Evolution of film temperature during magnetron sputtering

2 downloads 0 Views 185KB Size Report
Received 30 January 2006; accepted 15 May 2006; published 14 June 2006 ... only during film deposition and exhibits extremely low thermal conductivity.
Evolution of film temperature during magnetron sputtering L. R. Shaginyana兲 Institute for Materials Science Problems, National Academy of Sciences of Ukraine, Krzhizhanovsky Street, 3, Kiev 03142, Ukraine and Center for Advanced Plasma Surface Technology, SungKyunKwan University, 300 Chun-Chun-Dong, Jangan-gu, Suwon 440-746, Korea

J. G. Han Center for Advanced Plasma Surface Technology, SungKyunKwan University, 300 Chun-Chun-Dong, Jangan-gu, Suwon 440-746, Korea

V. R. Shaginyan Petersburg Nuclear Physics Institute, Gatchina 188300, Russia

J. Musil Department of Physics, University of West Bohemia, 306 14 Plzen, Czech Republic

共Received 30 January 2006; accepted 15 May 2006; published 14 June 2006兲 We report on the results of measurements of the temperature TFsurf which developed on the surface of films deposited by magnetron sputtering of chromium and copper targets on cooling and non-cooling silicon substrates. The TFsurf and substrate temperature 共Ts兲 were simultaneously measured using high-resolution IR camera and thermocouple, respectively. We revealed that the TFsurf steeply grows, keeps constant when it achieves saturation level, and rapidly drops to the value of the Ts after stopping the deposition. At the same time, the Ts either does not change for the case of cooling substrate or increases to a certain level for noncooling substrate. However, in both cases the Ts remains several times lower than the TFsurf. The TFsurf is proportional to the flux of energy delivered to the growth surface by sputtered atoms and other fast particles, weakly depends on the depositing metal and can achieve several hundreds of °C. This phenomenon is explained by a model assuming formation of a hot thin surface layer 共HTSL兲 on the top of the growing film, which exists only during film deposition and exhibits extremely low thermal conductivity. Due to this unique property the temperature TFsurf of HTSL is several times higher than the Ts. Variations in the TFsurf fairly correlate with structure changes of Cr films along thickness investigated in detail previously. © 2006 American Vacuum Society. 关DOI: 10.1116/1.2210947兴

I. INTRODUCTION It is known that condensation of evaporated atoms results in the increase of the temperature TF of the growing film, which can considerably exceed the substrate temperature Ts.1–3 Similar phenomenon also occurs during deposition of films by sputtering.4 Regular measurements of the Ts are performed by a thermocouple inserted into the substrate holder, which is normally not in a perfect thermal contact with a substrate. Therefore, Ts measured by thermocouple in most cases is somewhat lower than the real temperature of the substrate, that is, than the film temperature. Experiments performed with thermostrip pasted to the substrate surface confirm this assertion, showing that TF can be by ⬃100– 150 ° C higher than Ts measured by thermocouple inserted into the substrate holder.4 Recent measurements of the surface temperature TFsurf using in situ spectroscopic ellipsometry during plasma-enhanced chemical-vapor deposition 共PECVD兲 deposition of silicon5 and diamond6 films revealed that TFsurf is considerably higher 共by approximately 100 K兲 than the Ts measured by the thermocouple. The above reasoning shows that there can exist three different temperatures: one is conventional substrate temperaa兲

Electronic mail: [email protected]

1083

J. Vac. Sci. Technol. A 24„4…, Jul/Aug 2006

ture, Ts, and second and third are transient temperatures, temperature of the film TF, which is somewhat higher the Ts共TF ⬎ Ts兲, and temperature of the surface of growing film, TFsurf, which in turn, can be higher than TF, i.e., TFsurf ⬎ TF ⬎ Ts. Clearly, the two latter transient temperatures develop and exist only during film deposition. Simultaneous existence of the above three temperatures may have two principally different origins. The first is related to either inaccuracy or particularities of the methods of temperature measurement. In fact, in Refs. 1, 2, and 4 the temperature was measured using thin film temperature sensors attached to the substrate surface. In this case the measured temperature was related to the bulk of the film, i.e., TF, rather than to its surface, TFsurf on the other hand, in Refs. 3, 5, and 6 the measured temperature is related just to the surface of growing film, TFsurf, because these temperature measurements were based either on IR irradiation from the surface of growing film3 or on spectroscopic ellipsometry which deals with optical properties of the surface.5,6 The second possible reason of the temperature difference between the growth surface and bulk of the film 共or substrate兲 is a really existing physical effect7 rather than a result of inaccuracy or methods for temperature measurement. Reason for film temperature rise during condensation of evaporated metal films is an exothermic release of heat of

0734-2101/2006/24„4…/1083/8/$23.00

©2006 American Vacuum Society

1083

1084

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

1084

condensation, ⌬H, during vapor-solid transformation.1–3 In the case of condensation, sputtered atoms besides ⌬H atoms possess kinetic energy, Ek, which is more than an order of magnitude higher than that for evaporated atoms. Therefore the flux of energy 共i.e., heat兲 delivering to the growth surface during sputter deposition is noticeably higher compared to evaporation and thus, film temperature is expected to be considerably higher. Moreover, sputtering film is additionally heating by 共i兲 ions and fast neutrals bombarding the growth surface,8 共ii兲 the heat radiated by the sputtering target,5 and 共iii兲 the heat released in exothermic reactions during formation of compounds. The sum of the former three sources of heat flux to the substrate called “heating from the plasma” can result in high temperature rise during film growth.9 From the above discussion it is clear that the real temperature at which the film grows 共i.e., the growth temperature兲 is not equal to that often referred to as the substrate temperature. Just by this reason it is often difficult and sometimes even impossible to establish the correlation between the deposition conditions and the observed film microstructure, chemical and phase composition, surface morphology, etc., of sputtered films using only Ts measured by the thermocouple. Therefore, the knowledge of the real temperature at which the film grows and the relationship between Ts and the real growth temperature is of key importance in understanding the actual effect of temperature on the mechanisms of film growth. Based on the preceding discussion we have performed simultaneous in situ measurements of TFsurf and Ts developed during formation of Cu and Cr films deposited by conventional magnetron sputtering. The measurements were carried out using a high-resolution IR camera and thermocouple. The goal of this study is to establish the relationships between TFsurf, Ts, and their time dependences on the deposition rate aD, i.e., the flux of energy delivering to the growth surface.

holder cooled with a circulating coolant kept at a temperature range of 5 – 8 ° C. The Chromel-Alumel thermocouple, tightly pressed to the substrate surface by a flat spring, was used to measure the substrate temperature Ts. The thermocouple was screened by a shield to avoid the direct incidence of sputtered atoms 关see Fig. 1共b兲兴. The surface temperature of the film TFsurf was measured by means of VARIOSCAN high-resolution thermography system 共JENOPTIC Laser, Optic System GmbH兲 with postprocessing of thermograms recorded during deposition using the IRBIS Professional software. Temperature measurements within the range of 40– 1200 ° C with the accuracy ±1% of the full-scale value were carried out by comparing the radiation intensity of the heated object and reference source mounted inside the IR camera.

II. EXPERIMENTAL DETAILS

A. Determination of emittances of Cu and Cr films

The schematic diagram of the experimental setup is given in Fig. 1. The axes of the magnetron and IR camera intersect at the center of the substrate located at a distance 70 mm from the target plane generating the flux of metal atoms. A ZnSe window, transparent in the IR region 共6000– 20 000 nm兲, located at a distance of 450 mm from the substrate serves as a viewport for the IR camera. The magnetron is equipped with 4 mm thick Cr or Cu 共99.99兲 target of 50 mm in diameter bonded with Ag paste to the cooled Cu backing plate. The background and operating argon pressures are p0 = 共1 – 3兲 ⫻ 10−3 Pa and pAr = 0.2 Pa, respectively. The flux density of sputtered atoms was regulated by variation of the magnetron discharge current Id. Silicon plates 共20⫻ 20⫻ 0.5 mm3兲 precoated with 1500 nm thick Cr and Cu coatings were used as substrates. The coatings were prepared to be sure that the emittance of the depositing film is equal to the emittance of the substrate what substantially increased the accuracy of the surface temperature determination. The substrates were tightly attached to the substrate

The measurement of temperature by IR camera requires the emittance ␧ of the measuring object to be known. However, ␧ is very sensitive to the roughness and cleanliness of the surface of the measuring object. For the measurement of temperature dependences ␧共T兲 for Cr and Cu double-side polished Si 共100兲 wafers sputter deposited at Ts = 300 ° C, 1500 nm thick coatings of the corresponding metals 共objects兲 were prepared. Measurements of the emittances were performed in the same vacuum chamber evacuated to the base pressure and then filled with Ar at a working pressure. The ␧ of the object is determined from the condition of the thermal equilibrium state,

J. Vac. Sci. Technol. A, Vol. 24, No. 4, Jul/Aug 2006

FIG. 1. 共a兲 Schematic diagram of the experimental setup for in situ measurements of the film surface temperature TFsurf. 共b兲Details of measurement of a substrate temperature.

qin = qrad .

共1兲

Here, qin = mc共⌬T / ⌬t兲 is the flux of heat delivering to the object from the heater, qrad = ␴␧共T4 − T04兲 is the flux of heat radiating by the object at a given equilibrium temperature T 共the Stefan-Boltzmann law兲, m is the mass of the object, c is the specific heat of Si 共substrate兲, and ⌬T / ⌬t is taken from a

1085

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

1085

TABLE I. Discharge currents and corresponding deposition rates and atomic and power fluxes delivered to the growing films during surface temperature measurements. Depositing metal

Id 共A兲

Dep. rate, aD 共nm/s兲

Atomic flux, f d 共⫻1016 at./ cm2 s兲

Power flux, qin 共W / cm2兲

⌬Hc + Ek + E p 共eV/at.兲

Cr Cr Cr Cr Cu Cu Cu

0.2 0.4 0.6 1.0 0.2 0.4 1.0

1.6 2.6 4.4 7.4 3.1 6.2 15.2

1.4 2.2 3.8 6.3 2.6 5.3 13.0

0.04 0.07 0.12 0.2 0.06 0.14 0.35

20 20 20 20 17 17 17

linear part of the heating curve at the beginning of heating. The temperature measurements were performed simultaneously by the thermocouple clamped to the object’s surface and by the IR camera. Using Eq. 共1兲 the emissivity ␧ was found from the equation ␧ = qin/␴共T4 − T04兲,

共2兲

where ␴ is the Stefan-Boltzmann constant, T is the temperature of the object in the equilibrium state, and T0 = 300 K 共temperature in the chamber兲. The heating of the object tightly fixed to the heated substrate holder was performed in the deposition chamber evacuated to a base pressure p0 = 共1 – 3兲 ⫻ 10−3 Pa. The emittances ␧共T兲 = 0.08– 0.1 for Cr and ␧共T兲 = 0.025– 0.032 for Cu were found in the range of 25– 750 ° C from time dependences of T = f共t兲 for various values of qin. The initial values for ␧0 = 0.08 for Cr and ␧0 = 0.025 for Cu at T = 25 ° C were taken from the Ref. 10. For these values of ␧ the difference in T measured by the IR camera and thermocouple is ±共8 – 10兲 ° C in the whole temperature range. III. RESULTS AND DISCUSSION

B. Concept of HTSL

During deposition the growing film is heated by the energy qin / aD that results in the steep increase of its temperature 共see Fig. 2兲. In this figure the time dependences of two temperatures 关共i兲 the surface temperature of growing film, TFsurf, and 共ii兲 the surface temperature of substrate TSsurf = Ts兴 are given for the deposition of chromium. For clarity these temperatures are defined in Fig. 3, where TFsurf is measured by the IR camera and Ts is measured by the thermocouple. The big difference in time dependences of TFsurf and Ts is clearly seen from Fig. 2. From the beginning of the process and up to t ⬇ 30 s TFsurf increases rapidly and achieves a maximum value of ⬇320 ° C and after reaching this value continues to grow very slowly up to the end of the deposition at t = 300 s. On the contrary, Ts grows very slowly during the first ⬇60 s of the deposition; however, after t 艌 60 s the gradient dTs / dt is almost the same as the gradient dTFsurf / dt. That is, the difference between these temperatures becomes constant, ⌬T = TFsurf − Ts ⬇ const starting from t 艌 60 s. The existence of such a big temperature difference ⌬T = TFsurf − Ts between the growth and the substrate surfaces

A. Power flux density delivered to the surface of growing film

The power flux density qin delivered to the substrate surface surface is defined by Eq. 共3兲, qin = f d共⌬Hc + Ek + E p兲,

共3兲

where f d 共atom/ cm2 s兲 is the flux of atoms deposited per unit area, ⌬Hc is the heat of condensation, Ek is the average kinetic energy of sputtered atoms, and E p is the heat delivered from the plasma; ⌬Hc, Ek, and E p are expressed in eV/atom. The sums 共⌬Hc + Ek + E p兲 were taken from Ref. 9. The fluxes of sputtered atoms f d were calculated from the measured deposition rates aD as follows: f d共atom/cm2 s兲 = 共V f na/St兲 = hSna/St = aDna ,

共4兲

where V f is the volume of film, h and S are the thickness and surface of film, t is the time, na = ␳a / ma is the number of atoms in the unit of film volume, ␳a is the specific density, and ma is the mass of atom. The calculated values of atomic 共f d兲 and power 共qin兲 fluxes are summarized in Table I. JVST A - Vacuum, Surfaces, and Films

FIG. 2. Time dependences of TFsurf and TSsurf during sputtering of Cr film on noncooled substrate at qin = 0.07 W / cm2.

1086

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

FIG. 3. Illustration demonstrating the formation of hot top surface layer 共HTSL兲 and the method for temperature measurements used in these experiments.

indicates that the thermal properties of a substance between these surfaces, which forms and exists exceptionally during film deposition, strongly differ from those of metals. To comprehend this effect let us consider the growing film as consisting of three different parts with their own temperatures 共Fig. 3兲: 共1兲 thin continuous superficial layer formed by mobile atoms arriving at the growth surface from a vapor phase 共the layer is considered as a liquid due to high mobility of atoms forming the layer and because of its disordered structure,7 and the temperature of the layer is equal to TFsurf measured by IR camera兲; 共2兲 solid film beneath it; and 共3兲 substrate, which temperature Ts is measured by the thermocouple. Clearly, the thermal properties both of metal film and substrate do not change during deposition; therefore their temperatures are expected to be close to each other, TF ⬇ Ts. At the same time, the thermal properties of the superficial layer on the growth surface are not known and can strongly differ from that of the solid film and substrate. In further discussion this layer will be called the hot top surface layer 共HTSL兲. C. Grounds for the existence of HTSL

Let us now prove the competency of the idea about the existence of HTSL. For this purpose, first recall the “law of stages,” formulated by Ostwald.11 This law asserts that a metastable system will transform into the next more stable state, and from this intermediate state another transformation will finally yield the stable state. For the case of the vapor → solid 共v → s兲 transformation the intermediate state is a liquid state. That is, the v → s transformation occurs through formation of an intermediate liquid state: v → l → s. Realization of this law for the case of deposition of films of various materials was proved experimentally. It was shown that formation of a solid film from a vapor occurs by the ␯ → l → s mechanism when Ts / Tm 艌 2 / 3, that is, through formation of an intermediate liquid phase. Here Ts and Tm are substrate temperature and melting point of the depositing material, respectively 共see Refs. 5, 10, and 12 and references therein兲. This reasoning shows that the formation of an intermediate liquid layer on a growth surface during condensation of sputtered atoms is not something unexpected. Actually, the ␯ → l → s mechanism was revealed during deposition of films J. Vac. Sci. Technol. A, Vol. 24, No. 4, Jul/Aug 2006

1086

by conventional evaporation, which were formed from particles with very low kinetic energy 共0.05– 0.1 eV兲. In this case the substrate temperature was a leading factor in the realization of the ␯ → l → s mechanism. At the same time, the kinetic energy of sputtered atoms is one to two orders of magnitude higher than that of evaporated atoms. This means that the flux of energy delivered to the growth surface by sputtered atoms is several times higher compared to the evaporated atoms. That should result in much higher substrate temperature rise. Therefore, one may expect that the realization of the ␯ → l → s mechanism for sputtered films is quite probable for Ts / Tm ⬍ 2 / 3, depending on the flux density of sputtered atoms. Clearly, the temperature of the intermediate liquid layer that forms during growth of sputtered film should be noticeably higher than the temperature of a solid 共either substrate or film兲 underneath. It is also clear that the temperature of the liquid layer should be nonuniform across its thickness. In fact, the upper part of the layer is expected to have highest temperature because atoms arriving on its surface possess maximal kinetic energy and highly mobile. That results in reevaporation of part of these atoms which fraction achieves ⬃20%.13 On the contrary, part of the layer adjacent to already solidified film is formed of atoms, which partially dissipated their energy and thus possess lower mobility. Therefore the temperature of this part should be lower compared to its upper part. However, the mobility of atoms within this part is still noticeably higher than the vibrational amplitude of atoms in a solid film beneath. Formation of an intermediate liquid layer during condensation is a process reversal to that of a surface melting occurring during heating of a solid. This follows from the description of the process of surface melting, which is reproduced below from Ref. 14 “As the temperature of solid increases by heating the atoms acquire additional thermal energy and vibrate with bigger amplitude. The surface atoms are more loosely bound than in the bulk so that their vibrational amplitude is greater. At some higher temperature the surface atoms leave their sites and small fraction of these may escape from the surface as vapor. Others climb out of their sites that produces “roughening” on an atomic scale. At this stage the surface layer is mobile and may be considered as a liquid while the bulk still remains solid. The second layer is bound to the underlying solid and to the mobile layer above it. It is thus less strongly anchored to its site than atoms deep in the bulk. At a slightly higher temperature it is too melting.”13 Note that the formation of a liquid layer on solid nanosized particles during their heating to the temperature below melting point 共i.e., surface melting兲 was confirmed experimentally by direct observation.15–17 Comparison of liquid layers, one of which forms during surface melting and the other during atomic condensation, shows their similarity and the processes of formation of these layers are consistent with the Ostwald law of stages. The only difference is that the first forms in the s → l → ␯ direction while the other in the reversal, ␯ → l → s.

1087

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

1087

FIG. 5. Illustration of temperature distribution along the direction of film growth during the deposition.

FIG. 4. Approach for the determination of thickness hHTSL of HTSL which formed during deposition of Cr film on noncooled substrate at qin = 0.07 W / cm2.

The above discussion clearly demonstrates that the formation of a liquid layer during film deposition is completely approved from physical point of view and proved experimentally for similar objects. D. Determination of thickness of HTSL

The thickness of the HTSL and trend of its dependence on the power flux are the problems of a great importance. On one hand, the knowledge of the actual thickness of the HTSL will allow us to calculate the precise magnitude of its thermal conductivity and its dependence on the power flux; on the other hand, it will shed light upon the growth mechanism of the film. However, the data obtained in our investigations do not allow deriving this very important parameter. The maximal thickness hHTSL of HTSL can be very roughly estimated from the dependence ⌬T = TFsurf − Ts = F共h兲 given in Fig. 4. This dependence is obtained from the data in Fig. 6 and after the conversion of time t into thickness h using the measured deposition rate for chromium aD = 4.4 nm/ s. Multiplying the time of formation of HTSL during which the TFsurf has maximal gradient, by deposition rate we find maximal thickness of the layer. Note that during this period part of the HTSL can solidify. Therefore the thickness of HTSL calculated by this means is overestimated. Approximate thickness of HTSL calculated for these conditions is found to be hHTSL ⬇ 40 nm 共see Fig. 4兲. Note that the time of formation of HTSL depends on the flux of energy delivered to the growing film, that is, on the deposition rate. Therefore, the thickness hHTSL depends on conditions used in the film deposition process. At the beginning of film deposition the TFsurf is close to the Ts 共Figs. 2 and 5兲 because the HTSL not yet formed. It means that the fraction of film adjacent to the substrate forms at the Ts. With increasing deposition time the TFsurf steeply grows up to a saturation value at which HTSL formation is completed. From this time the film grows at a stable temJVST A - Vacuum, Surfaces, and Films

perature TFsurf from the solidifying “tail” of the HTSL while the HTSL continues moving in the direction of the film growth 共see Fig. 5兲. At the same time, the temperature TF of solidified film under the HTSL rapidly equilibrates with the Ts due to its high thermal conductivity, i.e., TF ⬇ Ts. From this reasoning it follows that a crystalline material in the substrate/film interface is composed of fine grains while the upper film fractions consist of noticeably larger grains as it is observed in many experiments.18–20 E. Thermal conductivity of HTSL

The thermal resistance of the layer can be estimated from the measured 共TFsurf , Ts , f d兲 and calculated 共qin , qrad兲 values using the following formula:21 Rth = 共TFsurf − Ts兲/共qin − qrad兲.

共5兲

The thermal resistance can be also expressed as Rth = h/kS,

共6兲

where k is the thermal conductivity and h and S are the thickness and surface of the HTSL, respectively. Knowing the layer thickness h, the thermal conductivity kth 共W / m K兲 can be calculated from Eq. 共6兲. These calculations were made for the case of sputtering of chromium at Id = 0.4 A. Necessary data were taken from Table I and Fig. 6. Substituting these data in Eq. 共6兲 we obtain the thermal conductivity of ⬃40 nm thick HTSL chromium layer of the order of ki ⬇ 10−8 W / m K. The thermal conductivity of the bulk chromium at T ⬇ 200 ° C is kCr = 94 W / m K.10 It means that the thermal conductivity kHTSL of chromium is very small compared to that of the bulk of film under HTSL; kHTSL / kCr ⬇ 10−10. Since the thermal conductivity of the HTSL is so low the heat transfer from it to the film below is very limited; this results in strong increase of the temperature of the HTSL. F. Physical explanation of extremely low thermal conductivity of HTSL

The thermal conductivity kHTSL of HTSL can be assessed using a recently developed model.7 This model is based on the assumption that during atomic condensation a liquid layer 共HTSL兲 described in detail in Sec. III C forms on the growth surface. Since atoms in HTSL are bonded to each other with metallic bonds, the HTSL consists of electron and

1088

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

1088

FIG. 6. Time dependences of TFsurf as a function of qin during deposition of Cr films on cooled substrates.

FIG. 7. Time dependences of TFsurf as a function of qin during deposition of Cu films on cooled substrates.

ion subsystems; the ion subsystem is immersed in the electron one. The energy exchange within each subsystem, i.e., between electrons within the electron subsystem and between ions within the ion subsystem, is very rapid. At the same time, the energy exchange between different subsystems 共i.e., between the ion and electron subsystems兲 is very limited. This is a result of a giant difference in the mass of the ions 共atoms兲 and electrons. Therefore, the main part of the energy stored in HTSL is accumulated within the ion subsystem. This assertion is based on the following reasoning. Inside the HTSL an average velocity of ions is vi = va = 共2Ea / ma兲1/2; here Ea, ma, and va are the energy, the mass, and velocity of atoms arriving on the condensation surface, respectively. The average velocity ve of electrons is the same as that of ions because prior to condensation and formation of the electron subsystem within HTSL all electrons were coupled to incident atoms, i.e., ve = vi = va. Since Ei = Ea = 1 / 2关ma共va兲2兴 and Ee = 1 / 2关me共ve兲2兴 with me Ⰶ ma we obtain that Ee Ⰶ Ei; here Ee and Ei are the average kinetic energies of electrons and ions, respectively, and me is the mass of electron. At the same time, the transmittance of energy of the ion subsystem to the electron one is strongly reduced due to me Ⰶ ma.22 Thus, the main part of energy qin / aD delivered to the growing film and stored in HTSL is accumulated within the ion subsystem. The energy of the electron subsystem rapidly equilibrates with that of electrons in a solid film beneath due to a higher mobility of electrons. Therefore, the thermal conductivity kHTSL is determined by the thermal conductivity of the ion subsystem and can be estimated as follows. Thermal conductivity kMe of metals is mostly determined by electrons and from the conventional kinetic theory is expressed by the equation14 共pp. 245–249兲

cific heat of metal. Since the heat of HTSL is accumulated within its ion subsystem, the thermal conductivity kHTSL of HTSL is determined by the ion subsystem. Therefore, to estimate the thermal conductivity kHTSL in Eq. 共7兲 we must replace ␭e with ␭a and ve with va. Then the kHTSL is defined as kHTSL = ␭acMeva共me / ma兲 / 3; the ratio me / ma is the factor determining the decrease in the energy transfer from ions to electrons. Assuming that the specific heat of the layer is equal to that of the bulk metal we obtain the ratio of thermal conductivities of HTSL to that of metal:

kMe = ␭ecMeve/3.

共7兲

Here, ␭e and ve are the mean free path and the average velocity of electrons in metals, respectively, and cMe is the speJ. Vac. Sci. Technol. A, Vol. 24, No. 4, Jul/Aug 2006

kHTSL/kMe ⬇ 共␭a/␭e兲共va/ve兲共me/ma兲.

共8兲

To estimate kHTSL for Cr we must substitute in Eq. 共8兲 ␭a / ␭e ⬇ 5 ⫻ 10−3, and me / mCr ⬇ 1.1⫻ 10−5, va / ve 1/2 −3 = 共me / mCr兲 = 3.28⫻ 10 . Values of ␭a ⬇ 0.2 nm 共average interatomic distance in liquid兲 and ␭e ⬇ 40 nm were taken from Refs. 14 and 23, respectively. After substitution we obtain kHTSL ⬇ 10−10 kMe. This means that the effective thermal conductivity of HTSL formed during growth of chromium film is ten orders of magnitude lower than the conventional thermal conductivity of bulk chromium. To estimate how properties of the depositing element influence the thermal conductivity of HTSL one should substitute the mass of the corresponding element to Eq. 共8兲. Doing this for the light carbon and heavy tungsten we find that kHTSL of these elements varies from ⬃10−9 to ⬃10−11. This means that the effective thermal conductivity of HTSL is very low and slightly depends on the sputtered material. G. Effect of qin on temperature TFsurf of HTSL

At the same time, the temperature TFsurf of HTSL strongly depends on the power flux density qin. This effect is clearly seen in Figs. 6 and 7, where the temperature time dependences TFsurf共t兲 as a function of qin for Cr and Cu depositions are displayed. From these measurements the following effects common for both of the metals can be drawn.

1089

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

1089

FIG. 8. Surface temperature TFsurf as a function of the power flux density qin during Cr and Cu film depositions.

FIG. 9. Time dependences of TFsurf during deposition of Cr films at qin = 0.07 W / cm2 on cooled and noncooled substrates.

共1兲 The TFsurf steeply increases at the beginning of the film growth and after reaching saturation value almost does not change. The steep increase of the TFsurf indicates that HTSL forms in a very short time and possesses a very low thermal conductivity. On the other hand, simultaneously measured substrate temperature reaches values several times lower 共Fig. 2兲, which confirms the above assertion. 共2兲 The TFsurf is proportional to qin. This experimental observation is in accord with the models developed in Refs. 7 and 24. The model7 also predicts the relation between the TFsurf and Ts:

IV. CONCLUSIONS

TFsurf = 共hqin兲/kHTSL + Ts .

共9兲

From Eq. 共9兲 it follows that the T surf is proportional to the flux of energy qin delivering to the growth surface. This effect is observed in our temperature measurements. From Fig. 8 the dependence of TFsurf on qin is clearly seen, while Fig. 9 demonstrates the dependence of TFsurf on Ts. Both of these dependences are quite clear and in consistence with conventional theory of the thermal conductivity.14 F

Based on the results and discussion above one can assume that the actual film growth temperature varies from Ts to TFsurf. However, since the TFsurf rapidly saturates, formation of the main film fraction occurs at the TFsurf rather than at the Ts. Thus, the bigger the difference ⌬T = TFsurf − Ts the stronger is the role of the TFsurf in the formation of film structure and properties—the factor which one usually does not take into account considering the correlation between film properties and deposition conditions. Detailed investigations of crystal and microstructure of Cr films as a function of the deposition conditions24,25 prove this assertion. In these works it was shown that the structure of these films varies across thickness24 and strongly depends on the flux of energy delivered to the growth surface25 that fairly correlates with the corresponding surface temperature variations, described in this article. JVST A - Vacuum, Surfaces, and Films

Systematic measurements of the surface temperature TFsurf which developed during deposition of Cr and Cu films by magnetron sputtering show that the TFsurf achieves several hundreds of °C which is considerably higher than the simultaneously measured substrate temperature Ts. The TFsurf is proportional to the flux of energy delivered to the growth surface by sputtered atoms, fast neutrals, and ions and weakly depends on the depositing metal. This phenomenon is explained by a model assuming formation of a hot thin surface layer 共HTSL兲 on the top of the growing film, which exists only during film deposition and exhibits extremely low thermal conductivity. Due to this unique property the temperature 共TFsurf兲 of HTSL is several times higher than the Ts. Variations in the TFsurf fairly correlate with structure changes of Cr films along thickness investigated in detail previously. The discovery of the HTSL is of great scientific importance because it provides deeper understanding of film growth phenomena and helps to explain such particularities of sputtered films as nonuniformity of crystalline structure, microstructure, and internal stress. ACKNOWLEDGMENTS This work was mainly supported by the Korea Science and Engineering Foundation through the Center for Advanced Plasma Surface Technology 共CAPST兲 at Sungkyunkwan University. The work was also supported in part by the Ministry of Education of the Czech Republic under Project No. MSM 4977751302. M. V. Belous and C. M. Wayman, J. Appl. Phys. 38, 5119 共1967兲. G. Breitweiser, B. N. Varadarajan, and J. Wafer, J. Vac. Sci. Technol. 7, 274 共1969兲. 3 E. Yoda, Proceedings of the Sixth Internation Conference on Electron Microscopy, Kyoto, 1966 共unpublished兲, p. 517. 4 J. Musil, D. Herman, and J. Sicha, J. Vac. Sci. Technol. A 24, 521 共2006兲. 5 D. Daineka, V. Suendo, and P. Roca I Cabarrocas, Thin Solid Films 468, 298 共2004兲. 1 2

1090

Shaginyan et al.: Evolution of film temperature during magnetron sputtering

M. Wakagi et al., J. Vac. Sci. Technol. A 13, 1917 共1995兲. L. R. Shaginyan, V. R. Shaginyan, and J. G. Han, Eur. Phys. J. B 46, 335 共2005兲. 8 J. Musil and J. Suna, Mater. Sci. Forum 502, 291 共2005兲. 9 M. Ohring, The Materials Science of Thin Films, 2nd ed. 共Academic, New York, 2002兲, p. 249. 10 Smithells Metals Reference Book, 7th ed., edited by E. A. Brandes and G. B. Brook 共Elsevier, Amsterdam, 1998兲, p. 17–19. 11 W. Ostwald, Z. Physik Chem. 22, 289 共1897兲. 12 K. H. Behrndt, J. Appl. Phys. 37, 3841 共1966兲. 13 L. R. Shaginyan, J. G. Han, and N. V. Britun, Vacuum 80, 828 共2006兲. 14 D. Tabor, Gases, Liquids and Solids, 3rd ed. 共Cambridge University Press, Cambridge, 1991兲, p. 158. 15 J. G. Lee, H. Mori, and H. Yasuda, Phys. Rev. B 66, 012105 共2002兲. 16 J. G. Lee and H. Mori, Phys. Rev. Lett. 93, 235501 共2004兲.

J. G. Lee, H. Mori, and H. Yasuda, J. Mater. Res. 20, 1708 共2005兲. R. Messier, J. Vac. Sci. Technol. A A4, 490 共1986兲. 19 S. P. Lau, Y. H. Cheng, J. Shi, P. Cao, B. K. Tay, and X. Shi, Thin Solid Films 398/399, 539 共2001兲. 20 L. R. Shaginyan, M. Misina, J. Zemek, J. Musil, F. Regent, and V. F. Britun, Thin Solid Films 408, 136 共2002兲. 21 J.-F. Daviet, L. Peccoud, and F. Mondon, J. Appl. Phys. 73, 1471 共1993兲. 22 E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics 共ButterworthHeinemann, Oxford, 2002兲, p. 173. 23 N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys 共Dover, New York, 1958兲. 24 L. R. Shaginyan, J. G. Han, and H. M. Lee, Jpn. J. Appl. Phys., Part 1 43, 2594 共2004兲. 25 L. R. Shaginyan, J. G. Han, and N. V. Britun, Jpn. J. Appl. Phys., Part 1 44, 3200 共2005兲.

6

17

7

18

J. Vac. Sci. Technol. A, Vol. 24, No. 4, Jul/Aug 2006

1090