Philips Res. Rep. 9, 225-230, 1954

R 244

THE SOLID SOLUBILITY AND THE DIFFUSION OF NICKEL IN GERMANIUM by F. van der MAESEN and

J. A. BRENKMAN 5460289: 546.74: 532.72/3

Summary Nickel produces rapidly diffusing acceptors in germanium, just as copper. Hall and resistivity measurements show the existence of a Ni acceptor level lying 0·23 cV above the valence band. On the basis of this picture the solid solubility between 700 and 900°C is derived from resistivity measurements. From these values and the liquidus curve of the phase diagram Gc-Ni, the distribution coefficients (k) at various temperatures are calculated. The distribution coefficient (k*) of Ni at the melting point of Gc is calculated at 1'8.10-6 aecording to a method of Thurmond and Struthers. The diffusion coefficient of Ni in Gc is measured between 700 and 850°C; the activation energy of diffusionis found to be 21 kcal/mole. Annealing of a Ni-saturated Gc sample restores the original resistivity. Résumé Le nickel, exactement comme Ie cuivre, pro duit des accepteurs à diffusion rapide dans Ie germanium. L'effet Hall et les mesures de la résistivité démontrent l'existence d'un niveau accepteur Ni qui se tient 0,23 eV au-dessus de la bande de valence. Sur la base de cette description, la solubilité solide entre 700 et 900°C fut tirée des mesures de résistivité. Les coefficients de distribution (k) à diffërentes tempëratures ont été calculës d'après ces valeurs et de la courbe de liquide du système Ge-Ni. Le coefficient de distribution (k*) de Ni au point de fusion de Ge a été calculé à 1,8 X 10-6 suivant la méthode de Thurmond et Struthers. Le coefficient de diffusion de Ni dans Gc entre 700 et 850°C a été mesurë, et l'on a trouvé comme valeur de l'énergie d'activation de la diffusion: 21 kcal/mol. Le reeuit d'un échantillon de Ge saturé de Ni fait revenir la résistivité criginale. Zusammenfassung Ebenso wie Kupfer erzeugt auch Nickel schnell diffundierende Akzeptoren in Germanium. Messungen des Hall-Effektes und des Widerstandes zeigen das Vorhandensein eines 0,23 cV über dem Valeneband liegenden Ni-Akzeptorniveaus an. Auf Grund dieser Vorstellung wird die feste Löslichkeit zwischen 700 und 900°C aus Widerstandsmessungen abgeleitet. Aus diesen Werten und der Flüssigkeitskurve des Phasendiagramms Ge-Niwerden die Verteilungskoeffizienten (k) bei verschiedenen Temperaturen bercchnet. Der Verteilungskoeffizient (k*) von Ni beim Schmelzpunkt von Ge wird errechnet zu 1,8 X 10-6 nach der Methode von Thurmond und Struthers. Es wird der Diffusionskoeffizientvon Ni in Ge gemessen zwischen 700 und 850°C; die Aktivierungsenergie fiir die Diffusion beträgt 21 kcal/Mol. Durch Ausglühen einer Ni-gesättigten Ge-Probe wird der ursprungliche Widerstand wieder zurückerhalten.

F. ven der MAESEN end 226 -------------------------,-

J. A. BRENKMk"l

,-,_.,,'-----_

1. Solid solubility It is known that nickel in germanium shows an acceptor activity 1),2) causing conversion of an n-type germanium sample of appropriate resistivity into p-type on heating at 800 In order to avoid the presence of copper impurities the Ge samples were cleaned with double-distilled concentrated HN032). After this the pieces were covered electrolytically with pure Ni and then heated for some time at the desired temperature. After quenching, the resistivity was measured. To be sure of saturation the samples were cleaned, plated again and reheated at the same temperature. After quenching no change in resistivity was found, showing saturation and the absence of copper impurities in the nickel at the same time. From measurements of the Hall constant at various temperatures of a sample saturated with Ni at 800 we calculated the position of the Ni acceptor level in the forbidden band. We found over the range of 170 to 250 "K a consistent value of 0·23 eV for the distance between the level and the valence band. This result is in good agreement with the value of 0·25 to 0·30 eV given by Burton 1). Assuming each Ni atom to give one acceptor level, we can evaluate the concentration of Ni atoms from resistivity measurements. Results of the saturation concentration Cs at various temperatures are given in

oe.

oe

table I. TABLE I Heating time (hours)

Temperature

(0C)

Cs

(at.jcm'') ,

22 18 7 3 2·5 2 2

700 750 800 850 875 900 920 Fig. 1 shows a plot of log is linear corresponding to

Cs

2.4.1014 7·6 16·0 36·8 43·9 47·5 46·4

versus liT. From 700 up to 850

(CS)Ni = 1.9.1023 exp (-

39500) RT at·/cm3

oe the

(RT in cal).

I I

i

graph

(1)

I

SOLID SOLUBILITY

AL'ID DIFFUSION

OF NICKEL

IN

GERJlIANIUl\[

227

Above 850°C the curve bends; at about 900 °C the solubility decreases rapidly showing a retrograde character. On the basis of quantitative thermodynamical considerations Meijering 8) has pointed out that when the solid solubility is very low compared with that in the liquid a retrograde solidus curve is normally expected.

920 1016940 900 875 850

800

750

at/cm3 (CSJNi

1

1014k-----;!;,----;b:,---;b;-----;;~-;!:;__+.----;&-__;:!;;;____.k;;;___.i:;:;~ 82 84 86 88 90 92 94 96 98 TOO T02 __

---I ..

JJt

TOl. 80296

T

Fig. 1. Plot of log (C.)Ni versus lIT. The rectilinear part of the curve can he represented hy equation (1).

2. Distribution coefficient (k) Recently Thurmond and Struthers 3) reported on alloys of Ge and of Si. They found the logarithm of the experimentally measured distribution coefficient k of Sb in Ge, Cu in Ge, and Cu in Si to be a linear function of the reciprocal of the absolute temperature:

A

logk = B--.

T

Values of k at the melting points

(2)

(T{) of Si and of Ge are obtained

F.

228 . by extrapolation.

VIDl

dor JlfAESEN

and

J. A. BRENKlIIAN

The solidus curves of these binary alloys show also a

retrograde character. Considering. the properties of a liquid solution in equilibrium with a dilute solid solution Thurmond and Struthers obtained the following thermodynamical

expression:

I k n

=

LlH{ RT

TH: +

(J -

LlS{ R

+

In

I

(3)

Y2'

where LlH{ is the heat of fusion and LlS{ the entropy of fusion of the pure solute (both at the melting point of the pure solute), Cf an extra positive entropy term occurring in the differential entropy of the solid solution, and Y~ the activity coefficient of the solute in the liquid phase, equal to 1 for an ideal liquid solution. Comparing (2) with (3) A and B can be related to thermodynamical properties. The differential heat of solution of the solute (LlH~) can be written as

LlH:

=

LlH{

+ 2·303 RA .

(4)

We will apply the above considerations also to the Ge-Ni system. The atomic fraction of Ni in the liquid solution (xl) at a certain temperature can he determined from the phase diagram, and the atomic fraction of ' Ni in the solid solution (xs) from Cs at the same temperature. The phase diagram Ge-Ni has a eutecticum at 775°C; so the distribution coefficient can be calculated only above this temperature. The results are given in table II and fig. 2. TABLE II Temp

(0C) 800 850 875 900 920

xs (at. fr.) 3.5.10-8 8·1 9·6 10·4 10·2

Xl

k

(at. fr.)

(= xslxl)

3.4.10-1

0.10.10-6

2·4 1·9 1·3 0·75

0·33 0·52 0·84 1·36

The plot of log k versus liT gives a straight line which can be represented by 11250 log k = 3·52 - -_.

T

SOLID SOLUBILITY

AND DIFFUSION

OF NICKEL

IN GERMANIUM

229

to T{ i. 1209 "K 5) gives the distribution coefficient 1.8.10-6• Measurements by Burton a.o. 6) with radioactive nickel give a distrihution coefficient k" = 5.10-6 in reasonable agreement

Extrapolation

k*

=

(Ni63) with our experiments. . With LJH[ = 4·2 kcaljmole for Ni 7) and A = 11250 we find, using equation (4) for the differential heat of solution of Ni, that LJH: =

55·6 kcal/mole. 920

900

875

850

k

1