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Conversion of BaF₂ to BaO for in-situ growth of Y-Ba-Cu-O thin films Gao, Yuan 1990

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CONVERSION O FB A F  2  T O B A O F O R IN-SITU G R O W T H O F  Y-BA-CU-O THIN  FILMS  By Yuan Gao B. Sc. (Physics) University of Science and Technology of China  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in  THE FACULTY OF GRADUATE STUDIES PHYSICS We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA January 1990 © Yuan Gao, 1990  In  presenting  degree at the  this  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department  of  Physics  The University of British Columbia Vancouver, Canada  D a t e  DE-6  (2/88)  Feb.  12,  1990  Abstract  The YiBa2Cu30 superconducting thin films were made by both sequential electronx  beam evaporation and co-evaporation of Cu, BaF and Y, followed with high temperature 2  post-deposition annealing. The possibility of making YiBa Cu30 superconducting film in situ with BaF2 as 2  x  the Ba source was investigated by studying the conditions of in situ conversion of BaF  2  to BaO. The BaO concentration in the film as function of the substrate temperature was estimated with an equilibrium thermodynamic model and found to agree with the experimental results. A brief experimental and theoretical exploration of BaCl also showed that BaCl does 2  2  not have any advantage over BaF as the Ba source for in situ growth of Y-Ba-Cu-0 films 2  from the growth temperature point of view.  11  Table of Contents  Abstract  ii  List of Tables  v  List of Figures  vi  Acknowledgement  vii  1 Introduction  1  1.1  High Te Superconductivity and High Te Superconductor Films  1  1.2  Y-Ba-Cu-0 Superconductor Film  3  1.3  Outline of This Thesis  5  2 Apparatus  7  2.1  Vacuum Evaporation System Description  2.2  Pressure Measurement  10  2.2.1  Pressure inside the Helical Resonator  13  2.2.2  Pressure in Front of Substrates  13  2.3  Hot Stage and the Temperature Measurement  14  2.4  Deposition Rate and Thickness Monitoring  15  3 Preparation of Y i B a C u O Films 2  3  x  7  18  3.1  Electron-Beam Evaporation  18  3.2  Substrate Preparation  18  iii  3.3  3.4  Film Deposition  19  3.3.1  Sequential Deposition  19  3.3.2  Co-deposition  19  Post-Deposition Annealing  20  4 Analysis of Prepared Y i B a C u O Films 2  3  x  21  4.1  EDX Composition Analysis  21  4.2  Resistance Measurement of the Films  22  4.3  Scanning Electron Micrograph  23  5 In-Situ Conversion of BaF and BaCl to BaO 2  2  26  5.1 Film Preparation . .  26  5.2  26  5.3  Thermodynamic Analysis 5.2.1  Conversion of BaF  5.2.2  Conversion of BaCl  26  2  35  2  X R D and EDX Analysis  35  5.3.1  X R D Analysis of BaF Films  35  5.3.2  EDX Analysis of BaCl Films  42  5.3.3  Discussion  42  2  2  6 Conclusions  44  Bibliography  46  iv  List of Tables  5.1  AH° and AS° values for some selected materials[30,31]  v  List of Figures  1.1  The structures of Y-Ba-Cu-0 superconductor [35]  4  2.2  Vacuum Evaporation System  8  .2.3  Substrate Holding Block  9  2.4  Top view of the evaporators showing the configuration of the evaporators and the substrate holding block  11  2.5  Plasma Discharge Unit  12  4.6  Four-Point-Probe  22  4.7  Resistance vs. Temperature Curve of Y i B a C u 3 0 Codeposited Film #890511. 2  T (onset) = 87K c  x  T (midpoint) = 68K  T ( R = 0) = 53K  c  24  C  4.8  S E M Picture of Codeposited Film #890511  25  5.9  The equilibrium curves of the B a F — > BaO reaction in the C B o T space. —  2  a  33  5.10 C e a O T equilibrium curves for P H O = 1 X 10 Torr and different deposi- . -  -4  2  tion rates  34  5.11 The equilibrium curves of the B a C l —• BaO reaction in the CB o—T space. 36 2  a  5.12 X-ray Diffraction Pattern of B a F Powders  37  5.13 X-ray Diffraction Pattern of BaO Powders  38  2  5.14 X R D Patterns of the Transition from B a F to BaO  40  5.15 BaO Concentration as a Function of Temperature  41  2  vi  Acknowledgement  I would like to thank my supervisors, Dr. Tom Tiedje and Dr. Richard Cline. It is their constant support and help that made this work possible. Especially, many ideas in this work came from the discussions with Dr. T . Tiedje. Thanks also to Norman Osborne for his kindly help in resistance and X R D measurements.  vii  Chapter 1 Introduction  1.1 High Tc Superconductivity and High Tc Superconductor Films Superconductivity was first discovered by H . K . Onnes in 1911 when he cooled mercury down to below 4.2K and found that the D C electrical resistance of the metal sharply droped to zero [1]. A number of materials were later found to exhibit superconductivity with transition temperature from near 4K to slightly above 20K during the following 70 years. These materials were also found to exhibit the total exclusion of magnetic field in the superconducting state. This is called the Meissner effect. However, the applied magnetic field must not exceed the critical field H , or the superconducting state will be c  lost and the magnetic field will penetrate perfectly into the sample. Some superconductors were found to exhibt the Meissner effect below the lower critical field H superconductivity above the higher critical field H  c 2  c l  and lose  but exhibit a mixed state between  H i and H 2 . In this mixed state, the applied magnetic field partially penetrates into the c  C  sample and is confined in vortex lines. These vortex lines are believed to be "pinned" by defects and form an array (flux lattice) so that the superconductivity is only destroyed in these local regions. These superconductors are called type II superconductors[2]. The microscopic nature of superconductivity was explained in 1957, 46 years after the discovery of superconductivity, by Bardeen,Cooper and Schrieffer (BCS) [2,3] based on the assumption that two electrons bind through the exchange of a phonon to form a Cooper pair at the temperature below the superconducting transition temperature T . c  1  Chapter 1. Introduction  2  The slow progress of studying superconductivity was changed, however, in April 1986 by the discovery by Bednorz and Muller that Ba doped L a 2 C u 0 4 becomes superconducting at a temperature of 35K [4]. Since then, this area has drawn a lot of attention and great effort has been made. Tl-Ba-Ca-Cu-0 has been found to have the highest T  c  of 120K [5] so far and Y - B a - C u - 0 film can have a critical current density as high as 6 x 1 0 A / c m at 77K [6]. All the superconductors found in the past three years with T 6  2  c  above 35K are called "high T superconductors". They are all found to be type II superc  conductors so they can maintain the superconducting state with relatively high magnetic field up to the higher critical field H 2. C  Also,, the conventional BCS theory is facing challenges from the results of the newly found high T  c  superconductors.  according to the BCS theory.  For example, T  c  is proportional to the energy gap  Thus, the newly found high T  c  materials should have  higher energy gaps. But this is not confirmed by the experiments. Questions about such topics as the nature of the charge carriers in the superconducting state and the type of pair coupling, are still controversial [7,8]. The high T superconducting mechanism is still c  not certain. Various mechanisms have been proposed. For example, Baskaran, Zou and Anderson proposed a mechanism based on the Resonating Valence Bonds concept with holons (unoccupied sites) carrying charges as bosons and spinons (unpaired spins in the sea of valence bonds) carrying spins as fermions so that Bose condensation of holons in doped samples leads to the superconductivity[33,34]. More experimental and theoretical effort is needed to explain the high T superconductivity mechanism. High quality thin c  film materials are very suitable for a variety of experiments in studying the mechanisms responsible for the high T , such as, optical transmission and tunneling experiments[16]. c  In addition, great effort has been made to apply high temperature superconductors in practical use, especially, in applications related to electronics, such as, SQUID detectors, faster electronic interconnects, passive electromagnetic filtering devices, e£c.[l].  Chapter 1.  1.2  Introduction  3  Y-Ba-Cu-O Superconductor F i l m  YiBa2Cu306.g was discovered by Chu e£a/[9] in 1987 to have a critical temperature around 90K, which is well above the boiling point of liquid nitrogen (77K). Cu-0 planes in the YiBajCuaOe.o. structure are found to be responsible for superconductivity at high temperatures [10]. Figure 1.1 shows the crystal structure of Y-Ba-Cu-0 superconductor as determined by neutron diffraction[35].  Several techniques have been used to make  superconducting YiBa Cu 06.9 films, such as, evaporation [11,15], sputtering [12], laser 2  3  ablation [13], etc.. YiBa2Cu306.9 superconductors, both bulk materials and thin films, were found to be sensitive to moisture and decompose to CuO,Ba(OH) and Y2BaCu0 in water and 2  5  lose superconductivity. Those films made with BaF as the Ba source were found to de2  compose less readily [14,15]. By using coevaporation of Y , C u and BaF , YiBa2Cu306.g 2  superconducting films made by Mankiewich et al were found not only insensitive to moisture but also having high critical current densities (10 A/cm at 8IK,about 2 orders of 6  2  magnitude higher than the best results obtained from bulk material) which is believed to be due to better aligned grains in the films [15]. Also, BaF2 is very easy to evaporate both with an electron-beam source or a thermal evaporator. In contrast, element metal Ba reacts actively with O 2 , H 2 O and C O 2 in the ambient resulting in inconsistent evaporation behavior [15,18]. As-deposited films made with absence of O2 are normally amorphous and insulating. Thus, post-deposition annealing is normally required for these as-deposited films. For films made by evaporation with BaF2 as the Ba source, typically a two-step annealing process is needed: a high temperature anneal at about 850 °C in the presence of oxygen and water vapour to convert the fluoride to oxide, and a low temperature anneal at about 400 °C - 700 °C in pure oxygen to form the superconducting phase, YiBa2Cu3U6.9  Chapter 1. Introduction  (a)  4  (b)  (a) The structure of the tetragonal parent phase, (b) The structure of the orthorhombic ordered phase.  Figure 1.1: The structures of Y-Ba-Cu-0 superconductor [35].  Chapter 1.  5  Introduction  [17,18]. For films made from BaO or Ba, only pure oxygen is needed during the annealing procedure and the temperature ranging from 300 °C to 700 °C is needed to crystallise the amorphous as-deposited film and form the right superconducting phase [18]. The technology of in situ growth of superconducting Y-Ba-Cu-0 films by coevaporation without annealing has also been developed [19,20]. One normally accomplishes this by heating up the substrate to about 600 °C and introducing activated oxygen (such as  ozone) into the deposition chamber during the deposition procedure [19,20]. In situ  growth has not yet been achieved with BaF as the Ba source material. 2  There are obvious advantages to the in situ method. The post-deposition annealing step is undesirable for the fabrication of various layered devices, including planar tunneling junctions where success depends upon the formation of clean surfaces and abrupt interfaces [20]. The in situ method also offers the advantage of low temperature fabrication. Superconducting thin film devices can be grown at a temperature compatible with semiconductor processing. It also gives a good prospect of attaining a highly-perfect, clean, and uniform film surface suitable for surface-sensitive measurements such as electron tunneling [21]. With the advantage of making Y-Ba-Cu-0 superconducting film from BaF in mind, 2  it is very useful to investigate the possibily of fabricating epitaxial Y-Ba-Cu-0 superconducting film in situ with BaF as a source. 2  1.3  Outline of This Thesis  In this project, the Y i B a C u O x superconducting films were made by sequential electron2  3  beam evaporation of Cu, BaF and Y and also by coevaporation of Cu,Y ( by electron2  beam ) and BaF (by thermal evaporator) followed with high temperature post-deposition 2  annealing. The possibility of making Y-Ba-Cu-0 superconducting film in situ with BaF  2  6  Chapter 1. Introduction  as the Ba source was investigated. The conditions for in situ conversion of BaF to BaO 2  were studied theoretically in the thermodynamic equilibrium limit and were found to be consistent with the experimental results. The conditions of in situ conversion of BaCl2 to BaO was also studied. Chapter 2 shows the apparatus used in this project. The preparation method of YiBa Cu30 superconductor films is shown in Chapter 3 and the analysis of those films 2  x  is shown in Chapter 4. In Chapter 5, the conditions for in situ conversion of BaF and 2  BaCl to BaO are studied theoretically and compared with the experimental results. 2  Chapter 2 Apparatus  2.1  Vacuum Evaporation System Description  The evaporation system used in this project consists of a vacuum chamber, two electronbeam guns, one thermal evaporator, a heated substrate holding unit, plasma discharge unit and some attendant instrumentation for pressure, temperature and film deposition rate/thickness measurements (See Figure 2.2). The vacuum system used is a commercial Varian/NRC 3117 Vacuum System, which has a 191 — inch water cooled metal bell jar sitting on a | — inch thick steel flange. The vacuum chamber is evacuated by a 6-inch diffusion pump with a Welch Duo Seal mechanical pump as foreline pump. Pressure is measured by a Varian ion gauge as shown in Figure 2.2. The lowest, or the base pressure, that has been achieved in this system, was 3 x 1 0  -7  Torr.  There are two electron-beam evaporation sources with crucible capacity of 6cc each mounted inside the chamber.  One is an Airco Temescal Model STIH270-1 4-hearth  electron-beam source which has a four-crucible turret to provide the means to evaporate ..four different materials sequentially. At the time that one crucible is at the evaporation position, the other three crucibles are isolated from stray beams and falling particles. The design also prevents cross-contamination of evaporants between crucibles. The second electron gun is an Airco Temescal Model SFIH-270 electron-beam source which has only one fixed hearth. Both electron-beam sources are water cooled and the power is supplied  7  Chapter 2. Apparatus  Figure 2.2: Vacuum Evaporation System  Chapter 2.  Apparatus  9  Thermocouple  PTT  lj  Wire  *«  Copper Block H  Substrates  Screws  Stainless Steel Substrate Holder  Figure 2.3: Substrate Holding Block by an Airco Temescal CV-8 power supply. The thermal evaporator is a home-made tantalum boat with 7cc capacity, constructed from 0.127mm thick tantalum sheet. Substrates were mounted by a stainless steel holder onto a copper block with four 150W cartridge heaters imbedded in it. A piece of stainless steel sheet covers the block as a radiation shield. The temperature is measured by a type-J (Iron-Constantan) thermocouple wire attached at the back of the copper block (See Figure 2.3). Substrates were 34cm above the centre of the three evaporators. The configuration of the evaporators  Chapter 2.  Apparatus  10  and the substrate holder is shown in Figure 2.4. There is also a 50W plasma discharge unit pointing to the substrates from 10cm away, fed from a Granville-Philip leak valve. This enables activated gas to be introduced during the deposition procedure (see Figure 2.2). The plasma discharge is produced by means of a Helical resonator with the resonant frequency of 50 MHz (see Figure 2.5). The gas flows through the coil and is ionized by the electric field generated by the rf power and then ejected from the 1.5mm hole at the front end of the quartz tube. The three quartz thickness/rate monitors, positioned 33cm directly above each evaporation source, moniter the deposition rate from each evaporator and provide the rate feedback to the evaporation sources. Three 3 inch long 1 inch in diameter stainless steel tubes are attached to each monitor sensor head as shown in Figure 2.2, and prevent the three evaporators from interfering with each other's thickness/rate readings. The measurement principle and details will be discussed in Section 2.4.  2.2  Pressure Measurement  The pressure of the system was monitored by a Varian ion gauge below the gate valve of the vacuum chamber (See Figure 2.2). The background pressure was about 2 x 1 0 during most runs though the lowest pressure ever measured was 3 x 1 0 the deposition process, 0  2  -7  -6  Torr  Torr. During  or H2O vapour was introduced through the leak valve and the  plasma discharge unit. Because this was the only major inlet gas source in the vacuum chamber during the process, the pressure inside the tube of the helical resonator and the pressure in front of the substrates can be estimated from the pressure measured by the ion gauge and from the geometry of the vacuum system.  Chapter 2. Apparatus  11  Substrate Holding Block (34cm above the 3 evaporators)  I I t  Thermal Evaporator  Figure 2.4: Top view of the evaporators showing the configuration of the evaporators and the substrate holding block  Chapter 2.  Apparatus  12  <  1^- " I.D.  • 1.5 mm  Figure 2.5: P l a s m a Discharge U n i t  Chapter 2. Apparatus  13  2.2.1 Pressure inside the Helical Resonator The gas throughput at the aperture at the front end of the helical resonater tube should be the same as the throughput of the diffusion pump. Therefore [22],  C (P 1  1  - P) = SP 2  2  (2.1)  2  Where C\ is the air flow conductance of the aperture, S  2  is the pumping speed of  the diffusion pump, Pi is the pressure inside the resonator tube and P is the chamber 2  pressure measured by the ion gauge. The conductance of an aperture in a flat sheet is known to be [22],  Cx(liter I sec) = U.6A(cm )  .  2  (2.2)  where A is the area of the aperture which is 1.77 x 10~ cm . The pumping speed 2  2  S is provided by the manufacturer as 2400 litre/sec in the pressure range of 10" Torr 4  2  10" Torr. Thus, P is related to P as, 8  x  2  Pi = 1.17 x 10 P  (2.3)  4  2  In most depositon runs, P was controlled at 1.5 x 10 Torr. -5  2  Therefore, the pressure  inside the resonator tube P can be estimated as 1.8 x 10 Torr. -1  2  2.2.2 Pressure in Front of Substrates One can estimate the pressure in front of the substrates by assuming that the flux intensity of the molecules coming out of the helical resonator tube has a cos 0 angular 2  distribution. Thus, the effective area covered by this flux in front of the substrates is,  Chapter 2. Apparatus  14  A  e f f  =  / cos; 0r dO 2  = 2wv I 2  Jo  2  cos 0sin0d0 2  (2.4) where r=10 cm is the distance between the helical resonator tube and the substrates. From Eq(2.2), the conductance of the aperture with area A ff can thus be estimated to e  be 2400 litre/sec.  The conductance of the 7"-diameter and 20"-long tube connecting  the pump and the vacuum chamber is 830 litre/sec [32]. Therefore, the total conductance between the substrates and the pump is 600 litre/sec.  By using the relation of  C(P — P ) = S2P2 shown in Eq(2.1), the pressure P in front of the substrates is esti2  mated to be 1 x 10 Torr. -4  2.3  Hot Stage and the Temperature Measurement  The substrate hot stage consists of a 2" x 2" x 0.5" copper block with four 150W cartridge heaters (Watlow #E2A56) uniformily imbedded in it. Four substrates can be mounted by a stainless steel holder tightly screwed on the copper block so that there is tight contact between substrates and the copper block. A piece of stainless steel sheet covering the whole block is used as a radiaton shield to increase the heating capability. The temperature is measured by a Iron-Constantan thermocouple tightly screwed on the back of the copper block (See Figure 2.3). The power of the heaters is provided by a variable autotransformer and about 250 W power was used to achieve 850 °C temperature reading. The heaters' lives were limited to a few hours time by running heaters at the temperature above 850 °C with power exceeding 300 W . Therefore, the highest temperature  Chapter 2. Apparatus  15  that the hot stage was operated at was limited to the temperature slightly above 850 °C. The temperature at the surface of the substrate is lower than the temperature measured at the back of the copper block due to the finite thermal conductivity of the substrate, the radiation of the substrate and the thermal contact between the substrate and the block. A lower limit to the temperature difference could be estimated by a simple model assuming perfect contact between the substrate and the copper block [23],  eaT*  (2.5)  Where T\ and Ti are the temperatures of the copper block and at the surface of the substrate respectively, k is the thermal conductivity of the substrate, A r is the thickness of the substrate, e is the tolal emissivity at the surface of the substate and a is the Stefan-Boltzmann constant. The substrates used in this project have been 0.5mm thick magnesium oxide single crystal. The thermal conductivity at 800 ° C was found to be lOWatts/m- K [24]. And the total emissivity is not greater than 0.43 [25].  Thus, the temperature drop at the  surface of the MgO substrate due to the radiation is estimated as about 2 °C at 800 °C. The temperature drop due to possible imperfect contact is unknown.  2.4  Deposition Rate and Thickness Monitoring  The success of making superconducting films largely depends on stoichiometric composition of the film. The stoichiometric composition of a film is determined by the deposition rate of each evaporant, in the case of coevaporation, or the thickness of each film layer, in the case of sequential evaporation. Three Inficon quartz crystal thickness monitors were used in this project. The three sensor heads were 33cm directly above each evaporation source to monitor the deposition  Chapter 2.  Apparatus  16  rate and thickness of each individual evaporant and provide the feedback to the evaporators. Three 3-inch-long 1-inch-diameter stainless steel tubes were attached to each sensor head so that evaporant molecules could only go straight to the sensor from the evaporation source directly below it. However, molecules from other two evaporation sources could still arrive at the sensor not directly above them by collisons between evaporants. Test runs showed that this effect gives an error of less than 1% with the pressure of 1 x 10~ Torr - 1 x 10~ Torr (mean free path 5m - 50m) and with deposition rates lower 6  5  than 15A/s. The deposited film thickness is determined by the monitor from the resonant frequency shift of the loaded quartz-crystal [26],  Tj =  -^-tan- {Ztan[ % }} i  h  7rif  (2.6)  fc)  Jq  L  where  Tj  =  film  f  =  resonant frequency  of unplated  f  =  resonant frequency  of loaded  C  — a constant depending on densities of quartz and of  Z  =  q  c  thickness crystal  crystal film  acoustic impedance ratio depending on the shear moduli of deposited film  and quartz  crystal  The quartz crystals used in this project all have / , = 6MHz and the monitor refers 100% of crystal life to a 1 MHz frequency shift from 6 MHz. The Z-ratio of some materials used in this project were not available. In those cases, the Z-ratio was set equal to 1. With the life of the crystal of thick),.'.ss monitor kept below 15% in those occassions, the  Chapter 2. Apparatus  17  error introduced from setting Z = 1 is less than 3%. One can easily see this from the Taylor expansion of Tj w i t h respect to  Jq  Jq  Jq  Jq  ^Jq  Jq  Jq  Chapter 3 Preparation of YiBa2Cu30 Films x  >  3.1  Electron-Beam Evaporation  The most involved technique in the film preparation of this work is electron-beam evaporation (see §3.2). In the electron-beam evaporation process,vaporization occurs at the surface of the evaporant by electron bombardment heating.  A stream of electrons is  emitted from a hot tungsten filament and accelerated by 5 to 10 kV electric field. The electron beam is confined longitudinally by a permanent magnet and swept laterally by an electro-magnet. The accelerating voltage used in this work was normally between 6 kV and 8 k V and the emission current was between 0.04 A to 0.06 A .  3.2  Substrate Preparation  Single crystal MgO (100) substrates were used in this work to promote epitaxial growth of Y B a C u O 1  2  3  x  films. Lattice mismatch between MgO substrate and Y i B a C u 0 6 . 9 is 2  only 8% [27]. Although single crystal S r T i 0  3  3  (100), which gives 1% mismatch, would  be a better choice, MgO (100) was chosen due to the relative costs. Substrates were about 10mm x 3mm x 0.5mm in dimension and cleaned with trichlorethylene, acetone and methanol prior to deposition.  18  Chapter 3. Preparation of Y i B a 2 C u a O Films  19  x  3.3  Film Deposition  Two major different methods were employed in the deposition of YiBa2Cu30  x  films  in this work. One is a sequential deposition technique in which a multilayer film is deposited by means of a four-hearth-rotating-turret electron beam source. The second is a co-deposition technique in which two electron beam sources and one thermal evaporator are used to deposit all materials simultaneously.  3.3.1  Sequential Deposition  In the sequential deposition, the sequence Cu — B a F — Y was deposited in 15 layers (5 2  periods) with a total thickness at about 1.5 — 2/im. The deposition of Cu and B a F was 2  carried out in a vacuum of about 1 x 10~ Torr while deposition of the Y was done at 6  1 x 10~ Torr with 0 5  2  leaked in. The deposition rates of Cu and Y were kept at 5A/s  and 1.5A/s respectively and the deposition rate of B a F was between 5A/s and 2 0 A / s . 2  3.3.2  Co-deposition  Y x B a C u 3 0 films were also made with simultaneous evaporation of Cu, B a F and Y . Cu 2  x  2  and Y were evaporated by electron-beam sources #1 and # 2 respectively (see Figure 2.2) and B a F  2  was evaporated by the thermal evaporator with a current between 160A -  180A. The deposition was done in 1.5 x 10 Torr 0 _5  2  with a background pressure of  1 x 10 Torr. The deposition rates of the three evaporants were repeateadly adjusted -6  against the E D X (Energy-Dispersive X-ray) composition analysis results of the films to achieve the right stoichiometry (See §4.1). As-deposited films were about 1/zm thick and deposition rates ranged from 1.5A/s to 5A/s.  Chapter 3. Preparation of Y i B a 2 C u s O Films  20  x  3.4  Post-Deposition A n n e a l i n g  High temperature post-deposition annealing of films is needed for two reasons: first, to remove fluorine from the film, second, to crystallise and oxygenate the amorphous as-depositedfilmto form the YiBaCu306.9 superconducting phase. 2  The as-deposited samples were put in a quartz tube furnace on a quartz boat with t h efilmside up. The furnace was heated up to 850 °C at the ramp rate of 5 °C/min and then dwelled for an hour at this temperature. During this period, wet 0 was introduced 2  into the furnace tube by bubbling 0 through distilled water. The water was heated 2  to about 60 °C - 70 °C to increase the water vapour pressure. The total airflowrate (0 + H 0 vapour) was about 1 cc/second. Then, theflowof wet 0 was replaced by the 2  2  2  flow of dry 0 at the sameflowrate. The temperature was kept at 850 °C for another 2  hour and then declined at the rate of 2 °C/min to 300 °C. The samples were taken out of the furnace and cooled to room temperature at this time.  Chapter 4 Analysis of Prepared YiBa2Cu30 Films x  4.1  EDX Composition Analysis  The compositional information of the prepared films were provided by the E D X (EnergyDispersive X-ray) analysis. A Hitachi S-570 Scanning Electron Microscope equipped with a Kevex 8000 E D X system was used. The characteristic X-rays generated by an electron beam striking the atoms of the sample were detected and matched to the standard. The standard was a | " - diameter yg" thick Y B a C u 0 . g pellet numbered 88 Jul. 2, 23 1  2  3  6  provided by U B C High T Superconductivity Group. The E D X system was not able to c  detect elements lighter than Na (atomic number smaller than 11). Therefore, the oxygen content of the films was not determined. For compositional analysis of each film, data was collected and random error calculated for several points (normally 4) on the sample. The size of the analysis spot on the sample was 0.3mm x 0.4mm. The E D X analysis results were used after each film making process to adjust the thickness of the individual layers, in sequential deposition, or the deposition rate of the individual evaporants, in the co-deposition case, to appoach the correct composition. The ratio of atomic composition of the best sequential deposited film is determined to be (with order of Y:Ba:Cu) 1.0:2.1:3.1 with a random error of 10%. co-deposited film, the ratio was 1.0:1.9:3.1 with a random error of 4%.  21  In the best  Chapter 4. Analysis of Prepared YiBa2Cu3 0  | 2 mm  |  2 mm  |  X  2  22  Films  mm  Substrate  Film  Figure 4.6: Four-Point-Probe 4.2  R e s i s t a n c e M e a s u r e m e n t of t h e F i l m s  One of the most important characteristics of superconducting t h i n films is the sharp transition of the electrical resistance to zero at some well-defined temperature.  Thus,  measuring the resistance as a function of temperature of the films, is necessary. T h e four-point-probe i n the T h i n F i l m Technology L a b (Parsons Lab) was used for this measurement. A s shown i n Figure 4.6, four contact leads were stuck on the sample w i t h silver paint. T h e leads were colinear and 2 m m apart.  T h e resistance was measured by passing a  current between the outer two contacts and measuring the voltage drop between the inner two. Because very little current flows i n the voltage sense leads, the contribution of the contact resistance to the resistance measurement is negligible. T h e sample was mounted on a copper block inside the bottom end of a stainless steel  Chapter 4. Analysis  of Prepared Y i B a 2 C u s O  x  Films  23  tube with the bottom end wall made of copper to enhance the temperature uniformity. The temperature of the sample was monitored by a silicon diode which was imbedded in the copper block. The diode was calibrated against a platinum resistor from 25K to 325K. The overall uncertainty is believed to be ± 0 . 5 K [28]. The measurement was taken with the probe being inserted into a liquid helium dewar and the probe tube being evacuated and backfilled with helium gas. Data was collected with a microcomputer controlled UBC Electronics Shop Model 87-033-5 system which has a resolution of 0.3mfl [28]. The resistance vs. temperature curve of the best codeposited YiBa2Cu30 film is shown in Figure 4.7. The current of 0.1 mA through the x  sample was used in the measurement. The low T ( R = 0) and the broad transition range is believed to be due to a stoiC  chiometry that is different from the ideal "1:2:3" ratio (see §4.1). To achieve narrow, sharp transition (within few Kelvins), one has to have the stoichiometry within about 0.1% of the ideal ratio [27]. For this purpose, an electron microprobe, which has the same mechanism as E D X but uses individual elements as standards instead of the compound and has higher resolution, should be used to determine and guide the film composition.  4.3  Scanning Electron M i c r o g r a p h  Scanning electron micrographs (SEM) were taken for the best co-deposited YiBa2Cu30  x  film. As shown in Figure 4.8, it had the texture of local oriented needles along (001) plane of the substrate. Good connectivity between long grains is also shown in the picture.  24  Chapter 4. Analysis of Prepared YiBa2Cu30 Films x  Resistance (Ohm)  Temperature (K)  Figure 4.7: Resistance vs. Temperature Curve of Y!Ba2Cu30 Codeposited Film #890511. T (onset) = 87K T (midpoint) = 68K T (R = 0) = 53K x  c  c  C  Chapter  4.  Analysis  of Prepared  YiBa Cu30 2  x  Films  Figure 4.8: S E M Picture of Codeposited F i l m #890511  25  Chapter 5 In-Situ Conversion of B a F 2 and BaCb to BaO  One of the main obstacles in the fabrication of superconducting Y B a C u O films in 1  2  3  x  situ with BaF as the Ba source is the undesired fluorine in the material. One would 2  like to convert BaF to BaO during the deposition process. Therefore, studying the 2  conditions of in situ conversion of BaF to BaO is very important. BaCl was studied as 2  2  an alternative of BaF in this chapter. 2  Film Preparation  5.1  BaF was evaporated from a tantalum boat onto a MgO (100) substrate. H 0 vapour 2  2  was introduced during the deposition. The H 0 background pressure was 1.5 x 10~ Torr 5  2  (see §2.2). The deposition rate was controlled at l.OA/s throughout the process and the substrate was heated to different temperatures to study the effect of temperature on the conversion. The films were 0.5/xm thick. BaCl was evaporated under the same conditions as BaF except for a two-hour 2  2  preheat to outgas water from BaCl • 2H 0 which is hydrated in its normal form. 2  5.2 5.2.1  2  Thermodynamic Analysis Conversion of B a F 2  The overall reaction taking place during the film deposition process is: BaF  2 ( s )  + H 0 2  ( g )  =BaO 26  ( s )  -r2HF  ( g )  Chapter 5. In-Situ Conversion of BaF 2 and BaCl 2 to BaO  27  The direction of the reaction is determined by the concentrations of reactants and products, the temperature, and the pressures of the gases. The equilibrium concentrations can be obtained by minimizing the total free energy. The equilibrium appoximation is valid when the deposition rate of B a F is much slower than the reaction rates in both 2  directions (infinite reaction rate).  The total Gibbs free energy of the system can be  written as  (5.8) where ^ hj is the total enthalpy and ^ Sj is the total entropy of the system summed j j over all the reactants and products. We assume there are N sites on the surface of the film and each site can only be occupied by B a F or by BaO. Therefore, 2  £  hj = . N C o h a O + N(l - C o ) h F B a  B  B a  B a  2  + 2NC  B a 0  h F + [N' - N C o ] h o H  Ba  (5.9)  H2  where CeaO is the BaO concentration and h; denotes the enthalpy of the ith material. Because H 0 vapour was constantly supplied during the deposition process, N' is a 2  independant constant. The total entropy can similarly be written as,  ^  Sj = N C a O S B a O + N ( l B  C a0)sBaF B  2  + 2 N C a O S F + [N' - N C B  H  B a  o]sH 0 + S e 2  sit  (5.10) where SB o> a  s  BaF > HF s  2  and  SH O 2  stand for entropies of BaO, B a F , H F and H 0 molecules. 2  2  S ite is the entropy due to the occupation of the surface sites by B a F or BaO. Therefore, s  2  S ite = kln( 8  N! nB o'nBaF ! a  2  )  (5.11)  Chapter 5.  In-Situ Conversion of B&F2 and B a C l 2 to BaO  28  where n n  B a F 2  = C  B a 0  B a 0  = (1 - C  N  B a 0  (5.12) )N  "  (5.13)  are the numbers of BaO and B a F molecules occupying the N surface sites respectively; 2  k is the Boltzmann constant. Minimizing the total free energy with respect to C o> Ba  dGtoui  dC o  o n  e has,  = 0  (5.14)  B a  Note that hup and hn o  a  2  r  e  dependent on the partial pressures PHF  h F = KF + H  kTln(|S5L) = h * tm  H F  a  n  + kTln^F  d PH O respectively, 2  (5.15)  a  h o = h^ o + k T l n ( ^ ) = h H2  2  H 2 0  + kTb^o  (5.16)  P  where hj\ and h F  H 2 0  are standard enthalpies at 1 atm. V = —— denotes the dimension* tm a  less pressure normalized by P  A T M  . Since the H F pressure is proportional to the rate at  which B a F is converted to BaO, 2  P  OC 2 N C  H F  (5.17)  B a 0  PH O OC (N' - N C 2  B a 0  )  (5.18)  then we have, dh F H  dC o B a  dh o H2  dC  B a 0  kT  C  B a  (5.19)  o  NkT N' - N C o B a  ( 5  '  2 0 )  Putting Eq(5.8),Eq(5.9),Eq(5.10),Eq(5.11) and Eq(5.14) together and using the appoximation InN! ~ N(lnN — 1), we obtain,  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  kT + Ah - TAs + Tkln(  *°  C b  29  )=  0  (5.21)  1 — ^BaO  where Ah = h o + As =  S  B a  -  2h F  Ba  H  h  F  B a  2  - h o  (5.22)  Hj  (5.23)  2SHF - S B a F j - SH O  Q +  2  so that, /As _  e^ k 'BaO  i \  /As  1  Ah  e kT  l  l  -I  + e^ k /•AS _  eS R  L  1 + e^ R  Ah  e kT  i \ L  /AS  \  )  A H  > e RT  _  \  -I  (5.24)  A H  ' e RT  where AH = N Ah  (5.25)  AS = N A s  (5.26)  A  A  NA  A H can be expressed as  = Avogadro constant.  (5.27)  [29,19],  AH = A H + R T l n ( ^ ^ ) 0  (5.28)  "PH O 2  where VHF and  are partial pressures of HF and H  PH O 2  AH = 0  AH° aO + 2AH?HF B  AS = A S ° f  B a 0  +  2AS ° F  H F  - AH° - AS ° f  B a F 2  B a F 2  2  0  normalized by P  - AH° o f  H 2 0  t  m  and (5.29)  H 2  - AS °  a  .  (5.30)  AH° and AS° are standard enthalpy and entropy of formation at 25 ° C and 1 atm which can be found in various handbooks shown in Table 5.1. Thus, we have,  [30,31].  AH° and AS° for the relevant materials are  30  Chapter 5. In-Situ Conversion of B a F 2 and B a C b to BaO  <p  1+  /AS  T^e - R 1  i \  AH°  ^ e  RT  From the above information, the equilibrium curves for different values of the Vu o/"^HF 2  ratio in CeaO—T space can be obtained (see Figure 5.9). The experimental value of ^HJO/^HF  cussed  m  front of the film during the deposition process, can be estimated as dis-  below. Because of the logarithmic dependence of the conversion temperature on  ^HJO/^HF  f° fi d CsaO) precise measurements of the ratio are not necessary. The r  xe  partial pressure of H2O in front of the film is estimated to be 1 x 10 Torr in §2.2.2. _4  The upper limit of the partial pressure of the reaction product HF just in front of the film can be estimated as follows: The total number of HF molecules in the chamber should be equal to the HF production rate times the residence time: N = Nt  (5.32)  The residence time is determined by: t=^-  (5.33)  where Sff is the effective pumping speed, V is the volume of the chamber. Since N PV = - R T , e  S i S fT e  is determined by the pumping speed of the pump S and the conductance of the pipe  connecting the pump and the chamber C [32], (5.35)  Chapter 5. In-Situ Conversion of B a F and B a C l to BaO 2  2  A H " (kcal/mol) -288.5  AS? (cal/K • mol) 23.03  BaO (s)  -131.000 [31]  17.225 [31]  H 0 (g)  -57.796  45.104  H F (g)  -64.8  41.508  B a C l (s)  -205.2  29.56  H C l (g)  -22.062  44.646  0.076  34.343  0  6.77  -168.3  26.45  BaF  (s)  2  2  2  H  2  (g)  A l (s) AICI3  (s)  Table 5.1: A H ° and A S ° values for some selected materials[30,31].  31  Chapter 5. In-Situ Conversion of B a F and B a C l 2 to BaO  32  2  The pipe is 7 inches in diameter and 20 inches long, so that, C = 830 litre/s [32]. The pumping speed S is 2400 litre/s (see page. 13). Thus, S fr = 6201itre/s. e  From the fact  that the B a F was deposited at a rate of lA/s (which is about | monolayer/s) and the 2  area size of a molecule is about 10A , the flux <j> of H F molecules coming out from the 2  reaction can be estimated as follows:  .  . 1  (p ~  . 3  ~  m o n  .  °^ y a  e r  /  molecules s e c  —io^2—  x  6.7 x 10 molecules/m sec. 18  (5.36)  2  where factor 2 represents the fact that each B a F  2  molecule generates 2 H F molecules.  Since the reaction takes place all over the hot area facing the deposition, which is the area of the bottom side of the heating block (2inch x 2inch, or 5.1cm x 5.1cm), the production rate of H F is,  N  =  4> x (5.1cm x 5.1cm)  ~  1.7 x 10  16  molecules/sec  (5.37)  Thus, the partial pressure P H F is estimated to be 9 x 10 Torr. It follows that the ratio _7  VH O/'PHF 2  1 S  a  hout 1 x 10 . The solid line in Figure 5.9 shows the equilibrium CBSO—T 11  curve with VfyofPuF = 1 x 10  11  which represents the experimental conditions in the  film preparation. Since P H F is proportional to the B a F  2  deposition rate (see Page 32),  changing the deposition rate will shift the C o — T curve. Figure 5.10 shows the C o — T Ba  Ba  curves with P H O = 1 X 10~ Torr and the deposition rates being O.lA/s, lA/s and lOA/s. 4  2  The rate of O.lA/s is probably too slow for practical film growth.  33  In-Situ Conversion of B a F 2 and B a C l 2 to BaO  Chapter 5.  BaO  600  650  700  750  800  850  Figure 5.9: T h e equilibrium curves of the B a F  2  900  950  1000  B a O reaction i n the CaaO—T space.  34  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  BaO  600  Figure 5.10: rates.  650  CB O—T B  700  750  800  equilibrium curves for P  850  900  950  o = 1 x 10 Torr and different deposition 4  H 2  1000  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  35  Conversion of B a C l 2  5.2.2  For B a C l conversion, the overall reaction can be written as: 2  BaCl  + H 0  a ( B )  2  (  g  BaO  r  (  8  )  +2HCl  (  g  )  Following procedure similar to § 5.2.1, we find,  ^-e TT (  Cfiao =  _  1  e TtT-  )  _  ™ „ o 1 + ^ 2 e ( i r - ) e"rer  (5.38)  r  Q 2 £  AH  1  •p  Here  A S = AS? A H  = A H ?  0  B  B a  A  0  o + 2AS ° ci - A S ° f  H  f  + 2AHf°HC1 -  AH ° F  B a C l 2  B A C L 2  - AS?H O  (5-39)  2  -  AH°  H 2  (5-40)  o  Similarly, the equilibrium curves for different values of the ratio PHao/^HCi  m  C  B a  o—T  space can also be drawn (see Figure 5.11). The solid line shows the CBaO—T curve with 'PHZO/^HCI =  3  1 ° - Comparing Figure 5.9 and Figure 5.11, one can find that BaClo  x  U  requires a higher temperature to convert than B a F Therefore, B a C l  2  is less favourable than B a F  2  2  does under the same conditions.  as the Ba source for in situ growth of  Y ! B a C u O films. 2  3  x  5.3 XRD and EDX Analysis 5.3.1 XRD Analysis of BaF Films 2  Because B a F  2  and BaO have different crystal structures, they exhibit different X-ray  diffraction (XRD) patterns. As shown in Figure 5.12 and Figure 5.13, B a F  2  has a very  simple pattern while BaO has a relatively complex pattern due to the existance of many hydrated forms of BaO.  B a F films made under different temperatures were studied by 2  Chapter 5. In-Situ Conversion of B a F  600  650  700  750  2  and B a C l  800  850  Figure 5.11: The equilibrium curves of the BaCl  2  2  36  to BaO  900  950  BaO reaction in the  1000  CBBO-T  space.  Chapter 5. In-Situ Conversion of B a F  15  20  25  30  35  and B a C l  2  40  Figure 5.12: X-ray Diffraction  45  2  to BaO  50  Pattern of B a F  2  37  55  Powders  60  Chapter 5. In-Situ Conversion of B a F j and B a C l 2 to BaO  Figure 5.13: X-ray Diffraction Pattern of B a O Powders  38  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  X-ray diffraction. Figure 5.14 shows the transition from B a F perature range 775 ° C — 850 °C.  2  39  to BaO over the tem-  Although the peak intensities of X R D pattern from  powder diffractometer are not useful for a quantitative comparison between B a F and 2  BaO concentrations due to the strong orientation dependence of the intensities, they can still provide a qualitative picture of the conversion. Figure 5.15 shows the BaO concentration in the films against the temperature at which the film was deposited. The BaO concentration is defined as,  C BaO  =  fBaOmax  J  —J  -* BaOmax  where  iBaOmax  a n <  i  iBaFimax  a  r  e  '  BaF^max  the highest peak intensities of BaO and B a F in the film 2  X R D patterns respectively. As shown in Figure 5.15, the experimental data are shifted to higher temperature from the theoretical prediction. However, we believe this difference in temperature is within the experimental error in the temperature determination. The surface temperature of the substrate is expected to be lower than the measured temperature of the heating block due to imperfect contact between the substrate and the heating block (see §2.3) and radiative cooling of the substrate.  The anomalous behaviour at  805 ° C to 820 ° C suggests that the random variations in the temperature of the substrate measurement are around 15 ° C . B a F films were also made under the same conditions as above, but with H 0 vapour 2  2  replaced by 1) H 0 vapour + 0 , 2) 0 2  2  2  plasma, and 3) H 0 plasma. No substantial 2  improvement of BaO conversion were found. This is not a surprising result, if the surface is already in thermodynamic equilibrium with the partial pressure of H 0 , in the absence 2  of the plasma. The plasma is expected to facilitate the achievement of equilibrium by breaking down activation barriers. The equilibrium concentration does not depend on the path, or the reaction rates. As shown above, it has already achieved the equilibrium with H 0 vapour. 2  Chapter 5. In-Situ Conversion of B a F  2  and B a C l  40  to BaO  2  (in) (200)  Ba$ Powder  BaKj BaKj  Deposited at 775 C  BaKj  v o  I  BaK,  Deposlted at 790 C BaKj  I Deposited at 805 C  CO CD CO  e BaF  2  f  Deposited at 820 C  A  Deposited  a t 8  3  5  °  c  e  Deposited at 850 C  f  15  20  25  30  BaO Powder  35  38  Figure 5.14: X R D Patterns of the Transition from B a F  29 ( ° ) 2  to B a O  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  A BaO 1  i  0.9  -  0.8  -  0.7  -  0.6  -  0.5  -  0.4  -  0.3  -  i  •  Experimental  • Theoretical •  1  • • • • • • • • •' • * •' u ^ . ' 1  1  1  1 1 1  jjj./  0.2 0.1  H  0  i i i | i i"iii i i i i | i  600  650  700  750  £r&\ i i i i | i i i i | i i i i j i i i i 800  850  900  950  1000  Figure 5.15: B a O Concentration as a Function of Temperature  Chapter 5. In-Situ Conversion of B a F 2 and B a C l 2 to BaO  5.3.2  E D X Analysis of B a C l  2  42  Films  In Situ conversion of B a C l to BaO was studied as an alternative to B a F conversion. Be2  2  cause both B a C l and BaO are hygroscopic, they both give complex X R D patterns which 2  are not easily distinguishable between each other. On the other hand, E D X provides a very effective way to detect elements heavier than Na such as C l (see §4.1). Therefore, the E D X technique was used to analyze the conversion of B a C l to BaO. One B a C l film 2  was made under the same conditions as those of the B a F  2  2  analysed in the last section  at substrate temperature of 740 °C. This sample was tested by E D X with B a C l • 2 H 0 2  2  powder as the standard. The atomic ratio between Ba and C l of the film was found to be 1:1.6 with a random error of 5%. This result of losing Cl in the film indicates that 20% of the B a C l has been converted to BaO in situ. The temperature requirement is similar 2  to that of B a F  5.3.3  2  conversion which is consistent with the prediction made in §5.2.2.  Discussion  As shown in §5.3.1, it was found that the substrate must be heated to 800 °C in order for the B a F  2  to convert to BaO in situ during the film deposition process. A n attempt was  made to grow a co-deposited Y-Ba-Cu-0 film at this temperature. The resulting film was transparent even though the thickness monitors gave the final thickness of the film as 1 fim (thickness monitors' crystals were water cooled to make the resonant frequency consistent). This temperature was found to be too high for the growth of Y-Ba-Cu-0 films presumeably because the deposited copper re-evaporates at these high temperatures. However, the growth temperature can be reduced by reducing the H F partial pressure (see §5.2.1). Adding an H F getter (such as quartz wool) to the film growth environment and reducing the heated area exposed to B a F would help reduce the H F partial pressure. 2  An experimental investigation of this might be worthwhile.  Chapter 5. In-Situ Conversion o / B a F 2 and B a C b to BaO  43  F r o m the growth temperature point of view, BaCl2 does not offer any advantages over B a F  2  as a source for B a i n the  in situ growth of YiBa2Cu30 films. Also, B a C l x  is hygroscopic, and the long preheating necessary to outgas water is an undesireable complication.  ,  2  Chapter 6  Conclusions  The Y j I ^ C u s O x superconducting films have been reproducibly made by both sequential evaporation and co-evaporation of Cu, B a F and Y , followed by high temperature post2  deposition annealing. The best film achieved the onset critical temperature of 87K and zero resistance critical temperature of 53K. The low T ( R = 0) and the broad transition C  range is believed to be due to stoichiometry different from the ideal "1:2:3" ratio. Thus^ more accurate control over the film stoichiometry is needed. The electron microprobe, instead of E D X , might be the choice. The possibility of making Y B a C u O superconducting film in situ with B a F as the 1  2  3  x  2  Ba source has also been investigated by studying the conditions for in situ conversion of B a F to BaO. The BaO concentration in the film as function of the substrate temperature 2  was provided by the equilibrium thermodynamic analysis.  The experimental results  showed agreement with the equilibrium model within the experimental measurement error. It was also found that producing a plasma of the gas reactant had no substantial effect on the conversion. This is believed to be due to the equilibrium nature of the conversion reaction at the given conditions. Under the current apparatus conditions, the substrate temperature was found to have to be as high as 800 °C to achieve the in situ conversion of B a F to BaO. However, this temperature can be reduced by reducing the 2  H F partial pressure in the reaction scene. Adding an H F getter (such as quartz wool) to the deposition chamber and reducing the heated area exposed to B a F are suggested. It 2  might be also be interesting to see the plasma effect at the lower substrate temperature  44  Chapter 6. Conclusions  45  if the above mentioned suggestions are practiced. A brief exploration of BaCl2 showed that BaCl2 does not have any advantage over B a F as the Ba source for in situ growth of Y-Ba-Cu-0 films from the growth temperature 2  point of view. In summary, a possible route of low temperature in situ fabrication of Y-Ba-Cu0 superconductor film using electron-beam evaporation technique with BaF2 as the Ba source was investigated and one of the key obstacles yet to be overcome for in situ growth is keeping the H F partial pressure low.  Bibliography  [1] A . M . Wolsky, R . F . Giese, E . J . Daniels, Scientific American, 260(2), 61, (1989) [2] N.W. Ashcroft, N.D. Merrnin, Solid State Physics, Holt, Rinehart and Winston, Philadelphia, 1976, pp. 726-753 [3] J . Bardeen, L.N. Cooper, and J.R. Schrieffer, Phys. Rev., 108, 1175 (1957) [4] J . G . Bednorz and K . A . Muller, Phys., B64, 189 (1986) [5] Z.Z. Sheng, A . M . Herman, Nature, 332, 58 (1988) [6] R . K . Singh, L . 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