Philips Res. Rep. 12, 303-308, .1957
R 321
INTERSTITIAL DIFFUSION Olf NICKEL
IN PbS SINGLE CRYSTALS
by
J. BLOEM and F. A. KRÖGER
532.72: 546.817.221: 548.55
Summary
Under reducing conditions, nickel may penetrate into PbS crystals at
temperatures T < 500°C at which the self-diffusion in PbS is negligible; it diminishes p-type conductivity and may cause n-type
conductivity with donors of a depth E ~ 0·03 eV. The diffusion
probably takes place via the interlattice with a diffusion constant
DNi = 17·8 exp (-22000/RT) cm2 sec-I. Under sulphurizing conditions (H2S)the nickel can he drawn out of the crystal again and the
original conductivity restored.
Résumé
Sous des conditions de réduction, il est possible de laisser diffuser le
Ni dans des cristaux de PbS à des températures T < 500°C, oü la
diffusion des ions Pb ou S est nëgligeable, Cette diffusion de Ni diminue
la conductibilité du type p et peut provoquer la conductibilité du
type n avec une énergie d'ionisation de 0,03 eVenviron. La diffusion
s'effectue probablement via des interstices avec une constante de
diffusion Dja = 17,8 exp (-22000/RT) cm2 sec-I. Dans une atmosphère
. contenant du soufre (H2S) il est possible d'extraire des atomes de
Ni du rëseau et de rétablir la rësistance criginale.
:Z;usammenfassung
In einer reduzierenden Umgebung kann Ni in PbS-Kristallen eindiffundieren bei Temperaturen T < 500°C, wo die Selhstdiffusion
in PbS zu vernachlässigen ist, Dadurch wird Defektleitung (p-Type)
herabgesetzt und kann UeberschuBleitung (n-Type) auftreten. Die
Donatorterme liegen etwa 0,03 eV unter dem Leitfähigkeitsband.
Die Diffusion verläuft wahrscheinlich im Zwischengitterraum. Die
Diffusionskonstante ist DNi = 17,8 exp (-22000/RT)
cm2 sec-I.
Bei Anwesenheit von Schwefel in der Atmosphäre (H2S) kann das
Ni dem Kristall wieder entzogen und die ursprüngliche Leitfähigkeit
wieder hergestellt werden.
1. Introduction
In a previous paper 1) it has been shown that copper may diffuse into
PbS at temperatures 100 < T < 500
at which the diffusivities of the
components of the crystal are negligible. The copper causes n-type conductivity. Both the diffusion and the electrical effects can be explained if it
is assumed that copper enters the crystal via interstitial sites, filling up
cation vacancies if present. The present paper is a. report on similar
experiments with nickel.
oe
304
J. BLOEM and F. A. KRÖGER
2. Experimental
2.1. The diffusion of nickel into virginal crystals
Samples of p-type PbS were electroplated with Ni and then re-treated
in H2 or H2S at T < 500°C. The following p-type PbS samples were used:
(a) undoped PbS, containing holes and ionized cation vacancies (Vii
centres) in equal concentrations.
(b) PbS doped with 1018 cm-3 Ag, and re-treated in such a way as to give
1018 holes per cm3 and the least number of vacancies (~1016 cm--3).
There is found to be a marked' difference in behaviour between the two
types of crystal, thus providing evidence for the assumptions needed to
evaluate the diffusion coefficients. Samples (b) covered 'with nickel and
heated in H2 did not suffer a marked change in their properties; they were
still p-type even after prolonged heating. Yet spectrographic analysis
showed that nickel had entered the crystals, up to a concentration of about
5.1018 cm-3• Samples (a) treated in the same way did show conversion to
n-type. The conversion started at the surface, and was similar as observed
with copper. If the experiment is carried on for a sufficiently long time,
the entire crystal becomes homogeneously n-type.
Data concerning the rate of penetration of the n-type region into the
crystal and the concentrations of electrons attained after prolonged heating
(t ~ 00 , nsat) are given in table I. It is seen that the diffusion is markedly
slower than in the case of copper. Further the final concentration of electrons is smaller than in the case of copper.
Measurements of the Hall effect and the resistivity as a function of
temperature
of samples (a) which have acquired a homogeneous Ni
concentration show that the ionization energy of the centre formed by
nickel is slightly greater than for interstitial copper, the donor depth being
about 0·03 eV. Nevertheless, at room temperature practically all the centres
are ionized, and a corresponding number of electrons is present in the
conduction band.
2.2. Reconversion
If crystals of group (a) which have been plated with Ni and converted
to n-type conductivity by heating in H2 are re-treated in H2S, a surface
layer of relatively high resistance is formed which extends from the surface
to the inside of the crystal: apparently the number of charge carriers is
greatly reduced. Reheating for a longer period of time (e.g. 24 hours at
400°C) restores the original p-type conductivity.
Spectrographic analysis of the interior of such crystals shows that the
nickel ccccentratton present is ~5.1018 cm-a, i.e. about the same as found
before the treatment with H2S.
INTERSTITIAL
DIFFUSION
305
OF Ni IN PbS SINGLE CRYSTALS
TABLE I
The diffusion of Ni into p-type PbS in H2; experimental data
Samples (a),
original
concentration
[Vt) = p(cm-3)
temp.
time
D
(min)
x
(mm)
nsat
(0C)
(cm-a)
(cm2 sec'")
1.3.1018
2.7.1018
2.0.1018
500
165
100
120
2·05
1·57
1·39
3.6.1017
6.0.1017
5.0.1017
7.5.10-6
9.35.10-0
5.35.19-6
2.2.1018
2.5.1018
3.0.1018
450
165
150
160
1·01
1·36
1·19
7.6.1017
5.0.1017
9.0.1017
1.55.10-6
6.12.10-7
2.50.10-6
5.6.1018
1.6.1018
4.0.1018
400
240
175
24.0
0·82
0·59
0·92
3.0.1018
8.7.1017
1.0.1018
4.25.10-7
3.0.10-7
1.17.10-7
2.6.1018
3.0.1018
3.3.1018
350
300
360
420
0·73
0·69
0·59
1.5.1018
1.3.1018
1.7.1018
2.45.10-7
2.50.10-7
1.30.10-7
2.1.1018
1.6.1018
300
465
470
0·46
0·52
9.1.1017
9,7.1017
8.75.10-8
2.10.10-7
2.5.1018
2.5.1018
200
3492
3492
0·22
0·12
2.3.1018
2.3.1018
1.10.10-9
3.74.10-10
3. Discussion
3.1. The activity of nickel in influencing the conductivity
The concentration of nickel that may be built up inside the crystal is
regulated by the thermodynamic potentialof the nickel atoms in the outer
phase, just as was the case for copper: under reducing conditions (H2) the
concentration tends to be large; under sulphurizing conditions (H2S) the
concentration tends to be low, the Ni forming a separate NiS phase at the
surfaces.
The nickel will either enter the crystal directly via interstitial sites, or it
will first penetrate via inner surfaces and then branch off into the interstices of the crystal proper. In the following it will be assumed that the .
former case applies.
306
J. BLOEM and F. A. KRÖGER
Let us :first consider the crystals of group (b), originally containing
1018 cm-S Ag+ and the same concentration of free holes, but no vacancies.
Ni atoms entering the crystal at interstitial sites tend to give off electrons,
which, recombining with the free holes, would lead to a decrease in the hole
concentration. As such effects are not observed, this indicates that under
the conditions of the experiments the solubility of Ni at interstitial sites
is less than the concentration of holes, i.e, < 1018 cm-s. As we shall see
below this is actually the case, the solubility at interstitial sites being
~ 5.1017 cm-s at the temperatures used.
Since spectrographic analysis showed the presence of ~ 5.1018 cm-3 Ni,
this indicates that most of the nickel is present in states in which it is
inactive; it is probably present as a sulphide absorbed at internal surfaces
(cracks, dislocations), as was also found to he the case for Cu 1).
In samples (a) originally containing Vii centres-and an equal concentration
oflioles, the nickel, migrating via interstitial sites, may meet and occupy
the lead vacancies. As nickel normally forms divalent ions, just as lead,
"the centre formed will tend to bind holes:
(1)
As in crystals (a) originally [Vii] = p, it will be clear that if all the Vii
centres are filled with nickel the crystal will have intrinsic properties. The
observed n-type conductivity with ~ 5.1017 electrons per cms must be due
to the presence of additional nickel atoms in the interlattice, which dissociate according to
(2)
Nii-? Nit
-ENi·
+e
The ionization energy found from the slope of the Hall constant as a
function of liT (assuming Nit = e) has the value E = 2 X 0·015 = 0·03
eV.
If the nickel ions that have :6.lledthe lead ion vacancies would give rise
to empty levels farther away from the conduction band than the levels due
to the interstitial nickel ions (Nit), then the ionization energy found would
correspond to the latter depth.
It seems most reasonable, however, to ascribe the level depth found
directly to the interstitial nickel atoms, the nickel ions at regular lattice
sites not giving rise to empty levels lying within the forbidden gap.
3.2. The diffusion process
Nickel caught at a Vii centre will be unable to move through the lattice.
If it is assumed that the probability of a jump from a lattice site into the
interlattice is relatively small, the diffusion of nickel into the crystal can
only take place by means of the atoms present in the interlattice.
INTERSTITIAL
DIFFUSION
vt
OF Ni IN PbS SINGLE
CRYSTALS
,
307
Owing to the presence of
which act as a sink, no nickel can be present
in the interlattice as long as
centres, are available. In the region in
which all the
have been filled, the concentration of interstitial nickel
will vary gradually from 'a value equal to the saturation value near the
surface (and this in turn is equal to the saturation value of n, nsat) to zero
at the front. If it is assumed that the concentration varies linearly, the
distribution pattern as shown in fig. lis arrived at. This model leads to the
following relation between the penetration depth of the nickel front (which
is at the same time the pin front, xp/n) and the diffusion coefficient of the
interstitial diffusion:
vt
vt
D
2,/
Po •
2t ,nsat
= Xp n
(3)
I
cone.
,1
--.l---p---'
_X
(distance from
91623
the surface)
Fig. 1. Simplified concentration pattern of nickel at a certain time t after the beginning of
the diffusion experiment.
',
Ana1ysis of the experimental data by means of this formula leads to the
values of D given in table I and fig. 2; D varies with temperature according
to
D = 17·8 exp (.
_!l_)
cm
RT
2
sec-1
(4)
with an activation energy Q of 22000 cal mole"! or 0·96 eV. The diffusion
of nickelis appreciably slower than that of copper, a va1ue of D = 10-5 cm2
sec-1 being reached at 500
for Ni and at 300
for Cu.
oe
oe
3.3. The mechanism of reconversion
If PbS saturated with nickel by heating in a .reducing atmosphere is
heated in H2S (or some other atmosphere of relatively high sulphurizing
power), the possibility of the formation of NiS lowers the thermodynamic
potential at the surface. As a consequence nickel tends to migrate out of the
crystal. In the first instance only the nickel present at interstitial sites is
able to move and the crystalis drained of the interstitial nickel atoms; as these
308 .
J. BLOEM and F. A. KRÖGER
-5
""~
I/)
-6
'"E
~
r-,
I~
=1"'.1"'-
Cl -7
""
-2
1
I1
I
-8
Ni dill. H2
:"'-
'"
-,
-,
-,
-9
to
.'\
1·5
91624
Fig. 2. The diffusion constant for the interstitial diffusion of nickel in PbS as a function of
temperature.
were the cause of the n-type conductivity a crystal with intrinsic properties
is left. In the course of time, however, nickel from lattice sites mayalso
escape into the interlattice and from there to the outer surface. According
to equation (1) this leads to the formation offree holes. The original p-type
conduction will thus );ierestored when all the nickel from lattice sites has
been drawn out of the crystal. From the fact that this is actually observed it
may be concluded that nickel from lattice sites indeed may be swept out
of the crystal *); yet the times involved are so long - i.e. the probability
of escape from a lattice site to the interlattice is so small - that the
assumption made in section 3.2 is justified.
As we have seen in sections 2.1 and 3.1, the bulk of the nickel is present
as NiS at internal surfaces. This nickel cannot be expected to be affected
by the treatment with H2S. This explains why H2S treatment does not
markedly reduce the total nickel concentration (section 2.2).
Acknowledgements
The authors are indebted to Mr E. A. Burns (M.LT.) for his aid in the
diffusion experiments during his stay at Eindhoven in summer 1955 and to
the spectrochemical department of Dr Addink for the analytical data.
*) A similar effect mayalso occur with copper in PbS. Since copper at lattice sites has
electrical properties which cannot be distinguished from those of
centres, the effect
cannot be proved in that case 1).
r:
Eindhoven, Morch. 1957
REFERENCE
1) J. Bloem and F. A. Kröger,
Philips Res. Rep. 12, 281-302, 1957.