THE MOBILITY OF THE COPPER AND SILVER EVAPORATED DEPOSITS. Rosalie Brandon. F. J. Bradshaw. CLEARfNGHOUSE FOB FEDERAL ^ISHTIFIC AND

Transcription

1 $ mi 1 liliiii»i mmm MARCH ROYAL AIRCP^n' ESTABLISHME TiCHNICAL REPORT No. fckh«i mi? i-h ; :. THE MOBILITY OF THE E ATOHS OF COPPER AND SILVER EVAPORATED DEPOSITS fey Roalie Brandon F. J. Bradhaw CLEARfNGHOUSE FOB FEDERAL ^ISHTIFIC AND TECHNICAL rnfob^ation ^_ r i c.. III; 0 o-a /7 ^'d C5ö p^- iiffluw! "S^S^e ;:)

2 ü.d.c Ho i ^ : ROYAL AIRCBAFT ESTABLISHMENT Technical Report Ho March 1966 THE MOBILITY OF THE SURFACE ATOMS OF COFFER AM) SILVER EVAPORATED DEPOSITS hy Roalie Brandon F. J. Bradhaw SUMMARY Etimate of the urface elf-diffuion coefficient of evaporated depoit were made from (l) the pread of material into a hadow cat by the placing of an object between ource and ubtrate, (2) the decay on annealing of the tep produced in a aetal film depoited onto a mica urface with a cleavage tep, (3) the thermal, grooving of grain boundarie in depoited film, and (4) the growth of hole in thin film. Rate law were propoed and verified experimentally for tep moothing and the growth of hole. Departmental Reference: CIM 67

3 COKEEETS p^ i ntcroiwcnon 5 2 THEORY The decay of a tep, (Method 2) Sitjoothing of a tep vhoe height i increaing at a 7 contant rate, (Method 1) 2.3 Grain boundary grooving, (Method 3) The growth of hole in thin evaporated film, 8 (Method 4) 2.5 The urface energy, EXPEMMEOTAL 11 4 THE SMOOTHING OF A STEP WHOSE HEIC2IP IS INCREASING AT A 12 CONSTANT RATE, (Method 1) 4.1 Introduction Experimental Reult Dicuion 13 5 THE DECAY OF A STEP, (Method 2) Introduction EjqperijQental Vacuum anneal Air anneal Reult Dicuion l6 6 GRAIN BOUNDARY GROOVUK}, (Method 5) Introduction Experimental Reult Dicuion 18 7 THE GROWTH OF HOLES IN THIN EVAPORATED FUm (Method 4) l8 7.1 Introduction Experimental Reult Dicuion 21 8 CONCLUSIONS 21 Symbol 22 Reference 23 Illutration Figure 1-20 Detachable abtract card

4 ILLUSTRATIONS The moothing of a tep of height a, due to urface diffuion 1 The hape of a grain boundary groove due to urface diffuion 2 The profile of a hole in an evaporated film which i growing by urface diffuion 5 Profile of hole edge k The variation of the urface tenion of ilver with environment 5 Subtrate heater 6 Shadow of a 10)i tungten wire formed on a copper ubtrate at -450 o C by evaporating copper for two minute 7 Step of ilver formed by the evaporation of ilver onto cleaved mica 8 Photograph of a tep of ilver on mica after heating at 480 o C in air for 64 hour 9-6 The urface diffuion coefficient for ilver in a vacuum of 5 X ICT torr 5X10' torr. Ehead' re cult in nitrogen plu 3 c r hydrogen end in vacuum are alo hewn 10 Surface elf-diffuion coefficient for ilver heated in air 11 Growth of the width of grain boundarie with tine for ilver heated in air at 800 o C 12 An example of the growth equence when a film of ilver on mica i heated in air at 560 o C. Thickne of film ~1100 Ä 15 A wedge haped film of ilver on mica after it ha been heated at C for 2 hour in air 14 Graph of (final diameter of hole) 5 / 2 - (initial diameter of hole) 5 / 2 againt time interval for hole in a ilver film of thickne iq 1.1 X 10 y cm on mica when heb.ed in air at C (a&b) Graph of (2r-.) - (2r.) ^ againt time interval for a hole in a Figi ilver film of thickne 1.1 X 10'^ cm on mica when heated in air at C (a&b) 5/2 5/2 Graph of (20 ' - (2r.) ' againt time interval for hole in a 1 1 -k ilver film of thickne 1,9 X 10 cm on mica when heated in air at 500 o C 17 Graph of log I) againt 10 /T for ilver on mica heated in air 18 Silver film of thickne ~1000 A on mica and gla ubtrate after 19 heating for J hour at ~500 o C in air (a&b) Graph of the diameter of a hole againt etimated time ince formation of hole for ilver on mica at C 20

5 OS 1 CTTRODüCTIOH Few quantitative experiment have been performed to meaure the mobility of atom in evaporated depoit, CaipbeH tried to meaure the mobility of evaporated atom by oberving the penetration of evaporated atom on a ubtrate into the umbra formed by placing a harp edge between the ource and ubtrate. The mobility wa decribed in term of the ditance in which the thickne of the evaporated depoit fell to l/e of it maximum value. He obtained value of thi ditance for evaporated gold on different ubtrate at room temperature which ranged from 1,2\i on carbon to l^n on lithium fluoride. 2 Pahley et al oberved the coalecence of two mall gold crytal into one on a ubtrate of molybdenum diulphide at 400*C. From the.rate of growth of the neck between two crytal he deduced that a urface elf-diffuion mechanim wa the dominant proce for the tranfer of material but he did not attempt to obtain quantitative data. The object of our exploratory experiment wa to obtain, if poible, quantitative data on the mobility of metal atom in metal film depoited by thermal evaporation on to variou ubtrate, (later called "evaporated film"). Meaurement were made of the ma tranfer of material and a with all uch experiment we obtained value of the product of the rorface elf- diffuion coefficient, D, and the urface energy, y. m order to deduce D, S So it i neceary to aume value for y. 8 The following method were ued to obtain D :- (1) the diffuion of evaporated material into the hadow cat by placing an object between the ource and ubtrate, i.e. the moothing of a tep whoe height i increaing at a contant rate; (2) the decay of the tep produced by the evaporation of a metal layer on to a mica urface with cleavage tep; (5) the thermal grooving of grain boundarie; and (4) the growth of hole in a thin evaporated layer. The mcbln boundary grooving method ha been uccefully aoplied previouly 4 TJ 5 to bull 1 ; ilver and copper'. In thee exploratory experiment the film were depoited in vacua of to 10 torr. However thee method can alo be ued for clean urface experiment if ultra high vacua ere ued for the depoition and ubequent heating. Thu the ucceful ue of evaporated film would make poible the

6 tudy of clean urface of the le refractory metal. Thee cannot eaily be tudied by the only other clean method of field emiion, 2 THEORY üfoe principle of the four method are a follow:- 2.1 The decay of a tep (Method 2) When a metal i evaporated onto a mica urface with cleavage tep the contour of the mica are reproduced by the evaporated, metal. The film thickne i arranged to be greater (-JOOO A) than the tep height (-2000 Ä), and harp tep are elected. However, the method i retricted to metal which depoit epitaxially on the ubtrate and have the ame crytal orientation on both ide of the tep. The tep can mooth by urface diffuion, volume diffuion, vicou flow or the evaporation and condenation of metal atom. For ilver and copper below temperature of C it ha been hown that urface diffuion i the dominant proce in the grooving of grain boundarie for boundary width le than about 20^, We therefore aume that for tep moothing below C where the characteritic width are le than 2öy. f urface diffuion i alo the dominant ma-tranfer mechanim. Thi argument alo applie to the other method ued, when the characteritic dimenion of the region in which ma tranfer i occurring i of order 20)i or le. 6,. Mullin obtained for the moothing by urface diffuion of a tep (x,t) of initial height a ituated at x = 0 after a time t x (x,t) * / g(e,t) de (1) where g(c,t) = a (Bt) 1 * L (Bt) lt -' (2) n=oo f(u) 'I n=0 (-1) \~. (5)

7 ex: B = D vfi 2 7 /kt, and S Sr 2 1 D «urface elf-diffuion coefficient (cm ec ) v = urface denity of atom (cm ) ß e atomic volume (cm ) 7 = urface free energy (dyne cm ) -1 k = Boltzmann' contant (erg deg ) o T = temperature K. Uing the fact that o. / g(e,t) de = a/2 -oc and integrating the erie obtained by ubtituting (5) and (2) in (l), ve obtain for (x,t) the converging erie (x,t) = + ^rr(i)u-r(^)^ ^r^^-lrg)^*...j (4) where u = j. A plot of (x / t) i hown in Hg."I. The abcia i in (Bt)'^ i term of the dimenionle quantity x/[(bt)\l, Hence the ditance from x = 0 (the initial poition of the tep)..to the point where (x,t) firt croe the x axi i approximately equal to 20 (Bt) 1 *. Since we did not oberve the "hump and dip" on the ide of the tep we take (ee Section 5.5) the total Vidth" of the tep to be W «4-6 (Bt)* (5) 2.2 Smoothing of a tep whoe height i increaing at a contant rate (Method 1) If during evaporation an object with a harp traight edge i placed between a ource and ubtrate, and cloe to the ubtrat^ a tep i obtained whoe vertical height increae at a contant rate, a*. If the temperature of the ubtrate i hot enough to allow appreciable urface migration during depoition there will be a continual moothing of the tep a material diffue into the umbra formed on the ubtrate by the object. In order that grain boundary grooving effect will not interfere with thoe due to tep moothing, depoition condition mut be uch a to lead to large crytal. In order to analye the above ituation we aume that the condening atom loe their exce kinetic energy on their firt impact. Thu from

8 ,Wl, K 8 para.2.1, the olution y(x,t) for the moothing of the tep edge i given by t y(x,t) = j (x,[t-t 1 ]) dt» (6) o vhere 8(x, t) i defined by equation (l), a i replaced by a* and t i the ^otal evaporation time. A ve could not produce a converging erie for thi integral, a rough etimate of the width of the tep ufficiently accurate for preent purpoe va taken to be W =* 4*6 (Bt) u (a given in 2.1). Thi lead in princi- ple, to em overetimate of D, but not by more than an order of magnitude. 2.3 Grain boundary grooving (Method 5) If a polycrytalline pecimen i annealed, groove develop at the inter- ection of the grain boundarie with the urface. (Thi i due to the etting up of local equilibria.) For Iotropie urface diffuion, with no lo of material into the grain boundary itelf, a "hill" hould develop on both ide of the groove, (Fig.2). 7 The groove deepen with time and Mullin ha hown that the groove width, w, i related to the time of anneal, t, by p where B = D vft y /k T. o w = 4.6 (Bt)^ (7) For our experiment uing thi method the pecimen conited of poly- crytalline ilver film on mica. A for bulk material, meaurement are made only on thoe grain boundarie which do not move during annealing. 2.4 The growth of hole in thin evaporated film (Method 4) Mot work wa done uing thi method. Given a uitable ubtrate on which the depoit can be formed with a ufficiently large crytal ize, the ubequent heating will enable the film to reduce it urface area, by the creation and growth of hole. The motive force for the growth of an exiting hole by urface diffuion i the urface tenion. Conider the growth of a hole of radiu r in an evaporated film of thickne d. We aume that the angle of contact of the film with the ubtrate at the edge of the hole i 9 and that, a the hole grow in ize by urface migration, the cro-ection of the edge of the hole i a "emi-circle" of radiu x at any intant, (Fig.3). In practice mall depreion are probably formed at the junction of the "emi-circle" and the unditurbed film but thee are neglected. The flow of migrating urface atom *

9 0«i due to difference of chemical potential \i at region of differing curvature. Thu the net flux, j, of atom at A along the urface i D J = -«v (8) kt where i the ditance along the metal urface, = 0 being the point where the edge of the metal film urface ^oin the ubtrate. The urface concentration of atom, v, can be put equal to that of a flat urface if change in i are mall with repect to k T. If the olid i conidered a bounded by a urface of uniform tenion y, A A then the preure difference acro the urface i 7 ( ), whence the difference in chemical potential due to the urface tenion, which i the Vdp term in the Gitb free energy change, i ^ -H* = -^(^-7) = - ft 7 /x for r» x (9) where the ubcript L refer to equilibrium with the local urface, the ubcript ^> to equilibrium with a flat urface, and ft i the atomic volume. Conidering equation(8) aid Fig.5, we aume that the curvature change from - to zero within a ditance «x. (Thi could be wrong by a factor of two or x three.) Putting ö = «x aid dpi = ft 7 /x in equation(6)we obtain S' D ft7 d * -^ i-v. 00) 5 k T «x The total perimeter acro which diffuion occur i 2«r, o that the volume rate of tranfer of material, dv/dt, by urface diffuion i ö r 2KT ft. Hence,.. 2 D ft 2 7 r Since the total volume of material i unaltered, <* ' ktx 2 ' * ^ or 2flr Z ~~ = n r 2 d n x 2 = r d. (12)

10 10 Hence ubtituting in equation (n) ve obtain AM 2 D Q 2 7 ä v. 05) dt k T d that From Pig.4 ve can ee that dv = 2nT x dr. Uing equation (12) it follow A* dt "- ^nr W < «A+ dt * \ lh i If we ubtitute for dv/dt uing equation (l4) e v ' equation (15) Integrating give. D n 2 7 v.--- dr f it dt Nr d " k T dr B?/ 2 «1 /2 7^ 5/2 3 llf B t = 2 d^ ^ = ) The merit of thi method over the other i that ve have a urface contour change vhoe time contant depend on film thickne. Thu for thin film (<5000 A), optically meaurable change occur in reaonably hort time even for value of E and D, one or two order of magnitude le than thoe producing meaurable change in practicable time interval by the other method. 2,5 The urface energy, 7 We ued Method 1 for copper and Method 2, 3 and 4 for ilver. A all the o above method yield data on B (where B = D V ft 7 /k T) we need to aume a value for 7 to obtain D. The value of 7 ued for copper in vacuo are thoe Q of Udin given by the equation 7 = O.5875 T erg/cm 2 where T i the temperature in degree abolute. The value of 7 ned for ilver are hown in Fig.5. Thoe in air are by q 10 Buttner et al and thoe in purified helium by Punk et al. From the data given for the adorption of oxygen on ilver in Section 5.^ it can be hown that oxygen adorption hould t; w» place (6 ^ ) for P 0 ^ lo' 5 '^ atmophere at

11 JI o C. From the graph given by Buttner et al for the oxygen partial preure dependence of the urface energy of olid ilver at 932 C it can be een that, -5.3 extrapolating to a P n of 10 ' atmophere we obtain the 7^ quoted for puri- fied helium. Thi mean that the value of 7 we quote for purified helium are for ilver free from adorbed oxygen and can be ued for 7 in a vacuum if no adorbed layer i preent. It can be een from Fig.5 that dicrepancie arie from extrapolating the reult ff 7 to low temperature a the two curve cro at a higher temperature th abolute zero. A we were primarily concerned with the order of magnitude of D in our experiment, 7 for ilver in air at 200 o C to ^00 o C wa taken to be equal to that for ilver in helium. (OSii give an upper limit to 7.) 5 EXPERIMEHIAL The evaporation experiment were done in a vacuum unit with a preure of -6-5 «5 X 10 torr before evaporation and of-j X 10 torr during evaporation. Thi,unit conited of a gla,belljar of 12" diameter by 14" high ealed to a mild-teel baeplate with a L-haped viton gaket, a baffle valve, liquid nitrogen trap and a FSOJ diffuion pump backed by a rotary pump. Current and rotary feed-through were ealed to the baeplate uing "0" ring, The rotary feed-through wa ued to operate a hutter placed between the ubtrate and the evaporation ource, Theroocoi^le feed-through were made by brazing ceramic- metal fecd-through into a mild teel "blanking off" plate..the evaporation ource wa a molybdenum boat 0»15 cm wide, 5*5 cm long and 0*6 cm deep heated by radiation from a U-haped tantalum trip which urrounded it. To reduce the heating of the be11jar and content, the ource wa orrounddd by three cylindrical heat hield. The evaporated beam paed through a lit onto the ubtrate. The ditance from ource to ubtrate wa 8 cm. The copper charge for the boat wa "pectrographically tandardied" copper wire, upplied by Johnon, Matthey and Co. Ltd., which had been urf^a cleaned by electropolihing in a bath of orthophophoric acid (denity l.jö gn/cc) uing 1-1 procedure imilar to Mullin and Shewmon.. It wa then wahed in 10^ by volume of orthophophoric acid (denity 1.75 gv cc ) to minimie phophate reidue, ditilled water, and Analar Acetone. The "pectrographically tandardied" ilver wire charge wa cleaned by dipping it in concentrated nitric acid, then wahed in boiling ditilled water, cold ditilled water and methyl alcohol and then dried. The temperature of all charge wa lowly brought up to the evaporation temperature and retained at thi for at leat one minute to outga before the molybdenum hutter wa opened and the depoition tarted. ^

12 12 Two ubtrate heater vere ued in thee experiment. The larger power heater conited of a t" thick copper block of urface ize n X 1^M. Heating element of platinum-15/' rhodium wire in 2 aa diameter pyrex tube and two thermocouple were inerted into hole drilled parallel to the ubtrate heating urface. The pecimen were clamped to the heater by a copper plate. The other heater conited of a piece of tantalum trip, inche thick and approxi-«mately a quarter of an inch wide, bent a hown in Fig.6. The trip wa heated directly by paing a current through it and it temperature wa meaured by thermocouple welded on to it back urface. The temperature of the depoit wa no doubt lightly different from that given by the thermocouple and it wa etimated that the temperature difference wa probably le than 10 o C. The ubtrate were clamped to thi heater with mall tantalum trip. The former heater wa ued in the experiment uing Method 1 and the latter in the other method, 4 THE SMOOTHIlKx OF A STEP WHOSE HEIGHT IS IMCREASIHG AT A COHSTAKT RATE (Method 1) " 4.1 Introduction Thi wa the firt method ued. The urface elf-diffuion of copper by grain boundary grooving with bulk pecimen ha been tudied earlier and thu comparable data on evaporated copper film wa of interet. Since the ue of a mica ubtrate to produce epitaxial film of copper i difficult, it wa decided to try copper itelf a a ubtrate and to work at high temperature in order to produce a uitably large crytal ize. The experiment wa one of imultaneou depoition and diffuion and, depite the reulting difficultie in analyi, erved to how if the ytem wa worth tudying. further. It wa one which can eaily be repeated under clean condition in ultra-high-vacua. 4.2 Experimental The hadow tep wa produced by claraping loji (and 90^) diameter tungten wire acro the pecimen uing the ame copper clamping plate a wa ued to hold the pecimen itelf. To reduce the width of the penumbra, the wire were parallel to the long dimenion of the boat; for the 10\i wire the penumbra wa 0»1}J. wide. Thu, ignificant_experimental reult require a half width of the tep after mooth- 5 ing of» 0*1 }i. Tbe previou work indicated that, to obtain mooth tep width of d«2[i with copper in vacuo, high temperature ( > C) or impoibly long evaporation time would be required.

13 TT Bulk copper pecimen 1.5 cm by 0.5 cm by 0.05 cm were ued a a ubtrate. The copper wa annealed to give a large grain ize, then prepared by electro- polihing and wahing a decrihed previouly for the copper charge (Section j). In order to promote rapid cooling of the ubtrate a oon a the eaqperlment wa completed the apparatu wa let down to atmopheric preure with dry nitrogen. l8 minute were required for the ubtrate to cool from 600 o C to 100 o C. After evaporation the pecimen were examined with a "Hilger and Watt" interference microcope and the width of the tep were meaured uing a adcrometer eyepiece. The region of ndlnimum width along the whole length of the hadow wa elected a being the point where the wire touched the ubtrate and therefore the region with minimum uncertainty due to penumbra. The preure during thee experiment wa of order 10"^ torr. 4.5 Reult It wa found that the type of evaporated film obtained depended on the orientation of the ubtrate grain. Some of the evaporated material wa produced in a granulated form (Fig.7). With uch film it wa more accurate to ue a graduated eyepiece than to meaure a photograph. The width of the tep varied uddenly from one ubtrate grain to the next and a. 1 o from ide to ide of the wire howing a large orientation dependence of D ; the maxi mum width of the tep correponded to the ubtrate grain with the mallet grain ize of depoit. The maximum oberved diffuion coefficient for copper were of order 10 cm /ec at 450''C and 10" 5 cm /ec at 600 o C. The minimum diffuion coefficient obtained were ~ l/t5 of thee. 4.4 Dicuion Thee experiment did not give better than an order of magnitude etimate of D due to the approximation ued in the analyi and to the large thermal inertia of the heater which caued cooling time comparable with the time of the experiment. The author previou experiment with bulk copper in a vacuum of "1 X 10~* torr gave a D^ at 603 o C of (2.5 ±0.5) X ;0' cin 2 /cec and at o C of (5.5 ±0.8) x 10 cm /ec. Becaue of the large pread in width of the hadow tep obtained in thee experiment it can only be een that the order of D r are the ame for the two experiment. Thi r.oan that within the rather poor accuracy of the method the urface mobility of atom immediately after depoition by evaporation i the ame a for urface atom of the bulk material.

14 14 5 THE DECAY OF A STEP (Method 2) 5.1 Introduction In view of the difficultie experienced vith copper film^ the ytem of 12 ilver on mica wa ued for thi method. The "bulk urface diffuion of ilver had previouly "been meaured try Rhead, and o comparative data on evaporated film va again of interet. Pahley found that if ilver wa evaporated at a rate of 10 A/ec on to cleaved mica heated to a temperature between 250 o C and 300 o C, a well orientated ingle crytal could be obtained -when the ilver reached a thickne of 1000 A. The orientation he found wa (ill} Ag // {ooi 1 mica cleavage and <?.1Q> Ag // to <PlQ>mica, By uing thee condition a ingle crytal of ilver wa produced on mica in which there wa no change in orientation acro the tep. However, in our experiment the mica tep height were about 2000 K, and thicknee > 5000 Ä were required to enure continuity of the ilver film. Uing toe Pahley method to produce uch thick film gave a crytal ize which wa too mall to prevent grain boundary grooving interfering with tep moothing. We therefore ued the modified method of Lowe ^ in which film of ~ 1000 Ä are depoited on to a ubtrate at 28o 0 C at a rate of ~ 20 Ä/ec and then growth continued at an increaed ubtrate temperature of 400 o C and at an increaed evaporation rate. In thi way a large crytal ize wa obtained in the required film thickne. It orientation i imilar to Pahley', i.e. I 111} Ag // {00l} mica cleavage plane <01Q> Ag // <P1Ö> mica. 5.2 Experimental The mica ubtrate were cleaved in air and quickly tranferred to the evaporation unit decribed in Section 5. The thicknee of the film were meaured with an interference microcope. Since mica i oft, a pyrex trip wa alo ued a a ubtrate in ome experimtnt o that the thicknee of the evaporated film could be checked with a Talyurf. The pyrex trip were prepared by wahing them in BBS 25 detergent (manufactured by "Medical Pharmaceutical Development Ltd.) rining in boiling ditilled water, then methyl alcohol and then heating them overnight at 500 o C in air. An example of the tep produced i hown in Fig.3. Such tep were annealed for a meaured time in either air or a vacuum. S Vacuum anneal Since the ubtrate heater ued in the preparation of ilver tep on mica did not allow very accurate temperature meaurement and the preure in -6 the evaporation chamber wa not le than 5 X 10 torr we tranferred the J

15 of. 15 pecimen to another vacuum furnace operating at5x10 tojxio torr for the diffuion experiment. Thi furnace wa a gla ytem which encloed a ilver boat and lid containing the pecimen, and wa pumped by a ilicone oil diffuion puxnp via a liquid-nitrogen trap. The pecimen were put in the illoa tube through a viton "O" ring eal. A furnace wa drawn over the ilica tube during anneal. Temperature were meaured by an external thermocouple, 5.2,2 Mr anneal For the anneal in air the pecimen, contained in a ilver boat, were placed in an open-ended ilica tube which wa put into a furnace whoe tempera- ture wa meaured by thermocouple. The change in width of the evaporated tep with time of heating wa meaured uing a micrometer eyepiece on a Hilger and Watt Interference microcope, 5.3 Reult An example of the revolting hape of the tep after annealing i hown in Fig,9. The hump and dip theoretically predicted and hown in Fig.1 were not oberved. Thi may be becaue the predicted height for the hump and dip wa only 5$ of the total height of the tep and therefore too mall to be een. At high temperature ome of the tep profile had a mall ridge intead of hung? on one ide. A thi may have been due to the tepped mica eparating from the heet (due to the evolution of water at high temperature) it wa decided to work at lower temperature. In ome of the experiment the face of the tep did not remain mooth; thi may have been due to the preence of adorbed oxygen cauing faceting. The value of D obtained by the analyi of the decay of a ilver tep in a vacuum of approximately 5X10 torr uing 7 for a clean urface (Fig.5) are 4 hown in Fig.10. Rhead' reult uing grain boundary grooving in bulk material -7 to obtain the D of ilver in a vacuum of 5 X 10 torr and hi reult in an atmophere coniting of nitrogen plu five per cent molar concentration of hydrogen at a minimmn dew point of -78,5 0 C are hown for conprion. The thick- ne of mot of the film ued were in the range 200C Ä to 4000 Ä and the tep height were in the range 1250 A to 5000 Ä, The meaured D for ilver in vacuo (ee Fig.10) wa mall (D K 2 X cm /ec at 7C0 o c) and of the order of the limit of detection. In order to invetigate the method further^ lower temperature experiment on tep moothing were therefore done in air ince it wa expected that the preence of oxygen would increae the apparent urface diffuion coefficient. Thi proved to be o 7 2 and urface mobility wa oberved at 400*0 with D ^ 1.5 X 10 cm /ec. The

16 16 value of 0 obtained from the analyi of the moothing of ilver tep in air 4 are hown in Fig.11. Bhead' reult, viing grain boundary grooving in bulk ilver, are alo hown for comparion. Ehead could not meaure the growth of grain boundarie below TOO'C a extenive faceting occurred. 5,4 Dicuion Jxygen i readily adorbed on the urface of ilver and becaue of the high heat of adorption involved it i generally accepted that oxygen i adorbed a atom. The reaction can be repreented a 0^ + 2 Ag = 2 (Ag - 0), where (Ag - 0) repreent an oxygen atom adorbed on a urface ite. Then,2 ^G = ^fl-o^s = -RTln [ 9-.1 P (i - er.i '! where ^6, ^H and ^6 are the free energy, enthalpy and entropy of adorption, & i the fractional urface coverage and P.. i the oxygen preure in atmophere, 14 2 Gonzalez and Parravano obtained, for mall Ö, AH = -108 Kcal/mole of oxygen and Ag = -66 cal/mol/degree. Thi indicate that oxygen adorption hould take place (0 S i) for P ^ 10 2 ' 7 torr at 800'C. In our vacuum experiment we vere working in a preure «5X10 torr with reidual gae probably tending to reduce Ö rather than increae it. Thi mean at thi preure and at a temperature of 800 o C the coverage 9 for oxygen «l/lo. The ame argument could reaonably apply to Rhead' reult in vacuo and the oxygen adorption in hi nitrogen-plu-hydrogen atmophere hould have been even le. It i not clear why hi experiment in the two environment which he ued gave different reult above 800*C ; but our own meaurement in vacuo agree reaoiably well at 800 o C with hi in nitrogen-plu-hydrogen. At lower temperature it i poible that oxygen adorption in our vacuum condi- tion would lead to value of D greater than Rhead r in nitrogen-plu-hydrogen. Cur reult for the urface elf-diffuion of ilver in air (ee Fig.11) when extrapolated interect thoe of Rhead at 800 o C, but, at 600 o C and below, the value we obtain for D are lightly higher than thoe expected from the extrapolation to 600 o C of Rhead f reult to lower temperature. Thi may be due to the fact that a the temperature of the experiment are reduced and pread obtained in D increae (ee pread in Rhead^ value in Fig.11) and, a we have picked mainly {m} plane by evaporating ilver on mica, we may have picked a particular plane which correponded to the upper value in Rhead,

17 catter. Choi and Sherwoon, tudying thermal grooving of copper in hydrogen found that D for {ill} plane va larger than that for {110} and {loc}, the ratio D (ml/d {loo} having a mean of 2.8. Blakely and l^rkura uing the ^M decay of a cratch on hulk nickel in a vacuum of 10 torr alo found that D wa greater near the {ill} plane, A Blakely and Hykura prchahly had oxygen adcrhed on their nickel it appear that, for both clean f.cc metal and f.c.c. metal with adorbed oxygen urface diffuion i fater near the {m} plane, 6 GRAIN BOUNDARY GROOVING IN EVAPORATED DEPOSITS (Method 3) 6.1 Introduction A the light difference between our reult and Rhead^ could be due to the method cf meauring D by the moothing of evaporated tep it wa decided to check our value for D by making ome meaurement on the growth in air of grain boundarie in evaporated ilver, 6.2 Experimental If Pahley^ and Lowe^ evaporation condition (ee J.l) are lightly altered, by uing either higher ubtrate temperature or different evaporation rate, Pahley ha hown, and we confirm, that the deired polycrytalline film reult. Such polycrytalline film were annealed in air a decribed in Section 5.2,2, In practice, grain boundary grooring experiment were carried out at the ame time a the moothing of evaporated tep. The change in width of the grain boundary groove with time after heating wa meaured, a before, with the interference microcope, 6,5 Reult The value of D obtained from the analyi (2,5) of the grain boundary grooving of evaporated ilver in air together with previou reult are hovn in Fig.n, On drawing the curvj mot weight wa placed on the value for D at C (10 /T = 9.5) and 600 o C (lo /T = 11.45) a thee are the average reult from at leat 6 groove. Fig,11 how that there i very good agreement between the value of D obtained from the moothing of an evaporated tep and from the growth of a grain boundary in evaporated film. A an example of the growth rate oberved, a plot of the width of the grain boundary groove againt time at 800 o C i hown in Fig,12. Each point on the graph i the average width of at leat ix grain boundarie, (The bar how the total pread in the actual value of width.) The reulting line of bet fit (Fig.12) repreent a line which approximate well to the t k law expected from the analyi giving upport to the aumption that the ma tranport wa due to urface diffuion. A C wa the highet temperature ued for thee experiment it wa even more likely that

18 T^ urface diffuion wa the dominant mechanim at ICTC temperature. However tte hape of the grain boundary groove found in thee experiment were not the 7 ame a thoe expected from Mullin analyi and hown in Fig.2 a they did not have uch ditinct hump on each ide of the grain.boundary, Khead alo oberved thi in hi experiment on ilver in nitrogen-plu-hydrogen. Lo of material down the grain boundary or poibly anitrcpy of urface diffuion may account for thi, 6,4 Dicuion The good agreement between diffuion data from tep moothing and grain boundary grooving in air lead u to ugget that our earlier comparion (Section 5»^) of tep moothing reult in vacuo with Ehead' data from grain boundary grooving in vacuo and nitrogen-plu-hydrogen wa reaonable. The value of D, from grain boundary grooving in air, are again greater than thoe of Rhead' and the reaon given in Section 5.^ may alo apply here, 7 THE GROWTH OF HOLES IN THIN EVAPORATED FILMS (Method k) 7,1 Introduction When evaporated film of ilver, of thickne le than approximately 5000 Ä, on mica are heated, in air, hole are nucleated in the film and grow with time. Let u conider equation (l5), i.e. r 5 ' d ' =2,5 JT 2 Bt, If the radiu of the hole, r, i equal to the thickne of the film,., we obtain r = 2,5 ^ 3t, If we coup are thi with the equation for the growth of a grain boundary w = 4,6 (Bt) 1 *,,,,(7) and if we et the ame obervable limit (i,e, 1 pi) on the order of the width, w, of the grain boundary groove and the S diameter of a hole 2 r, it can be een that the mallet B, and therefore D, obervable i the ame in each cae, Hovever if we chooe a film thickne much le than 1 u the obervable B and D can be decreaed by at leat an order; (two ordar would require a film thickne of approximately 500 Ä), Two limit were placed on the temperature of the experiment. Above approximately 800 o C mica releae water vapour and a lower limit of about C wa et by the very long time the hole took to nucleate in air. Film thicknee were choen o a to produce, on ubequent heating, dicreet hole of greater than 1 n diameter, (l \x being the practical lower limit for our optical meaurement of hole ize.) Within thee limit, we were unable to nucleate hole in ilver film in vacuo, though we were able to oberve hole growth.

19 vy E3g)erlmentRl Single crytal ilver film on mica vere made a decribed in Section 5.1. The ilver wa alo evaporated on to pyrex (prepared a decribed in 5.2) at the ame time in order to ccaapare the behaviour of the two film on annealing in a vacuum and in air. The thicknee of the ilver film varied from 270 * to 10 A, Some film were alo made in the form of wedge of maximum thickne 7500 A "by putting a mak at uch a ditance from the ubtrate a to produce a uitable penumbra. The change in the appearance of the film with time after heating (method decribed in and 5.2.2) wa recorded uing a tandard photo-micrographie method. A it wa hoped to lower the order of magnitude of D meaurable by thi method all anneal were in the temperature range C to 575 *C which wa below the range of previou meaurement made by grain boundary grooving method. 7,5 Reult We will conider firt thoe reult obtained from heating in air, ince here the break up of the film into hole wa rapid. The complete nucleation, growth and break up to produce channel with final hrinking of the film into globule i hown in Fig.lJ. The change in the appearance of the film on heating in air produced by changing the thickne of the ilver film on mica i hown in the wedge film in o Fig.l4, The thickne of thi film varied from zero to 2700 A, it can be een that it contained hole at ~ 23OO A thickne, channel at " 1000 Ä, and formed globule at 900 A, A expected the thicker the ilver film; the lower wa the nucleation and growth of hole and the larger the hole were before the channel "tage" occurred. In addition the globule finally formed were larger with a thick film. Little reliability can be placed on the abolute thicknee of the wedge film quoted due to the non-linearity of the decreae in thickne of the wedge. No meaurement were made uing wedge film. Equation (l5) give the relation between the radiu, r, of the hole and the time, t, ince the tart of the hole formation. Since the tart i never clearly oberved, our analyi for D i baed en meaurement of the radii of the hole, r- and r., at time t_ and t. repectively. The ubcript f and i refer to,final and initial obervation. The variation of (2r f ) ' - (2r.) '. with t f - t. hould be linear. Fig,!5, l6 and 17 how uch plot for experi- ment at C, 265*C and 500 o C, No plot are hown for experiemnt at jso'c ince the film agglomerated o quickly that only two point were obtained. Thee graph how that the theory propoed in Section 2,4 applie to the growth

20 20 of the hole. From the lope of the line in Fig, 15, l6 and 17, value of D were obtained and are hown in Fig.lS, The cro-ection of the film edge a hown in Fig.^ wa not alway een. In practice there wa ometime a flattening of the ridge producing a plane parallel to the ubtrate. Similar film were raade on pyrex gla uhtrate and were heated in air. For an equal thickne (~ 1000 k) the film on gla broke up into a tructure which wa much finer than that on mica (Fig,19)» Thi i to be expected ince without epitaxy the film wa probably polycrytalline on a very fine cale. Attempt were made to do imilar experiment in vacuo of «10 torr on film of Ä, However after heating to ^OO^ for 7^ hour.no change could be een on either pyrex or mica ubtrate. Either there wa a difficulty in hole nucleation or the diffuion coefficient wa much le. To overcome the nucleation difficulty and obtain a ratio for D in air to that in vacuo, hole were nacleated and grown in air and then tranferred to vacuum for obervation of any further growth. The reult of uch an experiment i hown in Fig,20. From the analyi in Section 2,4 ( 2 r f )5/2. {2ri) 5/ 2 t f If we had left the hole repreented in Fi2,20 of diameter 2r. = 2-1 \x to grow in air it would, have reached a diameter'2^ [air] of approximately 7*4 [x in / i -6 x ld7t hour, wherea In a vacuum of ~ 10 torr it actually reached a diameter 2r f Lvac] of 2,55 P- in the ame time. Therefore the ratio D inair ^^ (2r f [air] ) 5 / 2 - (2r 1 ) 5 / 2 y,^/ 2 r g.^/ 2 at 265 D in vacuum o 0 = ter^vac])^2-^/ 2 = ttw r^t^ =. 70 If the line of bet fit of the point in Fig.20 i extrapolated to give 2/5 2r f. air rather than the t line the ratio obtained i =* 150, o that a a rough guide, we can ay that D for ilver in a vacuum i at leat two order maller than in air at C. Further experiment of thi type are needed at temperature between C and 700, C to demontrate the ue of thi method for meauring mall value of D,

21 Dicuion The value for C of ilver in air from the growth of hole at low temperature are much lar^v,r than thoe obtained by extrapolating the value for I) hown in Fig. 11 to ewer temperature. The theory propoed in ection 2 A gave a growth law which eem to fit our reult a the lope of both our graph in Fig.18 and Fig, 11 are th-5 ame within experimental catter. Therefore formula(15)may only be wrong in it contant. Given that the value of D at 265*C in vacuo i approximately two order lower than that in air then it can reaonably be concluded that thi alone wa not reponible for our failure to ee the hole ir. vacuo but that there mut have been an additional factor in the nucleation tage, 8 CONCt TSIOMT) Uing mi-tranfer method, the order of the urface elf-diffuion coefficient, D, of ilver and copper ha been found to be Independent of whether the metal i in a bulk or evaporated film form. It ha alo been hown that an increae of oxygen preure increae the urface diffuion rate of ilver. The above eqoeriment have alo demontrated that D, can be meauicd uing the new technique of tep moothing and hole growth in evaporated depoit. The growth law for a hole viz, "the radiu of a hole, r, growing by urface diffuion i proportional to t ' d"''' where t i the time ince the formation of the hole and d the thickne of the film", wa propoed and verified experimentally. Uing thi method, D ' of two order of magnitude lower than that calculated from any of the other"method were meaured. The difficultie of nucleating hole in vacuo would be an obtacle to carrying out a complete evaporation and diffuion experiment in ultra high vacua (at l^at with ilver 01 mica), but more experiment could be done in which hole are nucleated by heating evaporated ilv Tilm in air and then grown at temperature between C and 700*0 in a vacuum. However lack of time prevented thi mot obviou extenion of the work and a more detailed confirmation of the obervation made, Aclmowle dgement Section 2, We wih to thank D, M. Gilbey for hi help with the theorie propoed in

22 SYMBOLS? -1 D = Eurface elf-diffuion coefficient (CEI ec ') v -2 7 = urface free energy (erg ca ) a = tep height (CPJ) V = urface denity of atom (cm ) 0 = atomic volune (cur; k = Boltzinann, contant (erg deg ) T = temperature ( 0 K) a 1 = rate of which a tep height i increaing (cm ec ) w = width of grain boundary due to urface diffuion (cm) 8 W = width of a tep due to urface diffuion (cm) t = time of anneal (ec) t«- t. = time interval for a hole^ rcdiu to increae from r. to r- (ec) r radiu of a hole (err;) r. = initial radiu of a hole (cm) r- = final radiu of a hole (cm) d = thickne of a film (cm) j = net flux of atom alon^ a urface ji = chemical potential of atom (erg) ÄH = enthalpy of adorption (k cal per mole) ß = entropy of adorption (cal per mole per degree) 9 = fractional urface coverage of oxygen

23 Hb. Author 1 D. S. CanpbelL 2 D. w. Pahley Title, etc..th Trane. 9 Vaciaan Syngpoium, 29, (1962) Phil. Ha«. 10, 127 («S^) M. J. StoweU M. H. Jacob T. J. Law 5 J. M. Blakely Progre in Material Science, Publihed Pergaxnon Pre 10, (1963) k G. E, Rhead Acta Met. 13, 225, 0965) 5 F. J. Bradhaw R. H. Brandon Acta Met.12, 1057, (1964) C. Wheeler 6 w. W. Mullin 7 W. w. Mil T Un 8 H. Udin 9 F. H. Buttner E. R. Funk J. Appl. Phy. 50, 77, (1959) J. Appl. Phy. 28, 553, (1957) Metal Interface, Publihed A.S.M. 114, (1951) J.Phy.Chem. 56, 657 (1952) H. Udin 10 E. R. I^mk Metal Interface, Publihed A.S.M. 122, (1951) n H. Udin J. Wulff w. W. Mullin P, G. Shewmon Acta. Met. 7, 165, (^59) 12 D. W. Pahley 15 R. M. Lowe Phil. Mag. 4, 316, 0959) Acta. Met. 12, 1111, (1964) ik 0. D. Gonzalez G. Parravano J.Am.Chem.Soc. 76, 4533, 0956) 15 J. V. Choi Tran. A.I.M.E. 224, 589, 0962) P. G. Shewnon 16 J. M. Blalcely Acta. Met. 9, 23, (1961) H. Mykura. 1-

24 (Bt) FIG. I. THE SMOOTHING OF A STEP OF HEIGHT <*: DUE TO SURFACE DIFFUSION WiDTH OFQROOVE,u> FIG 2. THE SHAPE OF A GRAIN BOUNDARY GROOVE DUE TO SURFACE DIFFUSION

25 FIG.3.THE PROFILE OF A HOLE IN AN EVAPORATED FILM WHICH IS GROWING BY SURFACE DIFFUSION (NOT DRAWN TO SCALE) TH\S AREA IS d v /2TTr" FIG. 4. PROFILE OF HOLE EDGE

26 Ofy 4-00 SOO feoo 700 BOO TEMPERATURE 0 C 900 looo FIG. 5. THE VARIATION OF THE SURFACE TENSION OF SILVER WITH ENVIRONMENT THERMOCOUPLES A,,4 THOU TANTALUM SHEET V STRAPS TO HOLD SPECIMENS FIG. 6. SUBSTRATE HEATER k

27 Fig.7. Shadow of a 10/4. tungten wire formed on a copper ubtrate at<v450 o C by evaporating copper for 2 minute Fig.8, Step of ilver formed by the evaporation of ilver on to cleaved mica

28 Net No C1925 Fig-9 Fig.9. A tep of ilver on mica after heating at 480 o C in air for 64 hour

29 IO O FROM THE SMOOTHINq OF A STEP IN A VACUUM OF -n. 5* IO" fa TORR O FROM QRAIN BOUNDARY QROOVINQ IN A VACUUM OF.«. 5* IO" 7 TORR [q E. RHEADj 10 -.d b O if) ni E o *r 0 A A A t -7!0 A A IO IO e IO IO* n 13 FIG 10 THE SURFACE DIFFUSION COEFFICIENT FOR SILVER IN A VACUUM OF 5XIO" 6 TORR.RHEADS RESULTS IN NITROGEN PLUS 5 0 /o HYDROGEN AND IN VACUUM ARE ALSO SHOWN

30 n [RHE:AO3 SILVER IN AIR GjRAlN BOUNDARY GiROOVIN^ SIUVER IN AIR GRAIN BOUNDARY firoovinq ÖÜR RESULTS A SILVER IN AIR STEP SMOOTHING OUR RESULTS 0 E 0 c h o II 12. I0 + /T 0 K FIG.M. SURFACE SF.LF-DIFFUSION COEFFICIENT FOR SILVER HEATED IN AIR in» '*** I 1 ^ I- - --r-n" ^, -r i 1, * _ **- -f V' c ' ' : ^ -» V^v (* ^1 J-j- ^J ^-» *- 1 [ _ 1 --l - *! ^^ ^, M - FH i, 1 i ' 1 to TIME HR5 IOO FIG.I2.GROWTH OF THE WIDTHS OF GRAIN BOUNDARIES WITH TIME FOR SILVER HEATED IN AIR AT 800 C

31 Time: V/i min. Time: 3/2 min. Time: 8 min. Time: 65 min Scale: 1(V Fig.13. An example of the growth equence when a film of ilver on mica i heated in air at 360 o C. 0 Thickne of \\\mco IIOOA

32 N«g. No. C1937 Fig.M Thickne of film 0 ^900A «v 1800 A A> 2700A Scale: J IG, Fig. 14. A wedge haped film of ilvt on mica after it ha been heated at 300 o C for 2 hour in air A

33 T o L 2x 10 - Jllo«1 X 10 - to SO TIME (hr) FIG. 5.(a) 11 X 'O lox. IO öx IO 6 6* IO ^ L 4 X 10 I 5l 2* IO - L O IO ao SO foo TO 80 TIME INTERVAL (hr) FIG 15. (b) FIG,! 5. GRAPHS OF(FINAL DIAMETER OF HOLE )^^NITIAL DIAMETER Of HOLE)% AGAINST TIME INTERVAL FOR A HOLE IN A SILVER FILM OF THICKNESS M X IO" 5 cm ON MICA WHEN HEATED IN AIR AT i75 0 C

34 - ü' lo SO TIME. (NTERVAL (hr) FIG- 16(a) 30x IO "h 10 E-O T\ME INTERVAL (hr) FIG- 16. (b) FIG. I6.GRAPHS OF{2rf)^ -(2rj)^ AGAINST TIME INTERVAL FOR HOLES IN A SILVER FILM OF THICKNESS II X I0 5 cfti ON MICA WHEN HEATED IN AIR AT C

35 ao 3o TIME INTERVAL (HR) F IG. 17 GRAPH OF (2r^^-(2^)4 AGAINST TIME INTERVAL FORA HOLE IN A SILVER FILM OF THICKNESS 19 X lo~ 4 cm ON MICA WHEN HEATED IN AIR AT C

36 1 1 \ 1 0 \ \ { \ -6 9 \ 1 \ \ -7 N 0 N \ k N in Ü D VT 0 J C) \ ^ - \ \ k 0 o \ X -9 k {(> \1 )6 19?.o Z\ ^^. 2.^ 0 K FIG. 18. GRAPH OF LOG D AGAINST I0 4 /T FOR SILVER ON MICA HEATED IN AIR

37 M ^ a. Silver on mica ^ «b. Silver on gla Scale: I J icv Fig.19a&b. Silver film of thickne ruloooa on mica and gla ubtrate after heating for % hour at 300 o C in air

38 OI Ng.^ü IÜ o i h- UJ 10 z < < UJ u o er UJ > O-r X < u_ o UJ h- UJ < ÜJ I ü_ o O UJ O I o o < o U- I So O CMß r- CM (H) -aioh JO ti3±3kmvia