structure and properties of sputtered zno...
TRANSCRIPT
STRUCTURE AND PROPERTIES OF SPUTTERED ZnO TRANSDUCERS
Aly Hassan Fahmy 1 B.Sc. (Eng.) 1 (Cairo Univ.)
STRUCTURE AND PROPERTIES OF SPUTTERED
ZINC-OXIDE TRANSDUCERS
by
Aly Hassan Fahmy, B. Sc. (Eng.), (Coiro Univ.)
A thesis submitted to the Faculty of Graduate Studies and Research
in portial fulfillment of the requirements for the degree of
Master of Engineering.
DeflOrtment ci Electrical Engineering,
McGi11 University,
Montreal, Canada.
March, 1971.
o .;ly Ha~sar. Fah:Dy lm
ABSTRACT
A technique has been perfected for depositing epitaxial Zinc-Oxide
films on c - axis oriented sapphire by R F sputtering of the compound in a reactive
atmosphere. The fi Ims produced are evaluated with regard to their use as ultrasonic
transducers at microwave frequencies. To include the effect of the metal electrode
layers in evaluating the performance of these transducers, a computational algorithm
has been developed for calculating the response of multilayer transducer structures which
also takes into account the effects of finite film resistivity and contact resistance. The
computed response is fitted to the measured data using a simple least squares procedure
in order to obtain the effective electromechanical coupl ing constant of the transducer.
It is demonstrated that films can be obtained which have an effective electromechanical
coupling factor of 0.25, very close to the bulk value of 0.28.
ACKNOWLEDGEMENTS
The author wishes to acknowledge his gratitude to Dr. E. L. Adler
for his valuable help and guidance.
i i
Many persons aided in the preparation of this thesis. Discussions with
Messrs. R. Mildenberger and P. Ramakrishna were particularly rewarding. Mr. J. Foldvari
has contributed in innumerable ways. 1 am also grateful to Mrs. P. Hyland for on ex
cellent typing job of a for from clear manuscript.
Thanks are also due to the Defence Research Board of Canada for financial
support (Grant 5525-07) and to Coiro University for granting the author leave of absence.
i i i
TABLE OF CONTENTS
A BSTRACT
ACKNOWLEDGEMENTS ii
TABLE OF CONTENTS iii
CHAPTER INTRODUCTION
CHAPTER
CHAPTER
CHAPTER
Il
2. 1 2.2 2.3 2.4 2.4 .1 2.5 2.6 2.7 2.8
III
3.1 3.2 3.3
3.3.1 3.3.2 3.3.3
IV
4.1 4.2 4.2.1 4.2.2 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1
PERFORMANCE OF MULTILAYER PIEZOELECTRIC TRANSDUCERS
Introduction Basic Equations The Multi layer Structure Problem Acoustic Power Generation Input Impedance and Transducer Loss Acoustic Power Detection The Non-Conducting Case Computer Program Computed Resu Its
R F SPUTTERING OF ZINC-OXIDE TRANSDUCERS
Introduction Sputtering of Zinc-Oxide Factors Affecting the Fabrication of ZnO Transducers Factors Pertaining to the Sputtering Station Factors Pertaining to the Substrate Independent Factors
TRANSDUCER FABRICATION
Introduction Experimental Sputtering Facility Main Vacuum System Instrumentation Pre 1 iminary Experiments Metallic Films Temperature Rise due to Sputtering Effect of R F Power on Deposition Rate Transducer Fabrication Procedure Cleaning Procedure
4
4 6
10 12 14 15 17 17 18
26
26 27
27 28 31 32
37
37 37 37 39 43 44 45 47 49 49
CHAPTER
CHAPTER
CHAPTER
APPENDIX
REFERENCES
4.4.2 4.4.3 4.4.4 4.4.5
V
5.1 5.2 5.2.1 5.2.2 5.2.3 5.3
5.3.1 5.3.2 5.3.3 5.3.4 5.3.5
VI
6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8
6.9 6.10 6.11
VII
DepCNitic~ of Beck Electrode Deposition of the ZnO Fi lm Deposition of the Top Electrode Chemical Etching of ZnO
TESTING OF THE TRANSDUCERS
Introduction Structure Analysis .. General Formulae Governing RED The Zinc-Oxide Structure Experimental Set-up and Procedure Evaluation of the Electrical Performance of the Tran:;ducer Overall Trnasducer Loss De 1 ay Rod Losses Delay Rod Holder Conjugate Matched Transducer Loss Untuned Transducer Loss
EXPERIMENTAL RESUL TS
Introduction Temperature and Deposition Rate
. Effect of Pressure Effect of Gas Composition Rate-Temperature Survey at 10 % Oxygen Crystal Size and C-axis Spread Input Impedance Effective Coupling Constant and Contact Resistance Post-Deposition Treatment Adhesion Reliability and Reproducibility
SUMMARY AND CONCLUSIONS
COMPUTER LISTING
iv
50 51 51 51
53
53 53 54 56 58
60 62 63 65 66 69
71
71 71 75 79 80 84 84
86 88 89 90
96
98
104
CHAPT ER 1
INTRODUCTION
ln the last decade, several techniques for obtaining piezoelectric thin
1-6 film transducers have been developed. The versatility of these transducers is demon-
strated by their use in a variety of applications su ch as non-destructive testing, low loss
delay lines, acoustic resonators and the processing of complex micraovave Signais?
The thin films used are primarily made of high gap semi-conducting com-
pounds such as CdS, CdSe, ZnS and ZnO. These materials have high crystallographic
symmetry and con be deposited as highly oriented thin films on a variety of substrates.
Other materials, both chemically and crystallographically more complex thon the simple
binary compounds, have also been used, such as L i Ga O2
and LiN b 03
.8
For microwave acoustic transducers in delay lines applications, a material
with high piezoelectric coupling coefficient, K .. , is required.6
The semiconducting •
material with the highest known value of Kt for compressional waves is zinc-oxide, having
a value of 0.28.
Techniques for obtaining thin ZnO films are numerous and have been in-
. d b h b 9 3,5 d R .10,11 h de vestlgate y many researc ers. Den urg, Foster an ozgonyl ove ma
ZnO transducers by D C sputtering of the compound. Wanuga 12 experimented by re
active sputtering of zinc in a mixture of argon and oxygen. Raimondi and Kay 13 obtained
high resistivity transparent ZnO thin films both by reactive D C sputtering of metallic
zinc and R F sputtering of ZnO . Reactive evaporation of zinc in an oxygen beam is
another technique used by de Klerk 6
and Malbon .14 Ohishi et 0115 successfully produced
ZnO films at low tempe ratures by the oxidotion of vacuum deposited Zn Se films.
2
Although the techniques for preparing the ZnO films are weil advanced,
little work has been done to corre lote the crystallographic structure of the thin film pro-
duced to the different parameters controlling the process of fabrication, and to the actual
performance of the film as an ultrasonic transducer. 6
Recently, de Klerk obtained single
crystal films by reactive evaporation on a substrate cooled to -lSOoC. Rozgonyi and
Polito 11 obtained epitaxial films of ZnO on (001) single crystal sopphire and c - axis
oriented CdS. However, the structure of the films was sometimes "random polycrystalline
or poorly oriented tt• The authors attributed this fact to changes and modifications brought
to the vacuum system prior to the fabrication of the se films. The sorne result was concluded
by Foster et al for the fabrication of ZnO films by D C sputtering3
and by triode sputter-
• 16 mg.
ln this thesis a study is made of the various parameters affecting the produc-
tion of ZnO films by R F diode sputtering of the compound in a reactive atmosphere.
ln Chapter Il, the frequency response of a multilayer semiconducting piezo-
electric transducer is obtained algorithmically. The multilayer transducer is first reduced
to a conventional three-port structure by defining recursively the mechanical impedance
loading each face of the piezoelectric layer. Electromechanical power conversion theory is
then used to obtain the transducer loss.
Chapter III presents a brief summary of sorne general concepts of R F
sputtering in relation to the formation of ZnO thin films.
The experimental method used for the fabrication of the transducers is
described in de ta il in Chopter IV, while the methods used for both structure analysis and
electrical testing are discussed in Chapter V .
3
Finally in Chapter VI, the results obtained frorn experiments carried out
according to the methods outlined in the earlier chapters are presented and discussed. Some
results of experiments on post-deposition heat treatment, film adhesion, as weil as sorne re
producibility tests are also described in this chapter.
ln summary, this thesis relates the fabrication procedure of zinc-oxide thin
films to their crystolline structure and their performance as microwave ultrasonic transducers,
and defines the guide lines to be followed for successfully depositing efficient transducers.
4
CHAPTER Il
PERFORMANCE OF MULTILAYER PIEZOELECTRIC TRANSDUCERS
2. 1 Introduction
The launching of plane acoustic waves into a certain medium by compo-
site layered transducers composed of a piezœlectric semiconducting thin film and other
lossless loyers has been extensively discussed in the recent literature .17,18,19
The coaxial geometry shown in Figure 2.1 is a typical one used in most
experimental and analytical studies. The top layer (s) - normally only one - preceding
the transducer is a metallic contact to which the electrical signal is applied. The trans-
ducer is followed by another metallic layer (second electrical terminal) and other layers
TOP ELECTRODE
PIEZOELECTRIC LAYER
BACK ELECTRODE
DELAY ROD
ADDITIONAL LAYERS
FIGURE 2.1. MULTILAYER TRANSDUCER STRUCTURE.
5
acting os a mechanical transformer to achieve sorne prescribed behaviour such os matching
to the de lay rod impedance. 19
For a theoretical treatment, a weil justified assumption Is that the
lateral dimensions of the structure ore large cornpared to the acoustic wavelength ; this
effectively reduces the problem to one dimension. Another assumption which is only
theoretically feasible, is that the crystal orientation of the piezoelectric layer is properly
chosen so that only one pure mode of vibration is excited.
To the author's knowledge, two approoches ore presently used for the
evaluation of the frequency response of the transducer. The first approoch starts from
the piezoelectric equations of state, Moxwelt's equations and Newton's equation of
motion, and works out the solution os an electrornechanical problem assuming a finite
. .. f h . d . • 1· • 1 20,21,22 reslstlvlty 0 t e semlcon uctrng plezoe ectrrc materra • the second approoch
23 is bosed on using an electric circuit model (known os "Mason circuit" after W. P. Mason )
f h . 1 1 h' h be . 1 d 17,18,24 Ith h h or t e plezoe ectric ayer. T IS as en extensIve y use • A oug t ere is
no basic difference in the computational wak between the two approoches, the first one
has the advantage of keeping the physical arguments of the problem, making it possible
to take the loss of the piezoelectric material into account and to handle "active" semi-
conducting films.
ln the following anolysis, the solution for "transducer loss" os obtained
previously for a piezoelectric film looded at one face bya hypothetical lood,22 is ex-
tended to multilayer structures looded at bath faces by real mechanical loods. First, the
case of a finite resistivity semiconducting piezoelectric thin film is considered. The case
of infinitely high resitivity is then approoched as a simplification of the more general case.
6
2.2 Basic Equations
For piezoelectric materials, which may also be semiconducting, the thermo-
dynamical equations of state are:
T c c 5 - e E 2. 1
2.2
where T and 5 are the stress and strain, 0 and Ethe electric displacement and field,
c the elastic stiffness tensor at constant field, Ethe electric permittivity tensor at constant
strain, and e the piezoelectric tensor. The assumptions of a one dimensional problem and
single mode of vibration (compressional or longitudinal) makes the variables in Equations
2. 1 and 2.2 sca lors, wi th the proper choice of the tensor e lements for c, e and E.
Consider plane waves of the form U • exp (i k x - i w t) where U is the_ ampl itude of
the displacement and x is the distance measured along the transducer axis toward the delay
rod (Figure 2.1). The above equations, together with Maxwell's equations, charge trans-
port equation and the equation of motion result in a quartic dispersion relation, k (w), in
20 the complex wave vector k.
where
With a little manipulation, this quartic can be written as :
w z = VT
s
z +
+ i ( wc) • z2 '. (z2 - 1) = 0 w
a dimensionless function of the wave vector,
2.3
2 e
s = e c
the square of the electromechanical coupling 2
constant (usually referred to as kt) ,
V D = - ~ EDe electron drift velocity in the presence of a
D e field, EDe '
W = c
wD
=
and v = s
ale
the conductivity and diffusion frequencies,2° and
v the longitudinal velocity of sound at constant s
field. Wc ' wD and Vs are related to the
physical constants as follows :
y2 ID s e
(clp) 1~
where a , De and p are the conductivity, diffusion constant for electrons, and mass
density respectively.
7
The solution to this quartic yields four allowed waves characterized by the
wave vectors k., i = l, 2, 3, 4 ; or alternatively z., i = l, 2, 3, 4. In 1 1
general, z. is a complex number causing k. to be complex of the form (101 1 v. - i a.) 1 1 1 1
where v. is the phase velocity of this porticular wave and a. an attenuation constant 1 1
associated with the space propagation of the wave. ( a. being positive for a wave at-1
tenuated as it advances in the positive x-axis direction).
For a finite piezoelectric film of thickness L and driven byan a c field
E , all four waves will be present. Following the derivation given in Reference 21, one o
8
ends up with expressions for the velocity, stress and electric field along the trans-
ducer * :
e E 0 [ Q. (ik-x)J v = ......- . exp
p Vs 1 1 2.4
T = e E . [ - 1 - Q. z. exp ( i k. x) ] 0 1 1 1
2.5
E = E . [ 1 + Q. (z. - 1 / z. ) . exp ( i k. x) ] 0 1 1 1 1
2.6
where ( pVs
) is the mechanical characteristic impedance of the piezoelectric material
and Q., i = l, 2, 3, 4 a set of amplitude ratios that depend on boundary conditions. 1
The time dependence exp ( - i Ct.) t) is implicit in the above equations. The voltage across
the transducer faces is then directly calculated :
E dx = EL o
[l-iQ. Ct.)o (i-l)'{exp(ik.L)-l}J 1 11 Ct.) 1 1
while the current flowing is given by
= E A E (Ct.) - i Ct.)) which con be rewritten o c
2.7
* The convention that repeated subscripts represents summation is used in the
rest d this work.
9
Ca) - i Ca)
= Ca) (EA)'E L • [_c __ J o L 0 Ca)
2.8 o
where A is the "acoustic beam cross-sectional area (defined by the top metal electrode)
and Ca) the angular frequency at which the length, L, is a half wavelength. o
For both machine computation and mathematical manipulation, it is useful
at this point to introduce the concept of normalization - while keeping the seme notations
for the normalized values:
v = Q. exp ( i k. x) 2.9 1 1
T = - 1 - Q. z. exp ( i k. x ) 2.10 1 1 1
E = 1 + Q. (z. - 1 / z. ) exp (i k. x) 2.11 1 1 1 1
Ca) 2
. { exp ( i kj L) 1} V 1 . Q 0 - 1 ) 2.12 = - 1 .- ( z. -11I'c.J 1
= (Ca) - i Ca) / c.J 2.13 c 0
It is now clear that Q. is a set of normalized velocities while z. is the corresponding set 1 1
of normalized mechanical impedances.
The normalizing electrical and mechanical impedances are
the magnitude of the transducer clamped reactance at f - and o
[ 1 ] 1
Ca) ( E A) o L
Z op
the piezoelectric material mechanical characteristic impedance. These normal izing factors
are functions only of the piezoelectric material and the geometry of the transducer .
10
2.3 The Mu 1 tilayer Structvre Problem
Referring to Figure 2.2 (a), showing a structure of N fi Ims on the top
of a delay rod of mechanical impedance ZDR' and with the free face loaded byan
impedance Z A (usuaHy set to zero) ; for each fi lm (n) we know the length, Ln'
sound velocity, v , and the mechanical characteristic impedance, Z sn on
The piezo-
electric layer is one of these films, e.g. number p •
PIEZOELECTRIC LAYER
.....,..---'-~ - - - - - ....... --,.-------4
2 P N DELAY ROD
ZON ZDR ZA Zol Z02 - - - Z op
~ ~ ~ 1+- ~ z zl z2 z z
p+l 0 P -1
(a)
(b)
FIGURE 2.2. (a) MULTILAYER STRUCTURE
(b) EQUIVALENT 3 - PORT.
1 1
A basic and justifiable assumption is that the acoustic loss in the coupling
layers is small and may be neglected.17
The boundary conditions which must be satisfied
at each interface are the continuity of stress and velocity in both media. Therefore, as
shown in Figure 2.2 (b), the acoustic impedances ZL and ZR which are the actual loads
on the "Ieft" and "right" of the transducer can be obtained by applying the principle of
travelling waves in lossless media .19 Defining 9 n
= wL
n v
sn of the n th film, we obtain
ZL = Z P - 1
with zp _ 1 defined by the recursive relation:
z = Z n on
z 1 + i Z tan 9 n- on n
Z + i z 1 tan 9 on n- n
where n = 1,2, .... , p-1
and
Similarly,
ZR = zp + 1
with
z defined by the recursive relation p + 1
the angular or radian length
2.14
2.14 (a)
2.15
12
z n+1
+ iZ tan 9 Z
on n z = i z 1 tan 9 n on Z +
on n+ n .2.15 (a)
where n = N, N - 1, ..... p + 1
and zN+1 - ZOR·
For a computational interpretation, the reader is referred to the computer listing -
Appendix 1. Equations 2.14 and 2.15, effectively reduce the multilayer structure to
the conventional single layer transducer loaded on each surface as shown in Figure 2.2.
2.4 Acoustic Power Generation
and
ln this case, the mechanical boundary conditions become :
T (0) =
T (L ) =
ZL • v (0 )
-Z ·v(L) R
Substituting for v and T from Equations 2.9 and 2. 10 we obtain
and
1 + Q. (z. - ZR) . exp ( i k. L) = 0 1 1 1
( = 1, 2, 3, 4 and the summoti on conventi on i s understood).
2.16
2.17
13
Two additional boundary conditions are required to obtain the four amplitude ratios Q .• 1
We examine the following possible Hreasonable tt boundary conditions: the plane wave
component of either the spa ce charge, the current density or the electric fie Id is made to
vanish at both ends of the transducer. Such choices may be thought of as defining an
ideal metallic contact.25
(a) Setting the current density equal to zero:
2 Q. (1 + s - z.) / z. = 0
1 1 1
2.18 (a)
Q. (1 + s - l) . exp (i k. L) / z. = 0 1 1 1 1
(b) Setting the space charge equal to zero:
2 2 Q. (1 +s -z.)/z. = 0
1 1 1
2.18(b)
2 exp (i k. L) / i 0 Q. (1 + s - z. ) =
1 1 1 1
(c) Setting the electric field equal ta zero
2 = 0 Q. (1 - z.) / z. 1 1 1
2.18 (c)
Q. 2
• exp (i k. L) / z. 0 (1 - z.) = 1 1 1 1
Only one pair ~ Equations 2~18 is required for the solution. While they 011 seem reasCYloble,
computations show negligible differences between the results obtained using sets a and b,
while the electric field assumptions yield slightly different results as will be shown later.
14
2.4 .. 1 Input hnpedëmce and Transducer Loss
Now that the boundary conditions are formulated, Equations 2. 16 to 2. 18
can be solved for the amplitude ratios Q. and by bock substitution into Equations 2.9 , 1
2.10 and 2.12, v, T and V are defined. The electrical input impedance of the trans-
ducer will then be 11" :'
z = V /1 e
Up to this point, only the lIintrinsic transducer· has been considered. In
practi ce 1 the contact to the top e lectrode may i ncl ude a series resistance, r , wh i ch may c
not be negligible compared to the input impedance .24 If the transducer is driven from a
source of internai impedance Z , the electrical port "mismatch loss·26 is: s
L ( E) = 4 Re [Z + r ] . Re [Z ]
e c s
Z + r e c
The voltage across the extrinsic terminais of the transducer is
VI = V + 1 r c
Therefore, the electrical and mechanical pa.vers are given by :
P ( E) = 1 / 2 • R e (VI • 1 * )
"
+ Since the time dependence ci the plane waves is assumed exp ( - i w t), the elec
trical impedances will be Z (- i w), i.e., a positive reactonce is a Copacitive
Load.
2.19
2.20
15
and
P ( M) = 1 /2 Re (- T R • vR*) 2.21
ln Equation 2.21 TRond vR
are the stress and velocity at the r. h. s. of the transducer.
P (M) is therefore the mechanical power intensity fed to ZR and delivered through the
lossless coupling films to the delay rode The power absorbed by ZL (in case Re (ZA):j 0)
is radiated at the free face of the device and presents a loss factor.
The actual "generation" conversion efficiency is :
11(G)= 5 p (M)
P ( E )
The term 5 /1f appearing in this equation is due to the normalizing factors carried along
the derivation.
2.22
The transducer loss defined as the ratio of the net power delivered to the load to the avai lable
power from the generator, is then :
TL (G) = L(E)' 11(G) 2.23
2.5 Acoustic Power Detection
ln this case, the generator - the deloy rod - suppl ies the transducer with
the mechanical power through the coupling films. The conversion to electrical power parallels
in 011 respects the acoustic power generation presented in the previous section. However,
16
since the acoustoelectric interactions due to drifted carriers are being taken into account,
the transducer 1055 in this case will differ from that obtained above.
To solve for this case we look again for the proper boundary conditions.
Those given in Equations 2.16 and 2.18 still apply, while the one given in Equation 2.17
is no longer applicable. Instead, one can state the condition on the voltage at the intrinsic
terminais as :
V= -1 (Z +r) 5 c
or fr~ 2.12
la) i Q. ~ ( z~ - 1) . [exp (i k. L) - 1 ] = 1 + 1 (Z + r )
Inla) 1 1 5 C 2.24
Again, 50lving Equations 2.16, 2.18 and 2.24, and bock substituting into Equations 2.9
and 2.10, v and Tare obtained. The mechanical input impedance, mismatch 1055, volt-
age output, conversion efficiency and detection transducer 1055 are respectively :
=
L (M) =
VI =
17(0) =
TR
/ v R
4 Re [Z M] . Re [ZR]
1 ZM + ZR 12
-IZ
.. 5
5
P (E ) P (M)
2.25
2.26
17
and
TL(D) = L(M)· 11(D) 2.27
where P ( E) and P ( M) are obta i ned by proper substi tuti on in Equations 2.20 and
2.21 .
2.6 The Non-conducting Case
ln the case of a high resistivity piezoelectric thin film or at frequencies
much ,higher than thec6ncNotlvifyJre.que,I'I,CY, one. .. con n'egj~c:t the ,conduction and diffusion
of the carries in the material. Equation 2.3 reduces in such a case to a quadratic giving :
z. 1
= :: (1 + s) 1/2 = l, 2
These roots correspond to the piezoe lectric stiffened conditions. The set Q. also rel
duces to a set d two amplitude ratios Ql and Q2. Equations 2.16 and 2.17 are
now sufficient in themselves for the complete solution and no additional boundary condi-
tions are needed. Further, the conditions for reciprocity are satisfied and the solution for
either the acoustic power generation or detection is sufficient.
2.7 Computer Program
A computer program has heeA .... rif*en-Gnd used to solve for the transducer
loss at any given frequency. This program is able to handle the different boundary condi-
18
tions given in Equations 2.18, as weil as different conditions for the input impedance tuning
which can be either "conjugate match ", ··series tuned", "shunt tuned" or "untunedll .22
The conjugate match case is when the source impedance is the conjugate
of the extrinsic input impedance of the transducer at each frequency. This can be achieved
b b • b h f • h'" 27 F • 1 • of • Y stu tunlng or y t e use 0 an active matc Ing circUit. rom a prachca pOint Vlew,
the conjugate match is only possible in an experimental set up.
ln the series tuned case, the source impedance has a reactive element
selected to tune out the input reactance of the transducer at a predefined frequency. The
real part of the source impedance is a fixed value. (e.g. the characteristic impedance of
the r f coupling lines).
The shunt tuning is similar to the series tuning but with the reactive element
connected in shunt with the transducer input. In the untuned case, the transducer is directly
connected to a source of a fixed impedance, usually the characteristic impedance of the
circuit.
The computer listing included in Appendix 1 shows the main features of this
program which displays the frequency response of the given transducer in different ranges of
other variables.
2.8 Computed Results
To illustrate the effect of the different conditions discussed above, the loss
of a multilayer transducer with zinc-oxide as the piezoelectric material, (k = 0.28), has t
19
been computed over the frequency range 0.5 - 3 GHz. The results obtained are
shown in Figures 2.3 to 2.11.
Solutions using the various boundary conditions discussed in Secti on 2.4.1,
ore shown in Figure 2.3. The space charge and cur.re.ntdensity assumptions yield practically
the sa me transducer loss. The assumption of zero plane wave components for the e lectri c
field at the boundaries, yields results with negligible differences over most of the frequency
bond. However, the validity of this assumption is in doubt, especially since calculations
predict "transducer gain" and "bonds of instability" which ore facts associated with high
carriers drift velocities,22 whereas the drift velocity is zero in these calculations.
ln Figure 2.4, the 2-wave solution - neglecting the conductivity -
is shown together with the frequency responses of a high conductivity and a low conductivity
zinc-oxide film. The structure of the transducer is similor to that shown in Figure 2.3. The
results indicate that the simplifying assumption of infinite resistivity con be used when the
zinc-oxide film resistivity is greater thon a few K ohm.m-l (f < 0.5 x 106
Hz). c
The effect of the contact resistance is shown in Figure 2.5. The
computed input impedonce of the "intrinsic" transducer is typically [0.14 + i 14.5J ohm
at 1.0 GHz, and [0.20 + i 7.5J ohm at 2.0 GHz. The small value of the real part
explains why the conjugately matched transducer is considerably affected bya contact re-
sistance of the order of a few tenths ohm, while in the untuned transducer, the additional
loss is minor and con be neglected for 011 practical calculations.
The effect of adding a passive tuning element to the source impedonce
is demonstrated in Figure 2.6, which shows that a series inductance that tunes out the capaci-
TRANSDUCER Au Zno Au LOSS (db) 0.15 1.5 0.15
30
25 UNTUNED
20
15
10 CONJUGATE MATCH
5
0.6 0.8 1 .0 1.5 2.0
20
SAPPHIRE D. R.
-SPACE CHARGE AND
CURRENT DENSITY
-- - ELECTRIC FIELD
r = 0.2 .n. e
f = 0.5 MHz e
3.0
FREQUENCY (GHz)
FIGURE 2.3. EFFECT OF APPLYING THE DIFFERENT BOUNDARY CONDITIONS.
TRANSDUCER LOSS (db) 30
25
20
FIGURE 2.4.
r = 0.2.n. e
f = 0.5 GHz ·e
= 0.5 MHz
= 0.0
=
~JUGATE +-- f 0.5 GHz
e MATCH
0.5 MHz
~ = = 0.0
0.6 0.8 1.0 1.5 2.0 3.0
FREQUENCY (GHz)
CONJUGATE MATCHED AND UNTUNED RESPONSES FOR A HIGH CONDUCTIVITY 1 LOW CONDUCTIVITY AND NON CON DUCTING PIEZOELECTRIC FILM.
TRANSDUCER LOSS (db)30
25
20
15
10
5
0.6 0.8 1 .0
f = 0.5 MHz c
CONJUGATE MATCH
1.5 2.0
1 .0 ohm
1.0
0.2
0.0
· 3.0
FREQUENCY (GHz)
21
FIGURE 2.5. CONJUGATE fv'IATCHED.·AND· UNTUNED RESPONSES
TRANSDUCE LOSS (db)30
25
20
15
10
5
FOR DIFFERENT CONTACT RESISTANCES.
f = 0.5 MHz c
'--- SHUNT TUNED AT 1.0 GHz
'-- SHUNT TUNED AT 2.0 GHz
r-CONJUGATE MATCH
~~ __ ~~~ ______ L-__ ~==~~_
0.6 0.8 1.0 1.5 2.0 3.0 FREQUENCY (GHz)
FIGURE 2.6. FREQUENCY RESPONSE UNDER DIFFERENT TUNING CONDITIONS.
22
tive part. of the input impedance at say 1 GHz, is actually ineffective. This is again
explained by the small input impedance compared to the 500hm characteristic impedance
of the source.
On the other hand, shunt tuning introduces considerable changes highly
dependent on the tuning frequency. Computations - show that shunting the transducer
by an inductance of 2.3 n H increases the input resistance at 1.0 GHz ta 1500 ohms
whi le 0.6 n H wi Il cause it to tune at 2.0 GHz with a tuned input resistance of 280 ohms.
The change of frequency response by shunt tuning con be used advantageously
in "response shoping'! by properly choosing the tuning frequency. Other factors that can be
used for frequency. respon.seshaping: are the :electrode niaterial's :andthicknesses. A thinner top
electrode - as it represents less mass loading on the free face of the transducer - gives a
frequency response with a broader bandwidth and lower transducer loss as shawn in Figure
2.7.
ln Figure 2.8, we see the effect of varying the material of the electrodes.
ln general, an acoustically Ilight" material ~ower Zo) yields responses of lower loss but
less bandwidth .
Frequency response shoping con also be achieved by additional loyers as
shown in Figures 2.9 and 2.10. Here, the piezoelectric film is separated from the delay
rod by two metallic loyers. Different combinations of materials are tried, and we see that
the combination (gold / aluminum) gives the broadest bandwidth while the (aluminum / gold)
gives the lowest transducer loss.
TRANSDUCER LOSS (db)
30
25
20
15
10
5
TRANSDUCE LOSS (éJb~
25
20
15
10
5
Au ZnO Au SAPPH IRE
L = 0.2 ~ L 1.5 0.1 D.R.
UNTUNED
0.6 0.8 1.0 1.5 2.0 3.0
FREQUENCY (GHz)
FIGURE 2.7. EFFECT OF TOP ELECTRODE THICKNESS.
X ZnO
0.1 1.5
UNTUNED
0.6 0.8 1.0 1.5
X
0.1
2.0
SAPPHIRE
D.R.
Zo
Au 65.5
Ag 40.0
A 1 18.4
3.0 FREQUENCY (GHz)
FIGURE 2.8. EFFECT OF DIFFERENT ELECTRODE MATERIAL.
23
TRANSDUCER LOSS (db)
30
25
UNTUNED
0.6 0.8 1.0 1.5
Au ZnO X y SAP PH IRE
0.1 1.5 0.15 0.15 D.R.
2.0
Agi Au
Agi AI
3.0
FREQUENCY (GHz)
FIGURE 2.9. SHAPING OF THE FREQUENCY RESPONSE.
UNTUNED Au 1 AI
........ ~_ 3 db B. W ____ ., __ ~
Ail Au
0.6 0.8 1 .0 1.5 2.0 3.0 4.0
FIGURE 2.10.
FREQUENCY (GHz)
SHAPING OF THE FREQUENCY RESPONSE.
24
25
The broad bandwidth obtained using a gold-aluminum "transformer ll
instead of a single gold coupling layer is better visualized by looking at the intrinsic input
impedance of the transducer in the two cases. This is shown in Figure 2.11 where we see
INPUT RESISTANCE (ohm) 0.5
0.4
0.3
0.2
0.1
0.6
F 1 GU RE 2. 11 .
INPUT CAPACITANCE - CONSTANT ~ 11.1 PF
Au, ZnO, AuJ
0.8 1.0 1.5 2.0 3.0
FREQUENCY (GHz)
INPUT IMPEDANCE OF MUlTiLAYER TRANSDUCERS.
that the addition of an aluminum layer causes the real part of the input impedance, as a
function of frequency, to have a double peak, resulting in a broader bandwidth.
At the present time, no general conclusions can be made about these
computed results. Further studies should be directed to a "design" program that con
synthesize a multilayer transducer, given a prescribed frequency response .
26
CHAPTER III
R F SPUTTERING OF ZINC-OXIDE TRÂNSDUCERS
3. 1 Introducti on
As defined by Davidse and Moissel,28 the term "sputtering" refers to
the ejection of atorns from a material through the impact of ions or atoms. The bombarding
particles are usually ionized particles of an inert 90S (e .g. argon), accelerated by an elec
tric field appl ied between two electrodes.
ln 0 C diode sputtering, the target is the cathode while the substrate is
at the anode. AOC glow discharge is clearly applicable to the sputtering of conducting
materials only. A high - frequency potential, applied to a metal electrode behind the tar
get con be used for R F sputtering non-conducting (or poorly conducting) materials.
Further, it is found that R F glow discharge con be sta:-ted and maintained at a mu ch lower
pressure thon that necessary for 0 C discharge. In bath 0 C and R F sputtering processes,
the ionization of the working 90S is enhanced by the accelerated free electrons and charged
particles that happen to he between the electrodes.
Triode sputtering differs in that the main ionizing perticles are electrons
provided bya hot filament and accelerated by an anode positioned so that these electrons
travel in a direction normal to the sputtering beam. A magnetic field is applied to make
these electrons spiral, thus increasing their ionizing ability.
If the 90S used as a sputtering medium contains reactive elements, film
growth is influenced. This property may oc tua Il y be advantageous in sorne appl ications,
particularly in sputtering metal oxides, which are found to deposit with an excess of the
27
metal element if sputtered in a pure inert 90S. This process is known as IIreactive
sputtering". For a more detaited description of the different processes, see Holland. 29
3.2 Sputtering of Zinc Oxide
From the above discussion, it is clear that RF sputtering has the advantage
of operating at a lower pressure, normally in the microns range. This low operating pres-
sure, considerably increases the mean free peth of the sputtered pertides which implies that
they con reach the substrate white they still have a high kinetic energy, hence giving better
adhesion ~ Also, diode sputtering is advantageous since the apparatus needed is less com-
plex thon that required for triode sputtering. Thirdly, since the material under considera-
tion is a metal oxide, it is mandatory to use reactive sputtering in an oxygen-rich medium.
To summarize, RF diode reactive sputtering is a simple and promising pro-
cess for the fabriaction of high quality zinc-oxide thin films.
3.3 Factors Affecting the Fabrication of Zn 0 Transducers
Uniformity of crystal structure, stoichiometry, orientation of the crystall ites
and good adhesion of the film to the substrate are necessary to obtain reliable and reproduc-
ible transducers.
28
The rate of deposition and the energy of the sputtered atoms at the moment
they strike the substrate (hereafter referred to as "deposition energy") widely affect the
above-mentioned conditions. The deposition rate and deposition energy are, in turn,
complicated functions of the different factors controlling the sputtering process, such as the
target and substrate positions, shapes and sizes, the substrate temperature, the input power
and the sputtering gas composition. To better understand how each factor affects the pro
duction of zinc-oxide thin films, they are grouped into the following categories:
3.3.1
Factors pertaining to the sputtering station.
Factors pertaining to the substrate.
Independent factors.
Factors Pertaining to the Sputtering Station
(a) Residual Gases in the Vacuum Cham ber
Even a small uncontrolled amount of a reactive element in the 90S present
in the chamber during sputtering may produce contaminants in the deposited film. Reducing
the amount of unwanted perticles before admitting the sputtering 90S into the chomber, ne
cessitates the use of a leak-free, non-out9Ossing system, preferably equipped with a 1 iquid
nitrogen cooled baffle. An optically dense baffle mounted directly above the diffusion
pump is used to prevent the oil vopor from backstreaming into the chamber. Also liquid
nitrogen cooling gives the added capability of trapping the condensables and thus reducing
the system pressure.
29
(b) Target and Substrate Shapes, Positions and Sizes
The geometry of the electrodes between which the discharge takes place
is primarily responsible for the uniformity of the thickness of the deposited film~' 31,32
For the plane parallel disk configuration shown in Figure 3.1, the de-
position intensity distribution at different radial locations on the receiver plane is given
30 by :
= A [ 1 2 2
. H + R - 1 ]
[ 1 - 2 ( R2 _ H2) + (R2 + H2 ) 2 ] 1 ï2
where is the intensity of the deposit, and A a constant depending on the other factors
also H h spacing between the 2 plates
= - = Target radius r
R ri radial location of receiver element
= -= r Target radius
A diagrammatic interpretation of the above equation is shown in Figure 3.2. It is clear that
for best uniformity of distribution, the substrate should be positioned at the centre of the re-
ceiver plane while its lateral dimensions in this plane should be small compared to the radius
of the electrode. The distance between the two electrodes, h, should be kept to a mini-
mum. Decreasing this distance has also the effect of increasing the energy of deposition,
since the average number of collisions a sputtered particle suffers, is reduced. However,
the interelectrode distance can not be decreased below a certain 1 imit determined by the RF
matching network. This constraint is due to the extreme difficulty in tuning the power supply
when h is small. Bock shielding of the target electrode is also another aspect of the tuning
limitations, since the distance between the shield and the electrode is constrained to be
H
R
h r
ri
r
1· S RECEIVER PLANE
C:;f=====I--===r;:::·1 =~~ ( SUBSTRATE)
h
t I-r --+1 , '-TARGET PLANE
FIGURE 3.1. PLANE PARALLEL DISC CONFIGURATION.
RELATIVE 1.00 INTENSITY
H = 0.1
0.95
0.3
0.90
0.85
0.80
r O. l 0.2 0.3 0.4 0.5 0.6 R
RELATIVE RADIAL LOCATION
FIGURE 3.2. RELATIVE INTENSITY OF DEPOSITION OVER
THE RECEIVER PLANE (REFERENCE 30).
30
31
within the tldark space" so that the sputtering plasma is confined to the unshielded
28 face. In our case, both for interelectrode distance and bock shield position, we found
that the values provided by the manufacturers allow an easy matching. (lnterelectrode
distance = 2 cm and bock shield at 0.5 cm from the electrode).
3.3.2 Factors Pertaining to the Substrate
(a) Type and Surface Preparation of the Substrate
Typical delay media are selected from single crystals of quartz, yttrium
iron garnet (YIG) , yttrium aluminum garnet (Y AG), and sapphire. The latter is usually
preferred because the crystals are chemically inert, easily cleaned, have good thermal and
f b .. l' . d Il . . 4 a rJcatlon qua Itles, an exce ent acoustlc propertles.
For use as a delay line in the microwave bands, the sapphire crystal shoù"ld
have an optically polished surface. This surface must be c1eaned prior to the deposition of
the transducer. The cleaning procedure must be efficient enough not to leave traces of the
cleaning substances on the substrate.
(!J) Metal Underlayer (s) Used
ln Chapter Il, the importance of a metallic underlayer was discussed. In
addition to the electrical and acoustical properties required, the bock electrode materiol
should provide a good hast for the zinc-axide depasit. Selt and Floria 4
experimented with
32
different materials and their best results were obtained with sil ver • Gold is extensive Iy
used as a bock electrode for zinc-oxide transducers on c-axis oriented sapphire delay rods
because it is easy to deposit and provide a good base material for epitaxial growth of zinc-
oxide and simi lar wurtzite structures.
(c) Substrate Temperature
The substrate temperature is one of the critical porameters in fi lm growth,
inf1uencing the sticking coefficient, nucleation conditions and the degree of epitaxy
obtainedll
,33 (Figure 3.3). Hussain34
and de Klerk6
remarked that the stoichiometry
of CdS and ZnO deposits depends on substrate temperature.
The effect of substrate temperature on the deposition rate is large. In
RF sputtering, the rate of deposition is found to decrease os the temperature rises, while in
DC • h' 1 •. 13 sputtenng t e Inverse re atlon IS true. The dependence of deposition rate on tem-
perature points out the importance of a uniform, stable, substrate temperature.
3.3.3 Independent Factors
(a) Sputtering Gas Composition
Zinc-oxide films grown by reactive sputtering are found to have varying
degrees of deviation from stoichiometry, depending on the percentage of oxygen in the
sputtering 90s. This fact is assumed to result From the chemisorption of oxygen both at the
DEPOSITION 10 RATE (AO
/ H) o
/
*
* 1 * * 1 * * * "1:
* * * "1<- * X
*
*
o Moderately Oriented
* Highly Oriented
X Epitaxial
*
*
100 200 300 400 500 600
SUBSTRATE TEMPERATURE (oC)
33
FIGURE 3.3. EFFECT OF DEPOSITION RATE AND SUBSTRATE TEMPERATURE ON
STRUCTURE OF ZnO FILMS ON SAPPHIRE SUBSTRATES (REFERENCE 11).
substrate and at the target. The oxygen collected at the substrate is bel ieved to come
from four sources :
Oxygen originally contained in the target and sputtered
as otoms.
Atomic oxygen formed in the discharge •
Molecular dissociation upon impact with the surface.
Absorption of energetic oxygeri which penetrates the
lattice.
34
At the target, the surface layer of sorbed oxygen - originating from the sputtering gas -
reduces the sputtering yield significantly.
(b) Input Power
As the input power (or the electrode potential in OC sputtering) in
creases, two effects contribute to the increase of the rate of deposition :
the increased number of ionized particles in the sputtering
gas ; and
the higher velocities these ionized particles reach before
bombarding the target.
The application of an axial magnetic field confines the plasma between the electrodes and
causes the electrons to spiral, increasing their ionizing abi! ity, thus increasing the rate of
deposition. An important side effect to the appl ication of a magnetic field is that it pro
vides a more stable glow, allowing for easier tuning and matching to the RF source.
35
SPUTTERING YIELD (Atom / ion)
0.5 -- - - --------
0.4
0.3
0.2
0.1
1
2 5 10 20 50 100 200
PRESSURE (millitorr)
FIGURE 3.4. SPUTTERING YIELD OF NICKEL IN ARGON (REFERENCE 36).
MEAN FREE PATH (cm)
PRESSURE (Torr)
FIGURE 3.5. MEAN FREE PATH IN ARGON.
36
(c) Chamber Pressure
As shown in Figure 3.4, the sputtering yield is nearly independent of
the gas pressure in the ronge 1 - 15 millitorr, which is used for RF sputtering, while
it decreases rapidly at higher pressures. This is explained by the balanced action of the
extra ionization available at on increased pressure, and on the other hand, the decrease
of the mean free pat.h at this pressure. (i.e. the increase in the average number of
collisions). Figure 3.5.
(d) Post-deposition Treatment of the Deposited Film
The effects of post-deposition heat treatment on the stoichiometry and
35 texture of vacuum deposits is not yet weIl studied. Desrumaux et al., found that
"bocking" a CdS evaporated film at 4000
C in CdS powder, compensates for the ex
cess of cadmium and improves the texture quality. For zinc-oxide, Rozgonyi and Polito10
suggest that a stoichiometric balance con be maintained "bya post-deposition treatment".
ln the present work, we have tried heating the zinc oxide films in vacuo and in on oxygen
rich atmosphere . The results of these experiments ore given in Chapter VI .
4.1 Introduction
CHAPTER IV
TRANSDUCER FABRICATION
37
The various parameters affecting thin film transducer fabrication have been
discussed briefly in Chapter III. The present chapter is concerned with the experimental
set-up for the fabrication of the transducers. The first part covers the description of the
vacuum system and the instruments and accessories used. In the second part, additional
important data are obtained frorn sorne preliminary experiments related to the sputtering
station. Finally, the fabrication procedure is presented.
4.2
4.2.1
Experimental Sputtering Facility
Main Vacuum System
The station used for the preparation of the transducers is an NRC - 3116
vacuum coater with a 6 inch oil diffusion pump and a liquid nitrogen cooled trap, as de
picted in Figure 4.1. The vacuum chamber -18 inch diameter - is equipped with a feed
through ring, three fixed water cooled electrodes and one movable grounded electrode . The
movable electrode can be rotated about a vertical axis to bring it - horizontally parai lei to
and vertically above - any of the fixed electrodes. Its vertical position is also adjustable
so that the spacing of the two plates can be changed. The fixed e lectrodes have a diameter
of 5 inches and are used as target holders, whi le the movable one carries the substrate holder
and heater, a thermocouple to measure the substrate temperature, and the thickness monitor
crystal.
2 x GAS 1 N LET====::()():===t F. T. R.
~--~------~--~ A . F • • L-----"""
A.R. V. T C 1
R. V. C.B.
TC2
M.P. D.P.
F. V.
38
"fMAGNETS
3 x ELECTRICAL POWER INLET
FIGURE 4.1. SCHEMATIC DIAGRAM OF THE VACUUM SYSTEM.
LEGEND
A.F.
A.R.V.
B.V.
C. B.
D. P.
F.E.
F.T.R.
F.V.
Air Filter.
Air Release Valve.
Baffle Valve.
Cryo Baffle.
Diffusion Pump.
Fixed Electrode.
Feed Through Ring.
Foreline Valve.
I.G.
M.P.
N.V.
P.G.
R.E.
R.V.
T .C.
Ion Gouge.
Mechanical Pump.
Needle Valve.
Pirani Gouge.
Rotating Electrode.
Roughning Valve.
Thermocouple Gouge.
39
Two coils, ring shaped, carrying currents of up to 10 amperes provide an
axial magnetic field between the electrodes of up to 100 gauss.
A Pirani gauge (CVC, GP - 210 C) provides an accurate reading of the
chamber pressure in the range 1 - 50 millitorr, which is the useful range for sputtering.
An ionization gouge and two thermocouples (NRC 720) monitor the chamber and fore-
1 i ne pressures from atmospheri c to 10-8
torr. (See Fi gure 4. 1) •
4.2.2 Instrumentation
(a) Substrate Heating and Temperature Control
The substrate heater is essentially a stainless steel block heated by a
Nichrome wire element. The substrate (sapphire delay rod) is fixed by holding it under
a slight mechanical pressure between two aluminum grips as shown in Figure 4.2. The
holder is designed so that the surface of the delay rod facing the target is emerging out of
the electrode plane, thus preventing any masking or shadowing effects.
To ensure good heat transfer, the sapphire crystal is wrapped in on indium
tinned copper shim.3
A chromel-alumel thermocouple is in contact with one of the side
faces of the substrate. This sensor is connected to a "Thermovolt" control 1er capable of
a temperature control of better thon :: 5 Oc in the ronge 50 to 500 oC. The control 1er
switches the current to the heater on and off. This current which can be adjusted up to 5
amperes is usually set at about 4 amperes.
40
HEATING WIRES THERMOCOUPLE
STAINLESS STEEL BLOCK
ALUMINUM GRI P
COPPER SHIM
SU BSTRATE
FIGURE 4.2. SUBSTRATE HEATER.
(b) Holder with Mask
To deposit the top electrodes, another holder is used. This is shown in
Figure 4.3 and consists of a block of aluminum in which two circular holes 0.5 mm dia-
meter and spaced 3 mm apart are drilled counter-sunk to minimize shadowing effects.
Two transducers are thus produced in each run under the some conditions, allowing for a
quick check on the re liabil ity of the results. Four centering screws enable positioning the
crystal to obtain the two transducers at nearly symmetrical places on its surface.
41
SU BSTRATE
r 4 x CENTERING SCREWS
ELECTRODE
(j 0.5 mm, COUNTER SUNK
FIGURE 4.3. HOlDER WITH MASKS.
(c) Film Thickness Monitor
A Slocn DTM - 3 frequency meter relates the thickness of the deposit
build-up on an osci lIating quartz crystal, to the change in frequency.36
where
T
T
Af
p
A f =
5.63 P
= thickness of the deposit in microns,
=
=
reading of the rneter in KHz,
3 mass density of the deposit material in 9 / cm ,
5 63 . .. f d .. . KH 3 / • = sensltlvlty or mass etermlllotlon, III z. cm g. ~
During sputtering, two kinds of difficulties are encountered. First, the sensor head being
42
sensitive to high temperatures, has to be thermally isolated from the heated electrode.
This introduces a source of error in thickness monitoring since the rate of deposition is a
function of temperature. The temperature dependent error is estimated during sorne pre
liminaryexperiments (see Section 4.3.3) and is accounted for in the rest of the work •.
Secondly, the interference between the RF sputtering fields and the crystal oscillator make
it impossible to read the instrument during sputtering. To overcorne this difficulty, the
sputtering is started with the thickness monitor crystal in the field of deposition and the in
strument adjusted for null indication. After 30 minutes, the RF ·source is switched off
to enable a measurement of the thickness. The rate of deposition is thus calculated and
the sputtering is continued under the same initial conditions for the time required to obtain
the proper thickness.
(d) DC and RF Power Sources
A DC high voltage power supply (NRC 1901) as weil as an RF one
(CVC Plasmavac Type AST 300) are avai lable .
A Bayly IW3 - 15A RF wattmeter is used to measure both forward and
reflected RF powers. Due to the high VSWR on the cable connecting the tuning network
to the electrodes, the power meter is inserted in the line connecting the RF power amplifier
to the tuning network, which is shown in Figure 4.4. Losses in the tuning network and cables
are assumed negligible, cornpared to the power fed to the discharge .
43
POWER METER
~ ,..-_____ TO VACUUM
RF
OSCILLATOR
POWER
AMPLIFIER
TUNING
NETWORK
CHAMBER
HIGHVSWR
FIGURE 4.4. R F POWER SUPPLY AND POWER METER.
4.3 Preliminary Experiments
Before proceeding with the main experiments, sorne preliminary tests were
necessary to establish the procedure to be followed in producing the transducers.
The various experiments done in this study are:
1. Evaluation of the metallic film deposition techniques.
2. Measurement of the temperature rise of an unheated substrate
as the sputteri ng process deve 1 ops.
3. Obtaining calibration charts for the rate of deposition of zinc-
oxide versus the net RF power input for different substrate
temperatures and 90S cornposi ti ons.
44
4.3.1 Metallic Films
The objective of this experiment is to establish the procedure for deposit
ing the gold metal electrodes. Since gold does not adhere weil to sapphire, an intermediate
layer of chromium is used.
(a) Chromium Deposition
A chromium film is formed on the face of a partially masked sapphire rod.
The conditions for sputtering are as follows :
Target : 5 inch diameter pure chromium disk.
Intere lectrode distance : 2 cm.
Working gas : pure argon at a pressure of 7 mill itorr.
Power supply: 150W RF.
Time of deposition: 5 minutes.
After removing the sample from the vacuum system, the film thickness is measured using a
Watson-Bornet interference microscope objective having a vertical resolution better than
1 /10 fringe with a green light source, (Thallium X = 535O~). The chromium layer
is found to be about 1000 i. thick, i.e., the rate of deposition is about 200 A / min.
(b) Gold Deposition
A gold film is deposited on a sopphire crystal on the top of a chromiun
loyer prepared os in (0) above. The gold target is a 2 inch diameter gold disk. Pure
45
argon at a pressure of 40 mill itorr is used as the working gas for DC sputtering at
2.5 KV and 2 cm interelectrode distance. After 5 minutes of sputtering, the sample
is removed from the cham ber and the thickness of the gold deposit is measured. About o
1470 A of gold is detected, i.e., the rate of deposition ~ 300 °A / min. A high re-
solution diffraction picture of this gold film showed that it is polycrystalline with the
(220) planes preferably oriented parallel to the substrate surface.
(c) Gold Top Electrodes
A gold layer is deposited as in (b) through a 0.5 mm mask. Micros-
copic inspection showed that the film has a convex shape which is due to the shadowing o
effect of the mask. It has a thickness of 1160 A at its centre corresponding to a rate of o
230 A / min, compared to 3000
A / min obtained in the unmasked case.
4.3.2 Temperature Rise Due to Sputtering
The substrate temperature was recorded during the deposition of a zinc
oxide layer on a sapphire rod, once using an input RF power of 200 w, and another time
with 125 watts. The results are in Figure 4.5, which show that the rate of temperature
rise is highly dependent on the input power. This experiment also tells us that in order to
maintain a fixed substrate tempe rature , we have either to heat the specimen to a temperature
level above that which it would have reached if unreated, or, to cool it at a certain rate
TEMPERATURE (oC) 1
100
80
60
40
20
P = 200 W·
30 60
p = 8 ~ , O2
= 10 %
t END OF SPUTTERING
r P = 125 W
90 120 150 180
TlME (min)
FIGURE 4.5. TEMPERATURE RISE DUE TO SPUTTERING.
balancing the rate of heating due to sputtering. A practical experimental set-up is to
46
have a cooled electrode (e .g. water cooled) with a controlled heating element 50 that
the adjustment of the flow of the cooling substance together with the heating current allows
us to operate at any temperature we wish. In our vacuum system, described in Section
4.2.1, a water cooled "movable" electrode presented a technical difficulty, and 50 we
were limited to operate at temperatures higher thon 150 Oc .
47
4.3.3 Effect of RF Power on Deposition Rate
Glass microscope slides are used as substrates in this set of experiments. o 0 .-
First, a 150 A thick chromium layer, followed bya 1500 A gold film, is deposited on the
glass substrate. Then, without breaking the vacuum, the substrate is moved to a masked
section of the electrode having a hole of 10 mm diameter, through which zinc-oxide is
sputtered for 30 minutes. This arrangement makes it possible to obtain 4 test samp les at
different power levels on one slide in each run.
The thickness of the zinc-oxide loyers is measured using the film thickness
monitor, (Section 4.2.2 (c)) , and 0150 - after breaking the vacuum - using the inter-
ferometric method. A comparison of the two readings gives the correction factor for the
thickness monitor calibration, thus compensating for the error due to temperature rise.
The rate of deposition calculated from the measured thickness is plotted
in Figures 4.6, 4.7 and 4.8, against the net RF input power. In Figure 4.6, we see
that within the accuracy of the actual measurement, the relation is linear and independent
of pressure. However, Figure 4.7 shows that at high input powers, the relation deviates
from linearity and is affected by the substrate temperature. The sputtering gas composition
is argon : oxygen = 50 : 50. In Figure 4.8, similor calibration chorts ore obtained
for the gas composition 90 : 10 .
The important conclusion drawn from these experiments is that a stable
temperature and a good control of the input power are necessary to maintain a fixed rate
of depositi on throughout the sputtering operation.
RATE 100 48 (Ao/min) PRESSURE
9 0
80 * 9.5 * , 10
x 11
60 0 12
+ 15 x
* 18 EXPERIMENTAL 0 ERROR
40
x + 20
*
20 40 60 80 100 120 140 W
FIGURE 4.6. RATE OF DEPOSITION vs. POWER INPUT AT DIFFERENT PRESSURES.
RATE
(A ° /min) 200
350
150 , __ - 300°C
10
50 UNHEATED / /
/ /
./' /
50 100 150 200 250 W
FIGURE 4.7. RATE OF DEPOSITION vs. POWER INPUT AT 50 % O2 .
RATE
(Ao/min) 200
150
100
50
UNHEATED /
/ /
/ /
50
49
350 Oc
100 . 150 200 250 W
FIGURE 4.8. RATE OF DEPOSITION vs. POWER INPUT AT 10 % 0 . 2
4.4 Transducer Fabrication Procedure
4.4.1 Cleaning Procedure
The sapphire crystal used as a delay rad is cleaned, prier to the deposi-
tions, using the following steps :
{a} Immerse in hot aqua-regia for 2 minutes to remove
previ ous deposits.
(b) Rinse in disti lied water.
50
(c) Remove organic residues using hot chromic acid.
(d) Rinse in running distilled water.
This method is found satisfactory (see Section 3.3.2 (a», especially if the substrate is dried
and put under vacuum immediately after cleaning.
4.4.2 Deposition of Bock Electrode
After cleaning, the substrate is fixed in the holder described in Section
4.2.2 (a». The vacuum chamber is then pumped down for several hours, usually over
night. This prolonged period of evacuation has two purposes : to reduce the residual gases
in the chamber to a minimum, a vacuum better than 10-7
torr is achieved, and to allow
for a uniform and stable substrate temperature.
Pure argon is introduced into the chamber through a needle valve whi le
the baffle valve is throttled to allow for a dynamic flow of the 90S. At an equilibrium
pressure of 7 millitorr the RF power supply is switched to the chromium target. After a
few minutes of pre -sputtering, the substrate is brought above the target for 45 seconds.
With an input power of 150 watts, this time gives a chromium thin fi lm of about 150 A 0
•
The pressure is then raised to 40 mill itorr and using the D. C. power supply at 2.5 KV
the gold bock electrode is formed after a pre-sputtering period of 5 minutes and another
active sputtering period of 5 minutes. The fi lm thus obtained has a thickness of about
1500Ao
.
51
4.4.3 Deposition of the Zinc-Oxide Film
Following the deposition of the gold e lectrode, the argon is pumped out
for one hour and then the proper Argon-oxygen mixture is admitted through a needle valve
to raise the pressure to the required value. A pre-sputtering of the zinc-oxide target for
15 minutes followed by the deposition of the required film using the RF power supply
terminates this step. Adjustment of the tuning network and the driver current, to obtain
the necessary power to the discharge, is made during the pre-sputtering periode
4.4.4 Deposition of the Top Electrodes
The substrate is allowed to cool for 6 hours before breaking the vacuum
to transfer it to the holder with the masks. (see Section 4.2.2 (b)). Under the same con
ditions described in Section 4.4.2 above, the gold top electrodes are deposited.
4.4.5 Chemical Etching of Zinc-Oxide
Since the zinc-oxide is deposited over the entire surface of the sapphire
crystal, it is necessary to etch the film at the corners of the delay rod to uncover the
gold bock electrode. This is done using diluted hydrochloric acid followed bya short rinse
in running distilled water.
Referring to Figure 4.2, one can see that gold - as weil as zinc-oxide -
deposit as a narrow' ribbon on the side faces of the substrate. Special care has to be given
52
to etch zinc-oxide from this area whereas the presence of gold is advantageous insofar as
it provides a good electrical contact to the holder used in the electron microscope,
(Chapter V) , thus providing a leakage path for the space charge build up on the sample
surface.
53
CHAPTER V
TESTING OF THE TRANSDUCERS
5. 1 !ntroducti on
ln this chapter, the methods used for testing the transducers are described
in detail. The major tests performed on each transducer are:
Determination of the crystallographic structure and orientation
of the zinc-oxide crystallites w ith respect to the substrate .
This gives an indication of how far the transducer is, ho,." the
ideal, c - axis oriented, single crystal one used in theoreti-
cal calculations.
Evaluation of the frequency response - transducer loss versus
frequency - which is the only meaningful representation of
the electrical performance of the transducer.
5.2 Structure Ana Iysi s
Reflection electron diffraction (RED) and X-ray reflectio'1 techr<que)
are used to study the crystal structure of the vacuum deposit,. However; a thin fil"., less
than a few microns thick can only be examined by the RED technique. Thi, i5 due to +he
fact that the interaction of electrons wjth atoms is much stronger. bya factor of rcughly
103
, than the interaction of X-rays. For RED, diffracted beams of intel"sity cQtT1poroble
wi th that of the incident beam can be given by less thon 100 A 0
of crysto l, ..... h 'Ie 0"
54
X-ray beam must traverse 5 to 10 mi.crons of perfect crystal before a diffracted beam ca~
achieve appreciable amplitude.37
5.2.1 General Formulae Governing RED
RED employs a stream or beam of high energy e lectrons (de Broglie waves)
contained in a vacuum better thon 10-4 torr. In the incident beam , it is assumed that
the electrons (also known as ~ particles) are monoenergetic, hence monochromatic. It
con be easily shown that the wave length , À 1 of such electrons is given by :
À == h
[2m eV(l+ o
where h is Pkmck's constant j m 1 electron rest mass j V 1 the accelerating o
potential ; e 1 electron charge ; and c, the speed of light.
If numerical values are substituted for constants in the above equation,
we get
À == 5.1
or
5.2
Equation 5.2 is accurate within an error of less thon 5 % for 100 KV.
55
The simple, elegant relation
2 d (hk 1) sin 9 (hk 1) = n À 5.3
known os Bragg1s Law, relates d (hkl) the distance or interplanar spocing between con
secutive parallel diffracting planes whose Miller indices ore (hkl) and 9 (hkl) the ongle
between the direction of the incident beam and the diffracting planes. 9 is also half the
diffraction angle, i.e., the ongle between the incident beam and the diffracted one. In
the above relation n is on integer giving the order of diffraction.
Applying Bragg1s law to single perfect crystals, gives electron diffraction
patterns consisting of arrays of spots. More often a spot pattern represents the average
pattern for a large number of separate small crystals aligned to have the sorne orientation.
The alignment of the individual single crystals is imperfect not only by
bending or rotations about axes Iying in the plane of the specimen but also by rotations
about on axis perpendicular to this plane. Thus, not only do we get a modification of in
tensity of the diffracted spots, but the spots ore spread into arcs and ore often also diHused
by the limitation of crystal size in the directions perpendicular to the incident beam ~7
On the photographic plate the radii of the arcs measured from the central
spot formed by the incident beam are given by :
r (hkl) = L ton 2 9 (hkl) 5.4
where L is the cornera length, i.e., the length from the specimen to the photographie
plate.
56
o For RED, 9 isusuallyverysmall, lessthan 1 , sothatEquations 5.3
and 5.4 con be combined to give :
r (hkl) ~
XL d (hkl)
5.5
line-broadening as mentioned above is due to the limited crystal size, t (hkl) , in the
direction (h k 1) normal to the incident beam. Using Sherrer formula: 38
t (hkl) X 5.6
49 . cos 9 (hkl)
one can estimate the crystal size. However, due to the small values of X and 49, the
estimate is very coarse.
5.2.2 The Zinc-Oxide Structure
The Zincite crystalite, (ZnO), is known as the Wurtzite structure. The
description of the crystal is in terms of two interpenetrating hexagonal lattices as shown in
Figure 5.1 ,
zinc atoms are at positions (0, 0, 0) + h c p trons-
lation, and
oxygenatomsareatpositions (0,0, u) + hcp
translation .
57
r 110
-! 100
002L
~~ t u + 1/2
Tl/2
b
/ ® ZINC ATOMS
• OXYGEN ATOMS a
FIGURE 5.1. ZINC - OXIDE CRYSTAL.
The ideal value of u for hexagonal closed pack is 0.375 while
39,40 0 measured values are 0.374 and 0.383. The lattice constants at 298 K are:
a = 3.249858 ± 6 A 0
and
c = 5.206619 ± 2 A 0
The c / a ratio is thus 1 .602 compared with the hexagonal closed pack value of
.i 8 /3 = 1 .633 .
58
For this structure, the only reflections systematically absent are the
( h h 1) for 1 = 2 n + 1 •
5.2.3 Experimental Set-up and Procedure
RED pictures were taken on a Philips EM 300 electron microscope using
an accelerating voltage of 80 KV and a camera length of 353.5 mm. Substituting
these values in Equations 5.1 and 5.5, we get :
À = 0.0416 AO
r (hkl) = 14.75/ d (hkl) 5.7
For convenience, rand d in Equation 5.7 are in millimeters and angstroms respectively.
Table 5.1 gives the values of d and r for different planes of the zinc-oxide structure.
To take a RED picture, the fi lm is first etched by short immersion in
dilute hydrochloric acid to remove any surface contamination. The sapphire crystal is
then introduced into the microscope column via an air-Iock device and diffraction patterns
at several positions on the surface are examined. The results obtained are discussed in
Chapter VI.
TABLE 5. 1 .
Zn 0 interplanar spacing (d) and radii of semi circles on
the photographie plate (r) based on :
Mi 11er Indices
h k 1
100
002
101
102
110
103
200
ZnO lattice parameters :
a
c
=
=
3.2498 A 0
5.2066 A 0
Electron microscope constants:
y = 80 KV
L = 353.5 mm
Formula d h k 1 d= A
O
a sin 600
2.8142
c /2 2.6033
2 a c sin 600
2.4754
j3a2 +4c2
. 600 a c Sin 1 .9109
)3 a2
+ c2
a /2 1 .6249
0 2 a c sin 60 1.4774
fz,;/ 2 . 27a +4c
a /2 . sin 60 0
1 .4071
XL r =
d
5.23
5.65
5.94
7.70
9.05
9.95
10.45
59
mm
60
5.3 Evaluation of the Electrical Performance of the Transducer
ln network theory, the transducer gain of a 2 - port is defined as the
ratio-expressed in decibels - of the power dei ivered to the load to that power available
26 from the generator. Referring to Figure 5.2 (a), the ability of a piezoelectric trans-
ducer to convert electrical power to mechanical power (acoustic power generation) is
expressed in terms of the generation transducer 1055 :
P T L (G)
a = - 10 10910 P 5.8
o
where P is the acoustic power delivered to the acoustic medium and P is the elec-a 0
trical power available from the generator.
The inverse function, namely converting mechanical power to electrical
power (acoustic power detection), Figl're 5.2 (b), is expressed as a detection transducer
loss :
T l (D) Pd
= -10 logP.
1
5.9
where Pd is the power dei ivered to the electrical load and Pi is the acoustical power
;.,cident on the transducer, ail of which is "available".
As discussed in Chapter Il, if there are no drifting carriers in the transducer
uf'1der consideration, then reciprocity holds and the generation and detection transducer
losses are equal.
----- TRANSDUCER ---~
P. 1
(a) (b)
61
ELECTRICAL LOAD
FIGURE 5.2. PIEZOELECTRIC TRANSDUCER AS (a) GEN ERATOR, (b) DETECTOR.
P o
P ~ o ~ P - - - - - - --, al , ~ Pil -- - - - ----'
~ P ------, 02 1
+ Pi2 - - - - --'
---..,,. Pa3
.... etc.
FIGURE 5.3. PULSE - ECHO DELAY LlNE.
1 ~Pal \
DELAY
L
rMIRROR PLANE
1 1 1
1 Pil
1 1 ROD 1
t
L~
-..P ~
dl
Il
FIGURE 5.4. UNFOLDED DELAY LlNE WITH RESPECT TO THE FIRST ROUND-TRIP.
62
5.3.1 Ove rai 1 Transducer Loss
ln the pulse echo technique of measurement~1 pulse modulated oscillations
cause the transducer to generate ultrasonic waves that travel in the delay rod, reflect at
the far-end face, and travel bock towards the transducer where they are detected (first
echo). Due to the acoustic impedance mismatch at the transducer-rod interface, a portion
of the mechanical power is repeatedly reflected bock into the delay rod causing higher
order echos as depicted in Figure 5.3.
As far as the first echo is concerned, the single ended delay line with a
reflecting endfac~ can be unfolded about the mirror reflecting plane and therefore re-
presented by the 2 - port network shown in Figure 5.4. An overall - device - transducer
1055 is then defined :
T L (device) 5.10
It is pointed out that the device transducer loss combines the generation and detection
transduce r losses as weil as the delay rod 1055, aDR
, where:
T L (device) = T L (G) + aDR
(1) + T L (D) 5.11
and
aDR
(1) Pil
5.12 = - 10 log-Pal
The subscript (1) in Equations 5.10, 5.11 and 5.12 refers to the first
rou.,d trip of the acoustic pulse .
63
5.3.2 De lay Rod Losses
For the nth round trip, the delay rod loss is :
p. a
DR (n) = - 10 log pin
an
This term is made up of several factors which are summarized as follows :
(a) Delay Rod Attenuation : 01
For c - axis oriented sapphire, the attenuation is 0.18 db / cm at
1 GHz, and varies as the square of the frequency ~2 Therefore we can write :
= - 0.18 L f2 x 10-16 db
5.13
5.14
where f is the frequency in Hz, and L the length of the round trip - twice the length
of the delay rod - in meters.
(b) Diffraction Loss : 02
Diffraction loss is a more complicated function of frequency, top elec
trode geometry, rod material and length ~3
ln Figure 5.5, the diffraction loss in c - axis oriented sapphire is plotted
against a normalized trip length. In Figure 5.6, the diffraction Joss of the first, second
and third round trips is plotted against frequency. The deJay rod length is taken to be
12 .5 mm and the top e Jectrode diameter 0.5 mm.
RELATIVE LOSS ( db)
4
2
2 4 6
SAPPHIRE, C - AXIS
b = 0.16
64
8 10 L/(02/ X)
FIGURE 5.5. DIFFRACTION ATTENUATION IN SAPPHIRE (REFERENCE 43).
O2
(n )
(db) 2
LOSS
(db)
2
=: 12.7 mm.
o = 0.5 mm.
n = 1
0.5 0.6 0.8 1.0 1.2 1.6 2.0
FREQUENCY ( GHz)
FIGURE 5.6. DIFFRACTION LOSS PER ROUND TRIP.
0.5 0.6 0.8 1.0 1.2 1.6
FREQUENCY (GHz)
FIGURE 5.7. DELAY ROD LOSSES.
2.0
65
(c) Other losses : 03
These are caused by imperfect reflection at the free face of the delay
rOO, non parallelism of the 2 faces and small deviations in the crystallographic orienta
tion. In general
5.15
a3
can be made negligible by properly choosing and machining the delay rod. The at
tenuation and diffraction losses are known and can be incorporated in the calculations.
Figure 5.7 is a plot of 01 ' a2
(1) and aDR
(1) for the first echo
in the de lay rOO described above .
5.3.3 Delay ROO Holder
ln Chapter Il, calculations have shown the importance of an effective
low loss contact to the metal electrOOes. The delay line holder used for transducer loss
measurements was specially designed to meet this requirement. As shown in Figure 5.8,
the holder is a type N male connector (lnitially a He~lett Packard 420 A crystal de
tector holder) to which a gold plated, spring loaded "POGO" contact is soldered.
Four centering screws enable accurate positioning of the delay rOO so that the top elec
trOOe of the transducer to be tested faces the spring loaded contact, while the delay rOO
is pressed from the other side by a spring loaded plastic piston. Short-circuit impedance
measurements showed that the parasitic contact resistance to a thin gold foil is less than
0.4 ohm.
66
DELAY ROD
4 CENTERING SCREWS
TYPE N CONNECTOR
FIGURE 5.8. DELAY ROD HOlDER.
5.3.4 Conjugate Motched Tronsducer loss
The circuit of Figure 5.9 is the basic circuit used to measure the con-
. h d d 1 l, 2 , 35, 41 lugate matc e trans ucer oss.
G is a pulse modulated UHF generator,
H a Hybridge with insertion loss Hab between
ports a and b,
67
M a "lossless" match ing network - e. g., Double Stub Tuner,
A a variable calibrated attenuator,
S an RF coaxial switch,
R a heterodyne receiver and amplifier. x
The method of measurement consists in adjusting the attenuator A until the power received
at switch position 2 is equal to the power detected from the first echo at switch position 1.
Therefore :
A Po = H24 P dl 5.16
where P is the power available from the generator after splitting equally in arms 2 and o
3 of the Hybridge. Equation 5.16 converted into decibels, together with Equation 5.10
gives the device loss :
T L (device) = A - H24
5.17
SÏ!1ce the Hybridge is operated with ail ports terminated in the characteristic impedance,
H24
is a known constant (6 db for the "Alford" Hybridges).
At this point, it is recalled that the generation and detection transducer
losses are equal since no acoustic amplification effects are involved. Therefore, using
Equati ons 5. 11 and 5. 17
T L (G) = T L (D) = A - 6 - a
DR (1)
2 5.18
G
--+ P
o
3
H
2 4
A
DELAY ROD
1 1 1 1 1 1
1 P 1
1 0 TRIGGER 1 L ______________ .. ______ --1
68
FIGURE 5.9. CIRCUIT USED FOR TUNED TRANSDUCER LOSS MEASUREMENT.
G
v o
2 S N
e
A
1
1
Pd1 1 +- DELAY 1
-- ROD 1 1 5 P
1 e 0 1 1 1 TRIGGER L_~_L _________ ~------.J
FIGURE 5.10. CIRCUIT USED FOR UNTUNED TRANSDUCER LOSS MEASUREMENT.
69
which is simply called the transducer loss, TL, and is plotted against the frequency to
give the frequency response of the transducer under test.
The use of a matching network (M) in this circuit is necessary to balance
the two arms of the Hybridge. Careful tuning to minimize the voltage standing wave ratio
seen by arm 2 of the Hybridge is carried out at each frequency. The transducer loss
obtained under such conditions is the conjugate matched transducer 1055.
ln a high resistivity (Iossless) transducer, the "intrinsic" conversion
efficiency is 100 %, so that the conjugate matched transducer loss is exclusively due to
the contact resistance and the matching network loss so far assumed negligible. The effect
of these parasitics is discussed in Chapter Il.
5.3.5 Untuned Transducer Loss
ln order to measure the untuned transducer loss the circuit of Figure 5.9
is modified, namely the matching circuit is removed and the Hybridge is replaced byan
electronic switch (S) as shown in Figure 5.10. The drive of the electronic switch is e
obtained From a pulse gene rator , Figure 5.11, synchronized with the pulse modulator of
the UHF source. The duration and delay of the driving pulse are adjusted 50 that it over-
laps the incident UHF burst providing the necessary isolation of the receiver.
Let S be the insertion loss of the switch (lncluding the 3 db pad). e
Therefore equating the pa.vers at terminais 1 and 2 of the manual switch S:
5.19
PULSE GENERATOR GR 1340
EXTERNAL
DRIVER
2 SWITCH
NO 1 1 NC L ______ J
TRIGGER 3 db PAD
70
D C POWER SUPPLY
FIGURE 5.11. DETAILED BLOCK DIAGRAM OF THE ELECTRONIC
SWITCH USED IN FIGURE 5.10 .
Converting 5.19 into decibels and combining with Equations 5.10 and 5.11, noting
that the incident power on the transducer is S P , we get e 0
T L ==
A - 2 S e - a DR (1)
2
which is the untuned transducer loss.
5.20
Typical frequency responses obtained using the above circuits are shown
and discussed in the following chapter.
71
CHAPTER VI
EXPERIMENTAL RESULTS
6.1 Introduction
A large number of zinc-oxide transducers were produced and tested in
accordance with the method of fabricati on outl ined in Chapter IV, and the testing pro-
cedures detai led in Chapter V.
ln order to investigate the effect of the different parameters affecting the
preparation of the transducers, the objective originally was to produce a set of samples
having 011 deposition parameters fixed - except one. However, as mentioned earlier, it
was found that preselecting the sputtering power does not allow a close control on the de-
position rate. This is due to the steepness of the rate-power relationship which was found
in the experiments described in Chapter IV and shown in Figures 4.7 and 4.8. It was
therefore decided to study the effect of varying each of the parameters, with the deposition
rate as another indepenCiient variable. The results obtained are thus presented as two dimen-
sional families of curves. An example is given in Figure 6.1 which shows a family of
constant temperature - minimum loss versus rate curves.
6.2 Temperature and Deposition Rate
1 •• Il h ba· f . d· 1.2 h f· of . n.tla y, on t e SIS 0 prevlous stu les, t e Irst set expenments
were performed using a sputtering gas of 50 : 50 - oxygen : argon - composition, while
the pressure was fixed at 8 millitorr. The distance between the electrodes was 2 cm.
72
A number of depositions (19 samples) were made at various rates and o
temperatures covering the ranges 40 - 200 A / min and 200 - 400 oC, respectively.
The results for these transducers are shown in Table 6. 1 ~
ln Figure 6.1, a plot of the minimum transducer loss (conjugately matched)
against the rate of deposition, with the temperature as a parametric variable, is shown.
For a certain fixed temperature, say 300 oC, the transducer loss is seen to decrease with
the increasing deposition rate. However, this relationship has a discontinuity at a certain
rate (hereafter called the critical rate) which seems to have very little correlation with
MIN TL 02 = 50 %
TEMPERATURE (db)
o 200 Oc 30 c 250 Oc
6 3OQoC
20 / 350 Oc x 400 Oc
10
50 100 150 200 RATE ( A 0 / MIN)
FIGURE 6.1. MINIMUM TRANSDUCER LOSS vs. RATE OF
DEPOSITION AT 50 % OXYGEN.
* Tables 6.1 to 6.7 are shawn at the end of the chapter.
73
the temperature. RED studies showed that the transducers produced below the critical rate
have in general weil ordered structures, with the c - axis oriented perpendicular to the
substrate surface, within :1: 200
as shown in Figure 6.2, for sample number 10. The
transducers fabricated at higher rates are polycrystalline with the (100) planes preferably
oriented parallel to the substrate surface as in RED picture for semple number 12 as shown
in Figure 6.3 (a). The latter, however, contain sufficient correctly oriented crystal lites
(c - axis normal) to be piezoelectrically active. A further increase in the deposition
rate apparently increases the percentage of correctly oriented crystal lites as shown in
Figure 6.3 (b), thus improving the transducer action.
ln general, the crystal structure was uniform throughout each sample and
no preferred orientation in the plane of the substrate surface was noticed. The randomness
is readily verified by checking that the pattern is completely independent of incident elec
tron beam directi on.
ln Figure 6.4, another representation of the results discussed above is
used. Here, the constant transducer-Ioss contours are drawn in the rate-temperature plane
with the experimental points shown by small circ les •
The frequency responses of some typical samples are shown in Figure 6.5.
The different responses are better expressed in terms of the 3 d b bandwidth as a percent
age of the central frequency (% B.W.) , which is drawn in Figure 6.6 against the rate
of deposition, and is found to be independent of the substrate temperature. It is also noted
that the minimum % B.W. occurs at - or about - the critical rate.
FIGURE 6.2. RED PICTURE OF
Zno FILM No. 10
(002)
FIGURE 6.3. RED PICTURES OF
(a) SAMPLE No. 12
(100)
~) SAMPLE No. 14
(100, 002)
74
FIGURE 6.2. RED PICTURE OF
ZnO FILM No. 10
(002)
FIGURE 6.3. RED PICTURES OF
(0) SAMPLE No. 12
(l00)
lb) SAMPLE No. 14
(l 00 , 002î
74
TL 30
( db)
20
10
0.5 0.6 0.8 1.0 1.2 1.6 2.0
FREQUENCY (GHz)
FIGURE 6.5. TYPICAL FREQUENCY RESPONSES FOR SAMPLES
PRODUCED AT 50 % OXYGEN.
%BW 100
o
o 50
o
.50 100 150 200 RATE (A
0 / MIN)
FIGURE 6.6. BANDWIDTH vs. RATE OF DEPOSITION
AT 50 % OXYGEN.
77
ln Figure 6.7, in spite of the small number of experimental points, we
see that the loss-rate re lationship at different pressures has the sorne general trend as was
shown earl ier •
MIN TL
(db) 30
20
10
12
8
50 100
~ 15 .... 12
~1O
150
FIGURE 6.7. EFFECT OF PRESSURE.
8
PRESSURE
6 10 m ili itorr
° 12
X 15
200 RATE (Ao/MIN)
A specially interesting somple is number 27 which showed shear mode
excitation near the quarter wavelength frequency. Figure 6.8 is an os ci 1 logram for the
echo pulses showing the shear mode superimposed on the longitudinal mode. RED picture
for this somple is shown in Figure 6.9. A c1ear (110) trace indicates that these planes
are stacked poralle 1 to the substrate surface.
Another interesting RED picture, Figure 6.10, is that obtained for
semple 20, which shows a very high orientation of the zinc-oxide film.
FIGURE 6.8. DETECTED ECHOES
SHOWING SHEAR AND
LONGITUDINAL WAVES.
Upper trace at 1 GHz.
Lower trace at 1.2 GHz.
(Vertical 17 db / cm,
Horizontal 2 ~ sec / cm.)
FIGURE 6.9. RED PICTURE OF
SAMPLE No. 27
(110, 002)
FIGURE 6.10. RED PICTURE OF
SAMPLE No. 20
(002, HIGH
ORIENTATION)
78
fl1ll II l
79
6.4 Effect of the Gas Composition
Table 6.3 summarizes the conditions and results obtained for 11 samples
fabricated at different gas compositions : 5, 10 and 20 % oxygen respectively with the
complementary balance of argon. The minimum transducer loss is plotted versus the rate
of deposition in Figure 6.11, which again shows the same type of relationship as above.
MIN. Tl ( db) 30 OXYGEN
50 X 5%
0 10 20
20 A
20
~ 10 AR A 10 ~ 10
50 100 150 200 RATE (A
o / MIN)
FIGURE 6.11. EFFECT OF THE GAS COMPOSITION.
ln addition, an attempt was made to deterniine the stoichiornetry of the samples produced in
this set of experiments. Visual microscopic inspection showed that the films produced in
5 % oxygen are - without exception - dark grey, characteristic ci excess zinc in the
deposit. Those produced at 10 and 20 % oxygen are transparent while the films obtained
in the previous set of experirnents at 50 % oxygen content were yellowish.
80
Methods of analytical chemistry 47 failed to give a stoichiometry index
for these films because the quantity of material available was too small (about 0.2 mg).
X-ray fluorescense also failed as a stoichiometry indicator because of the oxygen light
atomic weight compared to the zinc, (0 = 16, Zn = 65.38).
The electrical resistivity was then taken as a relatively more precise esti
mate of the stoichiometry than the color of the film. The samples produced at 10 % oxygen
had generally a high resistivity of about 15 K ohm. m. Those fabricated in the 20 % and
50 % oxygen atmospheres were also highly resistive. However, an erratic, unexpected
drift in their resistivity was noticed and could not be explained. The few samples made at
5 % oxygen showed lower resistivity (about 200 ohm. m) which is due to excess rne ta Il ic
(Zn) atoms in the deposited fi lm.
6.5 Rate - Temperature Survey at 10 % Oxygen
At this point, it was felt that the 10 % oxygen - 90 % Argon 90S com
position gives the best ZnO films with regard to their stoichiometric structure. Therefore
a rate - temperature survey similar to that done for the 50 - 50 gas composition was rele
vant. Table 6.4 and Figures 6.12, 6.13 and 6.14, show the results obtained end are
in ail respects similar to Table 6.1 and Figures 6.1, 6.4 and 6.6. The comparison
shows that lowe ... transducer losses and wider bandwidths can be achieved using the 10 %
oxygen atmosphere without being critically sensitive to the deposition rate - i.e. the R F
power input. Figure 6.15 is the frequency responses of typical transducers in this set.
MIN TL
(db) 30
20
10
50 100 150
81
TEMPERA TURE
o 200 Oc o 250 Oc Il 300 Oc / 350 Oc
200
RATE (Ao
/ MIN)
FIGURE 6.12. MINIMUM TRANSDUCER LOSS vs RATE OF
RATE 200
(Ao
/ MIN)
150
100
50
DEPOSITION AT 10 % OXYGEN.
o
200 250 300
PREDOMINANT ORIENTATION
002
100, 002
350 400 TEMPERATURE (oC)
FIGURE 6.13. CONSTANT TRANSDUCER LOSS CONTOURS
AT 10 % OXYGEN.
%BW
100
50
50 100 150
82
o
200 RATE (AO
/ MIN)
FIGURE 6.14. BANDWIDTH vs RATE OF DEPOSITION AT 10 % OXYGEN.
TL
( db)30
20
10
0.5 0.6 0.8 1.0 1.2 1.6 2.0
FREQUENCY (GHz)
FIGURE 6.15. TYPICAL FREQUENCY RESPONSES FOR SAMPLES
PRODUCED AT 10 % OXYGEN.
FIGURE 6.16. RED PICTURES OF
(a) SAMPLE No. 34
(002, EPITAXIAL)
(b) SAMPLE No. 46
(002, HIGH ORIENTATION)
(c) SAMPLE No. 48
(100, 002)
83
FIGURE 6.16. RED PICTURES OF
(a) SAMPLE No. 34
(002, EPITAXIAL)
(b) SAMPLE No. 46
(002, HIGH ORIENTA TlON)
(e) SAMPLE No. 48
(l 00, 002)
83
84
Epitaxial growth is noticed in RED pictures of samples made at 300 Oc and below the
critical rate (120 A 0
/ min in this case). Figure 6.16 •
6.6 Crystal Size and C - Axis Spread
The microcrystallite size was estimated from line broading (see Chapter V)
o to be about 200 A. An attempt was made to correlate the crystal size and the c - axis
spread about the film normal with respect to : transducer loss, rate of deposition and / or
temperature. Apparently there is no direct relation between these variables. However,
if we only look at samples with pol ycrysta Il ine structure, having a c - axis spread of
about :1: 200
the apparent crystal size seems to decrease slightly with increased rate of
deposition as shown in Figures 6.17 and 6.18. These conclusions are very tentative since
the error in crystal size measurement might be very large (:1: 100 A 0) .
6.7 Input Impedance
The input impedance of sorne samples have been measured at 2 MHz
using a high frequency bridge. In Table, 6.5, the measured C and R, as weil as the
calculated values for the input capacitance are listed. The resistivity of each film is de-
duced from the measured input resistance.
A comparison between the calculated and measured capacitances shows
that the latter are 2 to 3 times higher than the former. This suggests that the electrode
C-AXIS SPREAD
:1: 9° 30
20
10
50
0
a â
x
0
[)
!J. 0
/
!J.
!J.
100
85
TEMPERATURE
° 200 Oc o 250 Oc Il 300°C / a
!J. 1 350 Oc )( 4OQoC
0 / /
150 200
RATE (Ao / MIN)
FIGURE 6.17. C-AXIS SPREAD vs RATE OF DEPOSITION.
CRYSTAL SIZE
AO 400
300
200
100
o 0
~--H- Il 0
o l,a-~L- 0 A A-
o o
50 100 150 200
RATE (Ao /MIN)
FIGURE 6.18. CRYSTAL SIZE vs RATE OF DEPOSITION.
86
material (gold) diffuse (or is imbedded during sputtering) in the ZnO film to decrease
the effective length of the transducer and / or increase the effective area. It is to be
noted that the high substrate temperature and the process of depositing the top electrode
(sputtering, evaporation, ••• ) play a role as far as this effect is concerned.
6.8 Effective Coupling Constant and Contact Resistance
A technique commonly used for the evaluation of the electrical performance
of the transducer is to fit the computed frequency response to the experimental points by
adjusting an effective electromechanical coupling constant, Keff
' according to some best
fit criterion. (Keff
~ Kt' where Kt is the coupling constant of an oriented single
crystal of the piezoelectric material, Kt = 0.28 for ZnO).
ln Chapter ", the theory for the calculation of the transducer loss was
discussed and it was shown that the conjugate matched responses are highly sensitive to cir
cuit losses, while untuned responses mainly depend on the intrinsic transducer. This fact
makes it possible to evaluate both Keff
and the contact resistance r c by fitting computed
curves using a least squares criterion for both the tuned and untuned measured experimental
points. This has been carried out and results in Figure 6.19 for samples numbers 34 and
39. Here it can be seen that the circuit losses can adequately be modelled by a contact
resistance of about 1.0 - 2.0 ohm. The results obtained for these samples as weil as
other samples are summarized in Table 6.6. The effective coupling constant ranges from
0.04 to 0.25 : 0.01 and is higher for a transducer having a weil oriented structure.
The highest value of Keff
= 0.25 obtained for sample number 34, is approximately 10 %
belaN the value for bulk znO.
TL
(db)
TL
(db)
30
20
10
0.5
30
20
10
0.5
o untuned
Il tuned
A
0.6 0.8 1 .0
(a)
0 untuned
A tuned
0.6 0.8 1.0
(b)
87
SAMPLE 34
= 0.25
r = 1.7 ohm c
o
1.2 1.6 2.0
FREQUENCY (GHz)
SAMPLE 39
Keff = 0.17
r = 1.0 c
0
1.2 1.6 2.0
FREQUENCY (GHz)
FIGURE 6.19. COMPUTED CURVES FITTED TO EXPERIMENTAL POINTS.
88
This method of fitting curves for both tuned and untuned measurement:;
provides us with a better model for the extrinsic transducer and proves to be more accurate
than the methods used hereto.9,24
6.9 Post-Deposition Treatment
The effect of heat treating a sample to compensate for its stoichiometric
deficiency is studied.
Semple number 8, originally prepared in 50 % oxygen, showed an
improvement in the frequency response after baking for six hours at 300 Oc in a vacuum
better than 10-6 torr, Figure 6.20. The same treatment tried with samplenumber 35
prepared in a 10 % oxygen showed negligible differences.
TL (db) 30 SAMPLE 8
ORIGINAL~
AFTER HEAT TREATMENT
0.5 0.6 0.8 1.0 1.2 1.6 2.0
FREQUENCY (GHz)
FIGURE 6.20. POST-DEPOSITION HEAT TREATMENT.
89
A third sample (number 31) was heated for 6 hours at 300 Oc in an
atmosphere of 8 microns pressure of oxygen : argon - 20 : 80. The 90S was then
slowly pumped out white the sample was left to cool before breaking the vacuum. Neither
the frequency response, nor the microstructure, showed observable changes.
These three tests, affirms the conclusion that heating the zinc-oxide film
in vacuo causes the desorption of the chemically absorbed oxygen,44 thus causing the
compound to approach its stoichiometric composition.
6.10 Adhesion
Good adhesion of the different films to one another and to their substrate
is an important factor that affects the transducer performance. Methods of measuring ad-
hesion are quite a few : "Scotch tape" method and abrasion testing have been criticized
elsewhere.45
The scratch method consists of drawing a rounded steel point across the film
surface while a vertical load applied to the stylus is gradua Il y increased until a critical
value is reached at which the film is stripped cleanly from the substrate leaving a clear chan
nel. The critical load is taken as a measure of the adhesion. A more recent publication 46
adds sorne observations and comments to this method and concludes :
n The stylus method does, however, appecr capable of
providing a comparison of the adhesions of otherwise
identical film - substrate combinations. n
For a qualitative comparison of our specimens, an apparatus similar to the one sketched in
Reference 46 was specially constructed. Severa 1 specimens were tested and it was found
90
that the adhesion failure always occur at a load of about 10 grams. Microscopic inspec
tion showed that the failure is in the gold - chromium - sapphire bond. It is therefore
conc\uded - with reservation - that the adhesion of ZnO to gold is of a better quality
than that of gold to sepphire. The reservation here is referring to the fact that the pro
cesses of measuring adhesion have been developed and analysed only for the case of a single
film - i.e. the y have not yet been proven to work for multilayered structures.
6.11 Reliability and Reproducibility
Reliability of the results is readily verified throughout the work by checking
that the two transducers produced simultaneously on the same substrate have similar responses
and structures. Few semples showed differences of any significance and whenever this
happened microscopic inspection showed black lloases" in the gold top electrode of one of
the transducers, probably due to a foreign particle trapped on the substrate surface while
transferring it to the masked holder.
A check for reproducibil ity that was a Iso carried out, is the fabri cation of
complete transducers under exactly the seme conditions as previous ones. Conditions for
semples 11 and 34 were imitated to produce semples 11 Rand 34R. The critical control
of the rate of deposition reflects on the results obtained, while the reproducibility is con
firmed as shown in Table 6.7, where it can be seen that semples produced under the seme
conditions have the seme structure and almost the seme electrical performance.
91
TABLE 6.1 *.
O2 =50%, P = 8 mil li torr
N° T . P VSWR L R TL % B.W . Structure Oc Watts ~ A °lmin db
200 155 1.6 1.4 87 33 002
2 200 180 1.4 1.6 118 16 32 002
3 200 200 1.6 1.6 138 30.5 33 100, 002
4 200 210 1.4 1.5 170 11.5 61 100, 002
5 250 180 1.3 1.1 83 18 79 002
6 250 200 1.4 1.3 106 10 54 002
7 250 210 1.3 1.6 129 28 17 100, 002
8 250 220 1.3 1.8 200 15 60 100, 002
9 300 130 1.2 1.2 45 23 80 002
10 300 175 1.3 1.4 72 18.5 73 002
11 300 200 1.2 1.6 107 12 47 002
12 300 210 1.4 2.0 112 23 22 100, 002
13 300 215 1.2 1.6 136 20 30 100, 002
14 300 225 1.3 1.6 179 13 65 100, 002
15 350 200 1.4 1.6 105 20 46 002
16 350 225 1.5 1.5 144 9.5 42 002, 100
17 350 230 1.2 1.4 149 19.5 40 100, 002
18 400 250 1.2 1.3 85 25 33 002
19 400 280 1.4 1.3 174 20 65 002, 100
* ln this and ail subsequent tables O2
is the percentage oxygen in the sputtering gas ;
p, the pressure in millitorr i T, the substrate temperature in Oc ; P, the net R F input
92
power in watts ; VSWR, the voltage standing wave ratio j l, the ZnO film thickness
in microns j R, the rate of deposition in A 0
/ min ; T l, the minimum tuned transducer
loss in db j B.W., the 3 db bandwidth of the transducer loss in terms of percentage
from the central frequency. The number sets appearing under "structure '1 are the Mi 11er
indices of the planes preferably oriented porallel to the substrate surface. If 2 sets are
given the first one is the more dominant orientation. Additional letters: h. o. and
e p. stand for : high orientation and epitaxial respectively.
TABLE 6.2.
O2 = 50 % , T = 300 Oc
N° p P VWSR L R T.l % B.W. Structure
20 10 175 1.2 1.3 80 15 60 002 h .0.
21 10 200 1.3 1.6 120 13.5 32 100, 002
22 10 220 1.2 1.7 155 8.5 29 100, 002
23 12 125 1.2 1.6 40 17 002
24 12 170 1.2 1.5 77 11 40 002, 100
25 12 200 1.2 1.8 104 22.5 35 100, 002
26 12 220 1.4 1.5 150 16 58 100, 002
27 15 190 1.2 1.6 106 22 41 11 0, 002
28 15 220 1.6 1.2 134 17 61 100, 002
93
TABLE 6.3.
p = 8 mi Il itorr, T = 300°c
N° O2 P VSWR L R T .L. --% B. W. Structure
29 5 100 1.2 1.5 60 10.5 43 002
30 5 130 1.2 1.6 77 20 43 100, 002
_~.1 5 150 1.3 1.5 116 20 36 100, 002
32 5 200 1.3 1.8 144 18 36 100, 002
33 10 100 1.2 1.3 55 9 002 e p •
34 10 150 1.2 1.5 77 6.5 47 002 ep.
35 10 175 1.3 1.5 120 13 47 100, 002
36 10 200 1.4 1.6 160 8.5 75 100, 002
37 20 100 1.2 1.2 55 11 83 002 h. O.
38 20 125 1.3 1.7 83 10.5 58 002, 100
39 20 160 1.2 1.4 140 8 87 100, 002
TABLE 6.4.
o = 10 % , p = 8 millitorr 2 NO T P VSWR L R Llo % B.W. Structure
40 200 100 1.2 1.4 56 29 002
41 200 125 1.3 1.5 110 11.5 40 002
42 200 145 1.2 1.5 120 9 58 002
43 200 150 1.4 1.6 140 19 60 100, 002
44 200 160 1.2 1.7 170 9 79 100, 002
45 250 100 1.2 1.2 57 15 78 002
46 250 125 1.2 1.6 n 10.5 72 002
47 250 175 1.2 1.4 150 14 69 100, 002
-id 250 200 1.3 1.5 194 10 85 100, 002
(cont1d) ...•
94
TABLE 6.4 (cont'd)
o = 2 10 % , p = 8 mill itorr
N° T P VSWR L R LL- % B.W. Structure
49 350 125 1.2 1.8 55 18 72 002
50 350 lSO 1.2 1.6 97 14 60 002
51 350 175 1.2 1.6 120 29 100, 002
52 350 200 1.3 2.0 160 20 33 100, 002
TABLE 6.5
c = input capacitance ( P F) R = input Resistance ( K ohm) p = resistivity ( K ohm. m)
N° L C cale. C R P meas.
11 1.6 9.6 23 130 15.9
12 2.0 7.7 18 210 20.6
29 1.5 10.2 26 2 0.2
34 1.5 10.2 28 125 16.4
35 1.5 10.2 30 120 15.7
38 1.7 9.1 22 165 19.0
42 1.5 10.2 31 140 18.3
46 1.6 9.6 21 150 18.4
50 1.6 9.6 24 130 15.9
51 1.6 9.6 22 115 14.2
95
TABLE 6.6.
r = contact resistance (ohm) c
Keff
= effective coupling constant
TL TL Keff
r N° TUNED UNTUNED
c STRUCTURE
31 20 31 0.04 1.4 100, 002
34 6.5 15 0.25 1.7 002 e p •
35 13 20.5 0.13 1.3 100, 002
36 8.5 15.5 0.21 1.5 100, 002
39 8 19 0.17 1.0 100, 002
42 9 16.5 0.21 1.6 002
TABLE 6.7.
REPRODUCIBILITY CHECK
N° O2
, p, T, P, VSWR L R t.L. % B.W. STRUCTURE
11 1.6 107 12 47 002 Sorne Conditions
11 R 1.5 100 13 49 002
34 1.5 gJ 6.5 47 002 e p • Sorne Conditions
34R 1.4 90 7 50 002 e p •
CHAPTER VII
SUMMARY AND CONCLUSIONS
96
A procedure for computing the response of a multilayer transducer has
been described. Results of calculations using this procedure have been presented which
foc us attention on the effects of contact resistance, finite film conductivity, e lectric
tuning and different electrode materials c;>n the transducer performance. The possibility
of achieving very large bandwidths by means of multilayers has also been demonstrated •
. . -further, it has been shown that R F sputtering is a convenient method
for producing well-oriented ZnO transducers having electromechanical coupling constant
within 10 % of the bulk Value. The study of the influence of the deposition parameters
pointed out the fact that the film quality is highly dependent on the deposition rate, hence
the input R F power, the substrate temperature and the gas composition.
For a fixed temperature and gas composition, the results have shown that
a critical rate exists above which the crystallites of the ZnO film deposited on Z-oriented
sapphire have the c-axis Iying in the plane of the substrate surface, randomly oriented,
thus causing the transducer action to deteriorate • For a wide range of temperatures and
gas compositions, the critical rate is found to lie between 100 and 130 A 0
/ min, while
the best transducers are obtained at a rate just below the critical rate. Transducers having
tuned transducer loss as low as 6.5 db and bandwidths of about 0.6 GHz are reproducible
in an oxygen rich atmosphere (10 : 90 - O2
: A), on heated substrates (300 oC) .
It has also been shown that transducers having very wide bandwidths and
reasonably low transducer 1055 can be fabricated by properly selecting the deposition para-
97
meters. Such a performance was achieved in sample number 48 which had a bandwidth
of 1.2 GHz and a minimum transducer loss of 10 db.
Measurement of the input impedance showed that the resistivity of the
Zno film is about 15 - 20 K ohm.m for good transducers. The e lectromechanical
coupling coefficient, as weil as the circuit losses, were estimated by fitting calculated
frequency responses to both the tuned and untuned experimental points. Values of Keff
of from 0.04 to 0.25 were obtained while the circuit losses were modelled by an ex
trinsic contact resistance of about 1 - 2 ohm.
Although the transducers described here are canparable in performance
with those previously reported~,9, 16 sorne improvement in the vacuum station and the
measurement techniques are suggested.
To minimize circuit losses, soldered - or welded - leads should
be used instead of spring loaded contacts.
A tighter cootrol should be provided on the rate of deposition, sputter
ing gas mixture and rate of gas flow to facilitate the optimization of the transducer
performance, since these parameters affect the crystal orientation and stoichiometry of
the zinc-oxide fi lm.
APPENDIX 1
COMPUTER LISTING
98
OOOl
000. DilO 1 000 .. Oll'>' OuOI> 000 1
C THIS PROGRAM CALCULATES THE TRANSDUCER LOSS C OF A MULTILAYER SEMICONDUCTING PIE10ELECTRIC C TRANSDUCER. C MKS SYSTEM OF UNITS 15 USED. ACOuSTICAL IMPEDANCES t ARE IN 10 •• ' KG/CM.M.SECI UNITS. C C THE FOLLOWING 15 A LIST OF INPUT YARIABLES 1 C C yARIABLE MIANING c------------------------------.... -... -------------------. ___ ._ C N NUMBER OF LAYERS C 1DR DELAY ROD MECH. IMPEDANCE C lA FRIE FACE IMPEDANCE C AREA AREA OF TOP ELICTRODE C F1 TUNING FREQUENCY C 155 SOURCE IMPIDANCE CEPS PIRMITIYITY OF TRANSDUCER MATERIAL C FO DIFFUSION FREQUENCY C P INDICATES TYPE OF THE LAYER C ' .' FOR THE PIEZOELECTRIC LAYER C ILANK FOR OTHER FILMS C MAT MATERIAL OF THE FILM C IF FILM MECH. IMPEDANCI t L FILM LENGTH C VS SOUND VELOCITY C F FREQUENCY C K ELECTROMECHANICAL COUPLING CONSTANT C R SERIES CONTACT RESISTANCE C FC CONDUCTIVITY FREQUENCY C VR DRIFT VELOCITY/SOUND VELOCITY C MICF NO. OF 80UNOARY CONDITION CASES C BC BOUNDARY CONDITIONS 1 C '5.CHARGE',IEL.FIELD' AND/OR 'CUR,OEN,' C MSIF NO. OF SOURCE IMPEO. CASES C SI TYPE OF SOURCE IMPEDANCE TUNING C 'CO' FOR CONJUGATE MATCH C 'UN' FOR UNTUNED C 'SH' FOR SHUNT TUNED C 'SE' FOR SERIES TUNED C C FOR ~,A,F,FC t VR AOOITIONAL ~ETTERS I,F tS C STAND FOR INITIAL, FINAL AND STEP RESPECTIVELY. , C ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C
CUHMON ,BLK1/L,VS,ZF,ZA,ZOR,N,IP ~ ,BLKZ/FC,FD,FO,5,SS,R,RN,YR,ZFIP,ALPHA,LAMDA i IBLK)/1E,ZS,ZSO,BT,XT,F,F1,IS
DOuBLE PRECISION MAT,BOCOI31,BC')1 DIMENSION 51M141,S1141 olMENSION ZLRI501,ZRRI501,WRI'01 DIMENSION MAlI201,ZFIZ01,VSIZOI,L,ZOI COMPLEx ZE,ZR,ZRR.i~,lLR,ZS,ZSS,zso LJGICAL COND
0008 0009 0010
0011 0012 0013 0014 0015 0016 0017 00111 0019 0020 0021 0022 0023 0024
0025 0026 0027 0028 0029
0030 0031 0032 0033 00310
0035 0036 0037 0038 0039 0040
0041 DOlo'
0043 001010 0045
C
REAL DATA DATA
L,KI,KF,KS PIE10/1 .'I,SIH/'CO"IUN','SH','SE'I BOCO/IS,CHARGEI,IEL,FIELDI,ICUR,DEN.I/
C •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• ' C C READ INPUT DATA
C
C
C
READ,5,lOI N,lDR,ZA READC',3DI AREA,F1,lSS READC',301 EPS,FD DO 1 J a1,N READ15'201 P,HATIJI,lFIJI,LIJI,YSIJI IFIP.EQ.PIE10I IPaJ CONTINUE READC5,301 FI,FF,FS READ15,301 KI,KF,KS READ15,301 RJ,RF,RS READ15,301 FCJ,FCF,FCS READI5,3DI YRJ,YRF,YRS READ15,401 HBCF,eC READ(5,501 HSIF,SI
MFCPel.+(FCF-FCII/FCS MYRFal.+CVRF-YRII/VRS MKFa 1.+(KF-KII/KS MRFa 1.+(RF-RII/RS MFFa 1.+IFF-FII/FS
FO= O.5.VSIIPI/L(IPI RNaLIIPI/(6.Z8318.FO.EPS.AREAI RS"RS/RN RI"RI/R~~ ZFIPaZF(IPI
C •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• e C C CALCULATION OF ZL AND ZR
FaFI-FS
C
C
C
00 ,. Jal,HFF GO TO 3
2 WRITE(6,100I F 3 F.F+FS
w • 6.28)18.F
CALL ZLZR (W,ZL,ZR,IDI IFCID.EQ.11 GO TO 2
ZLRIJlaZL ZRRIJlaZR
4 WRIJlaW
C ••••••••••••••••••••••••••••••••••••••••••••••••• C C TRANSDUCER LOSS CALCULATION
00 00
00 .. 6 00 .. , OO"d 0\1"'. OO~O OO~I OO'~ OO~J OO~ .. OO~> OO~b 00' 1 00~6 OO~Q
OObCi OObl OOb, O()bJ OOb" OOb; 00b6 OObl 00b8 OOb'l ~OlO
00 Il OOU 001.1 001'0 007~ OU7b 001 ; 00111 007'1
0010 00111 OJllt OOUJ Oull .. OOIl~ 00110 0081 00811 0\)8'1
OO?I) OOQI OllQl 009) 009 .. OU'I)
C
t
NOTE TH! PROPER NESTING OF 'DO' LooPS FC- PCI DO 666 HFC-l,MFCF CoND - IFCfFOI .GT. 1.OE-Ob IFICoND' GD To , MSCP1-1 MVRF1-l GD To 6
, MICF1·M8CI' MVRF1·MVRF
b CONTINUE DO '" Mlt.l,MBCFl IFI.NoT.CoNDI GD TO 44 ALPHA-l. LA'1DA-l DO 11 1-1,' IFIBCIMSC'.EQ.SOCoII" GD To 122.,).44',1
11 CONTINUE 22 LAHDA·2
GD To lolo 3) ALPHhO. Iolt CONTINUE
VR- VRI DO 444 HVR-l,kVRFl DO J'3 I1SI.l,MSIF DO " 1 -1.1t IFISIIMSI,.EQ.SIMCI" 15.1
H CONTINUE AI( r _1(1 DO 222 HI(-l.MI(F S· ... KT.AKT ,;5-1.+5 "-RI DO 111 '1R-1.MRF RR-R.RN
C SELECT TUNING & WRITE "EADING OF PAGE lFIIS.LT." GD To 66
(.
W • 6.2nlUFl CALL lllR IW.ZL.lR.lD' CALL TLOSSIW,ZL,lR,CoND,l)
bb CALL SOURCECZSS,RN' IFICoNO, WRITEC6,90, BCIM8C,.VR,FC WRITEI6,60, lDR,lA,AREA,RR,AKT 00 11 J-l,N
77 WRITEI6,70, J,HATCJ),ZFIJ),LIJI,VSIJ) wR 1 TE 1 6,101
00 Il Hr.1,MFF W .WIIIH") ZL • ZL Il r '1 F ) ZRoZRIIP1FI CALL TLUSStW,ZL,ZR.CoND,21
Il CO~TINUl
0096 0097 0098 0099 0100 0101
0102 0103 0104 0105 OlOb 0107 0108
0109 0110
0111
0112
0113
C 111 R.R+RS 222 AKT-AKT+KS 333 CONTINUE 441t VR.VR+VRS '" CONTINUE 666 FC.FC+FtS
C C •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• C
STOP 10 FORMAT 115,lFIO.4' lO FORMAT IAl,AB,FIO.4,EIO.4,FIO.4' 30 FORMAT IIE10.4' 40 FoRMATI14,4X,4ABI 50 FoRMATI14,4X,4IAl,6X" 60 FoRMATI31X,'DELAY RoD IMPED •• ',FIO.2,
alOX,'FREE FACE IMPEO. -',FlO.2/'lX, a 'TOP ELECTRODE AREA .' ,E10.4,BX, a 'CONTACT RESISTANCE .',FI0.4/31X , a 'KT .',F10.) 1140X,' LAVER 1, a'MATERIALI,4X,'ZF',7X,'L IMICRoN,I,4X,'VS'/1
70 FoRMATC40X,I),lX,AB,F10.2, 6PF13.4,OPF12.ll 80 FoRMATI' 'III' FREQ GHZ',lOX,'TLG CDBI','X,IEL.M.L.I"X,
i 'ELECTRJCAL INPUT JMPEO.',llX,'TLO 10BI'"X,'MC.M.L.I, a ,x,'MECHANJCAL INPUT IHPED.'/I
90 FoRMATI)lX,IBoUNOARV CONDITIONS :',AB l'lX, a 'VO/VS ·',F10.2,21X,'FC .',El'.4'
100 FDRHATI' .WARNING. ZL OR ZR TENDS To " a'lNFINJTV AT ',-9PFlO.2,' GHZ'II 13X, a'CALCULATloNS AT THIS FREQ. ARE DELETED',
END
-OPTIONS IN EfFECT. JO.EBCDIC,SOURCE,NoLI5T,NoDECK,LoAD,NOMAP -OPTIONS IN EFFECT. NAME - HAIN , LINECNT • 56 -5TATI5TICS. SOURCE STATEHENT5 • 113,PRoGRAM SIZE • 4690 .51ATI5TIC5. NO DIAGNOSTICS GENERATED
-o o
000.
0(10'
OOOJ 00010 000; 0001, 0001 OOOd OOO'i 0010 Dili.
Oul~ OulJ 001,. OOI~ 001t.. 001' OUIII 001'1 OOlll Où" OOlL OOB OO~" OO/.'
Oll/t. 0017 OOll! OOi'l 001(, OJ11 OUJi OOH OiJH OoB OJ1C1 00].' 0,1)0 00)'1 Oll~'J OO~I
01)" t
0010) 00 ... OU .. ,
SUBROUTINE TLOSSIW,lL,ZR,CDND,ID) C SUIROUTINE TLOSS CAlCUlATES THE TRANSOUCER LOSS. C JT CALLS RonT le CINV 1 C ROOT SalVES COMPlEX POLVNOMIAlS C IC 15 THE HAX. NO OF ITERATIONS C CI~V SOlVES SYSTEMS OF COMPlEX EQUATIONS C DELTA 15 THE DETERHINENT OF THE COEFFICIENTS MATRIX
C
C
COHHON IllKZ/FC,FD,FO,S,SS,R,RN,VR,ZFIP,AlPHA,LAHOA i IllKJ/ZE,ZS,ZSO,BT,XT,F,Fl,IS
COMPlEX AI,),ZI4),OI4"BI4,51,BBI4,",EPI41,ENI4) CDHPLEX C,Cl,C2,C],DEtTA,T,Vl,VO,Vl,CU COMPLEX lE,ZOE,ZH,ZOH,ZR,ZRR,Zl,ZlR,ZS,ZSO lOGICAl CoNO F-W/b.ZIJ18 "'-Z Llll-CMPLXISQRTISSI,O.OI lIZ"-l(1) IFe.NOT.CONDI GD To 100
~-4 AI11-CHPlxI1.,FC/FI AIZI-CHPLxl-VR,O.OI A(ll-CHPLXI-SS,IF/FO-FC/FII AI41-CHPLXISS*VR,0.01 AI,,-CHPLxIO.O,-SS*F/FO) C -AIZI/12.*AI111 Cl·CSORrIC*C-SS-AllI/AII» Llll--C·CI 1141--C-Cl IC·ZOO CAll ROUT Il,5,4,1,0.0001 ,ICI BI4,"·CHPlXI0.0,0.01 813,"_CHPlXIO.0,0.01
100 H-~+l BI2,HI-'HPlX(-1.,0.1 B(l,HI-CHPlXI-l.,O.1 ~ -CHPl~(O.O,O.'*W/Fol Cl-CHPl(O.O,Z.·FO/WI CU·CHPlX(FC/FO,-F/FOI 00 10' 1-1,N CZ-CEXpeC/Z(111 IFI.NOT.CJNOI GO To 102 Cl-Ill.·S*AlPHAI-ZII)*ZII)I/IIII)·.LAHOA) IFIVR) 102,10Z,101
101 EP' II-C"PLXI 1.0,0.01 ENIII-l.le2 GO To 10)
10Z ENII hC,'1PLl(1 1.0,0.0) ePIII-C2
10) BI lilI-CIl II-ZRltEPe Il SI~,I)·IZI1)+Zl)*ENII) BB 1 1, 1 1 • O.llI 1 1 * Ill) -1 • ) • ' EPI 1 ) -EN 1 1 ) ) IF, .NOT .CONO) CO TO 105'
004b 0041 Ou48 004 .. 00)0 0051 00), 0053 0054 0055 OOSb 0057 OO)B 0059 OObO OObl
OObl
00b3 00b4 OOb5 OObo 00b7 OObB 00b9 0070 Don OOH
Don 0074 0075 0070
·0'077 007b 007'i OOB", 0081 OOBl OOBJ OOB ..
00B5 OOSCI 0\187 OOBt! Oull9 0090 009\ 0091. 0093 0'J9"
C
C
C
t
c
SI], 1 )-C1*EPII) B14, 1 ) -C l*EN Il )
10' CONTINUE DO lOb J-l,H DO lOb I-Z,N
lOb BBIl,J)-BII,JI CALL CINV 1 B,N,H,OELTA,O.lE-ZOI IFICABSIDELTA).lT. 1.E-301 RETURN VL·CO.O,O.OI vllli 1.,0.01 00 107 1-l,N QII )-BI l,HI Vl-VL+Olll*EPCII
107 vl=V1-C3*OII)*IZlll*ZIII-l.I*IEPII,-ENIIII T--VL*ZR ZE-V1/CU+R
IFIID .EQ.l) RETURN
IFIREAllZEl1 109,109,8 B VO.CU*ze
PE-REAlIVO*CoNJCCCUII PH-REAlI-T*CONJCIVLI) ETAG-PH/PE.S/3.14159 CALL TUNE CHLE-4. t REALIZSI.REALIZEI/REALIIZS+ZEI*CONJGIZS+ZEII n-CHLE.ETAC IFITL.LT.l.OE-lOI Tl.l.OE-lO TlC--10.*ALOG10ITLI
BBel,H)-l.+CU*IZSO+RI CALL CINV IBB,N,H,DELTA,O.lE-ZO) IFeCABSIDELTAI.LT. I.E-30) RETURN Vl·IO.O,O.OI T -1-1.,0.01 DO 108 l-l,N OIII.BBe l'MI VL-Vl+QIll*EPIII T ~T-OIII*ZII)*EPIII
108 CONTINUE ZM=T/Vl IF(REALIZMI) 109,109,9
9 CMLHa4 •• REALIZMI.REALIZRI/REALleZM+ZRI.CONJCIZH+ZRII VO·-CU.lSO PE-REALIVO·CONJGICUII PH=REALI-T.CONJCIVLII ET~O· PE/PH*3.14159/S n~CHlH·ETAO IF(TL.LT.l.OE-101 TL-l.OE-lO TLO--10.*AlOG10ITL) ZOE-lE.RN 10M_ZM*lFIP
... o ...
C III' lTE OUTPUT 009~ IIRITEI6,101 F,TLG,CHLE,ZDE,TLO,CMLH,ZOM OJ9~ RETURN 0097 109 IIRITEI6,201 F o"''Ie RETURN OO'l~ 10 FORMATe' ',-9PF7.3,6X, OP2F1Z.4'2E15,5,6X,2F1Z.4,Z~15.51 OIOU 20 FURMATe' ',-9PF7.3,' UNSTABLE'I 0101 ENO
·I)~'IONS IN EFFECT' 10,EBCOIC,SOURCE,NOLIST,NOOECK,LOAO,NOMAP -opriONS IN EFFEtT' NAHE - TLOSS , LINEtNT - 56 .~T~TI~TICS' SOURCE STATEMENTS - 101,PROGRAM SIZE - 5120 ·S1ATISTICS* NO UIAGNOSTICS GENERATEO
0001
0002 0003 0004 0005 0006 0007 0008 0009 0010 0011 0012 0013 0014 0015 0016
0017 0018 0019 OOZO OOZl 00Z2 0023 00Z4 OOZ5 0026 0027 0028 00Z9 0030 0031
SU8ROUTINE ZLZRIW,ZL,ZR,IOI C SUBROUTINE ZLZR CALCULATES ZL ANO ZR AT W, C ID 15 AN INTERNAL INDICATOR TO PREVENT OVERFLOW. C
C
COHHON IBLK1/L,VS,lF,ZA,ZOR,N,IP DIMENSION ZFCZO),VSI201,LI20) CoMPLEX ZL,ZR,DEN REAL L 10-0 n-cl"O.O)*ZA IFIJP.EQ,1) GOTo 3 JP1-IP-1 00 2 J-1,IP1 CS-COSIW*LCJ)/VSCJ)) SN-SINCW*L(II/VS(I)) OEN-ZFCJI·CS+ZL*SN*CO.,1,) IFICABSCDEN).LT,1,E-30) GO TO 6
Z ZL-ZFCJI*'ZL*CS.ZFCII*SN*CO.,l.I)/OeN :. ZL-ZL/ZFC IP)
ZR-Cl.,O.O)*ZOR JFIJP,EQ,N) GO TO , JP1-N-IP DO 4 II-l,IP1 J-N-II.1 CS-COSCW*L(II/VS(J)) SN-SINCW*L(II/VS(I)) OEN-ZFCII*CS.ZR*SN*IO"l.1 IFCCA8SCDEN),LT,l,E-30) GO TO 6
• ZR-ZFCI)*CZR*CS.ZFCI)*SN*CO.,l.))/DIN , ZR-ZR/ZFIIP)
RETURN 6 10-1
RETURN END
-OPTIONS IN EFFECT* .IO,EBCOJC,SOURCE,NOLIST,NOOECK,LOAD,NOHAP 'OPTIONS IN EFFECT- NAME - ZLZR , LINECNT • '6 _5TATI5TIC5* SOURCE STATEHENTS • 31,PROGRAM 51ZE - 1670 -STATI5TIC5* NO DIAGNOSTICS GINERATEO
-o ...,
0001
0002 000) 0001t 000' 000& 0007 00011 0009 0010 0011 0012 Oou 0014 OOU DOIt> 0017 00111 0019 0020
0021
0012
0023
SUIRaUTINE SOURCE IISS,RNI C SUI~OUTINE saUlCE CALCULATES TUNING ILEMENT AND. C MRITES PlDPER HEADING OF PAGE
- C eOMMON IILKI/IE,IS,ZSO,IT.XT,F,F1,IS COMPLIX II,ZS,Y,lSS,lSO lS.ZSS/RN GO Ta 111,11",,441 ,IS
11 MRITII&,lOOI RITURM
Il WRITII&.2001 ISS RITURN J, Y·l./ZE IT·-AIMAGIYI I·IT/RN WRITII&.IOOI 155,Fl,1 RITURM
44 xT.-AIMAGIZII X·XT.RN WRITII&.4001 ZSS,Fl.X RITURN
100 FORMATI'l',IOX, 'CONJUGATE MATCH TRANSOUCER LOSS'I 100 FO~MATI'l',IOX"UNTUNIO TRANSDUCIR LOSS'I
a J1X.'SOURCE IMPeDANCI .',2F11,4' 100 FO~MATI'l',IOX,'SHUNT TUNID T~ANSDUCIR LOSS'I
a J1X,'SOURCE IMPIDANCE .',2F12,41 a Jlx,'TUNING FRIQ. ·',11S,4,'X, a 'TUNING suseEPTANCE .',E1S.41
400 FORMATI'1',JOX,'SERI15 TUNED T.ANSDUCIR LOSS" a J1X.'SOURCE IMPIDANCI .',IFll,41 a J1X,'TUNING FRIQ •• ',llS,4.,X, a 'TUNING REACTANCI .',115.41
END
-OPTIONS IN !FFICT* ID.EICDIC,SOURCE,NOLIST,NODICK,LOAO,NDMAP *OPTIONS IN IPFleT* NAME. SOURCE • LINICNT • 5& *STATISTles. SOURCI STATIMINTS • II,PROGRA" SIZI • 1072 -STATISTles* NO DIAGNOSTICS GINERATID
0001
OOOl 0003 0004 OOO~ 000t> 0007 0008 0009 0010 0011 0012 0013 0014 0015 DOIt> 0017 0018 0019 0020 OOZI 0022 Don OOZ ..
5USROUTINE TUNE e SUIROUTINE TUNE CALCULATES THE 'TUNEDI INPUT C IMPEDANCE OF THE TRAN5DUCER. C
COMMON 18LK"IE,lS,lSO,8T,~T,F,Fl,IS COMPLEX lE.1S,150,Y GO Ta 111,22"3,441,15
11 U-CONJGCZEI 22 UO-U
RElURN 3J IFIBTI 1.1.2
1 &-eUF/Fl GO TO ,
2 a-aUFl/F ) Y-l.llE+IO.,l.'*&
ZE-l./Y Y-l.11S+10.,1.I*B UO-l./V RETURN
44 IFIXTI 'u4,' 4 X-XUF/Fl
GO TO 6 , XaXUFl/F 6 ZE-ZE+IO.,l.I*X
Z50-Z5+10.,1.I*X RETURN END
-OP1ION5 IN EFFECT. IO.EBCDIC,50URCE,NOLI5T.NODECK,LOAO.NOHAP -OPTIONS IN EFFECT. NAHE - TUNE • LINECNT - '6 .SIATISTICS* SOURCE STATEHENTS - 24.PROGRAM SIZE _ -ST4TISTICS. Na DIAGNOSTICS GENERATED
9&6
-o w
104
REFERENCES
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2. Lefebvre-Ganne, E., "OC and RF Sputtered ZnO Transdueers", M.Eng. Thesis,
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