Laver
1962
Depletion
The
White:
Thentheoutput envelope, as given below, is identical
v(!)
a displacement of
totheinput
envelope,exceptfor
[ap,- @1]/2wm in time,
s(t) = 1
+ m, cos
=
cos (uct
+
0
'
+
21
+ +.?>
m. cos (apt
+-(l -2 K> m, cos
(w,t
+ +.,>
2
e
2
Determination of the Mathematical Enuelope of an Ampli-
tude-Modulated
S ignal
in the Presence of Attenuation Distortion Delay line input signal:
e(t)
=
(1
+ m, cosw,t)
m.
COSW,~,
<
The envelope of theoutput
1.
Delay line transfer function:
F(w)
s(t) =
(1 - K)e'*'
at
w1 = W,
e'"'
at
W,,
=
+ K)e'"'
29, = -33 + a,.
(1
at o2 =
Byapplyingthistransferfunctionto
the output signal becomes
- W,
for K
<1
1
+ m. cos (w,t +
signalis given as
@2
2
"9
(umt
3- jKm, sin
W,
+
2
-l-U,,
Kotice that
the envelope
is
symmetric
in
time
about
the
point t = [-+,z - +J20m which representsthegroup
delay a t some frequency W located between w2 and wl.
The undistorted envelope may be obtained by letting
theinput signal,
K = 0.
The Depletion Layer Transducer*
range extends from near 300 MC to perhaps higher than
10,000M C .
The electromechanical coupling is due tothe piezoelectric effect in a material which is simultaneously a n
extrinsicsemiconductor.Examples of such materials are
gallium arsenide and cadmium sulfide. The novel feature
of this transducer is t'hat the electromechanically active
portion is a high-resistance depletion layer such as a p-n
junction or rectifying metal-semiconductorcont:wt instead
of the highresistancebulkmaterial
of ordinary piezoas quartz. As \vi11 be
electrictransducermaterialsuch
shown in the text, a flatdepletionlayer formed on the
surface of a low-resistivity piezoelectric semiconductor
behavesvery
similarly to a plat,e of high-resistivity
piezoelectric material bonded to a metal substrate.
I. INTRODUCTION
The two unique advantages of a depletionlayer used
as
a piezoelectric transducer are:
HE ULTRASONICdepletion layertransducer is a new transducerforconvertingelectricalenergy
1) Since the layer is so thin, it has its greatestefficiency
into ultrasonic energy and vice versa. Its frequency
a t very high frequencies;
2) The thickness of thelayer, hence the "resonant"
* Received M a y 7, 1962. frequency,canbe controlled by a dc bias voltage. t BellTelephoneLaboratories,Incorporated,
Whippany, N. J.
Summary-The
depletion
layer
transducer is a n ultrasonic
transducer for use atUHF and microwave frequencies. Its potential
advantages are high efficiency, large bandwidth, and comparative
simplicity in fabrication. The region which generates or detects the
ultrasonic waves is a thin flat high-resistance depletion layer, such
as a p-n junction or a rectifying metal to semiconductor contact, in
an extrinsicpiezoelectricsemiconductor.
When an ac voltage is
applied to the material, the depletion layer behaves in a manner
similar to an extremely thin piezoelectric crystal bonded to theconducting substrate. Since the depletion layer C a n be generated on the
surface of the semiconductor, the problems of handling extremely
thin piezoelectric plates are avoided.Depletion layer transducers
have worked a t frequencies as high as lo00 MC.It is anticipated
that improvements in circuit and fabrication techniques will greatly
extend their frequency range and efficiency.
22
TRdNSA4CTIOXS
IRE
OLV ULTRASOLVICS ENGINEERING
July
11. DEPLETIOS
LAYERTRASSDUCERS
The depletionlayertransducer
will be shown to be
analogous tothetype
of piczoelcctriccrystalor
poled
ceramic plate shown in Fig. 1. A flat plate of insulating
piezoelectric material is placed between metal electrodes
so the applied field is distributed uniformly through the
thickness of the plate. I n Fig. 1 the capacitance of the
transducer is antiresonated by the inductance and the reto the
sistance of the antiresonantcircuitismatched
source by the transformer. If the electrical losses in the
reactiveelements are smallcompared to the ultrasonic
power generated, almost all of incoming power would be
converted into ultrasonic energy. This ideal can best be
approached at the frequencyin which thetransducer
to a half wavelength of sound. The
thicknessisequal
reason for this is that the electromechanical coupling of
the transducerisgreatest
a t this frequency. Only in
is it possible to tune
extremelypiezoelectricmaterials
the circuit to frequencies fairly far away, say 30 per cent
above or below, the half wavelength condit.ion and still
obtain a largeconversion efficiency. Conversely,when
matched to the load the transducer converts almost all
the energy of an incident ultrasonicwave into an electricalsignal. Theplategenerates
planeshear or plane
dilatationalwaves. Since the t,hickness of theplateis
the frequency-determining
dimension,
fabrication
difficultiessetlimits to how thin a plate, hence how high
a frequency, one can obtain by using conventional piezoelectric materials. It is possible to operate the transducers
on overtones, i.e., the resonantfrequencyoccurswhen
the thickness is an odd .number of half wavelengths
thick.However in overtoneoperationthepiezoelectric
ccupling of the transducer decreases. This resultsin a
narrowedbandwidthandincreasedcircuit
difficulties.
Usuallysemiconductors aretooconducting
tosupport
suchlargeelectric fields without destructiveheating. If
high resistivity material is used, the semiconductor acts
likenormal piezoelectric insulators, such as quartz. The
novel feature of the depletionlayertransduceris
that
with an extrinsic semiconductor it is possible to maintain
as that
alargeelectric
field at a depletionlayer,such
which exists a t a p-n junctionor a rectifyingmetalsemiconductor contact.
Fig. 2 shows a bar of a semiconductorcontaining a
p-njunction which isreversebiasedby
a dcvoltage.
If the semiconductor is of low resistivity, almost all the
dc voltage drop occurs a t the junction. Since the junction
isthin,the electric field in that regionislarge. If the
semiconductor is piezoelectric, the large dcelectric field
layercreates a significantstress, andthedepletion
not the bulk semiconductor-is elastically strained. Since
fields of the order of lo' volts/meter are not uncommon
indepletionlayers,large
strainsare possible. If anac
signalissuperimposedupon
thedc bias, and if the resistancein the bulksemiconductor is smallcompared
withthe impedance of thejunctioncapacitance,most
of the ac voltage drop willbe across the junction. Thus
Fig. l-Conventional
piezoelectric transducer.
P-N JUNCTION1 DEPLETION LAYER METAL ELECTRODE N
Fig. 2-Depletion
layerdue to a piezoelectric junction acting
loaded transducer.
a
DEPLETION LAYER
METAL ELECTRODE
Fig. 3-Depletion layer due to a rectifying metal-semiconductor
contact acting as a resonant transducer.
an alternating stressis produced within the thin depletion
layerandthe
wave motionproducedthereisradiated
into the twoadjoining media.
An alternate design is shown inFig. 3. In this case
the depletion layer is formed by a rectifying metal-semiconductor contact. When reverse biased, a depletion layer
is formedin the n-type material
under the metalelectrode.
One could also use a verythinlayer
of a p-type semiconductor instead of metal in this design. If the depletion
electrode,
layer is considerablythicker thanthemetal
the transducer is very similar to the piezoelectric crystal
or ceramic plate of Fig. 1. The depletion layer, which is
the piezoelectricallyactiveregion,corresponds
to the
insulatingcrystal and the bulksemiconductorformsan
interiorelectrode which corresponds tothemetal
substrate. If the boundaries of the depletion layer are flat
and parallelone would expect the greatest coupling to
1962
Depletion
The
White:
occur a t bhe frequencycorresponding t.0 a wavelength
of soundtwice the depletionlayerthickness.
Thus the
depletion layer is expected t o behave in a manner similar
to a piezoelectric insulator of equal thickness.
When used as a transducer, the most significant property
is that the thickness is equal to a half wavelength a t a
high frequency. Since the depletion layer is usually very
lo-‘ cm
being
a normal range,
and
the
thin,
to
velocity of sound of these crystals ranges from 2-6 X lo5
cm/sec, the frequency of half wavelengththickness es100 &ICto above 30,000 MC.Under
tendsfromabout
ideal conditionsall
the electricalenergycan
be convertedto ultrasonicenergy and vice versa. I n practice
it is doubtfulif t,hese very high efficiencieswill be attained,
especially at’ the higher frequencies. Since the depletion
layer is so thin, it is inherently a low-impedance device.
For instance the impedance due to the capacitance
of a
1.5 X
cm
thick
and
a
l-mm
s quare
transducer
dielectric constant of 9 operating a t 1000 MC is about
2.5 ohms. To obtain efficient transfer of energy between
normalgeneratorcircuitsand
the low-impedance transducer requires high Q reactive elements andlow resistance
in the transducer itself because it is desirable to convert
all the electrical energy in the resonant circuit into ultrasonic waves, not heat. As the impedancemismatchbecomes greater this becomes very difficult.
The bandwidth of the transducer is also similar to that
of an ordinary piezoelectric plate. If the transducer circuit
is loadedprimarily by energy loss duetoradiation
of
ultrasonicwaves, the bandwidth will beapproximately
equal to the electromechanical coupling coefficient of the
transducer material. This would mean about a 5 per cent
bandfor gallium arsenide and a 20 percentbandfor
cadmium sulfide. If joule heating in the circuit elements
predominates, thebandwidth is usuallydeterminedby
the Q of the input or outputcircuits.
When used as a loaded transducer, as the p-n junction
in Fig. 2, the transducer is most sensitive when its thickness is a half wavelength of sound. The loaded transducer
usually hasgreaterbandwidthbut
less efficiency than
the unloaded transducer. When ohmic losses predominate
Q determines the
over ultrasonic radiation,thecircuit
bandwidth, but the loss is still greater than the unloaded
transducer.
Anotherimportantfeature
of thetransduceristhat
thethicknessisvoltagesensitive.
Thustheresonant
frequency (half wavelengththickness)can be controlled
at the breakdown
by a dc bias. A reversebiasalmost
voltage would correspond tothe lowest resonantf requency. The thinnest usable layer mould be at zero bias
or slightlyforward bias. As willbe seen in Section IV
another restriction is that toavoid nonlinear effects the ac
voltage must be small compared to the dc voltage.
l
I
l
I
111. MATERIAL
A depletionlayerisformedonlyin
an extrinsic semiconductor, and of course ultrasonicwavescanonlybe
Layer Transducer
23
generated by a piezoelectric material. Silicon and germanium, for instance, arc not piezoelectric, but there are
several materials which are piezoelectric semiconductors.
The most important ones c m be divided into two crystal
clnsses, those n-ith a zincblende structure and tho= Irith
a wurtzitestructure.l’*The
zincblende groupincludes
cubic zinc sulfide and more importantly for the present,
purpose, the A”’BV compounds such as gallium arsenide.
The wurtxite includes the hexagonal forms of zinc sulfide,
zinc oxide and cadmium sulfide. In general the zincblende
compounds show a smaller piezoelectric effect than quartz
and the wurtzite crystals have greater coupling.
Since the resistnnce of the bulkmaterial is in series
with the piezoelectric depletionlayer, it is desirable to
use a low-resistivity semiconductor. However,as indicated
above, for maximum efficiency in a particular frequency
band the depletion layer should be of the order of a half
wavelength of sound. Since the depletion layer thickness
as well as voltage
dependsonimpurityconcentration
[see (l)],limitson the optimum impurity concentration
areapproximately fixed. I n some cases gallium arsenide
may be preferable because of its high mobilit,y and resultant low resistivity and a t other times cadmium sulfide
may be superior because of its greater piezoelectric effect.
IV. THEDEPLETIONLAYERTHICKNESS
The depletionlayerassociatedwithrectifying
p-n
a region
junctionsormetalsemiconductorcontactsis
containing ionized impurityatomsin
which thereare
very few free-charge carriers.Although
theboundary
between the depletion layer and the bulk semiconductor
is not sharp(carriers enter the edge of the depletion layer
and are reflected back by the electric field) for the present
purpose we will consider the interface as sharp and distinct.
The piezoelectrically active region in the semiconductor
is the depletion layer. An oxide layer on the surface acts
as an insulating load onthetransducerand
a metal
electrode is a conducting load.
The simplest case is that of metal forming a rectifying
junction with uniformly doped n-type semiconductor, as
shown in Fig. 4(a). A very thin negative charge forms in
the metal a t the interface a t x = 0, and a comparatively
thick layer of positive charge (the depletion layer) forms
in the semiconductor,extendingfrom x = 0 to x = d.
Since there is almost novoltage drop in the metal, the
voltage a t x = 0 is that applied to the outer electrode.
If the resistivity of thebulkmaterial
is low, 1’ = 0
at x = d when the semiconductor is grounded. Since the
depletionlayeris a distributedcharge,the electric field
is zero a t x = d.
I n a normal semiconductor Gauss’s equation is
W. G. Cady, “Piezoelectricity,” McGraw-Hill Book CO., Inc.,
New York, N. Y., p. 228; 1946.
H. Jaffe, D. Berlincourt, H. H. A. Krueger, and L. R. Shiozon.~,
Proe. of the 14th Annual Symp. on Frequency Control, Atlantic City,
N. J.; “ a y 31, 1960.
24
J U Iy
IRE TRAMSACTIONS ON ULTRASOlVICS ENGINEERING
SEMICONDUCTOR
K I
l
I
(a)
ii
II
---- SPACECHARGE
.......... ELECTRICFIELD
(b)
electricdisplacement, S thestrain,a nd
t the electric
permittivity. If the piezoelectric constant were equal to
zero, (2a.) reduces to Hooke’s Law and (2b) becomes the
usualrelationbetween’displacementand
field. I n the
general case all thequantities are tensors. However if
me confine ourselves to the case where there is only one
piezoelectric constant whichcouples the electric field in
the thickness directiont,othe stress of either a dilatational
wave or one of the twoshear waves, all the quantities
in (2) will be scalar. Forinstance, if the thickness of a
galliumarsenide plate is inthe (111) direction,orthe
thickness of a cadmium sulfide plate is in the z-direction,
only dilatational waves will be generated. Conversely, no
matter what type of plane waves are incident upon the%
transducers,only
the dilatationalcomponent
will be
detected.
I n a piezoelectric material the correctvalue of the
displacement flux is given by (2b). Strain in (2) may be
written S = au,/dx,where U is the part’icle displacement.
Integrating Poisson’s equation twice and using the same
boundary conditions now yields
&(x)
- x)
e[S(d) - S(x)] - Nq(d
- E V ( X )= e[u(d) - U(.)]
X
0
=
- eS(d)(d
d
- x)
+ 2 (d - x)’.
-DC VOLTAGE
---_ WITH *C
(3)
(C)
Fig. H a ) Cross section of a resonant depletion layer transducer.
(b) Space charge
and
electric-field
distribution. (c) Voltage
distribution in the transducer.
(4)
If e = 0 and V = V , at x = 0, (4)reduces to (1). The
terms involving e in (4)are piezoelectric voltages due to
strainsinthe
depletionlayer. While it is possible to
calculate the thickness for a given set of conditions from
where N is the number of singly ionized impurity atoms
(4), there mould be great simplification if (1) were a
perunit volume and q istheir electriccharge.Since
sufficiently accurate approximation.
E = -aV/ax, by integrating the above expression twice
To estimate the maximum difference between (1) and
and using the boundary conditions E =,.V = 0 at x = d,
(4),
let us set [ U @ ) - u(O)] = Sd in (4).This is true if
Gauss’s equation yields
the strain is uniform and static, and when the strain is
-2 V,€
variable it isconservative if S isthe maximumstrain
d =
S = e/c V,/d. This
inthetrsnsducer.Nextletusset
is true for a dc voltage applied to an ordinary transducer
Here, V , isthevoltage at x = 0, given by the applied
of magnitude in the
andis also of t’hecorrectorder
volt,ageplus theinternalvoltage
which is due tothe
present case. Eliminatingthestrainanddisplacements
difference in Fermi levels.
in (4)with these approximations we see that at most (1)
Eq. (1) is for a nonpiezoelectric material. To. derive
differs from the d in (4) by (1
2 e2/cE)1’2. e2/ce is a
a similar equation for piezoelectric material, me must
dimensionless constant of the material. For a highly
include the effect of strain in the electrical displacement.
piezoelectric material like cadmium sulfide it is at most
Of the possible formulations of the equations of state for
0.04, and for most other materials considerably less. This
piezoelectric material, the form most useful in describing
is small compared to the effects which are of importance
plane wave transducers is3
in this study, and thus (1) may be used for the depletion
T = CS - eE
(24 layerthickness.Actually
(1) is a simple idealized case.
Otherimpuritydistributionsand
surface effects change
D = eS EE
(2b)
the relationshipbetween V and d. However in all these
where T is the stress, c the elasticstiffness constant, casesvariousresults to be developed such as nonlinear
e the piezoelectric constant, E the electric field, D the effectsfollow the same general pattern as (2).
If an acvoltageis superimposed onthedcbias,
V,
becomes
+
+
8 W. P. Mason, “Piezoelectric Crystals and their A plication t o
Ultrasonics,” D. Van Nostrand Co., Inc., New York,
Y., p. 452;
1950.
8.
V , = V,,
+ V.,,eiwl.
Layer
9G.2
Depletion
The
White:
25
[f do is the depletion layer thickness with only a dc bias, n-here,t.he electricfield may be taken as E = - Jr,,/d e-'"'.
xiththeaddition
of an accomponentt,hethickness
is At x = d boththe mechanicaldisplacement andthe
stress are continuous. This yields
lpproximated by,
+ 14-,e-ik1d =
~ , ~ i k * d
~ , i k , d
(10)
V
jkc,A,eikd - jklc, A-,e-jkd - e - = jk2cZBeiktd.(11)
d
rhus, not only does the thickness vary with the applied
;ignal (which is not the cEtse in an ordinary transducer)
ijut the time-varying component of the thickness contains These aresuEEcient condit.ionsto determine B, A , and
Knowing the strain in the transducer andhence D in (2b)
ilarmonics of the signal.
Using this value of thickness for t,he electric field in (3) the current is determined from I = aD/at.
I n the depletionlayertransducer
the electric field
xe obtain at x = 0
contains harmonics
c Ene-i"u'
m
E ( x l t)
=
n- 0
where the coefficients Eo,E l , etc., are given by ( G ) . Since
the driving force has harmonics,obviously thestrain
Thusthe displacement'swhich
Thus the ac component of the electric field also contains mill alsocontainthem.
harmonics of the appliedsignal.
Since the ultrasonic are equivalent to (7) and ( S ) , are
waves producedby thetransducerareproportionalto
m
A,ei"'k's-w" +
~ - ~ ~ i n ( - k ~ - lw I ) .
the electric field, they will also contain harmonics of the u , ( x , t ) =
"-n
signal. However by making Vdc>> V,, or by making the
transducer poorly coupled to the harmonics, the magniO l x S d
tude of the harmonics can be greatly suppressed.
m
Even
t hough
t he
electric field varies with
d epth
.
u z ( - x l t) =
B,e i n ( k . r - w I )
[Fig. 4(b)], it is important to notice that the accomponent
n- 1
is constantthroughoutthelayer.Hencethealternating
The boundary condition at the free surface z = 0 still
stress distribution is quite similar to ordinary transducers.
is that the stress be zero. Thus the coefficients of e-'"'
and e - 2 i w f yield
V. TRAKSDUCER
ACTION
c
c
c
So far qualitative arguments have been
used t.o show
the similarity between the depletion layer transducer and
conventionalplatetransducers.
Theproperties
of the
a morerigorous
transducer willnow
bedevelopedin
manner.
In an ordinary transducer the equations of state may
be used to deriveexpressionsfor
thecharacteristics of
thetransducerwhenitisincorporatedin
an electrical
circuit and also for the ultrasonic power generated by an
lpplied signal. The argument used is:
a freeface a t x = 0 and be
Letthetransducerhave
wave
bonded at x = d [as in Fig. 4(a)]. The ultrasonic
as:
which propagates into the right-hand medium is written
Clkl(A1
- A-1)
2clk,(A2 - A-2)
=
e V.,,
do
(12)
eK c
2vdC do
( 13)
___
The situation isdifferent at the otherboundary. The
interface between t'he active transducer medium
and the
transmission medium varies in spacea s afunction of time,
i.e., d is time dependent accordingto ( 5 ) .Since
d = do +
and for kd,
+ . ..
<< l
eikd
- eikdo(l+ jk, dle-jW'+
. . .);
where k , = @ / v 2 , v, is the velocity of sound in the trans- the second boundary condition now yields for the fundamission medium and B is t,he amplitude of the displace- mental
ment.Inside the transducerwavespropagateinboth
~ , ~ i +
k ~~ - d, ~ ~- i k x d o= B e i k * d o
directions, hence
(14)
ul(xl t)
=
A,ei ( k , z - w f )
+
~ - ~ ~ i ( - k ~ = - w l )
(8) and for the harmonic
If the left-hand boundary is a free surface there is no
stress a t x = 0.Using (2s) we have
+ k, d,(Aleikd"- A-,e-'"')
AZe2iktdr + ~ - ~ - 2 i k ~ d .
+ jk, dlBleiksdr.
= BZeZikado
(15)
The third condition, continuity of stress a t x = dl gives
OHMIC CONTACT
a similar set of equations.
jk I C 1 ~
~
~
GALLIUM ARSENIDE
-i jklclA4-le-ik~d*
k
~
d
~
-eT
v = jk PCPB l e i k a d o (16)
DEPLETION LAYER
7 O U A R T Z TRANSDUCER
d.
2jk IC1 A l e 2 j k z d o - 2 j k , C 1 ~ - , e - ? i " d ~
+
) - e - - - - -v"2- 2
d.
- elk: dl(.41eik'd" A - , e - i k l d o
= 2 j k ~ ~ B f i ~' "kki
~ d13,eik'dr
FTdC
(17)
The fundament,alcomponents of theboundary conditions of the depletionlayertransducer,
(12), (14) and
(16), are similar to those of theordinarytransducer,
(9)-(11). For small signal operation one then expects the
performance of the depletion layer traneducer to be similar
to ordinary transducers.
The harmonic power of the depletion layer transducer
an
is not that of an ordinarytransducerexperiencing
electric field E2e-*jW'.The terms involving A , , A - , and
B , in (13), (15) and (17), which arise of the variations
in thethickness, also affect the harmonic product,ion.I n all
cases the harmonic content is small if V,, << V d c .
VI.
Fig. 5-Quartz
crystal-depletion layer experiment.
CAVITY
DEPLETIONLAYER
MEASWREMEXTS
Initially normal piezoelectric transducers were used to
it hasbeen detest depletionlayertransducers.While
termined thatthe depletionlayer may beused as an
ultrasonictransducer,t,heexpectedhigh
efficiency has
not yet been realized. This is believed to be due to circuit
andfabrication difficulties ratherthantofundamental
limitations in the transducer itself.
was
In the first experiment anX-cutquartzcrystal
bonded to one end of a fused silica rod and the (111) face
of 0.1-ohm cm gallium arsenide crystal (supplied by J. hl.
Whelan) was bonded to the oppositeend as shownin
Fig. 5. A gold film, evaporated on the semiconductor face
joined to the silica, provided a rectifying contact and was
was
grounded.Eitherthe
signalgeneratorordetector
connected to the interior of the gallium arsenide via an
ohmic contact.
as a
When used t.his way the depletionlayeracted
highly loaded transducer as is depicted in Fig. 2. When
the quartz crystal was driven with one-microsecond pulse
of RF carrier centered a t 10G MC, a signal was detected
by thegallium arsenide. Whenobserved on an oscilloscope,
the first pulse wast,hat coupled directlyto the driver
circuitby electromagneticinduction. This mas followed
13, 39 and 65 microseconds later by pulses of decreasing
amplitude. Thisis the time required for dilatational waves
to travel the length of the rod one, three and five times.
Decreasing the debiasdecreased
theoutputv oltage.
This isexpected witha decrease in thickness.The depletion
layer thickness (as measured by its capacitance) and the
output voltage both varied withthe dc voltagein approximately the samemanner.Since the wavelength of
sound was much greater than
the thickness, the output
must be proportional to thickness if the voltage is being
generated in the depletion layer. The depletion layer was
Fig. 6-Resonsnt
cavity-depletion
layer experiment.
also used as a driverand signals were detected by the
quartz crystal. Again output voltage was approximately
proportional to depletion layer t'hickness.
Anothermethodforgenerating
anddetcctingnltrasonic waves a t high frequencies is shown in Fig. ( L 4 -4
quartz bar is inserted into a resonant microwave wvity.
The intense electric field generatesultrasonic wavcs in
the quartz. The piezoelectric coupling is so weak in this
method that thequartz does not significantly load the
cavity, i.e., most of the electrical energy is dissipated as
joule heating in the cavity, not in the generation of ultrasonic energy.Usually, less than 0.01 per cent of the
electrical
energy
is converted
into
ultrasonic
waves.
Despitethe high insertion loss thismcthod is still 3,
proven ultrasonic transducer and a reliable expcrirncnta.1
tool.
Again the (11 1) face of an 0.1-ohm cm gallium arsenide
crystal was used as a loaded transducer in the same manner
as in the preceding experiment. The length of the quartz
bar was in t,he 5 direction. The facc of the gallium arsenide
was polished optically flat. The two cavities usedwere
resonant at 530 hlc and 830 M C . In both eases one-microsecond pulses of ultrasonic waves generated in the quartz
in thecavity
were detectedbythe
gallium arsenide
4 H. E. Bommel and K. Dransfeld, "Excitation and atte~luation
of hypersonic waves in quartz," Phys. Rev., vol. 117, pp. 1245-1252;
March 1, 1960.
1962
White: The Depletion Lager Transduccr
17
depletionlayertransducer.Conversely,
waresgenerated
in the depletion layer could be detected with the cavity.
In both cases decreasing the dc bias decreased t,he output
signal.
I n noexperiment
to dat,e hasthed epletionlayer
mnsducer beenused successfully as a resonanttrans.lucer. However the experimentalevidencedoesprove
that the depletion layer acts as an ultrasonic transducer.
r h e magnitude of t.he insertion loss seems to be somewhat
less than that of a quartz rod betweentwomicrowave
cavit'ies, but it is definitely much greater than the theoretical loss. Apparently, excessive power is being wasted
due to resistancein thestub tuners,leadinductance,
semiconductor resistance and imperfect bonding between
the semiconductor and quartz. It isbelieved that much
higher efficiency and lower insertion loss can be obtained.
cm to cm,
its resonant freqtlcncy
is of the order of loW3
can range from 100 ;\ICto possibly well above 1O,OOO ~ I C .
The depletionlayerthicknessissensitive
to voltage.
This allows one to vary the resonant frequencyof a given
transducer by a factor of three or more by chnngiug the
dcb ias.The
voltagesensitivitymay
also introducc
harmonic distortion and frequencymixing to large signals.
Experimentshaveproven thatthe depletionlayer of n
piezoelectric semiconductor
behaves
as an electromcchanical transducer. So far in these studiesthe transducers
have not shown their theoretical high efficiency. However
it is anticipated that improvements incircuit' and fabrication techniques will demonstrate that the depletion layer
transducers is a practical, efficient and wide-band transducer for use in the UHF andmicrowave region.
VI. COSCLUSIOSS
The depletion layer transducer behaves very much like
.zn ext.remcly thin insulating piezoelectric cryst.al or ceramicultrasonictransducer.
Since the transducerthickness, dependingon impurityconcentrationandvoltage,
Theauthor wishes to thank F. G. Eggersfor use of
hismeasurementequipmentand
for valuableassistance
inmakingthemeasurements, S. S. Bearder for helping
in the construction of the transducers, and J. H. Rowen
and J. C. King for helpful advice.
VII. ACKNOWLEDGMERT