The Infrared Spectrum of Indium in Silicon Revisited A

The infrared spectrum of indium in silicon revisited A. Tardella, B. Pajot

To cite this version:

A. Tardella, B. Pajot. The infrared spectrum of indium in silicon revisited. Journal de Physique, 1982, 43 (12), pp.1789-1795. 10.1051/jphys:0198200430120178900. jpa-00209562

HAL Id: jpa-00209562 https://hal.archives-ouvertes.fr/jpa-00209562 Submitted on 1 Jan 1982

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Classification Physics Abstracts 71.55 - 78.50

The infrared spectrum of indium in silicon revisited

A. Tardella and B. Pajot Groupe de Physique des Solides de l’Ecole Normale Supérieure, Université Paris VII, Tour 23, 2, place Jussieu, 75251 Paris Cedex 05, France

(Reçu le 27 mai 1982, révisé le 22 juillet, accepté le 23 août 1982)

Résumé. 2014 Le spectre d’absorption de l’indium dans le silicium a été mesuré dans des conditions où l’élargisse- ment des raies par effet de concentration est négligeable. Avec une résolution appropriée, on détecte 17 transitions et les composantes d’un doublet serré sont attribuées à deux transitions calculées. A 6 K, la largeur intrinsèque des raies varie de 2,6 à 0,8 cm-1, ce qui indique un effet lié à la structure de la bande de valence du silicium. En utili- sant les résultats d’une mesure auto-cohérente de la concentration d’indium dans le silicium par une méthode spectroscopique, nous trouvons que l’élargissement par concentration est plus faible que ce qui avait été trouvé précédemment et que l’effet de paire semble inexistant dans les échantillons étudiés. Les mesures permettent aussi de détecter un élargissement thermique des raies entre 5 et 10 K.

Abstract 2014 The absorption spectrum of In acceptor in silicon has been measured under negligible concentration broadening in order to obtain the true profile of the lines. With adequate spectral resolution, 17 transitions are detected and the components of a closely-spaced doublet are attributed to calculated transitions. At 6 K, the intrinsic width of the lines varies from 2.6 to 0.8 cm-1, indicating some resonance effect linked with the split-off valence band structure in silicon. Using the results of a self-consistent determination of the indium concentration in silicon by a spectroscopic technique, we find that in the samples studied the concentration broadening is smaller than that found previously and that no evidence for pairing is observable. These measurements also detect temperature broadening of the lines between 5 and 10 K.

1. Introduction. - Considering its excited states, indium-doped Si for samples ranging from a low substitutional indium in silicon is an effective mass- concentration limit to the highest concentration like acceptor despite its ionization energy of 157 meV, available by the growing technique used. With the which reflects a trend for group III acceptors, namely, samples with low In concentration, we detect more the heavier the element the higher the ionization excited levels - actually 17 - than previously report- energy. It has been used as a dopant for integrated ed [3, 4] and we measure accurately the intrinsic extrinsic Si detector arrays operating in the near IR width of the lines of the In spectrum. The integrated atmospheric window [1]. This has led to the availabi- intensity of the line at 1 176 cm-1 for the different lity of well-characterized crystals allowing meaning- samples investigated is used to obtain their In concen- ful linewidth studies and concentration broadening tration. The concentration broadenings observed measurements. Such studies have been previously are compared with those previously published [5] undertaken [2] and the fundamental work of Onton and phonon (temperature) broadening is detected et al. [3] on the absorption spectra of group III accep- in the low temperature range. tors in Si has provided a guide line for the subsequent experimental and theoretical work on these impurities, 2. Measurement techniques. - The float zone crys- but the role of temperature and of concentration tals used in this study were grown at the CENG and broadening for the lines other than those correspond- they were checked spectroscopically for residual B, ing to the first three IR-allowed excited states above P, Al, C and for 0, whose main vibrational line at the ground state have been overestimated, precluding, 1 136.4 cm-1 is contiguous to the In spectrum (see for instance, significant comparisons between the Table I). The exact indium concentration will be given highly excited states of the different acceptors. later, but in these samples In is the main electrically We present here some spectroscopical data on FZ active impurity over several orders of magnitude in

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198200430120178900 1790

Table I. - Characteristics of the Si (In) samples. The Hall mobility is measured at room temperature with a magne- tic field of 0.2 T.

concentration. The samples, approximately con [8], suggest that a reflectivity value of 0.296 would 15 x 8 x d mm, d being a thickness appropriate to be more appropriate. the In concentration, were polished on the four large 3. results and discussion. - The In sides. They were fixed on their base by two dots of Experimental discrete observed between 1 145 and G.E. 7131 varnish on a sample holder in the compart- spectrum 1 255 to transitions the ment of a continuous flow cryostat (Oxford Instru- cm-’ corresponds from ground ments Model 204). The samples were cooled by the He state at Ev + 1 265 cm-1 (Ev + 156.9 meV) to excited states the of = valence exchange gas and their temperature was assum- having symmetry the j 3/2 bands of silicon One can also observe ed to be that of a Ge thermometer mounted parallel (P3/2 spectrum). near 1 580 cm-1 the lines associated with excited to the sample at - 1 mm from it, on the sample holder. plj2 states the of the valence The temperature of the exchange gas could be varied having symmetry p 1 /2 band, by adjustment of the liquid He flow and of the current split from the P3/2 valence band by a spin-orbit separation of 42.62 meV at k = 0. The in a heater mounted on the heat exchanger. The sample (343 cm-1) p1/2 lines interfere with the continuum could be pumped laterally by band gap light by focuss- P3/2 acceptor and are broadened a Fano ing on it the output of a 70 W quartz halogen lamp they asymmetrically by effect The between the 1 state through a narrow band interference filter centred at [9]. separation T8+ ground 1.2 eV. The monochromatic beam transmitted by the and the j = 1/2 valence band is 1609.4 cm -1 The two most intense In 2 sample was detected by a mercury-cadmium telluride (199.6 meV). Pl/2 lines, p’ and 3 are located at 1 565 and 1 590 (MCT) detector with an AR coated Ge window. The p’ [3], cm-1, spectra, recorded digitally, were smoothed and lineariz- ed on line by a Hewlett Packard 9845 desktop compu- ter and then stored on a floppy disk. In order to obtain reliable figures for the background and for the intensities, plane parallel samples were used in most cases. The optical axis of the cryostat was tilted by - 50 with respect to the IR beam while keeping the sample surface perpendicular to the beam. This avoids radiation reflected or transmitted by the sample being reflected back on it by the KRS5 cold windows distant by only 20 mm. Part of this reflected radiation, although defocussed, could reach the detector, lead- ing to an erroneous value of the absolute transmission of the sample. In some cases where interference fringes produced by the cold windows were observed in the spectra, they were eliminated by subsequent numerical filtering. The absorption coefficients of the In and 0 lines were measured either by taking the ratio of the transmission of a doped sample relative to that of an intrinsic sample or by measuring the absolute transmission of the doped sample and then removing the contribution We have assumed a phonon [6]. Fig. 1. - Recorder trace of the transmission spectrum of value of 0.300 for the silicon Measure- reflectivity. sample In-2, 4 mm thick. The two P1/2 lines observed are ments of the low-temperature refractive index of Si [7], at 1 565 and 1 590 cm-1. The two arrows indicate the reso- and the comparison between the calculated and experi- nance of the phonon replica of lines 1 and 2 of the P312 mental spacing of the excited states of donors in sili- spectrum with the P3/2 continuum. 1791

Fig. 2. - Ratioed spectrum of indium in sample In-1 Fig. 3. - Enlarged portion of the spectrum of figure 2. (Nln - 4 x 1015 at./cm3). The spectral band pass is 0.35 cm-1 The unresolved doublet 4AB is attributed to the 1 T$ - 1 r6 at 1250 cm-’. The losses of the detector response and and 1 r 8+ .... 4 r 8- transitions. in the grating efficiency are responsible for the noise increase below 1 160 cm-1. The sharp line at 1 136.4 cm-’1 is due to a vibrational transition of the quasi-molecule 28Si2160. the positions of the lines. The best fit is obtained with The dashed bar at 1 265.4 cm-1 to the calculat- corresponds Lorentz widths of o.95,1.2 and 1.2 cm - ’ ed limit of the discrete spectrum. shapes having for lines 4, 4A and 4B, respectively and we find that the relative intensity of line 4A with respect to line 4 is ~ 0.77. The impossibility of obtaining an exact and 4 p’ (In) has been detected recently [10] at the fit can be explained by a slight asymmetry of the lines. position expected (1 598 cm-1) from the positions of We are able to show that line 6 is a doublet with two 4 p’(B) (701.3 cm -1 ) and 4 p’(Al) (900.6 cm -1). Above components, 6 and 6A, of about equal intensities and these energies one also observes a resonant effect due 0.9 cm-1 apart In this domain of binding energies, to the coupling of the centre of zone optical phonon the calculations by Baldereschi and Lipari [13] give (519 cm-’) with the P3/2 transitions, resonating with levels, 2 r6 and b Tg , distant by 0.8 cm-’ and we the In P3/2 continuum. This effect has been reported attribute the final states of lines 6 and 6A to these and analysed by Watkins and Fowler in terms of a levels. This attribution, which is not the same as that Breit-Fano resonance [11]. Figure 1 shows part of of reference [4] where the doublet structure of peak 6 the transmission spectrum of sample In-2. The trans- was masked by concentration broadening, is further mission bump near 1 666 cm-1 corresponds to the resonance of the phonon assisted 1 T8 -> 1 T8 transition of the p3/2 spectrum and the onset of the plateau near 1 696 cm-1 to the same effect for the 1 r 8+ > 2 r 8" transition. The P3/2 spectrum of In is shown in figure 2. It is very similar to the corresponding spectra of Al and Ga, except for accidental phonon resonances in these two spectra [12]. The lines have been labelled 1, 2, etc... in order of increasing energy. The main diffe- rence with spectra previously published [3, 4] is due to the indium content in sample In-1, which reduces the concentration broadening. The spectral band pass (s.b.p.) used (0.35 cm-’ near 1 250 cm-’) mini- mizes instrumental broadening and the resolution of the spectrum of figure 2 is mainly limited by the intrinsic width of the lines and by the S/N ratio. The improvement on the spectrum above 1 200 cm -1 Fig. 4. - Enlarged portion of the indium specttum (sample can be seen in figure 3. The peak 4A cannot be resolved In-1). The higher S/N ratio of this spectrum allows a better into two because of their components, however, observation of lines 12-14 than the previous spectrum. intrinsic width. Covington et al. [4] have numerically Above line 8, the numbering of the lines does not follow resolved peak 4A into an asymmetrical doublet, that given by Onton et al. [3]. This spectrum was obtained 4A and 4B, with a separation of (0.9 ± 0.4 cm-1) under band gap light pumping, which improved the contrast and we have reached similar conclusions concerning of line 14. 1792

Table II. - Position (cm-1) of the P3/2 of In, Al and B Table III. - Intrinsic width at half maximum (cm -1 ) lines in silicon. The attributedfinal state of the corres- of some In lines compared with those of B. ponding transitions is given up to line 6A. For In and B, the accuracy is + 0.05 cm -1 and + 0.1 cm -1 for Al.

width and maximum absorption. This reveals a small asymmetry, on the high energy side and pre- sumably due to an intrinsic resonance effect for samples In-1 and 2. For sample In-4, the concentration broadening makes the intrinsic asymmetry less visible so that the line looks nearly Lorentzian, as can be seen in figure 5, where the profiles for In-1 and In-4 are quasi-normalized. (The parameters used are taken from table IV.) At that point, it becomes neces-

(*) Estimated from reference [15]. supported by the fact that a similar structure is found in the P3/2 spectrum of boron in silicon, although the relative intensity of the two B lines is different from that in In. In the case of Al only an asymmetrical broadening of line 6 is observed. Figure 4 also shows new lines at 1243.80,1247. 83 and 1254.1 cm -1 and a well- defined elbow at 1 250.9 cm-1. Table II gives a list of the P3/2 lines of In with the attribution of the excited states to all the calculated odd-parity levels. There is a close correspondence with the Al lines. Line 3 (Al) is undetected because of a strong interaction with optical phonons [12]. For boron the correspondence is less a weak line observed at 338.05 cm-1 evident; Fig. 5. - Comparison of the shape of line 2 observed with is ascribed to the forbidden I tentatively r 8+ -+ 4 r 8+ samples In-l and In-4 (solid line) with a Lorentz profile transition Line 7 is coincident with [14]. (B) nearly (broken line). a (outer line) : sample In-4, ordinate scale as 3 p , (P) and weaker than its counterparts in Al and In, indicated ; b (inner line) : sample In-1. The line is expanded as can be seen from the resonant photoconductivity by a factor of 12.5. spectra given in the paper by Skolnick et al. [15]. Above line 8 the numbering of the lines given here is different from that adopted previously, in order to Table IV. - Peak absorption coefficient, width at accomodate the new transitions detected. half maximum and integrated intensity of line 2 of In The natural width of the p3/2 lines of In depends in silicon for samples In-1, 2 and 4. on the energy of the transition considered, as can be seen from table III. This is also true for boron and aluminium, but for these impurities line 1 is sharper than line 2. This kind of broadening has not yet been explained, but it must be connected with the split- off valence band structure of silicon as it has not been observed for acceptors in germanium [17]. We have made a fit of line 2, for samples In-1, 2 and 4, with a Lorentzian line profile having the same 1793

Table V. - Optical indium concentration and calculated drift mobility of three In-doped Si samples.

(II) : N1n = 8 x 1014 x J (2). (III) : N,n = 2 x 1015 x J (2). (IV) : Using (II) and E1n = 140 meV. (V) : Using (III) and E1n = 155 meV. (VI) : Corresponding to the resistivity of (I) for boron-doped silicon.

sary to come back to a brief discussion of the deter- data for boron [21], aluminium [22] and even indium mination of the In concentration if we want to go [5], we see that the broadening of line 2 of In between further on concentration broadening. A calibration 3.8 x 1015 and 7 x 1016 In atoms/cm3 is moderate factor of 8 x 1014 In atoms/cm between the In concen- (12.4 %). This is not true for line 4, whose width increa- tration and the integrated intensity of line 2 has been ses by about 100 %. We believe that part of the diffe- obtained from measurements on neutron-compensat- rence with previous results for In can arise from unre- ed samples [18]. This figure is somewhat lower than cognized Stark broadening superimposed on concen- the value of 2 x 1015 In atoms/cm given by Jones tration broadening. (We have actually measured the et al. [19]. There are at least two reasons for this : Stark broadening contribution of line 2 in heavily a) when deducing an impurity concentration from a compensated In doped samples [23].) When compar- carrier concentration measured at room temperature, ing with boron and aluminium, we must admit that one must use a room temperature ionization energy. the higher ionization energy of indium reduces the For indium, from the change in the dielectric constant spreading of the ground state envelop function and and in the optical gap between liquid helium and limits the interaction between neighbouring atoms. room temperature and also from the coalescence of Thus charge transfer between the two In atoms of a the shallowest excited levels into the continuum, we pair is effective at distances closer for indium than for estimate the ionization energy of indium to be reduced boron and aluminium and this could be the reason to - 140 meV at ambient; b) in the case where the why no low-energy asymmetry due to pair interaction hole concentration is deduced from room temperature is observed on line 2 in the sample with 7 x 1016 In Hall measurements at low field, the Hall factor must atoms/cm3. be taken into account. In many cases it is set to unity, We measured the temperature broadening of line 2 whereas a value - 0.8 would be more realistic [20] between 5 and 35 K and an increase of 5 % of the at least for samples with p > 1015 cm- 3. We have width of the line in sample In-1 was already detected checked the consistency of a) by calculating the drift between 5 and 10 K. A more sensitive test of the broa- mobility JlD at 25 °C from the measured resistivity dening of the In lines is the value of the ratio of the and from the optical In concentration using our cali- amplitude of peak 4 to the minimum between peaks bration ratio and Ern = 140 meV, compared to 4 and 4AB : for samples In-1, this ratio decreases by the value obtained using the same resistivity but an 11 % between 5 and 10 K. optical In concentration using 2 x 1015 In atoms/cm From ultrasonic attenuation measurements on In and E1n = 155 meV. This is summarized in table V. doped Si, Schad and Lassmann [24] have inferred Referring to this table, we can see that the mobility the existence of an In state 4.2 meV (34 cm- 1) above for the high resistivity sample obtained in (V) is the ground state. On the other hand Elliot et al. [25] lower than expected and even lower than that for have attributed a luminescence line at 1 136.5 meV the lowest resistivity sample. The predicted drift to a two-hole transition of the In bound exciton mobility of 350 cm2/V . s obtained in column IV of involving this level, as the line is located 4.1 meV below table V for sample In-4 leads to a Hall mobility of the J = 0 bound exciton line of indium at 1 140.76 meV. 280 cm2/V . s using a Hall factor of 0.8 and this is This level would arise from the splitting of the r 8+ consistent with the measured value of 270 cm2/V . s. level of indium in a tetrahedral site under a dynamic The shape and width of impurity lines are affected Jahn-Teller distortion which should lower the site by several sample-dependent broadening mechanisms. symmetry to D2d and split this level into two sublevels. The two effects reported in this study are the concen- However, spectra of sample In-4 run at 20 K failed to tration broadening and the temperature broadening, reveal such an excited state from which a hole could be plus a combination of both effects. A detailed quanti- excited towards the other P3/2 excited levels. tative analysis of these phenomena is not intended in Lastly, we must note that we have observed a sam- this paper, but we can make however a few qualitative ple-dependent background for samples with similar remarks. First, by comparison with previous available concentration (In-3 and In-4). We do not believe it 1794

to be due to artefact. It could come from the photo- Appendix. - The effective mass Hamiltonian of ionization spectrum of acceptors shallower than a j = 3/2 acceptor in silicon can be expressed as the indium (In-X centre [19] or aluminium), but we failed sum of a term with spherical symmetry and of a term to observe the excitation spectra of these acceptors. with cubic symmetry [13]. Neglecting first the cubic term, the problem reduces formally to that of an hydrogenic atom with L-S interaction (S = j = 3/2). 4. Conclusion. - The IR spectra of In acceptor in The hydrogenic states of interest are those with L = 0 silicon in this paper have allowed us to presented and 1 (S and P states) and these states can be labelled detect lines whose is separation pre- = closely spaced using the projections of F L + 3/2, which is a dicted by and show that the binding theory they constant of the motion; hence, nS3/2, nP 1/2’ np3/2 energies of many excited states is still to be determined. and states. Under a cubic perturbation, the It is found that the In linewidths decrease with the nP 5/2 symmetry of the problem lowers to that of the cubic binding energy for the first excited levels and become point group Oh. The compatibility relations between constant 1 for the other levels. nearly (~ cm-1) the irreducible of the full rotation Another result is that the concentration representations broadening group and those of show that of the In lines in silicon is smaller than for oh Dj"/2’ 01/2’ D3/2 acceptors and transform as r 8+’ r 6-’ r 8- and r 7- + r 8-’ with a lower ionization to D5/2 energy, contrary prior and the states and data. The detection of respectively PSj2 split-into F7 F8 unambiguous temperature states. The calculated binding energy of the first odd- of the lines between 5 and 10 K must broadening parity excited states are given in table A-l, following allow meaningful quantitative comparisons with cur- this nomenclature. rent theoretical work on the broadening mechanism of acceptor impurity lines in silicon. Additionally, the optical calibration factor used in this study is Table A-l. - Calculated binding energy of the first levels in silicon. consistent with a room temperature ionization energy acceptor of - 140 meV for In at room temperature and with a Hall factor of - 0.8. With these figures, the solu- bility limit of indium in silicon is reduced to ~ 1 x 1018 atoms/cm3 compared with the value of 2.5 x 1018 at. /CM3 given by Scott and Hager.

Acknowledgments. - The authors wish to thank Mr. F. Blanc from CENG for the communication of the results of mobility measurements on the samples investigated. This work was supported in part under DRET contract 81-702.

References

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