Page 262 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Electron-Phonon
and a frequency of
produces a strain field with a spatial period of 2d
⁄
πcd where is the wave propagation velocity. At least part of this
c
strain field is of the right shape to propagate as a Love surface acoustic
wave, and clever design will maximize this ratio.
For our purposes it is sufficient to view the wave as generated by a row of
alternating point sources, each source placed exactly between the elec-
x
trode pairs [7.5]. At some point along the surface we now add up the
contributions of each electrode pair’s point source

N – 1 iω x – x)
(
n
n
u = ∑ – ( 1) A exp ------------------------- exp [ iωt] (7.64)
n
c
i = 1
where N is the number of electrode pairs, –( 1) n expresses the fact that
the pairs alternate in excitation direction, x is the position of the source,
n
and A is the amplitude of the excited wave. If we now denote the time
0
delay for a pulse at pair to arrive at as
n
x
( x + nd)
o
t = ---------------------- (7.65)
n
c
x
then we can write that the total displacement at is
f

(
1 – exp – iN – 1)π ----- – 1 
f  o 
u = A exp – [ i2πft ]------------------------------------------------------------------------ (7.66)
n
o
f

1 – exp iπ ----- – 1 
f  
o
⁄
where f = c 2d is the natural frequency of the interdigitated elec-
o
trodes, see Figure 7.5.
Usually such sensors are arranged as a pair of sending electrodes sepa-
rated by a sensor space (the delay line) and an identical pair of receiving
electrodes. The delay line is the space where the signal is allowed to
attenuate against a fluid. The receiver pair works in the reverse fashion of
the sender electrodes, i.e., the elastic wave induces a voltage in the elec-

Semiconductors for Micro and Nanosystem Technology 259