Atomic transport in germanium and the mechanism of arsenic diffusion

ARTICLE IN PRESS

Materials Science in Semiconductor Processing 9 (2006) 471–476

Atomic transport in germanium and the mechanism of arsenic diffusion Hartmut Bracht, Sergej Brotzmann Institute of Materials Physics, University of Muenster, D-48149 Muenster, Germany Available online 26 September 2006

Abstract The paper reviews some basic aspects of self- and foreign-atom diffusion in germanium (Ge) and provides new experimental results on the intrinsic and extrinsic diffusion of arsenic (As) in Ge. Experiments of As diffusion in Ge have been performed at temperatures between 640 and 920 1C utilizing a diluted Ge–As alloy as diffusion source. The As profiles were measured by means of the spreading resistance technique. Depending on the As concentration established at the surface, intrinsic and extrinsic As profiles were obtained. Arsenic diffusion in Ge is fully described on the basis of the vacancy mechanism taking into account singly negatively charged As-vacancy pairs. In contrast to a recent study of Vainonen-Ahlgren et al. (Appl. Phys. Lett. 77 (2000) 690), which claims that As diffusion is mediated by neutral and doubly negatively charged vacancies, we show that As diffusion is not sensitive to the properties of vacancies. From our experiments we determine an activation enthalpy of 2.70 eV and a pre-exponential factor of 30 cm2 s1 for intrinsic As diffusion in Ge. r 2006 Elsevier Ltd. All rights reserved. Keywords: Germanium; Self-diffusion; Dopant diffusion; Arsenic; Vacancy

1. Introduction The first bipolar transistor developed in December 1947 by J. Bardeen, W. Brattain, and W. Schockley was made of elemental Ge. However, the interest in Ge strongly decreased with the development of the Si-based field effect transistors (FET) with a metal-oxide-semiconductor (MOS) structure. Despite the fact that the electron and hole mobilities are higher in Ge than in Si, the extremely stable high ohmic Si oxide (SiO2) compared to the less stable

Corresponding author. Tel.: +49 251 833 9004; fax: +49 251 833 8346. E-mail address: [email protected] (H. Bracht).

1369-8001/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2006.08.041

Ge oxide (GeO2) made Si more attractive as the base material for the today microelectronics. Today an increasing interest in Ge and SiGe alloys exists. This renewed interest arises from their promising applications in Si-based integrated-circuit technology. With state-of-the-art epitaxial deposition techniques the former obstacles which strongly limited the use of Ge as the base material for electronic devices no longer exist. Using Ge or SiGe epitaxial layers instead of Si one can take advantage of the higher carrier mobility in Ge-rich layers. As in the case of Si, successful applications of Ge-based semiconductors demand the control of dopant distributions during device fabrication. This requires a detailed understanding about the atomic mechanisms of mass transport.

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In this paper the most basic process of matter transport in Ge, that is self-diffusion, is reviewed. The pressure dependence of self-diffusion and the interrelation between the diffusion of Ge and Cu provide strong evidence that vacancies mainly control self-diffusion. The dominance of vacancies also becomes evident in the diffusion behavior of mainly substitutionally dissolved n- and p-type dopants. Most recent data on the diffusion of foreign atoms are summarized and new results on the intrinsic and extrinsic diffusion of As in Ge are presented.

T (°C) 900 10-3

800

700

600

Ni

Cu Ag Fe

Ge:X

10-9 Au 10-12

Al Zn As

2. Self- and foreign-atom diffusion in Ge Werner et al. [1] investigated the diffusion of the radioactive isotope 71Ge in natural Ge as a function of temperature, doping, and pressure. In agreement with former studies [2,3] Werner et al. found an enhanced self-diffusion in n-type material and retardation in p-type Ge. The doping dependence is accurately described with neutral and singly negatively charged native defects. The pressure dependence of self-diffusion revealed activation volumes for the native defect mediating self-diffusion which are typical for relaxed vacancies. Based on these results Werner et al. concluded that selfdiffusion in Ge proceeds by a vacancy mechanism and that the vacancy acts as an acceptor. Additional evidence of the prevalence of vacancies in Ge is given by the diffusion of the hybrid element Cu. The strong structural dependence of Cu diffusion in Ge is fully explained on the basis of the dissociative mechanism (see Ref. [4] and references therein). Fig. 1 shows the temperature dependence of the diffusion coefficient of various foreign atoms in Ge in comparison to self-diffusion. The solid lines indicate the diffusivities of mainly substitutionally dissolved elements. The diffusion of the hybrid elements Cu [4–6], Ag [5], Au [5], and Ni [7], which are dissolved both on interstitial and substitutional sites, are indicated by the long-dashed lines. The data represent the interstitial foreign-atom controlled mode of diffusion via the dissociative mechanism. The upper thin-dashed line in Fig. 1 shows the diffusivity of interstitial Cui which was deduced in Ref. [4] from the interstitial controlled Cu diffusion coefficient and the solubility of Cu on interstitial and substitutional lattice sites. Cui is the fastest diffusing species among the other interstitial foreign atoms such as H [8] and Fe [9]. The data for B [10], Al [11], Si [12], and Zn [13] represent results

500

Cu

H

10-6

DX (cm2s-1)

472

10-15

Sb P

Si

B

Ge

10-18 0.9

1.0

1.1

1.2

103/T (K-1) Fig. 1. Temperature dependence of the diffusion of foreign atoms in Ge (thin lines) compared with self-diffusion (thick line). Details and references to the data are given in the text. Solid lines represent diffusion data of elements that are mainly dissolved on substitutional lattice sites. Long-dashed lines (— —) illustrate diffusion data of hybrid elements, which are mainly dissolved on substitutional sites, but diffuse in an interstitial configuration via the dissociative mechanism. The short-dashed lines (- - - -) indicate the diffusion of mainly interstitial dissolved elements. The upper short-dashed line shows the diffusivity deduced for interstitial Cui.

of most recent diffusion studies utilizing secondary ion mass spectrometry [10–12] and the spreading resistance technique [13] as profiling methods. The diffusivities of Sb [14] and P [15] shown in Fig. 1 were determined by means of incremental sheet resistivity measurements. The temperature dependence of As diffusion reflects the intrinsic diffusivity determined in this work. It is evident from Fig. 1 that the diffusivity of B and Si is slower than that of Ge. Assuming that vacancies mainly mediate the diffusion process this points to a repulsive interaction between the vacancy and the foreign atom. In the case of the semiconductor silicon, the diffusion of foreign atoms always exceeds self-diffusion [16]. This is related to the fact that both self-interstitials and vacancies contribute to almost the same extent to Si self-diffusion [17,18]. A comparison between self- and foreign-atom diffusion in Ge and Si as function of the homologous temperature Tm/T is shown in Fig. 2. This representation accounts for the different melting temperatures of Ge (T m ¼ 1210 K) and Si

ARTICLE IN PRESS H. Bracht, S. Brotzmann / Materials Science in Semiconductor Processing 9 (2006) 471–476

10-3

Cu

DX (cm2s-1)

Cu

Fe

10-6

Fe Zn

10-9

Zn ↓

Si:X Ge:X

10-12 As 10-15

B As B 1.0

Ge

Si

10-18 1.2

1.4

1.6

Tm/T Fig. 2. Representation of self- and foreign-atom diffusion in Ge (T m ¼ 1210 K) and Si (T m ¼ 1685 K) as function of the homologous temperature Tm/T. The solid lines show diffusion data for Ge and the dashed lines for Si. References to the data are given in the text.

(T m ¼ 1685 K). Referred to Tm, the self-diffusion coefficients in Ge [1] and Si [17,18] are of equal magnitude which reflects the similarity in the mechanisms of self-diffusion. Accordingly, the representation of DX versus the homologous temperature may also provide rough clues about the underlying diffusion mechanisms of the foreign atoms. The diffusion coefficients of interstitial Cui in Ge (upper solid line) [4] and Si (upper dashed line) [19] are of similar magnitude. The same holds for the diffusion coefficients of interstitial Fe in Ge [9] and Si [20]. The diffusion data of Zn in Ge [13] and Si [21] differ by several orders of magnitude whereas e.g. the data of As in Ge (this work) and Si [22] are again of similar magnitude. The difference in the diffusivity of Zn can be explained with the different mechanisms mediating the diffusion of this element in Ge and Si. Zinc in Si acts as a deep acceptor and diffuses by means of interstitial–substitutional exchange mechanisms, namely the kickout and dissociative mechanisms [21]. Zinc in Ge is a shallow acceptor which likely diffuses via the vacancy mechanism [13]. On the other hand As acts as shallow n-type dopant in both Si and Ge. In Si, As diffuses to the same degree via the vacancy and interstitialcy mechanism (see e.g. [23]). In Ge, As diffusion is concluded to take place mainly via the vacancy mechanism (see [24] and below). This similarity in the diffusion behavior obviously leads to similar DAs data in the homologous representation. In this context it is interesting to note the

473

difference between the diffusivity of B in Ge [10] and Si [25]. Boron acts as a shallow acceptor in both semiconductors but diffuses considerably slower in Ge than in Si. In Si, B is known to diffuse by means of self-interstitials via the kick-out or interstitialcy mechanism [23]. But, self-interstitials play a minor role in thermal self-diffusion in Ge. Accordingly, the low B diffusivity either reflects dopant diffusion via the vacancy mechanism or the contribution of selfinterstitials to B diffusion via the interstitialcy mechanism. The high activation enthalpy of 4.65 eV for B diffusion experimentally determined by Uppal et al. [10] and later verified by theoretical calculation of Delugas and Fiorentini [26] provides evidence for B diffusion via the interstitialcy mechanism. Recently, Vainonen-Ahlgren et al. [24] performed experiments on As diffusion in Ge using GaAs overlayers deposited on p-type Ge substrates as diffusion source. After diffusion annealing the profiles were recorded with secondary ion mass spectrometry. Vainonen-Ahlgren observed a concentration-dependent diffusion and concluded that As diffusion proceeds through neutral and doubly negatively charged vacancies. Our investigations show that their interpretation is misleading. The concentration-dependent diffusion of As is independent of the charge state of the vacancies and rather shows the charge difference between the mobile Asvacancy complex and the substitutional As donor than the charge states of the vacancies. This results from our analysis of the intrinsic and extrinsic diffusion of As in Ge described in the following.

3. Experimental Germanium samples with lateral dimensions of 5  5 mm2 were cut from a (1 0 0) oriented highohmic (430 O cm) p-type Ge wafer with a thickness of about 300 mm. After cleaning the samples in organic solvents, they were sealed in evacuated silica ampoules together with about 70 mg of a Ge–As alloy. Alloys with less than 1.0 at% As were used as diffusion source in order to protect the sample surface for strong degradation during annealing. The diffusion anneals were performed in a resistance heated furnace at temperatures between 640 and 920 1C for times which were appropriate to realize penetration depths of 10 mm up to 100 mm. The temperature was controlled with an accuracy of 2 K. The diffusion process was terminated by

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with a complementary error function ! x eq C As ðx; tÞ ¼ C As erfc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 2 DAs ðni Þt

1019

T = 730°C T = 770°C t=48 h

1018 1017

t=48 h t=96 h

1016 t=72 h

1015 0

40

80

120

depth (μm) Fig. 3. Concentration profiles of substitutional As in Ge obtained after diffusion annealing at 730 and 770 1C for times indicated in the figure. For As surface concentrations of CAs41019 cm3, which exceed the intrinsic carrier concentration, box-shaped As profiles are obtained. In the case when the As surface concentration is below the intrinsic carrier concentration the profile shape equals a complementary error function. Solid lines represent best fits obtained on the basis of the vacancy mechanism. For clarity only a reduced number of experimental data points are shown.

rapidly cooling the ampoule with ethylene glycol down to room temperature. Diffusion profiles of As were measured by means of the spreading resistance technique. The measured resistance profiles were converted into resistivity profiles taking into account the spreading resistance data of Ge samples with known resistivities. The transformation to As concentration was performed with the interrelation between donor concentration and respective resistivity reported by Cuttriss [27]. Typical concentration profiles of As are illustrated in Fig. 3. The profiles represent the distribution of the substitutionally dissolved donor As+ s . The shape of the profiles clearly depends on the surface concentration established by the Ge–As alloy. In the case the surface concentration is about 1018 cm3, which lies below the intrinsic carrier concentration ni [28], the profile resembles a complementary error function. For higher surface concentrations a box-shaped As profile is observed. These box-shaped profiles are characteristic for extrinsic As diffusion and were also observed by Vainonen-Ahlgren [24]. 4. Results The As profiles with surface concentrations below the intrinsic carrier concentration can be described

(1)

This is the solution of Fick’s law for diffusion in the case of an infinite source. The C eq As denotes the surface concentration of As which equals the thermal equilibrium concentration C eq of the substitutional Asþ s As donor. The x and t are the penetration depth and diffusion time, respectively, and DAs (ni) denotes the intrinsic As diffusivity. The data obtained for intrinsic conditions and temperatures between 640 und 920 1C are summarized in Fig. 4. The temperature dependence determined for intrinsic As diffusion is   ð2:70  0:06Þ eV DAs ðni Þ ¼ 30þ28  exp  cm2 s1 . 15 kB T (2) Extrinsic As diffusion yields box-shaped profiles (see Fig. 3). A simple analysis on the basis of Fick’s diffusion equation reveals that the profiles can be described with an effective As diffusion coefficient Deff As which is proportional to the square of the As concentration. This concentration dependence is in accord with the prediction of a foreign-atom 10-8

eq

concentration of arsenic (cm-3)

1020

DX and CAsVDAsV /Co (cm2/s)

474

10-10

10-12 As 10-14 Ge 10-16 (AsV)

-

10-18 0.9

1.0 10

3/T

1.1

(K-1)

Fig. 4. Temperature dependence of the intrinsic As diffusion coefficient DAs ðni Þ (filled symbol) and of the intrinsic transport  capacity C eq ðAsVÞ ðni ÞDðAsVÞ =C o of the singly negatively charged As-vacancy pairs (open symbols) in comparison to Ge selfdiffusion (thick solid line). The open circles (open squares)  represent data of C eq ðAsVÞ ðni ÞDðAsVÞ =C o deduced from intrinsic (extrinsic) As diffusion. The temperature dependence of intrinsic As diffusion (upper thin solid line) and of the transport capacity of As-vacancy pairs (lower thin solid line) are given by Eqs. (2) and (7), respectively.

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controlled mode of As diffusion via the vacancy mechanism [29] k  ðAsVÞ 3 Asþ s þ V þ ðk þ 2Þe

(3)

which yields Deff As

¼2

 C eq ðAsVÞ ðnÞDðAsVÞ

C eq ðnÞ Asþ s

¼ 2DAs ðnÞ

C Asþs ðx; tÞ

C Asþs ðx; tÞ !2

!2

ðnÞ C eq Asþ

ð4Þ

s

Modeling of As diffusion on the basis of reaction (3) eq  yields data for DAs ðnÞ ¼ C eq ðAsVÞ ðnÞDðAsVÞ =C Asþ ðnÞ. s

 The extrinsic transport capacity C eq ðAsVÞ ðnÞDðAsVÞ =C o eq eq is given by DAs ðnÞ  C Asþ ðnÞ=C o where C Asþ ðnÞ s

s

represents the surface concentration and Co ( ¼ 4.413  1022 cm3) the Ge atom density, respectively. The interrelation between the extrinsic and intrinsic transport capacity of ðAsVÞ is given by  C eq ðAsVÞ ðni ÞDðAsVÞ

Co

¼

 C eq ðAsVÞ ðnÞDðAsVÞ ni

Co

n

.

(5)

This equation follows from the impact of the Fermi level on the formation of charged point defects in semiconductors [30]. The n ð C eq Þ is Asþ s

the free electron concentration. Taking into account data of ni reported by Morin and Maita [28],  C eq ðAsVÞ ðni ÞDðAsVÞ =C o can be deduced from the extrinsic results by means of Eq. (5). The data are displayed in Fig. 4 by the open squares. The directly measured intrinsic As diffusion coefficient DAs ðni Þ is also associated with the intrinsic transport capacity of (AsV) DAs ðni Þ ¼

 C eq ðAsVÞ ðni ÞDðAsVÞ

C eq ðn Þ Asþ i

The good agreement between the intrinsic transport capacity of (AsV) deduced from intrinsic and extrinsic As diffusion confirms the relationships (4) and (6) for DAs ðnÞ and DAs ðni Þ. These diffusion coefficients are closely linked via  2 n DAs ðnÞ ¼ DAs ðni Þ  . (8) ni

s

.

ðnÞ C eq Asþ

475

.

(6)

s

This follows from reaction (3) in the foreign-atom controlled diffusion mode for mainly substitutioneq ally dissolved dopants ðC eq As bC ðAsVÞ Þ. According eq s to Eq. (6) the product C Asþ ðni Þ  DAs ðni Þ=C o yields s  C eq ðAsVÞ ðni ÞDðAsVÞ =C o . The transport capacity deduced from the intrinsic As diffusion coefficient is displayed in Fig. 4 by the open circles. All data for  C eq ðAsVÞ ðni ÞDðAsVÞ =C o are best described by  C eq ðAsVÞ ðni ÞDðAsVÞ

þ0:8 ¼ 1:10:5 Co   ð3:22  0:05Þ eV  exp  cm2 s1 . kB T

The quadratic dependence of DAs ðnÞ on the free electron concentration is a consequence of the eq doping dependence of C eq ðnÞ. ðAsVÞ ðnÞ and C Asþ s Fig. 4 demonstrates that the transport capacity of (AsV) is lower than the Ge self-diffusion, i.e. eq  C eq ðAsVÞ ðni ÞDðAsVÞ =C o 5C V ðni ÞDV =C o . This confirms ex post the foreign-atom controlled mode of As diffusion which was assumed in the derivation of Eqs. (4) and (6) [29]. 5. Discussion We have demonstrated that both the intrinsic and extrinsic diffusion of As in Ge is consistently explained on the basis of reaction (3) with singly negatively charged mobile (AsV) pairs. In fact all theoretical profiles illustrated in Fig. 3 are numerical solutions of the full differential equations of As diffusion via the vacancy mechanism (3). For the simulations only DAs ðni Þ and ni were optimized to describe the experimental profiles and a good agreement between the values for ni used in the simulations and those reported in the literature were found. For modeling we assumed neutral and singly negatively charged vacancies. Their individual contributions to Ge self-diffusion under intrinsic conditions were set according to the results given by Werner et al. [1]. However, irrespective of the settings for the vacancy contributions to self-diffusion, accurate fits are obtained as long as the relationship eq  C eq ðAsVÞ ðni ÞDðAsVÞ =C o 5C V ðni ÞDV =C o remains valid. This shows that As diffusion is insensitive to the properties of Ge vacancies. In the former work of Vainonen-Ahlgren [24] the concentration dependence of As diffusion was misattributed to the charge states of vacancies. In fact, the quadratic As concentration dependence of As diffusion is due to the difference in  the charge states of Asþ s and (AsV) . 6. Conclusions

ð7Þ

Vacancies mainly mediate the atomic transport of substitutional elements in Ge. An exception seems

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H. Bracht, S. Brotzmann / Materials Science in Semiconductor Processing 9 (2006) 471–476

to be the diffusion of B whose diffusion activation enthalpy is in accord with the theoretical predictions for B diffusion via an interstitialcy mechanism. We discussed the intrinsic and extrinsic diffusion of As in Ge which is accurately described on the basis of the vacancy mechanism taking into account singly negatively charged As-vacancy pairs. This pair controls the diffusion and formation of substitutional As in Ge. In contrast to recent results reported in the literature, the present work clearly shows that As diffusion in Ge is not sensitive to the properties of vacancies. We determined the temperature dependence of intrinsic As diffusion, which is given by Eq. (2), and found that extrinsic As diffusion is proportional to the square of the free electron concentration. We have performed additional studies which concern the diffusion of As in Ge isotope multilayer structures. From the simultaneous diffusion of As and Ge the charge states of vacancies can be determined. The results of these studies, which also comprise the impact of unintentionally carbon doping on As diffusion, will be published elsewhere. Acknowledgments We thank Dr. I. Romandic and Dr. A. Theuwis (Umicore, Olen, Belgium) for donating high-ohmic Ge wafers for the diffusion experiments and Ge material with specific doping levels for the calibration of the spreading resistance measurements. This work was supported by the Deutsche Forschungsgemeinschaft under the reference number Bra 1520/ 6-1. References [1] Werner M, Mehrer H, Hochheimer HD. Phys Rev B 1985;32:3930.

[2] [3] [4] [5]

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