From localization to superconductivity in granular niobium nitride thin films

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From localization to superconductivity in granular niobium nitride thin films

R. Cabanel, J. Chaussy, J. Mazuer, J.C. Villegier

To cite this version:

R. Cabanel, J. Chaussy, J. Mazuer, J.C. Villegier. From localization to superconductiv- ity in granular niobium nitride thin films. Journal de Physique, 1988, 49 (5), pp.795-802.

�10.1051/jphys:01988004905079500�. �jpa-00210756�

From localization to superconductivity ⁱⁿ granular niobium nitride thin films (*)

R. Cabanel (**), ^J. Chaussy, J. Mazuer and J. C. Villegier (1)

Centre de Recherches sur les Très Basses Températures, C.N.R.S., ^{BP 166} X, 38042 Grenoble Cedex, ^France (1) LETI, C.E.N.G., ^BP 85, 38041 Grenoble Cedex, ^France

(Requ le 3 décembre 1987, accepté ^{le 26} janvier 1988)

Résumé.

Nous avons étudié entre 1 et 300 K les variations de la résistivité de films de nitrure de niobium

préparés par pulvérisation cathodique réactive. En travaillant à des pressions d’azote de plus ^en plus élevées,

on augmente la concentration d’azote dans les couches qui deviennent de plus ^en plus poreuses. Ceci favorise leur oxydation ultérieure à l’ambiante. La concentration d’oxygène s’est révélée jouer ^{un rôle} primordial ^{sur la}

résistivité _p. Des séries d’échantillons ont ainsi été obtenues avec des résistivités à l’ambiante variant de 14 03A9.cm à 1 m03A9.cm. Les caractéristiques ^p (T) ^évoluent régulièrement depuis ^un comportement ^du type ^de celui observé dans des semiconducteurs désordonnés jusqu’à celui du NbN supraconducteur classique. ^Les

échantillons sont très hétérogènes, ^{avec une} large distribution des barrières d’énergie ^{entre les} grains

conducteurs. Dans les échantillons de haute résistivité, la conduction a lieu par ^sauts activés thermiquement ^et Ln p ^{~ T- n avec} 1/2 ~ n ~1/4. Pour les couches moins résistives, ^{un chemin} conducteur s’établit par

percolation ^{à travers les} barrières les plus ^{basses et} dès que T est supérieur ^{à une} certaine valeur critique T*, la conductivité devient linéaire en T. Il peut ^alors apparaître ^une transition supraconductrice ^{même sur des}

films dont le comportement à l’état normal est nettement du type semiconducteur. La plus haute résistivité observée avant transition a été de 60 m03A9.cm pour ^une résistivité à l’ambiante de 1 m03A9.cm, soit un rapport ^de 60. L’application ^d’un champ magnétique réglable de 0 à 4 T provoque la décroissance de la température critique selon la même loi linéaire que celle observée ^sur des supraconducteurs ^de type ^II homogènes.

Abstract.

The variations with temperature ^{T of the} resistivities of reactively sputtered ^NbN films have been studied from 1 to 300 K. The nitrogen concentration in the films has been increased by using higher ^and higher nitrogen ^pressures during sputtering. ^The porosity of the films is also increased and this favours their post oxidation at ambient atmosphere. The oxygen concentration in the films revealed ^to play a prime part ^{on the} resistivities _p. Series of samples ^{were obtained with room} temperature resistivities from 14 03A9.cm to 1 m03A9.cm.

The resistivity variations with T regularly evolve from a disordered semiconductor like behaviour to the bad metal behaviour of the classical superconducting ^{NbN. The} samples ^are highly inhomogeneous ^{with a wide}

distribution of the energy barriers between conducting grains. ^{In the} high resistivity samples, thermally

activated hopping ^is present ^{and Ln} p ^~ T-n with 1/2~ n ~1/4. In the less resistive samples, ^a percolating path is established through the lowest barriers and beyond ^{some critical} temperature ^{T* the} conductivity

becomes linear in T. A superconducting transition may then appear which could be observed ^{even on} samples

whose behaviour is markedly of the semiconductor type in the normal state. The highest resistivity ^before

transition was 60 m03A9.cm. This corresponds ^{to a} resistivity ratio of 60 with respect ^{to the value at room} temperature. Application ^{of a} magnetic ^{field up to 4 T} decreases the critical temperature ^{in the same} way ^as for

a homogeneous dirty type ^II superconductor.

Classification Physics ^Abstracts

73.60 - 74.70D - 81.15C

Introduction.

Niobium nitride studies extensively grew during ^the past twenty years, in close connection with the

development ^{of new} methods for thin-film depo-

sition. Among ^these methods, ^reactive sputtering

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01988004905079500

796

certainly ^{was the most} successful for NbN [1]. ^Initial

interest at that time was the high ^critical properties

of the superconducting (SC) ^5-NbN phase. ^{Values of} tc

^{15 K,} Bc2

^{20 T and} Jc

101° A. m-2 are now

currently achieved for the critical temperature ^field

at 4.2 K and current density ^at 4.2 K and 10 T [2]

respectively. Although ^{research to} improve ^these properties ^{is still} running [3, 4], ^{current studies are}

rather directed to the possible ^use of NbN films for

Josephson junctions ^based integrated ^circuits [5-7].

Superconducting properties actually ^are greatly ^con-

nected with the crystallographic structure, compo- sition and sputtering parameters of the films [8, 9].

For example, ^the highest ^critical temperatures ^are obtained on the 8-NbN phase, ^and superconductivity disappears as soon as the ratio [N ]/ [Nb ] ^{of the} nitrogen ^to the niobium atoms in the film reaches 1.5. At the same time, resistivity ^{at ambient} tempera-

ture drastically ^increases [8].

Much less attention has been paid ^{to the normal} phase ^{and to the} non-superconducting ^{films of}

niobium nitrides. Available results ^are concerning

either high ^ambient resistivity samples ^{with an} amorphous ^structure [10] ^or studies of the variations with temperature ^{of the} resistivity from ambient down to the SC transition [11]. ^{In both cases,} samples ^{exhibit a} semiconductor-like behaviour. A strong correlation has been found between the decrease of the critical temperature and the increase of the absolute value of the temperature coefficient of resistivity (TCR) which increases with the nitrogen

concentration in the reactive gas mixture in the

sputtering ^chamber [11]. ^These transport properties

have been proved ^to be reminiscent of a typical ^class

of materials, the so-called granular ^{films, which are}

mixtures of metal and insulators.

Granular films have been recognized ^{for some}

years ^as very convenient materials ^to study ^{the metal}

insulator transition (MIT) [12]. ^{Moreover, when the}

metal is ^a superconductor, ^an additional problem arises, i.e. the effect of localization on superconduc- tivity [13]. Interest of NbN as such a granular system then appears, inasmuch as it is possible ^to regularly modify ^the composition ^{of the films, so that} they

may regularly evolve between semi-metallic SC films and high resistivity films with a hopping type ^conduc- tivity. ^{It is to be} noted that these two limits only ^have

been studied up ^{to now.}

We report ^{below a} part of the work that we have undertaken to extend information on the transport properties of the NbN system [14]. ^{First we} briefly

describe our sputtering apparatus ^and analyse ^the

standard parameters ^{of the film} deposition. ^The

main parts played by ^{the structure and} post-oxi-

dation at ambient atmosphere of the films on their electronic properties ^{are then} emphasized. ^{We ob-}

tained a variety ^of samples ^{whose room} temperature resistivities (p RT ) lie between less than 1 mfLcm up

to p RT > 14 n. cm. The variations with the tempera-

ture of the resistivities are discussed in the frame of various hopping models. The last paragraph ^is specifically ^{devoted to the more} conducting ^{films for}

which a SC transition is appearing ^{even in a} highly semiconducting sample ⁱⁿ the normal state. The ratio reaches 60 between the low temperature peak resistivity ^{and that at room} temperature ; ^this is, ^to

our knowledge, ^the highest reported ^{value for a} granular ^film.

Film deposition and characterization.

The films were produced by reactive d.c. magnetron sputtering. ^The apparatus ^was specially designed ^at

the Centre de Recherches sur les Tres Basses

Temperatures, ^{in order to ensure a} close control of the sputtering parameters. ^{Since our aim was to} increase the nitrogen concentration, ^{we used a} pure

nitrogen atmosphere instead of a mixture of nitrogen

and argon ^as is usual in depositing the classical SC NbN’s [9, 15]. ^{As a} result, ^we avoid any pollution

of films by argon. We have prepared ^a variety ^of

NbN films whose thicknesses vary between 0.45 and 2.6 _fJ-m.

Details of the sputtering process and the prelimi-

nary characterization of the films ^are available in

previous papers [16, 17]. ^{A more extensive} report ^of the correlation between sputtering parameters, composition ^and resistivity of the films is in progress and will be published ^elsewhere [18]. We summarize below the typical sputtering conditions and our main conclusions.

For the room temperature resistivity p RT ^to be varied between the above mentioned limits, nitrogen

pressure has ^to be monitored from 1 to 10 Pa. The magnetron power density ranged between 8.5 to

28 W. cm-2 for a niobium target ^{6 cm in diameter.}

X-ray diffraction patterns ^showed i) the existence on

all samples ^{of a} rather well crystallized &NbN phase

and ii) ^a large ^diffusion peak typical ^{of an} amorphous

second phase. The columnar structure of the film

appeared ^on SEM and TEM photographs. ^{100 to}

200 nm in diameter columns are formed of grains

which stack to design cauliflowers. From the width of X-ray diffraction peak, ^the grain ^{diameters are}

found to be between 4 to 10 nm.

Diffraction patterns of transmitted electrons con-

firm that the small 8-NbN crystallites ^{are oriented}

with the [002] ^axis perpendicular ^to the substrate.

Careful analyses ^were performed ^{on four} samples

selected to overlap ^{the full} resistivity range. Results

are given in table I. Techniques of Rutherford Back

Scattering (RBS), ^{Nuclear Reactions} (NR) ^and Secondary ^{Ion Mass} Spectroscopy (SIMS) ^{were used}

to determine the atomic concentrations of niobium, nitrogen, carbon and oxygen in the films. A ^com-

parative study of the oxidation by ^{means of} Auger

Table I.

Sample characteristics.

electron spectroscopy [18, 19] ^{lead us to the con-}

clusion that oxygen concentration resulted from ^a

post-oxidation ^{at ambient} atmosphere ^of initially highly porous films. This concentration appeared ^to play a ^main part in both the TCR and the room

temperature resistivity which both increase almost

exponentially with the ratio [0]/[N] of the oxygen and nitrogen atomic concentrations.

To summarize, ^the studies of structure and compo- sition lead us to the conclusion that our granular

NbN films are made of metallic grains of the 5-NbN

phase embedded in an amorphous insulating phase.

For the most resistive samples, ^{this second} phase

most probably ^is amorphous Nb205 ^{so that the} general ^{formula must} be written in the form

NbN,,Oy. For the less resistive films, ^the amorphous phase is rather an inhomogeneous mixture of niobium and nitrogen ^{atoms and voids.}

Temperature variations of resistivities.

We have studied the variations of the resistivity ^{of a}

number of samples ^{from room} temperature ^{down to} 1 K. For films exhibiting high resistivities (p RT --

70 mO. cm) ^{we could not} explore ^{the whole} tempera-

ture range due ^to the off-limit values of the resist-

ances. Figure ^{1 shows a} logarithmic plot ^{of the} resistivity ^ratio p(T)/pRT ^{versus T-14 for some}

Fig. ^1.

Electrical resistivities of samples ^{A to F nor-}

malized with respect ^to their values at room temperature

versus T- 1/4. The lines. -. -. are used to separate approximately ^three regions where the conductivity ^ex-

hibits different behaviours.

samples illustrating ^{the three} typical behaviours that

we may distinguish ^{for our films :}

. when p RT > 10 mQ , cm, the conductivity cr ^{is of}

thermally ^activated hopping type (Region 1) ;

798

2022 when PRT’" 3 mO. cm, ^{we will see} that cr is linear versus T over a quite wide range of tempera-

ture (Region II) ;

2022 when P RT - 1 ^{mfL cm, a} SC transition occurs at T > 1 K (Region III).

All samples ^{exhibit a} negative temperature ^coef- ficient of resistivity ^TCR

(1/p ) (dp /dT) ^between

1 and 300 K. Therefore, ^{when we refer to Ander-}

son’s criterium [21] ^{for the} MIT, ^{all films are on the} insulating ^{side. In} agreement ^{with this} classification,

the low temperature conductivity ^is always ^lower

than the Mott minimum metallic conductivity [22]

(T mio ^~ 0.025 e2/ha ^{leading to P max}

^{if mio ~}

6 mfL cm for a lattice parameter a

⁴ A.

1. HOPPING CONDUCTIVITY (REGION I).

^{All the}

curves in region I exhibit over some range from the lowest temperature ^a linear variation versus T- 1/4 in the logarithmic plot ^of figure ^{1. The} temperature dependences ^are accounted for by ^{the now classical}

Mott law [22] of variable range hopping a = A T- 1/2 _{exp -} (ToIT)n. ⁿ depends ^on the dimen-

sionality ^D of the film n

1/4 at 3D and 1/3 at 2D.

Mott’s analysis ^is referring ^{to a} disordered homo- geneous medium with localized electrons. A ^more convenient representation ^of granular ^metals might

be that of the model of Ambegoakar, Halperin ^and

Langer (AHL) [23]. Here the medium is viewed as a

resistance network where regions ^of high conductivi- ty ^{are connected} by ^less conductive resistors through

which electrons are able to move by phonon ^assisted tunneling. ^{The same} T- 1/4 law is obtained as in Mott’s analysis. ^{It is to} be noted that both models consider a constant density ^{of states} N (E) ^{at the}

Fermi level EF ^and neglect electron interactions.

When Coulomb interactions between electrons

are considered, it has been shown that N (EF)

decreases and the conductivity ^{becomes oc} exp -

(Tol T)1/2 [24]. ^{The value n}

1/2 has been previously reported for NbN films [10]. ^{In order to} distinguish

between the various values for _n, we attempt ^{a more} detailed analysis ^{of our results} by plotting

Ln _p (T) / P RT ^{as a} function of T - n with n = 1/2, 1/3

and 1/4 (Fig. 2). ^{For the} specimens with p RT ~

10 mil. cm, ^{the best fit} clearly is obtained when

n

1/4, but the linear variation is limited within 2.5 and 35 K (Fig. 2a). ^{For the} highest resistivity samples (Fig. 2c, d) the differences is not striking ^{at all. The} temperature range investigated ^{is too narrow to}

allow for a final choice. Nevertheless, n ^{seems to}

evolve from 1/4 for P RT ’" 10 mO. cm ^{to 1/2 for} P RT :> 10 O. cm. ^{Such an} evolution has been pre-

viously reported ^for granular ^Al [25] ^{where a linear}

variation versus T- 1/2 could be observed over more

Fig. ^2.

Electrical resistivities of samples ^from region ^{I versus} T-n with n

1/2, 3/7, 1/3, 1/4. Different scales are used

from a) ^to d).

than two decades of temperature. It is also typical ^of

the cermets films [1].

From 1/4 to 1/2, n crosses over the value 1/3 which

unambiguously appears ^as the best fit for specimens

with _{p RT ~} 100 mn. cm (Fig. 2b). ^{In terms of Mott’s}

model this would correspond ^{to a 2D} hopping conductivity. ^{Such an} interpretation ^is quite ^unrealis-

tic for our sample whose thickness is - 700 nm. An

explanation ^{can be found} through ^a phenomenologi-

cal approach which takes into account a possible

variation of N (E) ^{at the} Fermi level. Pollak, by using percolation theory [26] ^{and E. M. Hamilton,} by extending ^the original Mott calculation [27] ^both proved independently that, ^{when the} density ^of

states is a power function of energy E ^near the Fermi level

then results for the 3D-conductivity u

No and p being ^{some constants.}

When we apply this model to our results, ^{we are}

led to the conclusion that an increase of the volumic fraction of the amorphous phase ^{in our} films induces the break and broadening ^{of a} potential ^{wall for the}

conduction electrons at the Fermi level. So when p

goes from 0 ^to 1/2 and up ^to 2, ^{then n takes the}

values 1/4, 1/3 ^{and 1/2} respectively and p RT increases from - 10 tao - 102 and - 104 mn. cm.

A new model has been recently proposed ^which

considers the fractal feature of the medium [28]. ^The

authors deduce a value n

3/7 i. e. not very different from 1/2 for samples ^{near the} percolation ^threshold

where states are strongly localized. This could be the

case of our specimens ^with p RT > 75 mfY. cm. From table I we are able to calculate the metallic concen-

tration in sample ^B (p RT

^{75 mQ .} cm) ^under rough hypothesis for the metal insulator arrangement ⁱⁿ the film : we assume the metal to be NbN and the insulator Nb205. ^{We find a NbN ratio} equal ^{to 20 %,}

which is not so far from the geometrical ^critical percolation threshold pc

15 % [13]. In the range of

applicability ^{of this} model, To - d-3 ^is composition independent (d ^{is the} grain diameter). ^{We have} previously pointed ^{out the} difficulty ^{to conclude for}

n. Yet we may ^{use our} experiments ^{to determine} To by ^means of least squares fits. Applying ^this

method to several samples having + 5 mn. cm - P RT 14 000 mn. cm leads to a regular increase of

To ^from 104 K to 2.55 x 104 K when n = 1/2. With

n

3/7, ^{the same} calculations give higher ^{but still}

realistic values : 3.25 x 104 K To M ^{9.25 x} 104 ^K.

Following To - d- 3 ^{this means that the} grain ^diame-

ter regularly decreases when the metallic NbN ratio decreases. The reduction coefficient does not fall below 0.7, ^{which seems} quite acceptable.

2. CONDUCTIVITIES WITH LINEAR DEPENDENCE ver- sus TEMPERATURE (REGION II).

^{When the am-}

bient resistivity lies between 1 and 10 mQ.cm the

logarithmic plot ^of figure ^{1 is no} longer ^{useful and}

we rather have to discuss our result by plotting ^the conductivity ^{ratio versus} temperature ^{in linear} scales,

as shown for two samples ⁱⁿ figure 3. A critical temperature ^{T* can} then be defined above which the temperature variation of a can be written :

Fig. ^3.

Electrical conductivity ^of samples ^{E and F}

normalized with respect ^to their values at room tempera-

ture versus T.

We observed this behaviour on several samples

with _{p RT ~} 3 mO. cm. T* ranged ^{from 10 to 80} K,

the constant u was either positive ^or negative ^and

the coefficient b varied between 1 and 4

(0. cm) - K-1, depending ^{on the} sample. ^{Such a}

linear variation has been previously reported ^for

GeAu granular ^films [29]. ^AHL [23] ^have suggested

that a conductivity proportional ^{to T} might ^follow

from their analysis when, in the resistance network,

a small number of high conductivity regions ^exist

which are randomly ^connected through ^{the whole}

film length. ^We expect ^{the film to be} highly ^in- homogeneous. ^{In our case, T* could be} interpreted

as the temperature ^{at which a} high conductivity path

is established throughout ^the sample by connecting

various conductive regions through small energy barriers of order kT*.

This interpretation emphasize ^the part played by

the barriers in our films. For low resistivity samples,

these barriers remain weak over the whole film.

When the ratio of the insulating phase increases,

some barriers become higher ^and begin ^{to live} apart

some high conductivity paths ; ^{there is a wide}

distribution of the barrier heights : this is the upper

linear conductivity regime.

800

When we go ^on increasing the insulator concen-

tration, ^{all the} high conductivity grains ^{are insulated}

from one another by large barriers and the hopping regime is reached.

At temperatures lower than T*, ^the slopes ^{of the}

or ( T) ^curves decrease and over a decade of tempera- ture, the conductivity is described by :

From the graphs ^of figure 4, ^for samples ^{E and} F, ^we deduced q

^0.86 and q

^0.75 respectively. Starting

Fig. ^4.

^The temperature dependent ^{term of} the conduc-

tivity ^of samples ^{E and F versus T.}

from the scaling theory of localization [30], Imry [31]

shows that inelastic scattering may govern the ^con-

ductivity when the inelastic mean free path lin ^is

greater ^{than some} localization length, ^{here the} grain

size. The mean time between inelastic events T;n increases when T goes down ^{to zero} like

T - 2 q, ^so that cr oc- 1 in oc T - 112 oc Tq. ^{’The value}

q

0.75 is typical of inelastic electron-electron interactions [32]. Such variations with some power of T for a (T ) ^{have been} reported ^{for NbN films} [33]

which exhibit q values of order 1.5 related to

electron-phonon interactions.

The values (Tõ ^{that we have} calculated for our

samples E and F are 380 mfl.cm and 175 mn.cm

respectively. ^{In the} scaling theory ^for localization in

a 3D system [30] the maximum metallic resistivity ^is proportional ^{to the} length scale of the sample. ^For granular metals this length is the metallic grain ^{size d}

rather than the lattice parameter of Mott’s model

[22]. Taking d - ⁵⁰ A for our films leads to p max ~ 40mn.cm. Thus samples E and F would be in- sulators at T

0 K, ^{and the} preceding analysis ^is by

no means pertinent. Actually ^{we have to} recall that

our films are highly inhomogeneous and the conduc-

tivity ^{can be} greater ^on preferential paths, ^{as em-} phasized ^above.

The superconducting samples.

For sample E, the decrease of the conductivity ^when

T is decreasing ^is sharply stopped ^at Tc ~ ^{2 K where}

a SC transition arises. We observed such a transition

at T > 1 K on almost all samples with p RT 1 mH.cm. Generally ^the resistivity slowly ^increased

from room temperature ^to liquid ^helium tempera- ture, ^{as shown in} figure ^{5 for} sample ^D. Sample ^E

was sputtered ^{under the same} conditions, ^{but it was}

further annealed at 350 °C and - 10-4 Pa for 12 h.

Fig. 5. - The variations versus temperature of the resis- tivities of samples ^{E and D. A} transition to a superconduct- ing ^{state occurs at} T, 1.5 K (sample D) ^and Tc ~

2 K (sample E).

The resulting resistivity behaviour is quite ^interest- ing : just ^before transition, ^{at 2.5} K, ^the resistivity

reaches 60 mfl.cm, ^the highest ^{value we} may observe

on these samples. ^It corresponds ^{to a ratio}

p (2.5 K)/ P300 ~ 60, ^{which is} greater, by ^{almost one}

order of magnitude, ^{than the} currently reported

results on granular ^materials [11, 34-36]. ^{The value}

60 mfl.cm is much larger than the critical resistivity

Pc

(h/e2) d ~ ^{3 mn. cm} associated with the grain

size d

7 ^nm for specimen ^{E. This means that this}

size is larger ^{than the critical} length dc ^{for which the} superconducting gap d ^is equal ^{to the} separation

between energy levels of ^a single grain ^{at Fermi}

energy :

For NbN, taking ^N (EF) - ^{1.4 x} 10" eV-1 cm-’ [37]

and 4 - 3 meV [6] ^{we find} de == ^{3 nm. Our} sample

then illustrates the large-grain ^{model of} Imry ^and Strongin [38] ^{where SC} may extend ^over the whole

film, ^even if the localization is governing the conduc- tion. The sharp transition at a well defined tempera-

ture Tc well below the critical temperature ^{of bulk} material would mean that the normal state resistivity

of the grains is very small compared ^to that of the

barriers between grains, ⁱⁿ agreement ^{with our}

conclusions on the microscopic ^{structure of the}

films. 7c ^{is the} temperature ^{at which the} Josephson coupling energy between ^a sufficient number of

grains ^over reach the energy barrier.

Our study of the variation of the upper critical field B,2 ^versus temperature ^near T, also confirms this idea (Fig. 6). Bc2(T) is linear in T as is the case

Fig. ^6.

Influence of an applied magnetic field from 0 to 3.67 T on the low temperature resistivity ^of sample ^{E. The}

insert shows the linear decrease of the upper critical field

Be2 ^{when T is increased.}

for ^a dirty type II SC. This behaviour has been

previously reported for NbN films [39] having

0.2 mil.cm _{p RT} 2.5 mQ . cm but with a resistivity

ratio which does not exceed 3. It disagrees ^{with what}

is generally observed in high resistivity granular

films made of a mixture of metal and insulator such

as InGe or PbGe [40]. ^{From the GLAG} theory ^the slope ^of Bc2(T) ^near Tc ^{for a} homogeneous dirty type ^{II SC is} proportional ^to the normal state resis-

tivity p,, and the electronic coefficient of the specific

heat _{y :}

The numerical factor is for a result in T. K-1 with _y in mJ . cm- 3 . K- 2 and p in >Q . cm. ^From the insert of

figure ^{6 we deduce} dBc2/dT == 5 T. K-1. Assuming

y

0.32 x 10- 3 mJ . cm- 3 . K- 2, ^as for bulk NbN

[39] ^we find Pn ^~ 350 _{um .} cm which is much lower than the film resistivity, ^as expected ^{from the} analysis just above, and which is physically accept- able as the resistivity of the NbN grains, compared

to the bulk resistivity of this material [39].

Conclusion.

By ensuring ^a close control of the sputtering par- ameters, ^we have been able to prepare series of NbN films with various nitrogen concentrations. Careful

analysis ^{of the structure and} composition of the films lead ^us to the conclusion that they always ^{are made}

of metallic grains of the ô-NbN phase separated by

an amorphous insulating phase. We have shown

that, ^{when the} nitrogen pressure in the sputtering

chamber is increased, ^the resulting ^films undergo

oxidation at ambient atmosphere. ^The fixed oxygen atoms play a prime part ⁱⁿ establishing ^the energy barriers for electrons between grains, ^{so that the}

room temperature resistivity of the films is well correlated to the ratio between oxygen and nitrogen

atoms. The variations with the temperature ^{of the} resistivities regularly ^{evolve from a} disordered semi- conductor-like behaviour to the bad-metal behaviour of the classical SC NbN. The samples ^are highly inhomogeneous ^{with a} wide distribution of the energy barriers between conducting grains. ^{In the}

less resistive samples, ^a percolating path ^{is estab-}

lished through the lowest barriers and beyond ^some

critical temperature ^{T* the} conductivity ^becomes

linear in T. For such samples, ^inelastic scattering ^can prevail ^{at low} temperatures. Increasing ^{the concen-}

tration of the &NbN phase in the films allows for a

semiconductor to superconductor transition to occur

at Tc by Josephson’s coupling ^of grains along ^a percolating path. ^{A value as} high ^as 60 has been observed between the low and room temperature resistivities of a previously annealed film. When a

magnetic ^{field is} applied, T, ^is depressed ^{in the same}

way ^as it would be for a homogeneous dirty type ^{II SC.} Finally, ^the granular ^NbN system ^has been shown to be very interesting ^{for the} study ^of

MIT at the same level as other metal insulator mixtures such as Al-Ge, ^{Pb-Ge or} Al-A1203, Sn-Sn02 which have been more widely ^studied.

Acknowledgments.

The authors wish to thank Dr. R. Rammal for

enlightening discussions and very fruitful ^comments

on the analysis of the results. The help of J. Geneste

during sample elaboration is gratefully ^acknow- ledged.

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