Splitting of the ground state of shallow acceptors in silicon

~)

Solid State Communications, Vol. 93, No. 5, pp. 379-382, 1995 Elsevier Science Ltd Printed in Great Britain 0038-1098(94)00802-7 0038-1098/95 $9.50+.00

Pergamon

SPLITTING O F THE GROUND STATE OF SHALLOW ACCEPTORS IN SILICON V. A. Karasyuk, S. An, M. L. W. Thewalt, Department of Physics, Simon Fraser University, Burnaby, B. C. VSAIS6, Canada, E.C Lightowlers, Physics Department, King's College London, Strand, London WC2R 2LS, UK., A. S. Kaminskii, Institute of

Radioengineering and Electronics RAS, Mokhovaya 11, Moscow 103907, Russia.

The results of near infra-red piezo-photoluminescence, phototuminescence excitation, and absorption spectroscopy of silicon doped with AI, Ga, and In performed at 2 K and 0.4 K show that the ground state of these shallow acceptors is split by 0.10 + 0.01, 0.10 + 0.01, and 0.015 + 0.03 cm- 1 respectively. This splitting is shown to be a fundamental intrinsic property of shallow acceptors and it may be explained by a dynamic Jahn-TeUer effect. Keywords: C. impurities in semiconductors D. electron-phonon interactions E. light absorbtion and luminescence

Splitting of the Ground State of ShallowAcceptorsin Silicon.

and In at 2x1015 cm -3 were immersed in a pumped liquid 4He or 3He bath and excited by a 0.98 I.tm Ti-sapphire laser radiation. For uniaxial stress measurements we used

Photoluminescence (PL) spectroscopy of excitons

the technique developed by Kaminskii et al. 4 which ensu-

bound to acceptors can provide information about the

red high homogeneity of the strain, The PL spectra were

acceptors themselves, as the final states for the optical

recorded with 0.02 cm-1 resolution by a BOMEM DA8

transitions. In the ground state of a shallow acceptor

Fourier transform spectrometer fitted with a Si avalanche

bound exciton (AOX) two holes form a spin singlet state

photodiode detector. The same spectrometer was used in

F1, and the electron occupies one of the valley-orbit states

the near infra-red (NIR) absorption experiments with a

F1, F 3 and F5.1 Accordingly, only three main optical

high pressure arc lamp coupled with a grating monochro-

transitions are expected in the spectra of AOX because the

mator ban@ass filter as a source of incident light. For the

final state, the ground state of the neutral acceptor (A0) in

PL excitation (PLE) experiments the laser was tuned conti-

Si is usually considered to be a fourfold degenerate purely

nuously by an intracavity thin etalon in the range of wave-

electronic state F 8 derived from the top of the valence

lengths corresponding to the AI A0X NP PL. The laser

band. In 1990 Thewalt and Brake 2 resolved six compo-

beam with stabilized power of 500 mW at 2 K and 10 mW

nents in no-phonon (NP) PL spectra of AOX in Si:A1, five

at 0.4 K was focused on the square face of the 2x2x25 mm

components in Si:Ga and four components in Si:In. The

sample. A double grating monochromator selected the PL

presence of the additional components indicated that an

from the TO phonon replica region, which was detected by

additional splitting takes place either in A0X or in A 0.

a Varian VPM- 129A3 photomultiplier tube.

Kaminskii and Safonov 3 suggested that the additional small doublet splitting observed in Si:AI is due to the A 0 ground

Without any external perturbation six different

state splitting, produced by the Jahn-Teller effect (JTE). In the present study we prove that the additional splitting

float zone silicon samples with A1 concentrations in the range from 2.7x1014 cm-3 to 3.3x1016 cm"3 produced PL

does indeed occur in the A 0 ground state, due to an intrin-

spectra with three well resolved doublets (Fig. 1). The

sic effect independent of random strains.

0.10 cm -1 splitting and the amplitude ratios in the doublets are the same for all six samples, so it is most unlikely that this splitting could be due to random strains or other ran-

Float zone silicon samples doped with AI in the range from 3x1014 to 3x1016 cm -3, Ga at lxl015 cm "3

dom fields, which would be expected to be sample depen379

380

Vol. 93, No. 5

SHALLOW ACCEPTORS IN SILICON I

I

I

\ ~

f)

I

I

I

I

I

I" ~ 1

vh~8.3xf~%m-S xl

I

Si:A1

t +'`'`-]

x4

I I I I I I I It

Ill

II

I II

I

II

Si:A1 <111>

Us USL~ i ~ @

I I II

I I II

2.1K

~ r n -r a --

~.,~ ,,,,++,,.~

i/

(

•

[fl

=

c) b)

9271

8.o __.A.

q '

9272

'

9275

Photon energy (cm -1)

II

[I

[]1

Us U5

$i:Al

II

I II

II

11

+.++

,,

UI L3 La

.

<111>

0.0

)1

11

II

,, . . . . . . . . . ~,, ,., ,.,, . . . . . . .

. .

. .

.

",, %1

% ' ~ ! %i ' !.

. . . . . . . .

L1

i

, i,,~/),l,,,,~l,

9270 9272 Photon energy (era -1)

Fig. 1 NP PL spectra of six different samples of float zone Si doped with AI in concentrations (a) 2.7×1014, (b) 5.5 xl014, (c) 1.5x 1015, (d) 4.6x 1015, (e) 1.1×1016, and (f)

Fig. 2 Positions of the peaks in the PL spectra as a function ofuniaxial stress in a (111) direction. The insert shows

3.3x1016 cm-3 recorded at T = 2 K with resolution 0.02

vels of the BE into the upper (U) or the lower (L) sublevel

cm"1. Line P ofexcitons bound to phosphorus has the FWHM = 0.048 cm"1 in spectrum (b).

of the acceptor ground state. The stress was calibrated according to the linear splitting of the phosphorus D0X line.

dent. This is confirmed also by the presence of a single narrow (FWHM = 0.05 cm"1) line P of excitons bound to

tra can be easily interpreted. The (111) strain does not change valley-orbit splitting and six components observed

neutral phosphorus donors (DOX) in some of the spectra,

in the spectra correspond to transitions from the three valley-orbit energy levels of the A0X initial state to one of

since random strains would affect the hole in D0X approximately to the same degree as the hole in A 0. They would also split the electron states F 3 and F 5 in A0X which would result in the additional splitting or broadening of the corresponding components labeled in Fig. l b y the subscripts 3 and 5 with respect to the components corresponding to the F 1 A0X state labeled by the subscript 1, yet to within our spectral resolution of 0.02 cm-1 the doublets

the scheme of optical transitions from the three energy le-

the two orbitally non-degenerate substates of the A 0 ground state split by the strain. Positions of the peaks corresponding to the transitions from the same initial state (labeled by the same subscript) extrapolate to different photon energies at zero stress, therefore the final state, the A 0 ground state, is split even in the absence of stress.

from each of the three valley-orbit A0X states are identical.

The PLE spectra (Figs. 3c and 3d) show the relative PL intensity of the integrated A0X TO phonon rep-

Under small (111) uniaxial stress, components in the three AI doublets move apart (Fig. 2) but do not split further. The amplitude ratios of the components in the

lica versus the energy of the photons in the incident beam

doublets change rapidly with increasing the stress from 0 to 0.9 MPa so that the high energy component becomes stronger than the lower energy component. In the same range of stress, polarizations of the components in the doublets increases gradually and than saturate. This indicates significant changes in the wavefunctions under very small uniaxial stress, again arguing against a splitting due to random static fields. In the limit of high stress the spec-

of laser radiation which was tuned continuously in the range of the A0X HP transitions. The PLE spectra look similar to the PL spectra (Figs. 3a and 31)) except for the differences in the relative amplitudes of the components. Comparison of the PL spectra recorded at 2.0 K (Fig. 3a) and 0.4 K (Fig. 3b) shows that the amplitude ratio of the components in the doublets does not change, although a strong thermalization of the components corresponding to the excited valley-orbit states of AOX is observed. On the contrary, the relative amplitudes of the low energy components

Vol. 93, No. 5 I

381

SHALLOW ACCEPTORS IN SILICON I

PLE

I

I

I

I

I

usL5 UsL 3 ~ / ~

I

I

I

I

I

I

I

I

I

I

I

rl

I

I

I

I

Si:Ga

~,~

I

I

I

I

I

I

I

I

I

1.7 K

~5

0.81 uP~ _ j / - q ~ / / , , \ \

_

Fi

°xlt 1.1,,,,°

5"01

I

J i

t

E t

i

n i

~ I

i

U3 I~ U5 I~ Ui L,

si:oa -..

L I

9271 Photon energy (err*-1)

t

I

9273

o.ot- I

".. ",

'. •

. . . . .

~ ! l ,

9266 Photon

energy

• ,/

,,( t

dl

9267 (era -1)

Fig. 3 PL and PLE spectra of the A1 BE. The PL spectra (bottom) were recorded with 300 mW (a) and 8 mW (b) excitation at T = 2.0 K and 0.4 K respectively. The PLE spectra (top) recorded at T = 2.2 K (c) and 0.4 K (d) show the integrated intensity of the TO phonon replica of A0X PL as a function of laser photon energy.

(U), in the PLE doublets (Figs. 3c and 3d), drop when the temperature is lowered from 2.2 down to 0.4 K, which is consistent with the assumption that they correspond to

Fig. 4 Top: evolution ofNP PL spectra ofGa A0X at T = 1.7 K with increasing (111) stress. Bottom: Ga A0X PL peak positions as a function of (111) stress.

the 0.4 K spectrum multiplied by a factor 1.2 which makes the low energy peak amplitudes equal. The resulting spectrum is shown by a dotted line in the bottom of Fig. 5. One can clearly see that it replicates the 4.2 K absorption spectrum with six times smaller amplitude and 0.15 cm"1 shift to higher energies. It is worth mentioning that, in the

transitions from the upper energy level (U) of the split

absence of external perturbations, for AI the transitions

acceptor ground state. Thus it is clear that the A 0 ground state is indeed split in Si:AI by 0.10 ± 0.01 cm-1.

between A0X and the upper A 0 level have a slightly higher oscillator strength than those associated with the lower A0X level, while for In this ratio is much larger and the transitions between A0X and the lower A 0 level can only

Similar A 0 results were obtained for Ga and In, with the ground state splitting for Ga equal to 0.10 + 0.01 cm-1 (Fig. 4). The 0.15 + 0.03 cm-1 splitting of the In A 0

be clearly observed in absorption at very low temperatures when the upper A 0 level is significantly depopulated.

ground state was deduced from the comparison of NIR absorption spectra recorded at 4.2K and 0.4 K (Fig. 5). The A0X PL spectra of Si:In contain four well resolved components and show little thermalization as opposed to Si:AI

near configuration of atoms, coupling between a degenerate electronic state and asymmetric vibrations of nuclei must

spectra, probably, because of the short lifetime (2.7 ns, ref. 5) of In AOx. We associate these four components with the A0X valley-orbit states, the state F 5 possibly being split by a spin-orbit coupling6. The asymmetric lineshape of the components, particularly the shoulder marked by an arrow in the top of Fig. 5, indicates the presence of other components which are not resolved. These unresolved extra components do appear in the NP absorption spectra when the temperature is lowered from 4.2 K to 0.4 K. The presence of these extra components can be seen more easily when the 4.2 K absorption spectrum is subtracted from

The Jahn-Teller theorem 7 states that in any nonli-

distort this configuration and lift the electronic degeneracy by reducing its symmetry. This theorem should apply also to the case of shallow acceptors with the F 8 ground state. According to modem theory of JTE 8-10 the ground vibronic state describing motion of the coupled electron-phonon system retains the degeneracy of the uncoupled electronic state. However, in the case of intermediate coupling when the vibrational quantum is comparable to the Jahn-Teller energy EjT the whole set of closely spaced vibronie states results in a typical "double-humped" spectral distribution observed in numerous experiments (see for instance ref.

382

SHALLOW ACCEPTORS IN SILICON I

I

I

i

I

Vol. 93, No. 5

the higher energy ones. If this is the case,/imp ~ EjT~ 0.1 cm"1 and thus the most effective coupling would be with very long wavelength acoustic phonons.

I

°.;t'

)

I

I

I

h

It.

1

I

A /11

,L,/'

Skln " - - , 2 K

I',i o,K
0.0~--" t I t I 9203 9201 Photon energy (cm -1) Fig. 5 PL (top) and absorption (bottom) spectra of In A0X recorded at the bath temperatures 4.2 K (dashed lines (a) and (c)) and 0.4 K (solid lines (b) and (d)). The dotted line (e) shows the result of the subtraction of the spectrum (c) from the spectrum (d) multiplied by a factor of 1.2. [1 I] p.188, ref. [9] p.49, or ref. [10] p.215) and matching very well the asymmetric lineshape of the doublets in Fig. 1, with the lower energy components being narrower than

1G. Kirczenow, Can. J. Phys. 55, 1787 (1977). 2M. L. W. Thewalt and D. M. Brake, Materials Science Forum 68-66, 187 (1990). 3A. S. Kaminskii and A. N. Safonov, Pis'ma ZETF 55, 245 (1992), (JETP Lett. 55, 242 (1992)). 4A. S. Kaminsidi, V. A. Karasyuk, and Ya. E. Pokrovsldi, Zh. Eksp. Teor. Fiz. 83, 2237 (1982) [Sov. Phys. JETP 56, 1295 (1982)]. 5R. Sauer, W. Schmid, and J. Weber, Solid St. Comm. 27, 705 (1978). 6A. J. Mayur, M. Dean Sciacca, A. K. Ramdas, and S. Rodriguez, Phys. Rev. B ,18, 10893 (1993).

The results of our experiments prove that the ground state of shallow acceptors in silicon is split by 0.10 + 0.01 cm"1 for AI and Ga, and 0.15 + 0.03 cm-1 for In, the splitting being an intrinsic property of these acceptors rather than the result of perturbations such as random strains. This splitting may be explained by a dynamic JaM-Teller effect due to coupling with the long wavelength acoustic phonons with the quanta smaller than the size of the splitting. This would explain the observed asymmetric "double-humped" lineshape of the doublets which may result from the convoluted optical transitions to/from the band of closely spaced vibronic states of the acceptor.

Acknowledgement - The authors wish to thank F. S. Ham for numerous and very useful discussions. This work was supported partly by the Natural Sciences and Engineering Research Council of Canada, by the Science and Engineering Research Council (U-K).

7H. A. Jahn and E. Teller, Proc. Roy. Soc. A 161, 220 (1937). 8F. S. Ham, in Electron Paramagnetic Resonance, edited by S. Geschwind (Plenum, New York, 1972) p. 38. 9R. Engleman, The dahn-Teller Effect in Molecules and Crystals (Wiley-Interscienee, New York, 1972), p. 37. 10I. B. Bersurker, V. Z. Polinger, VibronicInteractions in Molecules and Crystals, (Springer-Vedag, Berlin Heidelberg New York, 1989), p. 196. llM. D. Sturge, Sol. St. Phys. 20, 91 (1967).