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7/30/2019 Improved Current Efficiency Equation for the
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J O U R N A L O F A P P LIED ELEC TR O C H EM IS TR Y 2 5 (19 95
) 7 64 -7 69
Improved current e f f i c iency equat ion for thee l e c tr ode
pos i t i on o f c oppe rH . V O G TFachbereich V erfahrens-und U
mwelttechnik, Techn& che Faehhochschule Berlin, D-13353 Berlin,
GermanyReceived 3 October 1994 ; rev i sed 30 January 1995
T h e c u r r e n t e f fi c ie n c y o f c o p p e r d e p o s
i t i o n i s c o n t r o l l e d b y t h e e x t e n t o f th e c
o m p e t i n g h y d r o g e nf o r m a t i o n r e a c t i o n w
h i c h a c t s o n m a s s t r a n s f e r o f c o p p e r i o n s
t o g e t h e r w i t h f u r t h e r m a s s t r a n s f e rm e c
h a n i s m s . A n a v a i l a b l e c u r r e n t e f f i c ie n
c y e q u a t i o n t a k i n g a c c o u n t o n l y o f t h e b u
b b l e - i n d u c e dm i c r o c o n v e c t i o n f a i l s i n
t h e c a s e o f f o r c e d e l e c t r o ly t e f l ow . T h e e
q u a t i o n i s n o w e x t e n d e d t o a l l o t h e rm e c h
a n i s m s . R e s u l t s ar e c o m p a r e d w i t h e x p e r
i m e n t a l d a ta .
L i s t o f s y m b o l sc c o n c e n t r a t i o n (m o l m 3
)C 1 c o n s t a n t , Eq u a t i o n 1 5 (m2 s -1 A - '5 )d b u b
b l e b r e a k -o f f d i a m e t e r (m )D diffusion coefficient
(m 2 s -1)dh equ iva len t d iameter (m)F F a ra d a y c o n s t a
n t (F = 96 4 8 7 C m o 1 -1 )f~ g a s e v o l u t i o n e f fi ci
e nc y ( - )g a c c e l e r a ti o n d u e t o g r a v i t y (m s -
e )j to ta l cu r ren t dens i ty (A m -2 )J l p a r t i a l c u r
r e n t d e n s i t y o f c o p p e r d e p o s it i o n( A m - z
)J 2 p a r t i a l c u r r e n t d e n s i t y o f h y d ro g e n
fo rm a t i o n( A m - 2)k overa l l mass t rans fer coeff ic ien t
o f copp er ion ,Eq u a t i o n 1 6 (m s -1 )kb microconvec t ion
mass t rans fer coeff ic ien t(m s -1 )k n na tu ra l conve c t ion
m ass t ran s fer coeff ic ien t( m s - 1 )kv macroconvec t ion
mass t rans fer coeff ic ien t( m s - 1 )K1 d imens ion less g roup
, Eq uat io n 19K 2 d i m e n s i on l e s s g ro u p , Eq u a t i
o n 2 0/3 d imens ion less g roup , Eq uat io n 26K M m i g ra t i
o n fa c t o r ( - )L charac te r i s t i c l eng th in na tu ra l
conve c t ion (m)1 . I n t r o d u c t i o nIn d u s t r ia l h i g
h - ra t e d e p o s i t i o n o f c o p p e r i s c o m -monly
opera ted wi th cu rren t e f f i c ienc ies con-s iderab ly smal
le r than un i ty . The compet ing lossr e a c t i o n i s t h e fo
rm a t i o n o f h y d ro g e n . Th i sreac t ion i s no t s imply
de t r imen ta l in tha t i t lowersthe current efficiency. I t is
to lerated to gain largeproduct iv i ty ra tes in tha t i t ac t s
benef ic ia l ly wi threspec t to the increase in the l imi t ing
cu rren td e n s i t y o f c o p p e r d e p o s i t i o n . Th e s
e f a c t s c a n b ee luc ida ted on th e bas i s o f the in te r
fe r ing m asst r a n s f e r m e c h a n i s m s o f c o p p e r i
o n s a n d d i s s o l v e dh y d ro g e n .
L h channel leng th (m)n c h a rg e n u m b e r ( - )p p ressu
re (kg m -1 s -2 )R un iversa l gask g m 2 s - 2 m o l -1 K -1 )T t
e m p e ra t u r e (K , C )v f low ve loc i ty (m s -1 )X d i m e n
s io n l e ss p a r a m e t e r , Eq u a t i o n 2 2
cons ta n t (R = 8 .3143
Greek lettersc~ exp ansio n coefficient (m 3 mo1-1)e curr ent
efficiency (- )0 f rac t iona l sh ie ld ing o f the e lec t rode
su r face ( - )u s t o i c hi o m e t r i c n u m b e ruL k inem at
ic v i scos i ty o f liqu id (m 2 s -~)Transport numbersR e R e y n
o l d s n u m b e r , Eq u a t i o n 11ReG R e y n o l d s n u m b
e r o f g a s ev o l u t io n , Eq u a t i o n 1 3Sc S c h m i d t
n u m b e r , Eq u a t i o n s 5 a n d 6Sh S h e rw o o d n u m b e
r , Eq u a t i o n s 4 , 1 0 a n d 1 2SubscriptsB d i s s o lv e d
h y d ro g e nC c o p p e r i o nc cri t icalG gase e l iqu id bu
lk
I t i s t h e o b j e c t o f t h e p r e s e n t p a p e r t o
s h o w h o w ,a n d t o w h a t e x t e n t, t h e m a s s t r a n
s f e r o f c o p p e r i o n sto the ca thode i s a f fec ted by
var ious mechan ismsa n d h o w t h e c o m p e t i n g h y d ro g
e n e v o l u t i o n a f f e c t sthe mass t rans fer . The p
resen t paper wi l l d i scuss th i sef fec t qua l i t a t ive ly
and quan t i t a t ive ly . Resu l t s a recom pare d wi th those o
f a p rev ious res t r i c ted inves t i-ga t ion [1 ] . The p
resen t theo re t i ca l resu l t s a re f ina l lyc o m p a re d w
i t h e x p e ri m e n t a l l i te r a t u re d a t a .2 . T h e r
a n g e s o f m a s s t r a n s f e rTh e p o t e n t i a l o f a c
a t h o d e , w h e re c o p p e r i s d e p o s i t e df rom a su
l fu r ic e lec t ro ly te so lu t ion , i s show n as l ine 1
76 4 0021-891x/93 1993Chapman & Hall
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IMPROVED CURRENT EFFICIENCY EQUATION FOR THE ELECTRODEPOSITION
OF COPPER 765
, 0 ,E 1 0 a ) I:. ~ 0 . 613
0 . 4U
0 . 2
0, C i I , I , I f I ,0.0 0.2 0.4 0.6 0.8D i m e n s i o n l e s
s p a r a m e t e r , K 3
,0
Fig. 3. Current efficiency as a function of the parameter/3,
Equa-tion 25.
mass transfer coefficient used for evaluation ofEquation 23 are
k v =2 2 x 10-6ms -1 for one ofthe sets of Janssen's experimental
data with anominal velocity of v = 0.33ms -~, and kv =37 x 10-6ms
-1 for a second set o f v = 0.84ms -1.The mass transfer coefficient
for liquid-phase naturalco n v ec t i o n , kn, was calculated from
Equation 4. Thevalues turned out to be small enough compared
withthose of forced flow, kv, to be of virtually no effectin the
current density range applied. The masstransfer related to bubble
evolution was calculatedfrom Equat ion 12 with Equations 7 and
8.
The calculated partial current densities of bothcompeting
reactions are shown in Fig. 4. Reactionkinetic data for the
hydrogen formation reactionwere taken from Nieber [20]. The partial
currentdensity for copper deposition was calculated for thetwo flow
velocities and the conditions of Janssen'sexperiments [16] from
Equation 3 with Equations 14and 16 for given values of the partial
current densityJ2. The cathode potential shown in Fig. 4 is of
noeffect on the interrelation of the partial currentdensities.The
calculated current efficiencies for the same twoflow velocities are
shown in Fig. 5, lines (b) and (c).They are compared with the
experimental datapoints of Janssen [16].6 . Dis cus s ion
The restricted current efficiency Equation 24 based onthe
assumption that the mass transfer is controlledsolely by
bubble-induced microconvection, representsthe lower bound of the
current efficiency. This isshown in Fig. 5 as line (a).The
experimental values of the current efficiencyobta ined by Janssen
[16] for two flow velocities arelarger than line (a) thus
confirming the beneficialeffect of superimposed forced convection.
The
~ 'E 1 0 4 , ~ ~ ( l b )< \ ~ _ _ ( l a )
+ - 10 3-oEo. ~ 10 2
10 1- 0 . 8 - 0 . 6 - 0 . 4 -0 '. 2 0 . 0H y d r o g e n o v e r
p o t e n t i a l / V
Fig. 4. Increase in partial current density of the c opper
deposition(1) as the gas evolution (2) attains large values, l(a):
calculatedfor the conditions o f Janssen's experiments [16} for a
nom inal velo-city V = 0.3 3ms-1; l(b): v = 0.8 4ms 1.
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7/30/2019 Improved Current Efficiency Equation for the
Electrodeposition of Copper
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IMPROVED CURRENT EFFICIENCY EQUATION FOR THE ELECTRODEPOSITION
OF COPPER 769
1 ~ 0 . 9~ 0 , 7 -(3
0 . 6 ,
A
1 0 2 1 0 3 1 0 4Current de nsity j / A m 2
F i g . 5 . T h e c u r r e n t e f f ic i e n c y a s a f u n c
t i o n o f t h e t o t a l c u r r e n td e n s i t y , c a l c u
l a t e d f r o m E q u a t i o n s 2 5 a n d 2 6 . ( a ) : v = 0 ;
( b ):1 1v = 0 . 3 3 m s - . ( c ) v = 0 . 8 4 m s - . E x p e r i
m e n t a l d a t a p o i n t s f r o mJ a n s s e n [ 1 6] , ( C )
) : v = 0 . 3 3 m s - 1 ; ( 0 ) : v = 0 . 8 4 m s - 1 .
experimental data are slightly lower than thetheoretical lines
(b) and (c) for both experimentalsets of varying flow velocity. It
is difficult to becertain whether the reason for this discrepancy
is theunusual geometry used in the experiment orinaccuracy in the
properties data used in thecalculation, particularly in Equations 7
and 8.
Figure 5 expresses the well-known fact that thecurrent
efficiency generally decreases as the currentdens ity increases.
But the effect is negligible a t largevalues of flow velocity and
moderate values ofcurren t density. As the current density
increases, themass transfer mechanism of
bubble-inducedmicroconvection becomes dominant. This is visiblefrom
the asymptotic approach of the forced flowlines (b) and (c) to line
(a).
Equation 23 has been derived for the currentefficiency of copper
deposition. However, the
equation is a general one and may be used for theprediction of
current efficiency of other reactionsaccompanied by competing gas
evolution.7. SummaryThe current efficiency Equation 23 or 25,
derivedtheoretically, contains mass transfer coefficientsassociated
with forced flow and natural flow inaddition to that of
bubble-induced microconvection.Thus, it takes account of all the
three mass transfermechanisms acting in copper deposition and is
ageneralization of the prior Equation 24 [1]considering
microconvection alone.
Comparison with experimental results forelectrodeposition of
copper under forced flowconditions confirms the suitability of the
improvedcurrent efficiency equation.References
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C . K a y s e r , Z. E l e k t ro c h e m . 3 6 ( 1 9 3 0 ) 4 2 8
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n d H . V o g t , Eleetrochim. Acta 2 4 ( 1 9 7 9 ) 1 1 .[ 1 2] H .
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W . S e i l e r a n d H . V o g t , In t . o . H e a t Ma s
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