Novel elastic anomalies in ZrN films

~)

0038-1098/9255.00+.00 Pergamon Press Ltd

Solid State Communications, Vol. 83, No. 8, pp. 571-575, 1992. Printed in Great Britain.

NOVEL E L A S T I C A N O M A L I E S IN Zr-N FILMS M.Yoshizawa, H.Sugawara and Y.Nakamura Department of Metallurgy, Faculty of Engineering, Iwate University, Morioka 020, Japan N.Oki Basic Technology R&D Center, Kayaba Industry Co., Ltd., Sagamihara 228, Japan (received 22 April 1992 by T.Tsuzuki) Elastic anomalies have been observed as a function of temperature in Zr-N sputtered films. Both metallic and insulating samples show a broad minimum at high temperature. A remarkable elastic softening is found in the insulating sample at low temperature. The latter softening is characterized by T-I dependence above I K. Low temperature data below 2.5K are also fitted by IogT. The origin of the elastic anomalies is discussed from viewpoints of Two-Level System and electronic localization.

accompanied with the up-turn in resistance due to localization effect at low temperatures. This consequence does not accord with the fact that the up-turn due to localization in the resistivity would be a precursor of a metal-insulator transition. It is because the phase transition accompanies an elastic softening and an enhancement of ultrasonic attenuation near the transition point. This consideration has been theoretically investigated. First, Kotliar and Ramakrishnan showed a - ( ~ ) 1/2 for 3-dimensional weak localization, where ~ is the inelastic scattering time constant. 10 This term gives T-1/2, when xE varies as T-t. The effect of localization on ultrasonic attenuation has been modified for the cases with electron-electron interaction It and with many-valley transition in doped semiconductors 12 and for elastic constant 12. The theoretical works show that the above consideration is correct only for the case without interaction effect. The experimental check of the predictions seems very important, but the ultrasonic anomaly due to weak localization is so small 12 that the experiment is very difficult. Therefore we focus our attention on more strongly localized regime. In this work, we report a surface acoustic wave (SAW) measurements of the Zr-N sputtered films for the investigation of localized systems.

§I. I N T R O D U C T I O N Recently, Zr-N sputtered films have drawn attention as new type of thermometer, t They show an appropriate temperature dependence in resistivity, and a small magnetoresistance. 2 They are considered to have various features for the best candidate as an ideal thermometer such as very fast response time shorter than lgsec. 2 The electrical resistivity of Zr-N films as functions of temperature and magnetic field has been investigated so far. It has been reported that these interesting properties came mainly from electronic localization. 2-5 Zr-N sputtered films can be divided into two groups with a large and a small resistance ratio RR between at room and helium temperatures. 3 Especially, the samples with a large RR (hereafter abbreviated as the group 1) are very close to a metal-insulator transition. Some of the specimens in this group are expected to undergo the metalinsulator transition above 0K. 4 On the other hand, the specimens with a small RR (the group II) show rather moderate temperature dependence from room temperature down to 0.3K. 4,5 The ultrasonic method provides us with a powerful tool for the investigation on energy scheme in solids. The various types of energy-level systems have been intensively investigated so far. Energy level scheme due to Crystalline Electric Field effect, which is seen in rareearth and actinide compounds, has been determined by the ultrasonic methods. 6,7 Low-energy excitation in TwoLevel Systems (TLS) has been investigated by ultrasonics. 8 The band due to the itinerant electrons causes clear elastic anomalies, 7 and one can get various kinds of information on the band structure from the careful analysis of data. 9 An effect of localization on the longitudinal elastic wave is also interesting. First, we start with the Pippard's relation, that the ultrasonic attenuation is proportional to the electrical conductivity. It is known that the relation also holds various metallic systems including exotic metals such as heavy fermions. If the Pippard's relation holds in weakly localized systems, the ultrasonic attenuation a should increase with the decrease of resistivity at high temperatures, and decrease

§II. EXPERIMENTS Zr-N films are fabricated on the R-surface sapphire by the reactive rf sputter method with a mixed nitrogen and argon gas atmosphere. The sample B was fabricated at 200°C with 2.0mTorr nitrogen partial pressure, and the sample D at 200°C with 2.5reTort. The thickness of the films is about 270nm. The fabrication and precise properties of the films are reported elsewhere. 4,5 As shown in Fig.l, Inter-Digital-type Transducer (IDT) is fabricated on piezoelectric ZnO film, which is deposited on the sample to generate SAW. The thickness of the ZnO film is about 4gm. Ten finger pairs of IDT are made by the photolithographic technique. The room temperature resistance and the resistance 571

572

Vol. 83, No. 8

NOVEL ELASTIC A N O M A L I E S IN Zr-N FILMS Inter-Digital-type Transducer

o4 I

\

i

iltlllll i

L-l-1 Coaxial Cable

~

0 -0.2

-0.2

-0.4

-0.4

-0.6 I

~

9

-1.0 0

50

10

I

4

-1.2 300

250

!

I

l

I

Sample B

-

Sapphire

0 ~" ~

-10

"-" .~ -20 ,~ -30 -40 )

I

I

I

I

I

50

100

150

200

250

300

T(K) O. 1 m0

:o:if

-0.2

.

V,

-0.4

i 0 0 0

o: o SSaa m p l e I

m

0

t 0

~ ~

-0.5 06

i

-0105~ h m ~

0 -0.l

r~

200

the sample B and the sapphire substrate are shown as a function of temperature in Fig.3. The measurements are carried out with the frequency of I I5MHz. The propagating SAW evokes the circular displacement near the surface. The amount of displacement decreases exponentially as a function of the depth from the surface.

Experimental set-up.

,

150

Temperature dependence of relative SAW velocity of the sample B and sapphire substrate.

i

6

100

ZnO Film

ratio R R are 543[2 and 16 for the samples B, respectively, and 224f1 and 1.8 forD. The samples B and D belong to the groups I and II, respectively. The temperature dependence of the electrical conductivity ty of the samples B and D are shown in Fig.l. The sample D shows ~/T dependence in the conductivity in the wide temperature region between 25K and 250K. This would be a sign of 3-dimensional localization. Below 25K, the conductivity decreases as T0.2. On the other hand, the conductivity of the sample B shows T0.6-dependence above 4.2K. It would be considered that the sample B is either in a strongly localized regime or in an insulating side in whole temperature region, while the sample D shows a weak localization at high temperatures. The ultrasonic velocity change of the samples B and D were measured by a phase comparison method. The measurements are carried out in the temperature range above 0.3K. Sapphire substrate itself is also measured as reference. The relative changes in the sound velocity of

,,~

-0.8

BI

T(K) Fig.3

,

Sample

Sapphire Substrate

I

0.2

u

0

-1 .(~

Zr-N Film Sapphire Substrate

8

I

-0.8

l

Electrode

Fig. 1

i

Sapphire

-0.6

<1

Inter-Digital-type Transducer flnn nn

i

0.2! Film

J

m

40

1

D

50

T(K) 0

Fig.4 0

Fig.2

5

10 . f ~ ( K 1/2)

15

20

Electrical conductivity of the samples B and D is plotted as a function of ~/T. Line in the figure is expected from 3-dimensional weak localization.

Anomalous parts of relative SAW velocity of the samples (a) B and (b) D as a function of temperature. The contribution from the sapphire substrate is subtracted as a background. The insets in the figures are low temperature behaviors. A small minimum at IK that is clearly seen in the sample D is considered to be due to a superconducting transition of aluminium.

Vol. 83, No. 8

N O V E L ELASTIC ANOMALIES IN Zr-N FILMS

The penetration depth ;t of the S A W is calculated as number of SAW, co the measure angular frequency and v the bulk sound velocity. The penetration depth depends on the direction of the displacement. The values of ~ are 7.1 /.tm and 17 lam for the displacement components parallel to the propagation direction and normal to the surface, respectively, for 115 MHz at room temperature. Since the thickness of the Zr-N film is about 270nm, major part of SAW propagates in the sapphire substrate. Because we have no sound velocity data of bulk Zr-N, we cannot estimate the penetration depth of the Zr-N film on the sapphire. However, there would be no large difference in among the sapphire substrate and the samples B and D,

1

2rc(q2-o92/v2)-1/2, where q is the wave

because Zr-N films are very thin compared with A. In the phase comparison method used here, the wave number q is not affected by the SAW velocity change. Since the change of the measure frequency co proportional to the SAW velocity change is the same order of magnitude as the bulk velocity change v, then ,71.is considered to be almost temperature independent. Because the absolute value of sound velocity has a few percentages of error, we adopted the relative scale rather than absolute one in this work. According to the above consideration on the penetration depth, the basic feature of the elastic properties, such as temperature dependence due to anharmonic lattice vibration, of the Zr-N film on the sapphire substrate is considered to come mainly from the character of the substrate. This enables us to extract the contribution from sole Zr-N films by subtracting the velocity change of sapphire substrate from the samples. The results for the samples B and D are shown in Figs 4(a) and 4(b), respectively. Whereas the SAW velocity change of sapphire substrate shows a monotonous temperature dependence, the velocity change of Zr-N films is anomalous. The relative velocity change of the sample B shows a deviation from sapphire substrate. The deviation is small below 100K, and becomes remarkable with elevating temperature. This deviation seems to form a broad minimum at high temperatures. In addition to this anomalous T dependence, we found a remarkable elastic softening at low temperature below 20K, as indicated in the inset of Fig.4(a). The elastic softening shows an apparent T -l dependence between 1.25 and 20K (Fig.5). In the case of the sample D, the broad anomaly is found at around 15K. This anomalous behavior vanishes gradually with the increase of temperature. From the analogy with the sample D, the anomaly of B is considered to form a minimum structure above room temperature. The amount

I

I

I

I

I

|

Sample B

0

573

I

!

I

0

0.5

1

0

-4 -50. 5

1.5

Iog~o [ T(K) ] Anomalous part of relative SAW velocity of the samples B is shown as a function of logarithmic temperature below 20K.

Fig.6

of broad anomalies is 4x10 -3 and 7x10 -5 for the samples B and D, respectively. A very small minimum is also seen around 1K. This anomaly is considered to be due to a superconducting transition of aluminium, which is used as electrical leads for IDT. The thickness of the aluminium is about 150nm. It has been known that the A! film with 10nm thickness causes an elastic m i n i m u m at superconducting transition point with amount of 4x10 -7.13 This yields to 0.6x10 -5, which is comparable to 2x10 -5 for this case. Therefore, it would be considered that there is no anomalous part below 2K for the sample D. It is a remarkable difference from the sample B. The effect of the superconducting transition of AI would affect the elastic anomaly in the sample B. Since the amount of the low temperature anomaly of B is much larger than the effect from AI, the elastic softening is considered to be intrinsic. However, it surely gives the same amount of contribution to B. In Fig.6, the low T elastic softening of B is plotted as a function of logarithmic temperature. This figure shows a logarithmic T dependence below 2.5K. A small dip around 1K is considered to come from the effect of AI. §III.

DISCUSSIONS

An accurate ultrasonic apparatus enables us to make investigations on various energy levels in solids. Various types of energy scheme have been investigated by ultrasonic methods. Because Zr-N films were made by sputtering method, it is worth to check from the viewpoint of Two-level system (TLS) which is seen in glass systems. The absorption of ultrasound in insulating regime has been theoretically investigated based on TLS. 10 TLS shows anomalous temperature dependence as

-1 -2

C=C

;a.

-4 -50

|

i

0.5

1

|

I

i

1.5

2

2.5

T "l ( K "I ) Fig.5

0 -

A~

-3

The elastic anomaly at low temperature is plotted as a function of T -1.

~---T-- "

(1)

Here, N is the number of levels per unit volume. Ae is the energy separation between a ground state and an excited one, and fl=(kBT) -1. In eq.(l), ~and ~ are the coupling constants between the elastic wave and the level systems. The second term of the right hand side of eq.(l) comes from the excitation between the ground and the excited states through phonon. This is called vanVleck term from the analogy with magnetic susceptibility of two separate

574

N O V E L ELASTIC A N O M A L I E S IN Zr-N FILMS

energy levels. This mechanism gives a perturbation of -1Q2e2[Ae.to the ground state and Ig"12e2/Aeto the excited one, where e is the elastic strain. The third term of eq.(l) is due to a linear modulation of the levels by phonon. When the ground and excited states are modulated by the strain as ~0e and ~le, respectively, the coupling constant is described by (~1-~0).

Both contributions show T -1

dependence at high temperature above T=Ae/kB. At low temperatures, the second term approaches a constant -2NIg32/Ae, and the third term disappears as e'Ae/3/T. The energy separations responsible for the broad anomalies are about 1000K for the sample B, and 60K for D. Here, we estimate Ae for strongly localized systems where Variable Range Hopping (VRH) conduction is dominant. Equation (1) for TLS must be modified for electronic systems to take the particle conservation into account. 14 However, the formula is very similar, if the ground state and the excited one for TLS are replaced by the occupied electronic state below fermi level and the unoccupied one above fermi level, respectively. The difference between TLS and electronic system comes from an asymmetric configuration of states around fermi level. This causes an additional and small correction in eq.(l). This correction, which describes the temperature dependence of fermi energy, shows no anomalous behavior. Therefore, we can roughly discuss about electronic systems based on eq.(1) as well as TLS. In eq.(1), the energy separation Atr for TLS is replaced by the characteristic energy separation for d-dimensional VRH, Ae=kBTo(T/To) d/d+l. Here, the characteristic temperature TO is a measure for the inverse extent of electronic wave function, and is experimentally estimated from VRH conductivity ,:r=t:roexp(-(To/T)~) with tS=(d+l) -1. In the case that interaction effect is important, the exponent t5 is taken place by 0.5.15 Hereafter, we assumed &=0.25 for d=3. If we put this formula of Ae for VRH into eq.(l), a minimum structure is expected to be found at around T=To/4 due to the third term of the right hand of eq.(l). A large elastic softening is also expected from the VanVleck term. The latter softening will be discussed later. The value of TO shows strong temperature dependence, and increases rapidly with elevating temperature. The analysis by VRH gives T0=268K for the data below 15K and T0=1600K at 40K for the sample B. The values of TO are 0.7K for the data below 15K and 18K at 40K for the sample D. These values would not be able to explain the experiments quantitatively. In the frame of our qualitative discussion, however, this mechanism would be a possible origin for the broad anomalies found at high temperatures. It would be noted that the other characteristic scale of the energy is needed to interpret the softening found at low temperatures. In the case of the sample B, the elastic softening is characterized by T -1 above 1.25K. This may indicate that the fairly confined energy scheme is responsible for this anomaly. On the other hand, low T data can be considered to have logT dependence between 0.3 and 2.5K. This would be consistent with the glass nature, where the logT dependence in elastic constant is obtained from the second term of eq.(1) by assuming the suitable distribution in level scheme. 8 However, it must be asked whether this logT behavior really comes from the glass nature for Zr-N. According to Auger and X-ray diffraction experiments, Zr-N films consist of about 40% of Zr and 60% of N, 2 and form the same structure as ZrN. 16 It means that excess nitrogen may share interstitial

Vol. 83, No. 8

sites in the crystal. The sputtering method introduces unstable structures in solid, and often becomes a trigger to form amorphous structure. The samples measured in this work were annealed at 400°C for several hours to remove the structural instabilities. However, unstable structures may be still rest in high resistance samples like B after such heat treatment. In any way, the elastic softening' of the sample B surely requests the characteristic energy separation Ae to be order of IK in the frame of eq.(1). Such small Ae is not inconsistent with the structural origin. According to VRH mechanism, the temperature variation of the characteristic energy scale Ae decreases as T d/d+l with decreasing temperature. As mentioned above, it is found that the second term in eq.(1) with Ae of VRH gives an anomalous part that diverges as T -°.75 for 3dimensional system. It is inconsistent with the experimental results. Therefore, it can be concluded that the elastic anomalies at low temperature can not be discussed based on VRH. It seems correct, because VRH between interatomic levels does not satisfy the momentum conservation for the transition through the ultrasonic wave having a long wave length. The third term in eq.(l) has no such restriction. If the anomalies observed here would be a precursor for the metal-insulator transition (MIT), the analogy with critical phenomena seems very useful. The effect of localization on elastic constant has been theoretically investigated for heavily doped semiconductors in weakly localized regime. 12 It has been shown that there is no anomaly due to localization in the first-order perturbation for single valley system. The question is whether the MIT accompanies a critical anomaly at the transition point. In the case of interaction-driven MIT, no anomaly is e x p e c t e d , t7 In the case of Zr-N films, the elastic softening at low temperature deviate from T -1 dependence below 1.25K. Lower temperature measurements of elastic constant should be carried out to investigate this problem. In this paper, we reported elastic anomalies in Zr-N sputtered films. Similar behaviors are seen for the samples both in the metallic and insulating regions. There is a broad minimum at high temperature for both samples. An additional softening is found at low temperature for the high resistivity sample. Various origins for the anomalies were discussed. The total feature can be explained by eq.(1) with two kinds of the energy separation Ae in twolevel systems. The origin of Ae and the relation to the localized electronic state should be further investigated. Investigations on the other films are now going on.

ACKNOWLEDGMENT

We would like to thank Mr. T.Yotsuya and Mr. M.Yoshitake of Osaka Prefectural Industrial Institute for providing Zr-N samples, and Mr. N.Mizuno of Basic T e c h n o l o g y R & D Center, Kayaba Co., Ltd., for preparing S A W device. We wish to express the best thank to Prof. P.Wyder, Max-Planck-lnstitut, HochfeldMagnetlabor, Grenoble, for encouraging us at early stage of this work. The help of Mr. M.Saito for experiments is appreciated. We thank the machine shop of Research Institute for Scientific Measurements, Tohoku University, Sendai, for constructing 3He cryostat. This work is supported by Grant-in-Aid for Scientific Research from Japanese Ministry of Education (Grant No. 02640244).

Vol. 8~ No. 8

NOVEL ELASTIC ANOMALIES IN Zr-N FILMS

575

REFERENCES

1. 2.

3. 4. 5. 6. 7.

T.Yotsuya, M.Yoshitake, Y.Suzuki, S.Ogawa and J.Yamamoto, Proc.5th Sensor Symposium (1985)9. T.Yotsuya, M.Yoshitake and J.Yamamoto: Appl. Phys.Lett. 51(1987)235, T.Yotsuya, M.Yoshitake, S.Ogawa, Y.Suzuki and J.Yamamoto, Jpn.J.Appl. Phys. 26(1987)1743. M.Yoshizawa, K.Ikeda, N.Toyota, T.Yotsuya, T.MiJller and P.Wyder, Physica B, 165& 166(1990)293. M.Yoshizawa, K.Ikeda, H.Sugawara, N.Toyota, T.Yotsuya and M.Yoshitake, submitted to Jpn.J.Appi.Phys. H.Sugawara, M.Yoshizawa, T.Yotsuya and M.Yoshitake, submitted to Jpn.J.AppI.Phys. B.Liithi, Dynamical Properties of Solids, NorthHolland, Amsterdam, 3(1980)245. P.Thalmeier and B.Liithi , Handbook on the Physical and Chemistry of Rare Earths, North-

8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Holland, Amsterdam, 14(1991)225. S.Hunklinger and W.Amold, Physical Acoustics, Academic Press, XII(1976)155. M.Yoshizawa, B.Liithi and K.D.Schotte, Z.Phys. B, 64(1986)169. B.G.Kotliar and T.V.Ramakrishnan, Phys.Rev.B 31(1985)8188. M.Yu.Reizer, Phys.Rev.B 40(1989)7461. T.Sota and K.Suzuki, Phys.Rev.B 33(1986) 8458. M.Yoshizawa, J-K.Maan, G.Bruls, P.Wyder, K.Ploog and G.Weimann, in preparation. M.Yoshizawa, l.Shirotani and T.Fujimura, J.Phys.Soc.Jpn. 55(1986)1196. A.L.Efros and B.I.Shklovskii, J.Phys. C 8(1975) L49. M.Yoshitake, S.Ogawa and K.Takiguchi, unpublished. V.Dobrosavijevic, T.R.Kirkpatrick, C.Chen and D.Belitz, Phys.Rev.B 44(1991)5432.