Lattice distortion energy spectra of thin evaporated silver films

Thin Solid Films, 139 (1986) 33-40

33

ELECTRONICS AND OPTICS

LATTICE DISTORTION SILVER FILMS D. SCHUMACHER

SPECTRA

OF THIN

EVAPORATED

AND D. STARK

Institut fir Angewandte (Received

ENERGY

Physik,

Universitdt DtisseldorJ

August 9, 1985; accepted

November

UniversitiitsstraJe

I, 4000 Dtisseldorf I (F. R.G.)

26, 1985)

Thin silver films (thickness, 12.5160nm) were evaporated under ultrahigh vacuum conditions onto clean glass substrates (substrate temperature, 225 K). During the growth process a large number of lattice defects were incorporated (condensation rate, 0.2 and 0.01 nm s-i). The films were subjected to heat treatment (constant heating rate, 0.1 K s-i) and the variation in the electrical resistance was measured as a function of temperature. Using Vand’s theory the initial lattice distortion energy spectra of the films were determined from the resistancetemperature data. The lattice distortion energy function has maximum values. While the number of distortions with a decay energy of about 0.8 eV increases rapidly with decreasing film thickness, the number of distortions with a decay energy of about 0.93 eV varies only slightly.

1. INTRODUCTION

Vacuum-deposited metal films show a high electrical resistivity compared with that of the bulk. Apart from size effects this is caused by the large number of defects in the films frozen in during the condensation process. Following Vand’s ideas it can be explained that the initial electrical resistance of metal films decreases irreversibly during annealing, owing to the removal of lattice distortions formed of interstitials and vacancies close to one another’. For the removal of each of these so-called combined-type3 defects only a low activation energy is necessary. The energy E required for the decay of such a distortion can vary from zero to the value of the activation energy of self-diffusion. One can imagine these distortions as small “clusters” of n atoms with an approximately regular lattice arrangement relative to each other, but the whole “cluster” is tilted with respect to the surrounding lattice. (1) The number of atoms forming such a distortion is not a constant one but may reach values of about several tens. (2) For a given number of atoms forming the distortion more than one arrangement is possible. Therefore there cannot exist only one decay energy of all distortions but a “spectrum”. Several studies have been made during recent years?14. With only a 0040-6090/86/$3.50

0 Elsevier Sequoia/Printed

in The Netherlands

I).

34

SC’HUMAC’HER,

D. STARK

few exceptions the films were evaporated under insufficient vacuum conditions. However, the influence of residual gas cannot be neglected. The film resistance can be influenced by adsorption and desorption as well as by incorporation and degassing of residual gas molecules during the evaporation and the subsequent heating and cooling cycle. Therefore ultrahigh vacuum conditions are absolutely essential. We have studied the size dependence of the *‘initial lattice distortion spectra” of thin evaporated silver films. _. 7

EXPERIMENTAL

DETAILS

Thin silver films were evaporated onto clean glass substrates held at 225 K under ultrahigh vacuum conditions (5 x 10 lo mbar) at different deposition rates (0.2 and 0.01 nm s I). The film thickness, controlled with a quartz crystal thickness monitor, was varied between 12.5 and 160 nm. The specimen temperature was determined by means of an (Au/Fe)-chrome1 thermocouple. The heating and resistance measurements were carried out without breaking the vacuum after the deposition of the films. The residual gas pressure during the annealing and cooling cycle was lower than 1 x lo- ‘” mbar to exclude resistance changes caused by gas adsorption. The films were heated at a constant heating rate of 0.1 K s ’ up to a maximum temperature of about 350 K. The annealing process was stopped as soon as the film resistance reached a minimum. Above this temperature the films start to burst. The resistance was continuously measured using a four-terminal arrangement. The application of the lock-in technique (a.c. frequency, 1 kHz) for the current and voltage measurement eliminates thermovoltages and provides a high signal-tonoise ratio. The latter was necessary because the R(T) characteristics had to be differentiated for the further evaluation. 3.

RESULTS

AND DISCUSSION

Silver films were prepared by evaporation, two different evaporation rates and various film thicknesses being chosen. During the subsequent annealing and cooling cycle the film resistance was measured continuously as a function of the specimen temperature. Figure 1 shows a resistivity cersus temperature plot for a silver film 15 nm thick (evaporation rate, 0.2 nm s ‘). It is characteristic of most metals. The resistivity decreases with increasing temperature, as the defect density diminishes. The defects, which act as scattering centres for the conduction electrons, are annealed. The resistivity does not decrease uniformly but the plot possesses a weak structure, which contains some information about the initial structure of the evaporated film. During the cooling cycle the resistivity decreases uniformly with decreasing temperature, owing to the contribution of the phonons. No irreversible change in resistivity during a second or further heating and cooling cycle can be observed. This means that the defect density remains constant below the maximum temperature reached in the first cycle. Following Vand’s theory, we consider that the part of the resistivity pi caused by the lattice defects can be expressed as follows’: +I pi = r(E)&‘(E) dE (1) I ,

LATTICE

DISTORTION

ENERGY SPECTRA

OF EVAPORATED

Ag FILMS

Fig. I. Resistivity vs. temperature plot for a silver film (evaporation temperature during evaporation, 225 K): -, first heating cycle; -. -, cycle.

35

rate, 0.2nms-‘; substrate cooling and second heating

where N(E) dE is the number of distortions per unit volume that have decay energies between E and E + dE and r(E) is the contribution to the resistivity caused by one distortion with decay energy E per unit volume. The function F,(E), defined as F,,(E): = r(E)&(E)

(2)

is called the initial lattice distortion given by

The decay energy can be calculated

energy spectrum.

According

to Vand F,(E) is

from the temperature:

E = ukT where k is the Boltzmann

constant

and U and u are related by

u =$;+ and can be determined

by solving the equationI

(6)

D. SCHUMACHER.

36

D. STARK

Here a is the heating rate, f the Debye cut-off frequency and n the estimated number of atoms forming a single distortion. In eqn. (3) dp,/dT can be calculated from the resistance characteristic. The resistivity is composed of two parts (Matthiessen’s rule): P = Pi + Pr

(7)

where pr is caused by scattering on phonons distortions and impurities, Differentiating temperature T gives

dp ---~

dpi

dT

dT+dT dp,ldT

2.

dP= be

and pi is caused by scattering at lattice this equation with respect to the

LATTICE

DISTORTION

ENERGY

SPECTRA

OF EVAPORATED

Ag FILMS

37

0

0. 7

Cl. 8

0. 9

1. 0 s” 1. 1

i Fig. 3. Lattice distortion

0. 7

I). 8

energy spectra of thin evaporated

0. 9

silver films (evaporation rate, 0.2 nm s- I),

1. 0 a’4 1. 1

E

Fig. 4. Lattice distortion

energy spectra of thin evaporated

silver films (evaporation

rate, 0.01 nm s-l).

Distortions of type B predominate at a film thickness of 20 nm (Table I and Fig. 6). The decay energy amounts to 0.93 eV. For higher as well as for lower film thicknesses the number of these distortions decreases, whereas the corresponding decay energy increases slightly. The number of these distortions can be reduced by choosing a lower evaporation rate in the case of film thicknesses higher than 20 nm (see Fig. 6).

I>. SCHUMACHER.

38 TABLE

Il. STARK

I

VAKlATlOh

IS

Em,,

AND

F,,(t,,,

) AS bX!N(‘TIOYS

Of

THk I-IL%, THIC’KNtSb

,I

E “la” A

L‘rnllX ”

F,,( c 111114 1

(nm)

tew

(eV)

(PQcmeV

C‘rdlvWrlorl

rtllf’, 0.2 ?I!??\

F,,( E “l&(XH J

‘1

(@cmeV

’

12.5

0.78 f 2”,,

IS

0.x0

O.YY + ?,,

21.x

5.6

17.5

0.x I

0.Y6

I 6. I

x3

20

0.79

0.Y.J

5.0

1.x

60

0.x0

0.93

2.9

Il.6

X0

0.80

O.Y4

I.5

I

0.82

O.Yh

0.x

I60 C‘~~rlrl~~rl.\cJr/on

r(II<‘, 0.01

,I,?1 ,

‘1

37.5 + lo”,,

Ok lo”,,

I .o 41

’

IS

0.84 * 2”,,

I .(X) * 2”,,

x.0 z IO’,,

‘0

0.84

0.97

5.5

I I.0

40

0.84

0.93

3.5

IO.5

80

0.84

0.96

I.5

7Y

I 60

0.84

O.YX

0.x

6. I

Y.5 f lo”,,

f m

Fig. 0.0.2

5. Variation

in F,,(E,,,)

with

lilm thickness

t

for

type

A distortions

and two evaporatton

rates:

nm b ’ : +.O.Ol nm b ‘.

The thickness dependence of both types of lattice defects can be explained in a two-layer model of the films. The films were evaporated onto glass substrates. Their roughness and the residual impurities influence about the first IO nm of each film. Hence this part of the film has a different structure and consequently a different defect structure from those of the rest of the film. Type A distortions exist only in the lower layer and type B distortions appear only in the upper layer. In addition, the density of the latter may fall slightly with increasing film thickness. This rough model of the film composition shows why the density of type A distortions increases rapidly with decreasing film thickness, whereas the density of type B defects decreases to

LATTICE

DISTORTION

ENERGY SPECTRA

OF EVAPORATED

39

Ag FILMS

o-

Fig. 6. Variation in F,(E,,,) 0.2nms.-‘; O,O.Ol rims-‘.

with film thickness

for type B distortions

and two evaporation

rates: 0,

zero. The defect density in the small lower layer does not depend on the condensation rate, because these defects are caused by the substrate. In most size effect theories the assumption is made that the films have a homogeneous structure which does not depend on the film thickness. This investigation shows that the structure of as-grown silver films can clearly be inhomogeneous. 4. CONCLUSION Thin silver films were prepared by evaporation onto glass substrates. During a subsequent annealing and cooling cycle the film resistivity was measured as a function of temperature. Using Vand’s theory the initial lattice distortion energy spectra of the films were calculated from the resistance-temperature data. These spectra show that the films contain at least two different types of defects which were annealed in the temperature range between 225 and 350 K. There exist different and very inhomogeneous distributions of both sorts of defects in the films. The structure of these as-grown films depends clearly on the film thickness. ACKNOWLEDGMENT

We should like to thank Professor

Dr. J. Kranz for the provision

REFERENCES

I V. Vand, Proc. Phys. Ser., London, 55 (1943) 222. 2 3 4 5 6

P. G. Wilkinson and L. S. Birks, J. Appl. Phys., 20 (1949) 1168. P. G. Wilkinson, J. Appl. Phys., 22 (1951) 419. V. Damodara Das and M. S. Jagadeesh, Thin Solid Films, 24 (1974) 203. V. Damodara Das and M. S.Jagadeesh, J. Phys. Chem. Solid.v, 38 (1977) 167. L. Olumekor and J. Beynon, Thin SolidFilms, 53 (1978) L13.

of means.

40

7

D. SCHUMACHER.

M. Radhakrishnan and C. Balasubramaman, Phy.s. S/rr/u.r Solidi A. 48 ( 1978) M. Radhakrishnan and C. Balasubramanian, PhJ.\. .S/uru.c Solidi .4.56 (1979) 195. S. K. Saha and P. C. Mahanta. Indim J. Pure Appl. Ph~x., 18 (1980) 159. K. Narayandas, M. Radhakrishnan and C. Balasubramanian. Thin Solid Film. 67 ( 1980) 357. S.K. Saha, In&n J. Purr Appl. Phys.. IY (I 98 I ) I I I. V. Damodara Das and A. S. Talawat, Thin Solid Films. HI ( 198 I ) 21. A. R. Patel. N. C. Pandya. N. C. Chourasia and G. K. Shivakumar. PIr~.v. Srrrtu.t Solrdr A, 71 (1982) K. Narayandas,

8 K. Narayandas, 9 IO II I2

13

.lL.>.

14

D. STARK

P. Renucci,

15 V. Damodara

L. Gaudart. J. P. Petrakian and D. Roux, 73~1 SolidFilms, Das. J. Appl. PhJ.v.. 5.5 (1984) 1023.

123 (19X5) 2X I