Ultrasonic spectroscopy in p-type silicon

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Ultrasonic spectroscopy in p-type silicon

H. Zeile, O. Mathuni, K. Lassmann

To cite this version:

H. Zeile, O. Mathuni, K. Lassmann. Ultrasonic spectroscopy in p-type silicon. Journal de Physique

Lettres, Edp sciences, 1979, 40 (3), pp.53-55. �10.1051/jphyslet:0197900400305300�. �jpa-00231568�

L-53

Ultrasonic

_spectroscopy

in

_p-type

silicon

_(*)

H.

Zeile,

O. Mathuni and K. Lassmann

Universität _{Stuttgart, Physikalisches Institut,} Teilinstitut 1, 7000 Stuttgart 80, F.R.G.

(Re~u le 23 aofit 1978, revise le 4 decembre _{1978, accepte} le 11 decembre ₁₉₇₈₎

Résumé. 2014

On a déterminé la distribution des _séparations en _énergie des niveaux de l’état fondamental de

l’accep-teur dans des cristaux Si(B) très purs en mesurant _{l’absorption} résonnante ultrasonore dans une _{gamme importante} de _fréquences. Les distributions mesurées se _comparent bien avec les distributions attendues des champs électriques

des ~ 1012 cm-3 donneurs résiduels. On a mesuré l’intensité

critique

_pour saturer l’atténuation résonnante dans des cristaux avec différentes concentrations

_{d’accepteurs}

et en fonction de la

_{température.}

Bien que la distance moyenne des accepteurs soit

_beaucoup

_{plus grande}

_{que le rayon de Bohr des} trous liés on trouve _{que les} temps

de relaxation sont _{raccourcis par l’interaction accepteur-accepteur.}

Abstract. 2014 From ultrasonic resonant

absorption

over a wide

_frequency

_range we have determined the distri-bution of the energy

splittings

of the acceptor ground state _{in very pure Si(B) crystals.} The measured distributions with maxima of the order of 10

_{03BCeV fit}

well to the _expected electric field distribution from the ~ 1012 cm-3 residual donors. The critical _intensity for _saturating the resonance attenuation has been measured in

_crystals

of various

acceptor concentrations and as a function of temperature. Although the average distance of acceptor atoms is much _greater than the Bohr-radius of the bound defect-electrons, relaxation times are found to be shortened _by the acceptor-acceptor interaction.

LE JOURNAL DE _PHYSIQUE - LETTRES _TOME 40, ler FEVRIER

1979,

Classification

Physics Abstracts

71.70E - 71.55 - 62.65

1. Introduction. - The

ground

state of a hole

bound to an

_acceptor

in cubic semiconductors at low

temperatures is a fourfold

_{degenerate r 8}

state which

may be

split

into a doublet

by

elastic or electric

fields.

_Thus,

random internal fields of the

_crystal

originating

from defects

_give

rise to a distribution

of

_splittings

which in turn _may be

_regarded

as an

indicator of residual defects.

Furthermore,

such

a distribution of two-level

_systems

(T.L.S.)

is

quite

analogous

to that in

_glasses,

and the same

_questions

arise as to the relaxation times and the

_possibility

of a

long

range interaction between the T.L.S.

[1].

Information on these

questions

can be obtained

from

_measuring

the ultrasonic resonant attenuation

over a wide

_frequency

range. Since the attenuation

is

_proportional

to the

_{spectral density}

of the

_splittings

at a certain

_frequency,

the distribution is thus

probed

in the

_{corresponding}

_{energy range. From}

_measuring

the critical

_intensity

for

_saturating

the resonance

attenuation one obtains the

_{product ’r 1 . T2}

of the

longitudinal

and transverse relaxation times. We

report

here measurements of the ultrasonic attenuation

at

_frequencies

between 0.4 to 4 GHz in various silicon

_{crystals doped}

with boron and indium

acceptors of concentrations between 9 x

1015

and 5 x 1017

cm-3

with the aim

_(i)

of

_correlating

the measured distributions to the residual

_crystal

defects, (ii)

of

_determining

the

_temperature

depen-dence of the critical

_intensity;

i.e.,

of

_{i1(T). z2(T) ;}

and

_(iii)

of

_seeing

how the critical

_{intensity depends}

on

_acceptor

_{concentration; i.e.,}

on the mean

acceptor-acceptor distance.

2. Determination of the distribution of the

_splittings.

- The

resonance attenuation is

_{given by}

where

_N(E)

is the

_{spectral density}

of those

_splittings

E

of the distribution that are in resonance hv = E with the ultrasonic wave of

_frequency

_{v ;}

_Dres

is an effective

deformation

_potential

_{constant; p} is the mass

_density;

and v is the sound

_velocity.

To

_separate

_(Xres from other attenuation mechanisms

_(relaxation,

geome-trical

_effects)

we make use of the saturation of _(Xres at

high

acoustic intensities to obtain the residual

atte-nuation to be subtracted.

_Figure

1 shows a

_typical

L-54 JOURNAL DE PHYSIQUE - LETTRES

Fig. 1. - Distribution of splittings of the

acceptor ground state

in _Si(B); curve fitted for _splittings due to electric fields between residual ionized donors and acceptors.

distribution obtained in this way. We have assumed

Dres

to be

_independent

of _E, which seems

_plausible

if the _symmetry of the random field does not vary

strongly

with the field

_strength.

In contrast to our

earlier

_findings

in GaAs

_[2]

and Ge

_[3],

where the distribution function was constant in the

_measuring

range, the

spectral

density

falls off at low

_energies

for all the silicon

_crystals

we have measured.

_Furthermore,

for three _{very pure}

_crystals

from the same

supplier

[4],

but with different boron concentrations

_NA

=

0.9,

5.5,

8.5 x

1016

cm - 3,

the observed maxima lie

bet-ween 1.5 and 2

_GHz,

whilst for indium

_{doped crystals}

and for a less _pure boron

_{doped crystal}

the maxima lie

at

_{higher energies.}

If we _try now to correlate the measured distribution to internal random

fields,

we

find that elastic fields are of no

_importance

and can be

ruled _out, since the

_crystals

are

dislocation-free,

of

low _oxygen content

₍

10"

_{cm - 3),}

and the misfit of the boron atom in the silicon lattice is too small at

our concentrations to have an effect. Carbon and

oxygen

impurities

cause

_splittings

of the

_acceptor

ground

state which are

_{significant only}

in

concen-trations above

1016

cm- 3,

as seen in ESR

_by

Neubrand

_[9].

At small

_impurity

concentrations a

residital ESR linewidth is observed. We _suppose that these residual

_splittings

are of the same nature as the

splittings

observed

_by

ultrasonic

_{spectroscopy.}

It

should be

_mentioned,

_however,

that

_etching

of the

sample

side walls was _necessary to avoid strain field effects from the surface

_perturbed

_by

_grinding

_[9].

Another

_possibility

is the electric fields of the residual ^-’

1012 cm-3

donors

_(as

seen

_{by luminescence),}

which are ionized

by giving

their extra electron to

some

_neighbouring

_acceptors.

Larsen

_[5]

has calcu-lated the

_expected

electric field distribution

_assuming

random distribution of ionized donors and _acceptors.

(At

low _temperatures nearest

_{neighbour pairs}

should be more

_probable

_[6].)

_Taking

into account linear and

quadratic

Stark

_effects,

we can fit Larsen’s Holtzmark

distribution to our

N(E)

with reasonable

_parameters

for the residual donor concentration

_ND

_(comparable

to the estimate from luminescence

_{experiments),}

the

coefficient #

for the

_quadratic

Stark effect

_(as

esti-mated

_{by Pikus, Bir,}

and Butikov

_[7])

and the coeffi-cient _X for the linear Stark effect

_(three

times

_larger

than the estimate

_[7]

for shallow

_acceptors).

To check

our

_hypothesis

we are

_{preparing experiments}

with

varying compensation

ratios

_by

neutron irradiation which leads to a uniform distribution of

_phosphorous

donors

_by

Si -~ P transformation which should result in a

_{corresponding}

shift of the distribution.

3. Critical

_intensity

and relaxation times. - The

critical

_intensity

_Ic

for

_saturating

the resonance

attenuation is obtained

_{by measuring}

the

_dependence

on the acoustic

intensity

I

We relate I to the

_applied

microwave _power

_by

an

insertion loss measurement

_[8].

In a Bloch

equation

formalism we _get from

_Ic

the

product

’t 1 . ’t 2 of the

spin-lattice

or _energy relaxation

_{time T,}

₁ and the

transverse or

_dephasing

relaxation time _i2

If

_{only spin-lattice}

relaxation were

effective,

one

might

assume _{1’1 . l’ 2} =

2. il

[1],

that

_{is, Ic}

should not

_depend

on concentration

_NA.

To see whether an interaction

between the _acceptors

_{(spin-spin relaxation)}

plays

a

role,

we have measured

_Ic

for three _{very pure}

_Si(B)

crystals

from the same

_supplier

with different

_acceptor

concentrations

_NA

but otherwise

_essentially

identical. The result is shown in

_figure

2. The value of a fourth

crystal

with the lowest concentration

_NA

but otherwise less _pure, shows a

_{leveling-off.}

This _may be due to the

Fig. 2. - Critical intensity for saturating the _resonance attenuation

L-55

ULTRASONIC SPECTROSCOPY IN _p-TYPE SILICON

extra

_impurities

or _may indicate a

_tendency

to

non-interaction. As can be seen from the _upper

abscissa,

the most

_probable

distances are at least 10 times

larger

than the

Bohr-radius,

so that direct

_overlap

effects can be excluded. This is in accordance with the fact that we do not see a

dependence

of the

dis-tribution of the

_splittings

on

_NA.

If we know the

temperature

dependence

of _Ti, we can deduce

’t2(T)

by measuring

the _temperature

_dependence

of

_7~.

This is valid

only

if the

_measuring

_{pulse length}

(2

Jls)

is

_{longer than ’t1}

which is true in the case of

Si(B)

for

temperatures

higher

than 2 K at 1 GHz. For

instance,

at 4.15 K and 1 GHz for

_Si(B)

we have

as

_extrapolated

from an

_analysis

of the relaxation

attenuation between 5 K and 20 K. In this _{case 1’1 1} is determined

by

Raman and Orbach _processes

(relaxation

via a Jahn-Teller level of the

_{r 8 state).}

In

this

_temperature

_range, in the case of

_Si(B),

we would

expect the relaxation time to _vary

_{as T}

1 oc T 5

However,

the measured

_temperature

_dependence

of the

critical

_intensity

varies more

_slowly

than

_expected

and

_depends

on _acceptor concentration. We find

Ic

oc T5 for the

_crystal

with

_NA

= 9 _x

1 O 15 cm - 3

and

_1~

oc T for

_NA

= 8.5 x

1016 cm-3.

The

fre-quency

dependence of 1~

is

roughly

as

c~ 1 ~ 5

in _{the range}

from 0.5 to 3 GHz at 4.2 K. This would mean

1’2 OC

(,~-1.5,

, since at 4.2 K Raman and Orbach

processes dominate in Ti, both

being frequency

independent.

In the case

of Si(In)

we find at _temperatures between

0.5 and 4.0 K a

T2

_dependence

of

_7~

_(Fig.

_3),

as one

might

expect if direct relaxation were dominant.

However,

the absolute value

_7~

is too

_{high by}

two

orders of

_magnitude,

and also at

_temperatures

above

Fig. 3. - Critical

intensity for saturating the resonance attenuation

versus _temperature in the case _Si(In).

2 K we estimate the _{Raman process} to be the most

important,

whilst for

_temperatures

below 3

_{K, L1}

is estimated to be

_longer

than the duration of the ultrasonic

_pulse.

This shows that measurements of the

critical

_intensity

alone do not

_give

sufficient informa-tion on the relaxation _processes.

Clearly,

a more direct determination

_{of i2}

is

necessary before

discussing

the

_possible

interaction mechanisms.

In

_conclusion,

we have shown that in _{very pure} silicon

_crystals

the

_splitting

of the acceptor

ground

state is determined

_by

the random electric fields from residual donors and that there is a

_dynamical

inter-action between the _acceptors.

References

[1] JOFFRIN, J. and LEVELUT, A., J. _Physique 36 (1975) 811.

[2] LASSMANN, K. and _{SCHAD, Hp.,} Solid State Commun. 18 (1976)

449.

[3] ORTLIEB, E., SCHAD, Hp. and LASSMANN, K., Solid State

Com-mun. 19 (1976) 599.

[4] Wacker Chemitronic GmbH, D-8268 Burghausen,

Waso-quality.

[5] LARSEN, D., Phys. Rev. B 13 (1976) 1681.

[6] GOLKA, J., TRYLSKI, J., SKOLNICK, M. _{W., STRADLING,} R. A. and COUDER, Y., Solid State Commun. 22 (1977) 623. [7] BIR, G., BUTIKOV, E. and PIKUS, G., J. Phys. Chem. Solids 24

(1963) 1475.

[8] WAUK, M. T. and WINSLOW, D. K., IEEE Transactions on Sonics and Ultrasonics SU-16 ₍₁₉₆₉₎ 86.

[9] NEUBRAND, H., Phys. Status Solidi (b) 86 (1978) 269 and NEUBRAND, H., Phys. Status Solidi _(b) 90 (1978) 301.