantly as a function ofdoping concentration suggesting diffusion dominated by negatively charged vacancy-Sn complexes.Gallium diffusion is practically unaffected by doping, suggesting diffusion dominated byvacancy-Ga complexes having the same charge state as isolated, negatively charged Ga ions. Theevident two orders of magnitude higher diffusivity of group V elements in germanium than of groupIII and IV elements can be well explicated by means of the present findings. © 2007 AmericanInstitute of Physics. �DOI: 10.1063/1.2778540�

Recently, a renewed interest in diffusion properties ofgermanium has appeared, e.g., due to its thermal, mechani-cal, and radiation hardness properties. However, the micro-scopic picture and the role of vacancies in impurity atomdiffusion in germanium are still incomplete. It is commonlyaccepted that germanium-self-diffusion is vacancymediated.1 This is most probably due to the high migrationenergy of Ge interstitials2 or to the low formation energy ofGe vacancies.3 In germanium, all dopants as well as groupIV impurities occupy practically only substitutional latticesites. With the exceptions of boron4,5 and phosphorus,6 it iscommonly adopted that they diffuse via vacancies. Underintrinsic conditions, the difference between self- andvacancy-mediated impurity diffusion is caused by vacancy-impurity interactions. It is practical to separate these interac-tions into two main categories, Coulomb and elastic. Theelastic interactions originate from the elastic stress caused bynative point defects and impurity atoms to the host lattice.The relevance of the elastic interactions for impurity atomdiffusion in germanium was studied in detail for group IVelements in our recent work.7 At typical diffusion tempera-tures, the charge state of group III impurity atoms is −1 andof group V atoms is +1, whereas vacancies in Ge can befound with several charge states. The long range Coulombinteraction prevails between the ionized impurity atoms andthe charged point defects.

In this work, we shed light on the role of the charge stateof the vacancy-impurity complexes by studying the effect ofdoping on Ga and Sn diffusions in germanium. For galliumdiffusion in intrinsic germanium, one previous study is avail-able in the literature,8 but the effect of doping has not beenstudied. For tin diffusion in germanium, four previous stud-ies exist9–12 of which the values of Ref. 10 differ clearly fromthe others. The effect of doping on tin diffusion has beenstudied by Valenta11 and the data were reevaluated later byShaw,13 but the results fail to provide consistent knowledge.The only attempt to study the effect of doping for group IIIelements is the study by Valenta11 carried out for indium

�data reevaluated in Ref. 13�, but unfortunately these resultsare also inconsistent. It should be noted that in all previousstudies, the employed impurity atom concentrations havebeen significantly high. In case of intrinsic material, caremust be taken that the impurity atom concentrations are keptlow. An ideal method for such experiments is the presentlyemployed radiotracer technique.14

Recent calculations predict15 that germanium vacanciescan have charge states of ��, �, 0, �, and ��. Accordingto calculations, relaxation of the lattice around a vacancy candiffer significantly for the different charge states. Corre-spondingly, vacancy formation and migration energiesstrongly depend on the vacancy charge state contributingvery distinctively to self-diffusion. For the diffusion of sub-stitutional impurity atoms, the situation is even more com-plicated. When the distance between an isolated vacancy andimpurity atom decreases, the vacancy-impurity interactionsstart to affect the charge distribution and the lattice relaxationaround both of them. Depending on the properties of theseinteractions, various kinds of vacancy-impurity complexescan be formed. During the complex formation, excess elec-trons or holes may also be incorporated to the complex.

The concentration of free charge carriers can be alteredby doping, e.g., p-type doping decreases the concentration offree electrons and increases, respectively, the hole concentra-tion. Due to the shift of the Fermi level, a change in thecharge carrier concentration also affects the concentration ofcharged vacancies.16,17 However, it does not affect the con-centration of neutral vacancies nor the charge state of substi-tutional impurity atoms. At typical diffusion temperatures,practically all isolated dopant atoms have the same chargestate, i.e., −1 for group III impurities, 0 for group IV impu-rities, and +1 for group V impurities. Semiconductor dopingcan therefore be taken advantage of in determining thecharge states of mobile vacancy-impurity complexes. If thecharge state of the mobile vacancy-impurity complex differsfrom the charge state of an isolated impurity atom, excesscharge is needed to form the complex. This may originatefrom a charged vacancy or from the capture of a free chargecarrier. In both cases, the complex formation energy will bealtered by doping. With n-type doping, the formation energy

a�Author to whom correspondence should be addressed; electronic mail:jyrki.raisanen@helsinki.fi

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decreases for complexes with “excess” �compared to thecharge state of an isolated impurity� negative charge andincreases for complexes with excess positive charge. If thecharge state of the mobile vacancy-impurity complex is thesame as of an isolated impurity, excess charge is not neededand doping does not have a significant effect on the complexformation energy nor impurity atom diffusivity. It is alsopossible that complexes with several charge states contributeto diffusion.

The intrinsic and p-doped �Ga; 3.5�1018 and 2.5�1019 cm−3� germanium samples were fabricated by Umi-core Ltd., Olen, Belgium. The tin and gallium depth profil-ings were carried out by means of the modified radiotracertechnique14 using 123Sn �T1/2=129.2 days, decay mode �−�and 66Ga �T1/2=9.49 h, decay mode �++EC� as the tracers.The 123Sn implantation was carried out at the online isotopeseparator ISOLDE at CERN. The implantation energy was60 keV and the total fluence was 5.2�1011 ions/cm2

corresponding to a peak concentration of about2.8�1017 at. /cm3. The 66Ga tracers were implanted at theion guide isotope separator online �IGISOL� of the Univer-sity of Jyväskylä, Finland. The implantation energy was40 keV and the fluence was 2�109 ions/cm2 correspondingto a peak concentration of approximately 7�1014 at. /cm3.Sample annealing �575–910 °C� was performed in avacuum furnace under a pressure of 1�10−9 mbar with aprotective Ge cap placed on top of each sample. The anneal-ing times varied from 4 min to 113 h. The subsequentsample serial sectioning was done by ion beam sputtering.The activity of the removed material was determined by twolarge area silicon particle detectors with active volume thick-ness of 0.5 mm.

Typical 123Sn profiles are shown in Fig. 1. Details of theprocedures and extracting the diffusion coefficients D can befound from Refs. 18 and 19. In Fig. 2, diffusion coefficientsas functions of the inverse diffusion temperature are dis-played. Arrhenius plots were fitted by taking into accounterrors in D and 1/T axis for each data point individually.20

The deduced activation enthalpies and preexponential factorsare compiled in Table I.

From the obtained results, several interesting and sub-stantial conclusions can be made. Vogel et al.,1 Werneret al.21 as well as Valenta and Ramasastry22 have studied theeffect of doping on germanium self-diffusion and found out

that n-type doping enhances and p-type doping retards self-diffusion. The doping dependence is accurately described,taking account only neutral and singly negatively chargedvacancies.21,23 In the work of Valenta,11 the effect of dopingwas studied for tin diffusion at two temperatures for whichcontradictory results were obtained and thus, no definite con-clusions can be made on this basis. However, according tothe present results, as can be clearly noted from Figs. 1 and2, p-type doping has a significant effect on Sn diffusion. Theeffect depends clearly systematically on the doping concen-tration and the fact that p-type doping retards Sn diffusionindicates that the mobile Sn-vacancy complex has a negativecharge state �isolated Sn atom is neutral�.

For group III elements, the only attempt to define theeffect of doping on diffusion in germanium is the work ofValenta11 concerning indium diffusion. Measurements wereconducted at three temperatures and the highest diffusivity

FIG. 1. 123Sn profiles in intrinsic and p-doped germanium produced by60 keV implantation ��� and subsequent diffusion annealing at 578 °C for112 h �x, intrinsic; �, Ga-doped �3.5�1018 at. /cm3�; and �, Ga-doped�2.5�1019 at. /cm3��. The solid line represents a fit of the appropriate solu-tion of the diffusion equation to the diffusion profile.

FIG. 2. Diffusion coefficients for Sn �a� and Ga �b� diffusions in intrinsic��� and gallium-doped ��, 3.5�1018 at. /cm3 and �, 2.5�1019 at. /cm3�germanium. Experimental uncertainties are of the order of the data-pointsizes and the solid lines are the fittings. In case of Ga diffusion, only the datapoints for intrinsic material are included in the shown fit.

TABLE I. Activation enthalpies H and preexponential factors D0 for Sn andGa diffusions in intrinsic and p-type �2.5�1019 at. /cm3� germanium. Errorsin the preexponential factor D0 correspond to positive/negative direction ofthe vertical axis, respectively.

Ge type

Sn Ga

H �eV�D0

�10−3 m2/s� H �eV�D0

�10−3 m2/s�

Intrinsic 2.90±0.03 1.5±0.7/0.5 3.21±0.07 8±9/4p type 3.33±0.05 80±80/40 3.4±0.2 80±700/70

091922-2 Riihimäki et al. Appl. Phys. Lett. 91, 091922 �2007�

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was obtained for n-doped germanium and the lowest forp-doped material. These results would mean that the chargestate of the mobile negatively charged vacancy-In complex ishigher than of an isolated In atom. This is actually quitesurprising, since it would lead to a repulsive Coulomb forcebetween the In− ion and the rest of the complex. Accordingto our present findings, gallium diffusion is unaffected bydoping, indicating that the charge state of the mobilevacancy-Ga complex is −1 �same as of an isolated Ga atom�.

Clear systematics in the literature diffusion data of groupIII, IV, and V elements in germanium may be noted. Diffu-sivities of group III and IV elements are comparable but thediffusivities of group V elements �P, As, Sb, and Bi� areabout two orders of magnitude higher. In case of the rathersmall P atom, the interstitial mechanism has also beensuggested6 and due to the prevailing strong elastic attractionwith interstitials, this possibility cannot be definitely ruledout. However, at least in case of As, Sb, and Bi, which are allvacancy diffusers,23 the most probable explanation for thefast diffusion are the forces acting inside the vacancy impu-rity complex. In the diamond cubic structure, a vacancy be-ing next to a substitutional impurity atom after diffusionjump, in order to cause another jump, must move to at leastthird coordination site from the impurity and return by an-other path. Thus, if the attractive interaction potential be-tween a substitutionally dissolved impurity atom and va-cancy is sufficiently strong and extends at least to a thirdnearest neighbor site,24–26 it is possible for the impurity todiffuse as a pair with the vacancy via so-called E-centerdiffusion.

For all group V dopants, singly negative E centers havebeen identified3 and their stability has been found to increasewith increasing atom size, as expected due to the effect ofelastic interactions. For Sb and Bi, the charge states of themobile vacancy-Sb/Bi complexes have not been determinedbut Bracht and Brotzmann23 have shown that As diffusion inGe is conducted by singly negative As-vacancy complexes.Since the isolated As atom is singly positively charged, anattractive long range Coulomb potential prevails between theAs atom and the rest of the complex, making effectiveE-center diffusion feasible. In the case of group III and IVimpurities, this does not hold. For gallium, the charge stateof the complex is the same as the charge state of an isolatedGa atom. In case of group IV impurities, no long range Cou-lomb interactions exist since at typical diffusion tempera-tures, isolated group IV atoms are neutral in germanium. Thefaster diffusion of group V elements �As, Sb, and Bi� can bebest understood by considering that the attractive long rangeCoulomb interaction prevailing between the impurity and therest of the complex prevents complex dissociation when thevacancy-impurity distance is increased which in turn enableseffective E-center diffusion.

The definite reason why group III elements do not dif-fuse via neutral or positively charged complexes is still un-clear. In the case of neutral or positively charged complexes,an attractive Coulomb force would prevail between the im-purity and the rest of the complex, preventing dissociationduring the vacancy diffusion path between successive jumps.The most probable reason for the lack of mobile neutral andpositively charged vacancy-impurity complexes is the lowerflux factor �=DV

x CVx , where DV

x is the diffusivity and CVx is the

concentration of charged vacancies� of positively charged va-

cancies compared to neutral and negatively charged vacan-cies. This conclusion can be deduced from self-diffusion datashowing that positively charged vacancies do not play a rolein self-diffusion of germanium. For germanium, no indepen-dent formation and migration energy measurements of va-cancies exist but for silicon, it has been observed that themigration energy for doubly positively charged vacancies issignificantly higher than for neutral and negatively chargedvacancies24 �singly positive vacancy is not stable in silicon�.

In conclusion, the effect of p-type doping on Ga and Sndiffusions in germanium revealed the important role of thevacancy-impurity atom complex charge state in understand-ing the diffusion systematics of group III, IV, and V elementsin germanium. The two orders of magnitude higher diffusiv-ity of As, Sb, and Bi compared to group III and IV elementsis due to the more effective E-center diffusion made possibleby the attractive Coulomb interaction prevailing betweengroup V dopants and the rest of the mobile complex.

Implantations at ISOLDE and IGISOL are highly appre-ciated. This work was supported by the European UnionSixth Framework through RII3-EURONS �Contract No.506065�. The financial support from the Academy of Finland�Project No. 203736� and from the Finnish Society of Sci-ence and Letters, Magnus Ehrnrooth Foundation is gratefullyacknowledged.

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