Teledyne HASTINGS 2002, Instruction Manual, Page: 21 / 49

page 21
Boron ion implanted doped Si matrix resistance elements are employed as shown in Figure 5.2.
The die is electrostatically bonded on to a Pyrex substrate in a good vacuum so that the die cavity
is evacuated, this provides maximum deflection at atmospheric pressure. When the sensor is
exposed to vacuum the deflection becomes less and less as the die cavity pressure and the vacuum
system pressure equalizes. Eventually the strain in the membrane due to D P becomes zero and
only the residual strain in the lattice remains. The bridge resistive elements are oriented to give
maximum change in bridge resistance which in turn gives maximum voltage out for a given strain.
5.2 Pirani Sensor
Figure 5.3a shows a thin film Pt resistive element on a one micron thick Si
3
N
4
continuous mem-
brane surrounded by a thin film Pt reference resistor on a Si substrate. The membrane is heated to
a constant 8
0
C above ambient temperature that is monitored by the substrate resistor. The
membrane resistor is approximately 60 W and a constant substrate to membrane resistance ratio is
maintained at 3.86. Figure 5.3b shows the Pirani die in cross section. A parallel Si lid is eutectically
bonded to the Au pads and sits 5 microns above the membrane. As shown, this dimension gives a
Knudson number of greater than 0.01 up to atmospheric pressure, which insures a molecular flow
component. At 10 Torr the region above the membrane is totally in the molecular flow regime and
thus provides a relatively linear output verses pressure region overlapping the linear output versus
pressure of the piezo.
The measurement technique is to produce an output signal that is proportional to the power
supplied to the heated resistor by using the product of the current and voltage. This rejects errors
introduced by resistance changes since the sensor resistance is no longer part of the power equa-
tion.
A signal proportional to the power is obtained by multiplying the voltage across the heated sensor
and the voltage impressed by the direct current across a constant series resistance. The power
supplied to the sensor resistor must equal the heat dissipated (E
t
). The three main heat loss routes
from the heated sensor are thermal conduction through the silicon nitride membrane to the silicon
substrate (E
s
), radiation losses (E
r
), and thermal conduction through the gas to the silicon substrate;
thus, as shown in Figure 5.3c,
E
t
= E
s
+ E
r
+ E
g
The first term, E
s
, is dependent on the thermal conductivity of the silicon nitride (K), the tempera-
ture difference ( D T) between the heater and silicon substrate and geometric factors (A
M
& L). E
S
is given by
E
s
= (K D T A
m
)/L
A
m
is the membrane area through which the heat transfer occurs. This is, approximately, the outer
circumference of the chamber multiplied by the membrane thickness. L is the distance from the
edge of Rs through the membrane to silicon substrate.
For any particular sensor, all of the factors except
D T are constants dependent on its construction.
The D T is held constant by the control circuit. The thermal loss through the silicon nitride will be a
constant value independent of the thermal conductivity and pressure of the gas.
Radiation is another source of thermal losses. It can be determined from
E
r
= se (T
h
4
-T
a
4
)A
s
where
s = Stefan-Boltzmann radiation constant
e = thermal emissivity of the silicon nitride membrane
A
S
= surface area of the heated portion of the membrane
T
h
= temperature of R
s
T
a
= ambient temperature