The infrared spectrum of indium in silicon revisited

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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�

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

été mesuré dans des conditions où l’élargisse-

ment des raies par effet de concentration ^est négligeable. ^Avec

résolution appropriée,

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,

qui indique

^{effet lié à la structure de la bande de valence du silicium. En utili-}

sant les résultats d’une

auto-cohérente de la concentration d’indium dans le silicium par

méthode

spectroscopique,

^trouvons que l’élargissement par concentration ^est plus faible que

qui avait été trouvé

précédemment ^et que l’effet de paire ^semble inexistant dans les échantillons étudiés. Les

permettent ^aussi de détecter

élargissement thermique ^{des raies entre 5 et 10 K.}

Abstract

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

detected and the components ^of

closely-spaced ^doublet

attributed to calculated transitions. At 6 K, the intrinsic width of the lines varies from 2.6 to 0.8 cm-1, indicating

^effect linked with the split-off

valence band structure in silicon. Using the results of

self-consistent determination of the indium concentration in silicon by

spectroscopic technique,

^{find that in the} samples studied the concentration broadening ^{is smaller}

than that found previously ^{and that}

evidence for pairing ^is observable. These measurements also detect tem-

perature broadening ^{of the lines} between 5 and 10 K.

Classification Physics ^Abstracts

71.55

78.50

1. Introduction.

Considering ^{its excited} states, substitutional indium in silicon is ^an effective mass-

like acceptor despite its ionization _energy of 157 meV,

which reflects a trend for group III acceptors, namely,

the heavier the element the higher the ionization energy. It has been used as a dopant ^for integrated

extrinsic Si detector _arrays operating ^{in the near IR} atmospheric ^window [1]. ^{This has led to} the availabi-

lity ^of well-characterized crystals allowing meaning-

ful linewidth studies and concentration broadening

measurements. Such studies have been previously

undertaken [2] ^{and the} fundamental work of Onton

et al. [3] ^{on the} absorption spectra of group III accep- tors in Si has provided ^a guide line for the subsequent experimental and theoretical work on these impurities,

but the role of temperature and of concentration

broadening for the lines other than those correspond- ing ^to the first three IR-allowed excited states above the ground ^{state have been} overestimated, precluding,

for instance, significant comparisons between the

highly ^{excited states of the different} acceptors.

We present ^{here some} spectroscopical ^{data on FZ}

indium-doped ^{Si for} samples ranging ^{from a low}

concentration limit to the highest concentration available by ^the growing technique used. With the

samples with low In concentration, ^{we detect more}

excited levels

actually ¹⁷

^than previously report- ed [3, 4] ^and we measure accurately the intrinsic width of the lines of the In spectrum. ^The integrated intensity of the line at 1 176 cm-1 for the different

samples investigated ^{is used to obtain their In concen-}

tration. The concentration broadenings ^observed

are compared with those previously published [5]

and phonon (temperature) broadening is detected in the low temperature range.

2. Measurement techniques.

^{The float zone} crys- tals used in this study ^were grown ^at the CENG and

they ^{were checked} spectroscopically for residual B, P, Al, ^{C and for} 0, whose main vibrational line at 1 136.4 cm-1 is contiguous ^{to the In} spectrum (see

Table I). ^{The exact indium} concentration will be given later, but in these samples ^In is the main electrically

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}

temperature ^with

magne- tic field of 0.2 ^T.

concentration. The samples, approximately

15

8 x d mm, d being ^{a thickness} appropriate ^to

the In concentration, ^were polished ^{on the four} large

sides. They ^{were fixed on} their base by ^{two dots of}

G.E. 7131 varnish on a sample holder in the compart-

ment of a continuous flow cryostat (Oxford ^Instru-

ments Model 204). ^The samples ^{were cooled} by ^{the He} exchange gas and their temperature

^assum- ed to be that of a Ge thermometer mounted parallel

to the sample ^{at - 1 mm from} it, ^{on the} sample ^holder.

The temperature ^{of the} exchange gas could be varied

by adjustment ^{of the} liquid ^He flow and of the current in a heater mounted

the heat exchanger. ^The sample

could be pumped laterally by ^band gap light by ^focuss- ing ^{on it the} output ^of

^{70 W} quartz halogen lamp through ^{a narrow} band interference filter centred at 1.2 eV. The monochromatic beam transmitted by ^the sample ^{was detected} by

mercury-cadmium ^telluride (MCT) detector with an AR coated Ge window. The 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 inten-

sities, 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 sam-} ple ^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 phonon contribution [6]. We have assumed a

value of 0.300 for the silicon reflectivity. ^Measure-

ments of the low-temperature refractive index of Si [7],

and the comparison between the calculated and experi-

mental spacing of the excited states of donors in sili-

con [8], suggest ^{that a} reflectivity value of 0.296 would be more appropriate.

3. Experimental results and discussion.

The In discrete spectrum observed between 1 145 and 1 255 cm-’ corresponds ^to transitions from the ground

state at Ev ^{+ 1 265 cm-1} (Ev ^{+ 156.9} meV) ^{to excit-}

ed states having ^the symmetry ^of the j

3/2 ^valence

bands of silicon (P3/2 spectrum). ^{One can} also observe

near 1 580 cm-1 the plj2 lines associated with excited states having ^the symmetry ^{of the} p 1 /2 ^valence band, split ^{from the} _P3/2 valence band by

spin-orbit sepa- ration of 42.62 meV (343 cm-1) ^{at k}

^{0. The} _p1/2

lines interfere with the P3/2 acceptor ^continuum and they ^are asymmetrically ^broadened by ^{a Fano}

effect [9]. ^The separation between the 1 T8+ ground ^state

and the j = 1/2 valence band is 1609.4 cm -1 (199.6 meV). ^{The two most} intense In Pl/2 lines, ² p’

and 3 p’ [3], ^{are located at 1 565} and 1 590 cm-1,

Fig. ^1.

^{Recorder trace of the} transmission spectrum ^of sample In-2, ⁴

thick. The ^two P1/2 ^{lines observed}

at 1 565 and 1 590 cm-1. ^{The two}

indicate the

of the phonon replica of lines 1 and 2 of the P312

spectrum ^{with the} P3/2 continuum.

Fig. ^2.

^Ratioed spectrum of indium in sample ^In-1 (Nln - 4

¹⁰¹⁵ at./cm3). ^The spectral band pass is 0.35 cm-1

at 1250 cm-’. The losses of the detector response and in the grating efficiency

responsible ^for the noise increase below 1 160 cm-1. The sharp ^{line at 1 136.4 cm-’}

^{is due}

to

vibrational transition of the quasi-molecule 28Si2160.

The dashed bar at 1 265.4 cm-1 corresponds ^to the calculat- ed limit of the discrete spectrum.

and 4 p’ (In) has been detected recently [10] ^{at the} position expected (1 598 cm-1) ^{from the} positions ^of

4 p’(B) (701.3 cm -1 ) ^{and 4} p’(Al) (900.6 cm -1). ^Above

these energies ^one also observes a resonant effect due to the coupling ^{of the centre of zone} optical phonon (519 cm-’) ^{with the} _P3/2 transitions, resonating ^with

the In P3/2 continuum. This effect has been reported

and analysed by Watkins and Fowler in terms of a

Breit-Fano ^resonance [11]. Figure ^{1 shows} part ^of the transmission spectrum ^of sample ^{In-2. The trans-}

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

can be seen in figure ^{3. The} peak ^{4A cannot} be resolved into two components, however, because of their intrinsic width. Covington et ^al. [4] ^have numerically

resolved peak ^{4A into an} asymmetrical doublet,

4A and 4B, ^{with a} separation ^of (0.9 ± ^0.4 cm-1)

and we have reached similar conclusions concerning

Fig. ^3.

Enlarged portion ^{of the} spectrum ^of figure ^2.

The unresolved doublet 4AB is attributed to the 1 T$ - 1 r6

and 1 r 8+ .... ⁴ r 8- transitions.

the positions ^of the lines. The best fit is obtained with Lorentz shapes having ^{widths of o.95,1.2 and 1.2 cm - ’}

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}

fit can be explained by ^a slight asymmetry ^{of the lines.}

We are able to show that line 6 is a doublet with two

components, ^{6 and} 6A, of about equal intensities and 0.9 cm-1 apart In this domain of binding energies,

the calculations by Baldereschi and Lipari [13] give levels, 2 r6 ^and b Tg , ^distant by ^{0.8 cm-’ and we}

attribute the final states of lines 6 and 6A to these levels. This attribution, ^{which is not the same as that}

of reference [4] where the doublet structure of peak ⁶

was masked by concentration broadening, ^{is further}

Fig. ^4.

Enlarged portion of the indium specttum (sample In-1). ^The higher S/N ^{ratio of this} spectrum ^allows

^better observation of lines 12-14 than the previous spectrum.

Above line 8, ^the numbering of the lines does not follow that given by ^{Onton et al.} [3]. ^This spectrum

^obtained under band gap light pumping, ^which improved ^{the contrast}

of line 14.

1792

Table II.

Position (cm-1) of ^the _P3/2 of In, ^{Al and B} lines in silicon. The attributedfinal ^state of ^the

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.

(*) 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 ^broa- dening of line 6 is observed. Figure ⁴ also shows new

lines at 1243.80,1247. 83 and 1254.1 cm -1 and

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 evident; ^{a weak line observed at 338.05 cm-1}

is tentatively ^{ascribed to the forbidden I} r 8+ -+ 4 r 8+

transition [14]. ^{Line 7} (B) ^is nearly coincident with 3 p , (P) and weaker than its counterparts ^{in Al and} In,

as can be seen from the resonant photoconductivity 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}

accomodate the new transitions detected.

The natural width of the p3/2 ^{lines of In} depends

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}

Table III.

Intrinsic width at half ^maximum (cm -1 ) of some ^{In lines} compared with those of B.

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 concentra-}

tion 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-

Fig. ^5.

Comparison ^{of the} shape ^of line 2 observed with

samples ^{In-l and In-4} (solid line) ^with

^Lorentz profile (broken line).

(outer line) : sample In-4, ^{ordinate scale}

indicated ; ^b (inner line) : sample ^{In-1. The line is} expanded by

factor of 12.5.

Table IV. - Peak absorption coefficient, ^{width at} half ^{maximum and} integrated intensity of ^{line 2} of ^In

in silicon for samples In-1, 2 and 4.

Table V.

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

(II) : N1n

⁸

¹⁰¹⁴

^J (2). (III) : N,n

²

¹⁰¹⁵

^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- mination of the In concentration if we want to go further on concentration broadening. ^A calibration factor of 8

1014 In atoms/cm between the In concen-

tration and the integrated intensity ^of line 2 has been obtained from measurements on neutron-compensat- ed samples [18]. ^This figure is somewhat lower than the value of 2

1015 In atoms/cm given by ^Jones

et al. [19]. ^{There are at least two reasons for this :} a) ^when deducing ^an impurity concentration from a

carrier concentration measured at room temperature,

one must use a room temperature ionization energy.

For indium, ^{from the} change ^{in the} dielectric constant and in the optical gap between liquid ^{helium and}

room temperature and also from the coalescence of the shallowest excited levels into the continuum,

estimate the ionization _energy of indium to be reduced

to - 140 meV at ambient; b) ^{in the case where the}

hole concentration is deduced from room temperature Hall measurements at low field, the Hall factor must be taken into account. In many ^cases it is set to unity,

whereas a value - 0.8 would be more realistic [20]

at least for samples with p > 1015 cm- 3. We have checked the consistency ^of a) by calculating ^{the drift} mobility JlD at 25 °C from the measured resistivity

and from the optical In concentration using ^{our cali-}

bration ratio and Ern = 140 meV, compared ^to

the value obtained using ^{the same} resistivity ^{but an} optical In concentration using ²

^{1015 In} atoms/cm

and E1n

155 ^{meV. This is} summarized in table V.

Referring ^{to this table,} we can see that the mobility

for the high resistivity sample obtained in (V) ^is

lower than expected ^{and even} lower than that for the lowest resistivity sample. ^The predicted ^drift mobility ^{of 350} cm2/V . s ^{obtained in} column IV of table V for sample In-4 leads to

Hall mobility ^of

280 cm2/V . s using ^a Hall factor of 0.8 and this is consistent with the measured value of 270 cm2/V . s.

The shape and width of impurity ^{lines are affected} by ^several sample-dependent broadening mechanisms.

The two effects reported ^{in this} study ^{are the concen-}

tration broadening ^{and the} temperature broadening, plus ^a combination of both effects. A detailed quanti-

tative analysis ^{of these} phenomena ^{is not intended in}

this paper, but ^{we can} make however a few qualitative

remarks. First, by comparison ^with previous ^available

data for boron [21], ^aluminium [22] ^{and even indium} [5], ^{we see that the} broadening ^{of line 2 of In between}

3.8

1015 and 7

1016 In atoms/cm3 is moderate

(12.4 %). ^{This is not true for line} 4, whose width increa-

ses by ^{about 100} %. ^We believe that part of the diffe-

rence with previous results for In can arise from unre-

cognized ^Stark broadening superimposed ^{on concen-}

tration broadening. (We ^{have actually} measured the Stark broadening contribution of line 2 in heavily compensated ^In doped samples [23].) When compar-

ing with boron and aluminium, ^{we must admit that}

the higher ionization energy of indium reduces the

spreading ^{of the} ground ^state envelop ^{function and}

limits the interaction between neighbouring ^atoms.

Thus charge transfer between the two In atoms of a

pair is effective at distances closer for indium than for boron and aluminium and this could be the reason

why ^no low-energy asymmetry ^{due to} pair interaction is observed on line 2 in the sample ^{with 7}

^{1016 In} atoms/cm3.

We measured the temperature broadening ^{of line 2}

between 5 and 35 K and an increase of 5 % ^{of the}

width of the line in sample ^{In-1 was} already ^detected

between 5 and 10 K. A more sensitive test of the broa-

dening ^{of the In} lines is the value of the ratio of the

amplitude ^of peak ^{4 to} the minimum between peaks

4 and 4AB : for samples In-1, this ratio decreases by

11 % between 5 and 10 K.

From ultrasonic attenuation measurements on In

doped ^Si, Schad and Lassmann [24] ^{have inferred}

the existence of an In state 4.2 meV (34 cm- 1) ^above

the ground ^state. On the other hand Elliot et al. [25]

have attributed a luminescence line at 1 136.5 meV to a two-hole transition of the In bound exciton

involving ^this level, ^as the line is located 4.1 meV below the J = 0 bound exciton line of indium at 1 140.76 meV.

This level would arise from the splitting ^{of the} r 8+

level of indium in a tetrahedral site under a dynamic

Jahn-Teller distortion which should lower the site symmetry ^to D2d ^and split this level into two sublevels.

However, spectra of sample ^{In-4 run at 20 K failed to}

reveal such an excited state from which a hole could be excited towards the other P3/2 excited levels.

Lastly, ^{we must note that we have observed a sam-}

ple-dependent background ^for samples with similar

concentration (In-3 ^and In-4). ^{We do not believe it}

1794

to be due to artefact. It could come from the photo-

ionization spectrum ^of acceptors shallower than indium (In-X ^{centre [19] or} aluminium), ^but

^failed

to observe the excitation spectra ^{of these} acceptors.

4. Conclusion.

The IR spectra ^{of In} acceptor ⁱⁿ silicon presented ^{in this} paper have allowed

to detect closely spaced lines whose separation ^is pre- dicted by theory ^and they show that the binding energies ^of many excited states is still to be determined.

It is found that the In linewidths decrease with the

binding energy for the first excited levels and become

nearly ^constant (~ ¹ cm-1) for the other levels.

Another result is that the concentration broadening

of the In lines in silicon is smaller than for acceptors with a lower ionization energy, contrary ^to prior

data. The unambiguous detection of temperature broadening of the lines between 5 and 10 K must allow meaningful quantitative comparisons ^{with cur-}

rent theoretical work on the broadening ^mechanism

of acceptor impurity lines in silicon. Additionally,

the optical calibration factor used in this study ^is

consistent with a room temperature ionization _energy 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

1018 atoms/cm3 compared with the value of 2.5

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.

Appendix.

The effective mass Hamiltonian of

a j

3/2 acceptor in silicon can be expressed ^{as the}

sum of a term with spherical symmetry ^{and of}

^term 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).

The hydrogenic ^states of interest are those with L

0 and 1 (S ^{and P} states) ^{and these states can} be labelled

using ^the projections ^{of F}

^{L +} 3/2, ^{which is}

constant of the motion; hence, nS3/2, nP 1/2’ np3/2

and nP 5/2 ^{states. Under}

^cubic perturbation, ^the symmetry ^{of the} problem ^{lowers to} that of the cubic

point group Oh. ^The compatibility relations between the irreducible representations of the full rotation group and those of oh ^{show that} Dj"/2’ 01/2’ D3/2

and D5/2 transform as r 8+’ r 6-’ r 8- and r 7- + r 8-’

respectively ^{and the} PSj2 ^states split-into F7 ^and F8

states. The calculated binding energy of the first odd-

parity ^{excited states are} given ^{in table} A-l, following

this nomenclature.

Table A-l.

Calculated binding energy of ^the first

acceptor ^{levels in silicon.}

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