physical properties of ion-implanted laser annealed n-type germanium

G. CONTRERAS et al. : Ion-Implanted Laser Annealed n-Type Germanium 475

phys. stat. sol. (b) 131, 475 (1985)

Subject classification: 6 and 13.4; 14.3; 20.1; 22.1.1

Max- Plawck- Institut fur FestkorperjoruchuNg, Stuttgert')

Physical Properties of Ion-Implanted Laser Annealed n-Type Germanium

BY

G. CONTRERAS~), L. TAPFER, A. K. SOOD~), and M. CARDONA

Dedicated to Prof. Dr. Dr. h. c. Dr. E. h. P. GORLICH on the occasion of his 80th birthday

An investigation is made of the impurity distribution and carrier concentration in n-type germanium layers doped with P, As, and Sb by ion implantation and recrystallized by laser annealing. The impurity distribution is determined with SIMS. The electzon concentration is obtained from Hall effect and from ir reflectivity measurements. Impurity concentrations as high as 2 X x loz1 cm-3 are reached, with carrier concentrations N , as high as 2.4 x lozo ~ m - ~ , much higher than in bulk doped samples ( N , 5 4 X IOl9 ern+). For the P-doped samples the implanted layers are found to have a lattice constant larger than the substrate for small implantation doses and smaller for larger doses. An analysis of these data leads to the conclusion that most of the ions are implanted substitutionally and, a t high concentrations, they aze compensated by pairing defects, probably vacancies. With this hypothesis it is also possible to interpret the dependence of the strength of the phosphorus local mode on implantation dose, as found with Raman spectroscopy. The softening of the Raman phonon with dose observed experimentally is also compatible with this hypothesis. A soStening of the acoustic phonons with dose found with Brillouin spectroscopy is also reported and discussed.

Es wird die Storstellenverteilung und die Ladungstragerkanzentration in n-leitenden, durch Ionenimplantation P-, As- und Sb-dotierten und mittels Laserausheilung rekristallisierten Ger- maniumschichten untersucht. Die Storstellenverteilung wird mit SIMS bestimmt und die Elek- tronenkonzentration aus Hall-Effekts- und aus IR-Iieflexionsmessungen erhalten. Storstellen- konzentrationen bis zu 2 x loz1 cm-3 werden erreicht mit Ladungstragerkonzentrationen N , bis zu 2,4 x lozo ~ r n - ~ , die vie1 hoher als in volumendotierten I'roben ( N , 5 4 x 1019 sind. Fur P-dotierte Proben wird gefunden, daB die implantierten Schichten eine Gitterkonstante auf- weisen, die fur geringe Implantationsdosen groSer ist als die des Substrats und kleiner fur grol3e Dosen. Eine Analyse dieser Werte fiihrt zu dem SchluS, daO die meisten der Ionen substitutionell implantiert sind und bei hohen Konzentrationen durch paarbildende Defekte, wahrscheinlich Leerstellen, kompensiert werden. Mit dieser Hypothese ist es auch moglich, die Abhangigkeit der Starke der lokalen Phosphormode von der Implantationsdosis zu erklaren, wie mit Raman- spektroskopie gefunden wird. Die Erweichung des Ramanphonons mit der Dosis, die experimentell beobachtet wird, ist mit dieser Hypothese ebenfalls kompatibel. Eine Erweichung des akustischen Phonons mit der Dosis, die mit Brillouin-Spektroskopie gefunden wird, wird ebenfalls mitgeteilt und diskutiert.

Heisenbergstr. 1, D-7000 Stuttgart 80, FRG. 2) DAAD Bellow, on leave from E.S.F.M.-I.P.N., Edif. 6, U.P.A.L.M., Deleg. G. A. Madero,

3) Present address: Materials Science Laboratory, Reactor Research Centre, Kalpakkam 07300 Mbxico, D.F. N6xico.

603 102, India.

476 G. CONTRERAS, L. TAPFER, A. K. SOOD, and M. CARDONA

1. Introduction

Laser annealing of ion-implanted semiconductors, especially Si [l to 61, Ge [7], and GaAs [8] offers the possibility of reaching higher carrier concentrations than those governed by solubility limits in the bulk. In this sense, ion implantation and laser annealing have been particularly successful for Si [9]. In this case ions such as P, As, and B are incorporated substitutionally to very high concentrations (=z 10%). They are electrically active and the ion-implanted, laser-annealed (IILA) layers seem to have a relatively small number of defects. In the case of IILA germanium considerable coarse damage, in the form of craters and voids, has been observed [7,10]. Because of this fact, and of the technological applications of Si, much less work has been published for IILA Ge than for similarly treated Si.

In this paper we present investigations of IILA samples implanted with either phosphorus, arsenic, or antimony and annealed with a pulsed excimer laser. The IILA layers are single crystalline with the orientation of the substrate, as shown by Raman scattering. The implantation profiles were investigated by secondary ion mass spectroscopy (SIMS). The free-electron concentration was obtained from the infrared reflection and the Hall effect. It was found to be as high as 2.4 x lozo c111-~, although, in this case, a much larger concentration of electrically inactive ions existed. These ions were shown, in the case of phosphorus, to occupy substitutional sites by Raman measurements of the local vibrational modes induced by the phosphorus. A niodel for this electrical inactivity, based on compensation or passivation of the donor impurities by neighboring vacancies, was developed.

The presence of active and inactive implanted impurities is also revealed by measurements of the change in the lattice constant of the IILA layers implanted with P with concentration: a t low P concentrations the lattice constant is larger than that of the intrinsic substrate while a t high concentrations it is smaller.

Shifts and broadenings of the Raman phonon are also observed in the IILA samples. They can be attributed to the presence of impurities. The effect of doping on the LA phonons has also been investigated by means of Brillouin spectroscopy. A large softening is observed. It can be partly attributed to electron-phonon interaction and partly to a decrease in refractive index produced by the presence of voids.

2 . Experiment

2.1 Sample preparation and determination of the carrier concentration

Instrinsic Ge substrates were implanted with different donor ions (P, As, and Sb) and varying doses N , (2 x 1015 cm-2 5 N , 5 6 x l0ls cm-2). The implanted samples were laser annealed with a XeCl laser (A = 308 nm, 10 ns pulse duration, 0.8 J/cm2 energy density). The carrier concentrations of the samples were determined by ir reflectivity [ll to 131 and Hall effect measurements (van der Pauw geometry [14]). The Hall measurements were performed a t room temperature with the sample on the original substrate (x 1 mm thick) and with this substrate thinned down to 0.6 and 0.3 nim. The data were then linearly extrapolated to zero substrate thickness so as to remove the influence of the intrinsic Ge substrate (x l0l4 carriers/cm3) on the measurements. The carrier concentration N , is related to ,the Hall constant R through

1 Rec ’ N , = f -

where e is the electron charge and c the speed of light. The scattering and mass anisotropy factor f was taken equal to unity for simplicity. The scattering part of it is

Physical Properties of Ion-Implanted Laser Annealed n-Type Germanium 477

Pig. 1. I r reflectivity spectra measured a t room temperature for two IILA samples; - - - Ge:P, 1 x 1016cm-2, (110) face;-Ge:P, 6 x 10l6 cm-2, (110) face. The insert shows the SIMS profile of phosphorus atoms obtained for one of these samples (Ge(P), 6 x 1OI6 cm-2, (1 10) face). The ir spectra show the reflectivity mi- nima vh, and the first interference extrema v;, v;,+ At the inset read ~ 1 1 1 ~ ~ instead of cm2. The wave-number scale has t o be interupted left to ZOO0 em-'

i

41(M 3200 Z O O U O O 800 200

uncertain. The mass anisotropy alone would give f = 0.8 1151. Recent data for silicon [la] suggest that the value of f should be close to that calculated from the mass anisotropy alone for dopings in the 1020 cm-3 range (cf. [16] and references therein).

The determination of the Hall constant R from the van der Pauw data requires the knowledge of the sample thickness. Three avenues are open for its approximate determination : measurement of optical interferences in the implanted layer, SIMS, and Rutherford backscattering (RBS). The latter can only be used to determine thicknesses of layers implanted with atoms much heavier than Ge, in our case Sb. RBS results for our Sb-implanted Ge layers yield thicknesses of about 300 nm, in reasonable agreement with the other measurements (see Table 1 ) [17].

A typical SIMS doping profile obtained with 12 keV 0; primary ions for a P-doped Ge sample is shown in the insert of Fig. 1. The ion concentration scale was calibrated by equating the integrated surface density to the total implantation dose. The depth a t which the density decreases to one-half of its maximum value is seen to be 380 nni.

We have also shown in Fig. 1 the infrared reflectivity spectra of two P-doped samples including that for which the SIMS profile is given. These measurements were perfornied with a Nicolet M10 (2.0 ym < il < 50 pm) and a Cary 17D (0.6 pm < 2 < < 2.0 pm) spectrometers. We derive the carrier concentration N , from the wave number of the reflectivity minimum vh, by assuming that this minimum occurs in our layers a t approximately the same position as for bulk material [ l l ] . The correct- ness of this assumption is supported by detailed studies performed for IILA layers of n-type Si 1181. The qualitative justification is that only the front surface, with the sharp refractive index discontinuity, should have nearly zero reflectivity when its refractive index equals one. The interface between the implanted layer and the substrate shows a gradual decrease in the impurity concentration and is expected to have a small reflectivity, nearly independent of wave number. The back surface between intrinsic Ge and air should only contribute a weak, incoherent background to the reflection of the front surface. Within the region of our measurement (vin between 1500 and 3500 cn-1) we found that the experimental data which exist for the bulk can be written as a function of the plasma wave number v6 as


where m* is the optical effective mass of the free electrons (m* = 0.12m,J4) and = 16 the dielectric constant of the intrinsic semiconductor. The values of N , so

obtained for our samples are listed in Table 1.

T a b l e 1

List of the samples used with their corresponding carrier and impurity concentrations and the thickness determined from interferences in the near ir (optical thickness), see text

sample dopant sur- N , Ne N , optical

dose cm-?) concentration concentration d (nm) face implantation carrier impurity thickness

(1020 ~ m - ~ ) (1020 cm-3)

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

phosphorus [loo] 1 2 3 4 6

0.5 1 6

2 arsenic [lll] 1

2 6

[loo] 6 antimony [loo] 1

2

[110] 0.2

[lll] 1

1.5 1.8 1.7 1.5 1.1 0.55 0.96 1.5 1.2 1.6 2 1.8 2.4 2.2 2.1 2.1 2.2

2.9 5.3 7 8.46

12 0.6 1.5 2.9

14 3 5.1 3.3 6.3

19 19

3.2 6.2

353.2 380.0 432.0 473.0 489.0 332.0 340.0 340.0 421.8 335.1 392.1 302.2 316.1 319.6 319.7 312.0 321.7

Our samples also exhibit interference fringes for wave numbers above vd. Fig. 1 shows fringes of order m = 1 and 1.5(v;, &). Prom these fringes the “optical thickness” d of the implanted layer can be determined by means of the expression

Using the plasma wave numbers vk obtained from vh, with (2) we found the “optical thicknesses” listed in Table 1. The “optical thickness” is indicated by a mark in the insert of Fig. 1. We see that i t is only about 10~/o higher than that determined by SIMS at the point where the ion density is half that a t the maximum. This deviation is found systematically for all samples measured. The reason for i t may lie in uncer- tainties in the SIMS work related to initial variations of the sputtering rate. We thus take the optical thickness to be the nominal thickness of our samples as listed in Table 1. With these thicknesses, the values of N , listed in Table 1 were determined from the van der Pauw measurements.

4, The optical effective mass is given by l/m* = (2/mt + l/ml); values of mt and ml a t room temperature are found in [19].


2.2 X-ray diffraction measurements

An X-ray double-crystal diffractometer in (+1, -1) non-dispersive Bragg geometry [ Z O ] was used to measure the difference between the lattice constant of the IILA samples and that of the substrate. The X-ray rocking curves on IILA samples were obtained with CuKa, radiation (1 = 0.1514 nm) on the net planes (004), (333), and (044), (022) for the [OOl], [lll], and [ O l l ] sample orientations, respectively. The X-ray beam was collimated and rendered nearly monochromatic. by asymmetric reflection on a dislocation-free single crystal of Ge.

2.3 Raman and Brillouin scattering measurements

The Raman spectra of our IILA samples were measured a t room temperature in the backscattering geometry with a Spex 1 m double rnonochromator in the photon counting mode. As exciting radiation we used several laser lines of Kr+ and Ar+ lasers. Brillouin measurements were made in backscattering geometry from samples with [ill] orientation a t 1 = 647.1 nm (= 200 mW) using a piezoelectrically scanned five-pass Fabry-Perot interferometer [Sl] having an instrumental contrast of 2 los and finesse x 40. The spectra were recorded in a single, slow scan.

3. Results

3.1 X-Fay diffraction

A typical X-ray diffractogram, taken for sample 4 (Qe:P), [loo] orientation, N , = = 4 x 10l6 cm-2 is shown in Pig. 2 for the (400) reflection as a function of scattering angle 0. This diffractogram shows two peaks which are easy to attribute to the diffraction from the substrate (sharp peak taken to be the origin of 8 ) and to the IILA layer (broad peak). This assignment is easily accomplished by considering the extinction length of the (400) reflection for CuKa, radiation [20]. The double-peak structure was observed for all P-doped Ge IILA samples investigated, regardless of orientation, but neither for Sb-doped nor for As-doped Ge. For N , smaller than 10l6 cm-2 the diffraction peak of the IILA layer shifted to negative values of A0, this fact indicates that the distance between lattice planes parallel to the layer is larger than that of the substrate for N , s 10l6 cm-2 and smaller for N , >= 10l6 cm-2. The relative change in d for the IILA layer, as compared with the substrate, is obtained with [22]

IILA - Ge iP)

Pig. 2. X-ray diffractogram of a P-IILA Ge sample showing the (400) peak of the substrate (pure Ge) and that of the IILA layer (4 x 10le cm-2, (100) face)

- 1000" 0 2000"

480

IILA-Ge iPl

m q R

-3 t

G. CONTRERAS, L. TAPFER, A. K. SOOD, and M. CARDONA

Fig. 3. Relative change in the lattice constant as a function of the impurity concentration Ni. The samples measured were those with the numbers l, 3, 4, 5, 7, 9, and 10 with (400), (440), and (333) as reflection planes (see Table 1). The solid line represents a f i t t o the experimental points with (6) for Be = 7.4 x c d , pi = -3.0 x cm3

-7 04 1 10 4a

N~ (1a%i3)--

where 6JB is the kinematic Bragg angle. The values of Adld obtained with (4) for the (400), (440), (220), and (333) reflexes of correspondingly oriented samples have to be converted into values of Aala for bulk material by taking into account the fact that the lattice constant parallel to the substrate remains the same as that of the substrate. This conversion is made with

Aa Ad 2C12 --I

- a d = - (1 + .q) for (100) surfaces. For (110) and (111) surfaces the elastic stiffness constants Cl, and

0

Fig. 4

for (110) surfaces,

for (111) surfaces.

A 1 I

Ramon shift(c17i') - Fig. 5

Fig. 4. Integrated intensities of the local vibrational modes of P implanted in Ge vs. impurity concentration; T = 300 I<, A = 647.1 nm. The intensities are normalized to those of the Raman phonon of Ge Fig. 5. Room temperature spectra of the Raman phonon in intrinsic Ge and in two IILA samples showing phonon softening and broadening of the latter. __ pure Ge, - - - Ge:As ( N , =

-: 1.8 X lozo ~ r n - ~ ) , -.- Ge:As ( N , = 2.1 x lozo


h- I

Fig. 6. Raman phonon softeningobserved for IILA Ge samples a t room temperature. The hollow points are as measured, the solid points after correction for changes in lattice constant, Aala, induced by the doping. The solid line w-as calculated as induced by vacancies (see text). Squares P, circles As, triangles Sb doping

l I I I l I I I I l 1 1 1 1 1 1 1 1 1

0

The values of Aa/a obtained with ( 5 ) are shown in Fig. 3 as a function of Ni (from Table 1). This figure shows clearly the reversal in the sign of Aala referred to above.

Raman measurements have been shown to reveal the localized vibrational modes of the phosphorus impurities in Ge (at x 336 em-') [23]. Their integrated strength, normalized to that of the Raman phonon, is shown in Fig. 4. Within the estimated error in the determination of these strengths, the intensity ratios of Fig. 4 are seen to vary linearly with impurity concentration Ni.

Fig. 5 shows the Stokes spectra of the Raman phonon of intrinsic Ge and two As- IILA Ge samples. A softening and a broadening of the phonons of the IILA sample, which seems to depend on Ni rather than N,, is seen. Similar softenings were observed for P- and Sb-implanted layers, as displayed in Fig. 6. The hollow points in this fi-

3.2 Raman measurements

fregoency shift - Fig. 7. Rrillouin spectra of two Ge samples, an intrinsic and an IILA one, showing the softening of the LA phonons of the latter. R Rayleigh line, FSR free spectral range, S and AS in paren- theses Stokes and anti-Stokes

31 physica (b) 131/2


Fig. 8. Softening in Lid induced by electron-phonon interaction in n-Ge a t room temperature. The squares represent ultrasonic data for a bulk sample [24, 251 and the line the theoretical prediction (Keyes theory). The circles (0 as measured, corrected for n (Drude model)) were obtained from Brillouin data for IILA samples. They can be brought to agree with theory by assuming that the samples have = 3% of spherical voids (see text)

50 " 19 -3 1 N,(IO cm I -

gure represent raw data while the filled points represent data after correction for changes in lattice constant induced by the doping (see Fig. 3 and discussion). The abscissa represent the number of electrically inactive impurities Ni - N,. Within the estimated scatter of the experimental points (= f 1 cm-l) the dependence of the frequency softening on ATi - N , can be assumed to be linear.

3.3 Brillouin scattering

Fig. 7 shows the Brillouin spectra of longitudinal acoustic phonons (LA) obtained for intrinsic Ge and for an As-doped IILA layer. A softening of these LA phonons is seen. A similar softening has also been found from ultrasonic propagation measurements for less doped samples [24, 251 (see Fig. 8).

4. Discussion

The above results show that the IILA n-Ge samples have much higher electron concentrations ( N , up to 2.4 x 1020 Table 1) than similar bulk doped samples (the N , limit is quoted to be (4 to 5) x 1019 cm-3 for bulk samples [ll]). Nevertheless the most heavily implanted samples must contain a large number of electrically inactive impurities according to the data of Table 1. The electrically active impurities can be assumed to be substitutional. One of the main questions to be approached below is the structure of the electrically inactive impurities, in particular whether they are substitutional (with their electrical activity compensated by other defects, such as vacancies) or simply correspond to precipitated large clusters of the dopant atoms. No evidence of large impurity segregation at the surface or a t the interface between the IILA layer and the substrate was seen in either SIMS or RBS [17] measurements. We should point out that heating of the samples to only = 200 "C led to the lowering of N , to the standard values for bulk samples.

4.1 X-ray diffraction data

Data for the dependence of the lattice constant of silicon on doping are quite extensive [26 to 281 but much less extensive in the case of germanium [28,29]. It is known [26] that two contributions to this dependence exist: one due to the free carriers themselves and the other due to the hard cores of the dopant ions. The former can be estimated from the deformation potential of the free carriers for hydrostatic deformations, which is known to be negative in the case of electrons in Ge [26, 30].5)

5) The magnitude of this deformation potential is the subject of some controversy, nevertheless we believe the sign of [26] should be correct, see [30].


Hence the presence of free electrons should cause the lattice constant to expand so as to reduce their free energy 1311. By substitutional doping, however, we not only introduce free carriers but also change atomic cores. This is expected to lead, in the case of Sb, to an increase in the lattice constant because of the larger covalent radius of Sb as compared to Ge. For As this effect should be small while in the case of P a decrease of the lattice constant should be obtained.

I n view of the discussion below (Section 4.2) we assume that all of the dopant atoms are substitutional, compensated, in the case of the N , - N , fraction of electrically inactive ones, by defects such as vacancies or dangling bonds a t the internal surfaces of voids. Donor-vacancy pairs have indeed been shown to lead to electrically inactive defects [32]. We further assume that these vacancies do not lead to significant changes in the lattice constant a. We can thus write

Using the relationship between N e and Ni given in Table 1 we have determined 8, and pi by fitting (6) to the experimental data of Fig. 3 (solid line). We find

Be = 7.4 x 10-24 cm3, pi = -3 x cm3. (7)

The value of pi can be estimated from the covalent radius of Ge and the ionic radius of P obtained by extrapolation between those of Po (covalent radius) and P-3 1331. In this manner one finds Pi = -5.7 x cm3 [26], in reasonable agreement with the results of our fit. The value of Be has been theoretically estimated in 1261 to be be = 2.8 x cm3 although the value obtained from experimental data for As, Sb [28], and P 1291 seems to be smaller (= 4 x cm3 on the average) and more in line with the one found here. We note that a value Be + Bi = cm3 was obtained in [29] for P-doped Ge.

We should also note that the bond lengths of As-doped IILA silicon also shortened when the dopant becomes electrically inactive through furnace annealing [34].

In view of the excellent data and the theoretical interpretation given above for Aafa we must try to answer the question of why we do not observe separate X-ray diffraction peaks in the case of As and Sb. In the case of As the answer may lie in the smallness of the Adld shifts expected. In the case of Sb i t should be quite large. Variation of the lattice constant in the neighborhood of the impurities may lead to rather large widths for the diffraction lines, making them inobservable.

4.2 Raman measurements

We believe that the data of Fig. 4 give strong evidence of substitutional doping by most of the Ni atoms. If the intensities of the local mode are plotted against N , the simple linear dependence of Fig. 4 is not obtained. Interstitials and other segregated clusters of P should have local vibrational frequencies very different from those of the local modes.

Softenings of Raman phonons upon doping have been observed in heavily doped n-Si [35,36] and in p-Si 137, 381 and p-Ge 1391 and interpreted as due to electron- phonon interaction. The theory used for this interpretation, however, requires the existence of a very small excitation gap for the free carriers [40] which applies to n-Si, p-Si, and p-Ge but not to n-Ge. We have calculated the softening due to phonon- induced intraband transitions in n-Ge [41] and found it to be about an order of 31'

484 G. CONTRERAS, 1,. TAPPER, A. K. SOOD, and M. CARDONA

magnitude smaller than the results of Fig. 5 and 6. Hence another explanation for this data has to be found.

We should point out that the data of Fig. 6 are shown as “raw data” (hollow points) and also as data corrected for changes in lattice constants of the type discussed in Section 4.1. For this correction we have considered only the hydrostatic component of the strain (one third of Adld) . The uniaxial component, which pro- duces splittings of the phonons, should be negligible in most measurements performed with unpolarized light [42]. For this correction we have used the mode Griineisen parameter for the Raman phonons of Ge [43]. In the case of P doping we have used experimental values of Adld (Fig. 3). For Sb and As we have used the Be and Bi co- efficients as given by [26], in order to calculate Aala with the values of N , and Ni as given in Table 1. Note that the corrected data of Fig. 6 vary more linearly with Ni - N , than the uncorrected ones.

One may also ask whether one should apply a correction to take into account the different atomic masses of the dopants. It is easy to see along the lines of [44] that the mass correction is unnecessary. In fact, the eigenvectors of optical phonons tend to avoid the atoms with large differences in mass, Hence the effect of such differences is negligible.

We attribute the softening of Fig. 6 mainly to broken bonds of the vacancies or voids which compensate the donor impurities, The frequency of the Raman phonons oR can be written as [45]

where 01 and @ are Keating’s bond stretching and bending force constants, respectively, and M is the atomic mass. The factor 4 in (8) corresponds to the four bonds attached to each atom. A vacancy breaks one of the four bonds and three of the six bond angles of four atoms, hence a vacancy concentration Nv = Ni - N , should give a frequency softening

where we have made use of the fact that B = 0.301 for Ge [45]. The straight line of Fig. 6 represents (9) with v k = 300 crn-l. It accounts remarkably well for the observed softening.

The softening of the LA modes of Fig. 7 can be attributed, a t least in part, to electron-phonon interaction [46, 471. Since the measurements were performed in the backscattering configuration we can relate the observed Brillouin shift to the stiffness constants Cll, C12, and C,, through 1481

where 1 is the laser wavelength, n the refractive index of the material a t this wavelength, and @ its density. The electron-phonon interaction should soften C,, in n-type Ge but not C,, + 2C1, [46]. Hence the observed softening must be related, a t least in part, to a softening in C44. From (10) we easily find


The change in n, An can be estimated from the Drucle contribution to the dielectric constant (radicand of (3)). Using the values of vb found from ir reflectivity measurements (cf. (2) ) we obtain Anln = -0.021 and -0.024 for N , = 1.8 x 1020 and 2.5 x lozo respectively. Inserting these values and the experimental AmL into (11) we find the values of AC44/C44 shown by full circles in Fig. 8. The open circles represent the softening obtained for Anln = 0, for comparison. These values are more than twice as large as those calculated from the electron-phonon interaction 1461 (solid line in Fig. 8). Hence we conclude that the electron-phonon interaction does not suffice to explain the observed softening.

We next consider the possibility that vacancies or voids also contribute to the lowering of the Brillouin frequency. If such defects are present, they should not, to a first approximation, lower the radicand in (10) since both e and C, should be affected in roughly the same way. Following Landau and Lifschitz [49] the effective dielectric constant E of a composite medium with spherical voids ( E ~ = 1) imbedded uniformly in the host medium ( E ~ = 16) is given by

where C is the volume fraction of the voids. Using the Anln corresponding to (12) we can fit the difference between the full circles and the calculated curve in Fig. 8 provided we take C = 0.03 for sample 12 and C = 0.0.4 for sample 13. Such a volume fraction of voids is compatible with reports of the existence of voids in IILA Ge which are found in the literature [7].

5. Conclusions

It has been shown that electron concentrations as high as 2.4 x lozo can be obtained in IILA Ge implanted with column-five atoms. In this case, however, a larger number of electrically inactive donors is also present. A model, involving donor- vacancy pairs, is proposed for the electrically inactive donors. This model explains the anomalous dependence of the lattice constant on implantation dose, the intensities of the local vibrational modes of phosphorus, and the softening of the Raman phonon. The observed softening of the LA Brillouin peaks observed for (111) surfaces requires the existence of = 3% of voids in the IILA layer.

Acknowledgements

We would like to thank H. Hirt, M. Siemers, and P. Wurster for expert technical assistance and W. Stolz for the Hall measurements, H. Breitschwerdt and W. Konig for help with the ir measurements, and Dr. P. Eichinger and Mrs. Elisabeth Frenzel of the Fraunhofer-Institut fur Festkorpertechnologie for performing the SIMS measurements. Thanks are also due to A. Axmann for the ion implantation which was performed a t the Fraunhofer-Institut fur Angewandte Festkorperphysik in Preiburg, Federal Republic of Germany.

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(Received June 11, 1985)

physical properties of ion-implanted laser annealed n-type germanium

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