Introduction
The demand for miniature pressure sensors is increasing steadily due to
various kinds of application. New fields of application are established
because of miniaturization of sensors and sensor systems. Additionally,
smaller devices and cost-effective production cause lower unit prices. One
area of application is low pressure measurement. Measuring instruments for
ultra-high vacuum are usually needed in fields of highly specialized industry
or research, for example in scanning electron microscopes or particle
accelerators; whereas measurement devices for low to high vacuum are employed
in broad fields of industry, from automotive sensor applications to food
processing. Even in the fabrication of micro-electro-mechanical systems
(MEMS), vacuum is needed to increase reliability and endurance .
Due to the growth of the market for micro-structured vacuum sensors there are
already many approaches for fabricating such devices. One popular idea is the
miniaturization of Pirani gauges that use the dependence of thermal
conductivity on ambient pressure . The concepts for
micro-Pirani gauges have been improved for decades and in the meantime
MEMS-type gauges with a very wide pressure range from 10-5 to
103 mbar have been presented .
It is not surprising that measuring the electrical conductance of thinned
gaseous substances has not been of interest for low pressure measurements so
far. In general miniaturization of well-known sensor types is the typical
approach regarding the development of microsensors and most MEMS-type vacuum
sensors make use of effects that are known from conservative, macroscopic
gauges . Some newer concepts of micro-structured vacuum gauges,
based on field emission, were established during the last few years. Even though
there is skepticism about whether or not the miniaturization of ionization vacuum
gauges will be advantageous, some approaches with field emitter arrays have
been presented . One concept for pressure sensors operates
with the effect of field emission from silicon tip arrays. A difficulty here
was the need for high sensitivities that seems to exclude the need for high
currents .
In general, gases are considered to be very good insulators. On a macroscopic
scale the electrical current through a gas volume is very small. To measure these
currents a high level of measurement technique is necessary: digital
multimeters are usually suitable for measuring currents greater than 1 µA.
For low current measurements, picoammeters are required, triaxial
cables must be used to achieve a good guarding of the signals and the overall
measurement setup must also be shielded from electromagnetic interference in
order to minimize the noise level . That is why this
sensor principle is not attractive on a macroscopic scale. The manufacturing
of a gas chamber with electrodes at a distance of some 100 nm provides a chance
to use electrical conductivity measurements for the measurement of
low pressure. Even if gases are considered to be very good insulators, there
is always a small number of charge carriers depending on the gas
pressure. The miniaturization of the MEMS-type gas chamber leads to an increase in
the electrical conductance of the device and thus to an increase in the
currents to be measured. This reduces the requirements of measurement
technique and opens up an interesting new measurement concept for the
determination of vacuum pressures.
This study aims to examine whether conductivity measurements with
MEMS devices are a promising concept for simple and competitive microscopic
sensors for low pressure measurements. In the following, some theoretical
background concerning the principle of electrical conductance in gases will
be summarized. The design, the fabrication in standard CMOS technology and
the electrical characterization of the sensor chip will be explained
afterwards. Finally, the results of the electrical characterization will be
presented, analyzed and discussed.
Conductivity in gases
Assuming that the number of charge carriers in a gas
volume is a function of the total number of particles in that volume and
thereby a function of pressure, the measurement of the electrical conductance
G of a gas volume is a way to determine the gas pressure. Measuring the
current–voltage characteristics is general practice to determine the
electrical conductance G, which is the derivative
G=dIdUU
of the current I with respect to the voltage U. The challenge of
measuring electrical conductances in hardly conductive materials is the low
current measurement. Therefore, the sensitivity of the experimental setup is
crucial for measuring conductivities of gases. The conductance of a resistive
volume will increase with the area perpendicular to the electric field A
and decrease with the length of the gas volume, or more precisely the distance
between the two electrodes d. Thus, a gas volume of a small length and large area,
that can be realized by the application of surface micro-machining technology,
will provide enlarged conductances and currents.
Certainly, the current–voltage characteristics of two electrodes with more or
less gas molecules in-between cannot be described by Ohm's law. First of all,
the electrical conductivity κ may be a function of the electric field.
In addition, the total current is affected by diffusion and the source of
charge carriers. For understanding the behavior of the sensor chip, it is
necessary to examine the conduction mechanisms that might take place. Two
special cases shall be discussed in the following paragraphs.
In the first case, a number of gamma electrons are emitted from a cathode per unit area and time. The constant
emission current density is causing an emission-limited current flow
. The electrons released from the cathode either drift to the
anode due to the electric field E or return to the cathode by diffusion
with the thermal mean speed u. Therefore the sum
of the current densities,
γe-ρμE-ρu4=0,
equals zero, where e is the elementary charge, ρ is the charge density
and μ is the electrical mobility of the charge carriers. The current
between cathode and anode results in
Icath.=γeAμU+du4μU,
where d is the distance between those two electrodes, A is the area
perpendicular to the electric field E and U is the voltage across the
electrodes.
In the second special case, the charge carriers originate from ionization in
the volume between two electrodes. Some charge carriers generated diffuse
towards the edge of the volume and some of them drift towards the electrodes.
Neglecting recombination, in equilibrium the number of charge carriers N
does not change over time and can be described by
dNdt=ngν0V-Nτ-2Nud=0,
where ng is the density of the gaseous substance, ν0 is
the frequency of generating charge carriers by ionization, V is the volume
between the two electrodes, τ is the mean residence time due to
diffusion to the boundaries of the gas volume and u is the average drift velocity in electric field. This
results in the total current
Iion.=eτν0ngdA2τμU+d2μU
between cathode and anode .
Ohm's law works for these experimental setups in the case of small electric
fields. If μU is substantially less than du4, Eq. () may be approximated by
Icath., ohm.≈4γeuAdμU
and if μU is substantially less than d22τ, Eq. () may be approximated by
Iion., ohm.≈eτν0ngAdμU.
Whether these presumptions for a linear approximation are true has to be
decided in individual cases.
These characteristics show a pressure-depending behavior as the gas density
ng and the electrical mobility μ are functions of the pressure.
The ideal gas law states that ng is proportional to the pressure
p. The electrical mobility μ is depending on the ratio of electric
field to pressure. Wasserrab states that the mobility is proportional to
1/p for small electric fields and high pressures, and that it is
proportional to 1/p for experimental setups with low pressures
and higher electric fields . For mercury vapor, for example, it
is shown that the electron's mobility dependence on the pressure can be
described by
μ-(p)=μ0-⋅p0p
with μ0-=22.7 m2 V-1 s-1 and
p0=1 mbar for an electric field to pressure ratio
E/p less than 1.5×104 V m-1 mbar-1. The mercury
ion's mobility is indicated as
μ+,1(p)=μ0+,1⋅p0p,
with μ0+,1=2.4×10-2 m2 V-1 s-1 for an
electric field to pressure ratio E/p less than 7.5×103 V m-1 mbar-1 and
μ+,2(p)=μ0+,2⋅1Ep,
with μ0+,2=2.1 m s-1 (m mbar V-1)1/2 for an
electric field to pressure ratio E/p higher than 7.5×103 V m-1 mbar-1.
The combination of Eqs. () and () with the
different parts of mobility (Eqs. –) results in
different forms of dependencies between current and pressure, respectively,
conductance and pressure. Assuming that the pressure dependence of the
conductance is due only to the pressure dependence of the gas density
ng (given by the ideal gas law) and the electrical mobility μ,
the following proportionalities can be estimated: in the case of electrons
emitted from a cathode, the conductance is proportional to 1/p for E/p
less than 1.5×104 V m-1 mbar-1. In the case of
ionization in the gas volume, the comparison of Eqs. () to
() with Eq. () shows that the dependence of the
conductance on the pressure at smaller pressures is essentially determined by
the mobility of the ions. In this case the pressure dependency of the
electrical conductance is given by
G+,2(p)=G0+,2⋅p/p0,
with p0=1 mbar and the conductance G0+,2 for
p=1 mbar for E/p higher than 7.5×103 V m-1 mbar-1. The pressure dependency of the mobility of ions at
higher pressures and of electrons cancels the pressure dependence of the gas
density in Eq. () and then results in a conductance that is
independent of pressure.
For the evaluation of the experimental results, a determination of the
electric field to pressure ratio is needed. Although the electric field may
not be homogeneous, for the experimental setups presented in this article
the magnitude of the electric field E may be approximated by
E≈Ud,
where d is the distance between the electrodes.
If the distance between the electrodes d is in the range of the mean free
path of electrons or smaller, another effect has to be considered. The mean
free path of electrons in kinetic gas theory is given by
λ=1ngσ,
where σ is the effective cross-sectional area for collision. In
perfect vacuum, electrons are accelerated to the anode undamped by collisions
and the mobility becomes independent of ambient pressure. With rising
pressure, the number of collisions of electrons with gas molecules increases, the mean
free path decreases and the fraction of electrons that arrive at the anode
without collisions with gas molecules falls off. The pressure dependence of
the electrical conductance can then be described by
Gλ(p)=G0,λe-d/λ(p)=G0,λe-dσpkBT,
where G0,λ denotes the electrical conductance in vacuum,
kB is the Boltzmann constant and T is the temperature
.
Design and realization
One possibility to handle the difficulty of measuring low currents is to use
energy sources like ultraviolet light to increase the rate of ionized
particles within the gas. This is done in conventional gas sensors like photo
ionization detectors for example. In contrast, the idea discussed in
this article is about optimizing the dimensions of the gas volume to increase
the conductance. In the following, the design and realization of the sensor
chip will be presented and the experimental setup will be described.
Design and principle of operation
Design study of a chip to measure the conductivity of gaseous
substances: levitating honeycombed grid electrode and substrate electrode are
isolated by spacers made of SiO2.
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An increased conductance can be obtained by using a gas volume with a large
area A perpendicular to the electric field and a short distance d between
the electrodes. A design study for a chip that complies with these
requirements is shown in Fig. . The sensor chip consists of
two electrodes, namely the silicon substrate and a levitating grid. The
hexagonal grid made of titanium nitride (TiN) is supported by abutments made of
silicon dioxide (SiO2). The honeycombed structure of the grid
originates from an optimization of the mechanical strength of freely
suspended grids . The wide, honeycombed vent holes of the grid
provide fast gas exchange and therefore a fast response time. The final
layout of the chip results in a grid of 5 mm × 5 mm and a
length of the gas volume (distance between
grid and substrate) of 300 nm.
Fabrication of the sensor chip
Cross sections of the fabrication using planar technology. (a) Deposition
of SiO2 and TiN, (b) structuring with reactive ion etching, (c) contact of the
substrate, (d) isolation with plasma enhanced chemical vapor deposition
(PECVD) silicon dioxide, (e) bond pads made of TiN/Ti/Al
and (f) final suspension of the levitating grid.
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The sensor chip was manufactured in planar technology on a p-doped
silicon substrate. A flow-chart with cross-section illustrations of the
fabrication process is displayed in Fig. . The first step
was the plasma enhanced chemical vapor deposition (PECVD) of a
300 nm SiO2 layer. This layer was coated with
300 nm TiN, deposited with reactive magnetron
sputtering. The honeycombed grid structures were patterned by
photo-lithography (with MicroChemicals AZ MIR 701) and structured by reactive
ion etching with chlorine gas (Cl2), methane (CH4) and
silicon tetrachloride (SiCl4) at 40 ∘C (see Fig. b).
To provide good electrical contact to the substrate, TiN was deposited on the
marginal parts of the chip. Therefore, a photo-lithography with image reversal
photoresist (MicroChemicals AZ 5214 E) was done in positive mode. Silicon
dioxide was removed using wet etching with buffered oxide etch (BOE) followed
by the deposition of TiN with reactive magnetron sputtering. For structuring
the TiN layer, a lift-off procedure was performed with acetone at
40 ∘C supported by sonication (see Fig. c).
Afterwards, another 300 nm thick layer of silicon dioxide was
deposited to avoid short circuits between substrate- and grid-electrode
(Fig. d).
The next process steps are needed to build contact pads on the grid and on
the titanium nitride margin. This is done because electrical contact to the
chip will be provided by ultrasonic bonding later on, when the chip is
mounted on a circuit board. Figure e shows the contact
pads on the grid and the TiN margin. Photo-lithography with image reversal
photoresist (MicroChemicals AZ 5214 E) was done in positive mode, before the
silicon dioxide layer was removed with BOE. The contact pads
are made of titanium nitride, titanium (Ti) and aluminum (Al), deposited
with reactive magnetron sputtering and structured by lift-off.
The final step to obtain the levitation of the grid (Fig. f)
is done by wet etching with BOE after another photo-lithography with
MicroChemicals AZ 5214 E in positive mode. Figure shows the
scanning electron micrograph of a levitating grid. In the
cross-sectional view it is possible to evaluate the removal of the silicon
dioxide sacrificial layer under the grid. The bars have a width of
approximately 800 nm and the diameter of the holes is about 6 µm.
On the brink of the grid the abutments of SiO2 are visible
underneath.
Cross-sectional scanning electron micrograph of a micro-structured, levitating grid
made of titanium nitride based on silicon dioxide abutments.
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Experimental setup
For the electrical characterization, the chip with a size of
8 mm × 8 mm was attached on a circuit board. Electrical contact
was provided by ultrasonic wire bonding. Inside the vacuum chamber the
circuit board was soldered to the measuring lines. The vacuum chamber was
specially designed to offer the possibility of measuring low currents at
different vacuum pressures. It is placed inside a measurement cabinet to
avoid vibration and disturbing noise. The pump is a Pfeiffer Vacuum TMU 065
turbo-molecular pump, the pressure was measured with a Pfeiffer Vacuum MPT 100 gauge.
Additionally there is a throttle valve to control the
flow of gaseous substances into the chamber. To run the electrical
measurements an Agilent 4156C precision semiconductor parameter analyzer was
used. This setup provides the measurement of currents between femtoamperes
and milliamperes at pressures between 1 ×10-6 and 1000 mbar. In
sweep measurements at different pressures, the current I is monitored while
the voltage UG is swept. These current–voltage characteristics
supply the information that is needed to determine the electrical conductance
G as a function of pressure.
To evaluate the advantage of the sensor chip over a macroscopic setup
concerning the measurement of conductivity due to optimized dimensions, a
reference experiment with grids on circuit boards at a distance of
approximately 1 mm was passed. The area of these grids perpendicular to the
electric field is approximately the same as the area of the grid on the
sensor chip. Subsequently, similar measurements were carried out with the
sensor chip, where the gap between the electrodes is reduced by a factor
of 3 ×10-4 compared to the dimensions of the reference setup.
Results
In the following, the measurements with both experimental setups will be
presented and analyzed. Determination and quantitative analysis of the
conductance–pressure characteristic of the reference setup with a gap of
1 mm between cathode and anode will be described. Subsequently, analogues
measurements with the sensor chip with a gap of 300 nm are presented and
compared with the previous results.
Current–voltage characteristics with 1 mm gap
Current–voltage characteristics with electrodes at a distance of
1 mm at different pressures. The solid lines represent simple linear regressions.
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Eight out of 13 sweep measurements with electrodes 1 mm apart at
different pressures are shown in Fig. . Measurements
were executed at pressures between 3.8 ×10-6 and 1000 mbar. Grid
voltage was swept from -20 to 20 V twice at each pressure to verify
reproducibility. The current is a linear function depending of the applied voltage
(the electric field) and depends on the pressure. Current–voltage characteristics measured at the same pressure hardly differ from each other.
Referring to Eq. (), an electric field of about 20 V mm-1
is estimated for an applied voltage of 20 V. The linearity of the
characteristic curves is consistent with the theoretic background presented
in Sect. as the experimental setup complies with the
requirements for the linear approximations in Eqs. ()
and ().
For further evaluation, simple linear regression was used. The slope of the
fitted lines is equal to the electrical conductance G according to
Eq. (). The mean value of the slope with error bars calculated from
the two measurements at each pressure is displayed in Fig.
as a function of pressure. The error bars are nearly invisible as the
standard deviation is very small. The solid line in Fig.
results from non-linear curve fitting with the “trust region reflective”
algorithm to the function
G1mm(p)=mp/p0+b,
with p0=1 mbar and the fitting parameters m=27.6±0.8 fS (femto siemens) and b=1.71±0.01 pS referring to
Eq. () for ions ionized in the gas volume at lower pressures.
The electrical conductance G as a function of pressure with
electrodes at a distance of 1 mm. The values for the electrical conductance
result from linear regression of the sweep measurements. The solid line is a
non-linear fit to the data according to Eq. ().
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The results of data analysis correspond to the expectation that the
electrical conductance is a function of the charge carrier density and
therefore will be a function of the pressure. The electrical conductance G
is increasing with rising pressure in particular in the range above 1 mbar.
This might be due to the fact that the electron's mean free path becomes
smaller than the distance between the electrodes of 1 mm for pressures
higher than 0.4 mbar. This could result in a larger number of collisions and
therefore more charge carriers in the volume due to ionization. Obviously the
fitted curve is in quite good agreement with the data. For mercury vapor,
Eq. () applies up to a pressure of 3 mbar, but it seems that
this limit shifts to higher pressures for air. It is likely that the
conductance mechanism is due to ionization in the gas volume with a pressure-dependent
charge carrier mobility but a final conclusion of this question is
not possible at the moment as the mobility of ions in strong electric fields
has not been entirely understood and is still of interest in current research
.
Current–voltage characteristics with 300 nm gap
Seven examples for sweep measurements at different pressures with the sensor
chip are displayed in Fig. . The gap between the
electrodes is 300 nm. The grid voltage was swept from -1 to 1 V. It is
worth mentioning that the electric field on the chip is more than 2 orders
of magnitude higher than the electric field applied during the reference
measurements due to the small distance between substrate and grid. According
to Eq. (), an electric field of about 3 kV mm-1 can be
estimated when a voltage of 1 V is applied to the grid. Measurements were
carried out at pressures between 5.0 ×10-6 and 1000 mbar. The
measurements were repeated once or twice at each pressure to ensure
reproducibility of the results. The characteristics differ clearly from the
ohmic behavior observed in the reference measurements
(see Fig. ), which is reasonable because the prerequisites
for a linear approach do not apply due to the large electric fields. For
small electric fields, there is a residual current region where an ohmic
behavior may be estimated. For higher values of the electric field, the
current approaches a saturation current.
Current–voltage characteristics with the sensor chip (electrodes at
a distance of 300 nm) at different pressures. The solid black lines are fitted
curves.
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For further evaluation, a curve of the form
I=c1Uc2U+c3
was fitted to the current–voltage characteristics in the positive range of
voltage (solid black lines in Fig. ) with the fitting
parameters c1, c2 and c3. This curve describes
the current–voltage characteristics for both special cases discussed in
Sect. , Eqs. () and (). For curve
fitting, the “trust region reflective” algorithm was used. The values for the
slope in the ohmic region with small electric fields,
G=c1c3,
correspond to the conductance G in Eq. () and should show a
dependence on pressure that is similar to the linear approximations in
Eqs. () and () if one of the two special
cases applies. The mean values of the results of the curve fitting for
measurements at different pressures are displayed in Fig. .
The conductance drops from more than 25 µS at low pressures to less
than 10 µS at atmospheric pressure.
The electrical conductance G as a function of pressure with
electrodes at a distance of 300 nm. The values for the electrical
conductance result from the fitted curves of the sweep measurements (cf.
Eqs. and ). The solid line is a non-linear fit to
the data according to Eq. ().
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The decrement of conduction with rising pressure points to the fact that the
current between substrate and grid does not result from ionization in the gas
in contrast to the results deduced in Sect. . The emission of
electrons from the substrate seems to be more likely instead. However, the
dependence of the conductance on the pressure cannot be explained by
Eq. (). This is reasonable as the electron's mean free path
is larger than 300 nm for pressures below 1400 mbar and Eqs. ()
to () do not apply. The solid line in Fig.
is the outcome of fitting Eq. () to the mean values of the
conductance. As a result, the scattering cross section σ=2.7±0.8×10-19 m2 can be calculated from the parameters of
the fitted curve, given by
G300nm=G0e-p/p0,
referring to Eq. () with the fitting parameters
G0=23±1 µS, p0=510±150 mbar and a distance between grid and substrate of d=300 nm.
The value for the cross section is in the range of the values of electrons
with a kinetic energy of 1 eV colliding with oxygen and nitrogen
(σO2=5.97×10-20 m2,
σN2=1×10-19 m2), reported in literature
. Even though the shape of the curve does not fit the data
very well, and the standard deviation of the fitting parameter p0
is rather high, the deceleration of electrons due to collisions with gas
molecules is likely to be the reason for decreasing conductances with rising
pressures. However, there have to be further mechanisms of conductivity not
considered yet.
Contrary to the measurements with a gap of 1 mm, the current increases on the
sensor chip when the pressure drops and the currents are thereabout 5
orders of magnitude larger than in the reference measurements. This cannot
simply be explained by a reduced distance between the electrodes. Both
Eqs. () and () indicate that the current is
proportional to 1/d and a rise of 3 orders of magnitude in the current
would be sensible. Thus, a supplemental effect that causes higher currents has
to be taken into consideration.
Discussion
This work is the first research testing conductance measurements as a
measurement principle for MEMS-type vacuum sensors. With regard to the
question of whether this concept is promising for the development of vacuum
sensors, the findings presented above have revealed that the sensitivity,
defined as dG/dlg(p) , is approximately
1 µS per decade for pressures smaller than 1 mbar. For this
pressure range, the sensitivity of the sensor chip is low but it is not zero
as predicted in Eq. (). The proposed model explains one
aspect of the results but cannot explain the overall behavior of the sensor
chip yet. Further research on the causes of the decreasing conductance in
this pressure range could also reveal possibilities to improve the
sensitivity. The fabricated sensor chip shows a good sensitivity of
approximately 12 µS per decade from 1 to 1000 mbar. Compared
to other sensor principles, this is a narrow range of pressure as there are
already many suggestions for MEMS-type vacuum sensors with a pressure range over
8 orders of magnitude. However, most of the sensors presented in
literature work on sensor principles that have been improved over years .
The analysis of the measurements indicates that the sensitive
range of the sensor could be adapted by varying the distance between
substrate and grid. Previous studies have shown that the sensitivity of ion
gauges, both conventional and field-emission-based vacuum gauges, is
determined by the shape, dimensions and the material of the electrodes
. In the future, further research should be carried out to
examine if the variation of design and materials of the sensor chip first
presented in this article will allow the extension of the sensitive range
towards lower pressures.
Knowing that low current measurements are a challenge for this type of
sensor,
this study aimed to reach higher currents by miniaturization of the sensor.
The results show clearly that the increase in current exceeds the
expectations and that this effect cannot be explained by a reduced distance
between the electrodes. One possible explanation is that field emission due
to inhomogeneities of the electric field is the reason for this discrepancy.
In previous studies, field emission structures have been used as electron
sources. However, these studies are predominantly focused on tip arrays and
did not examine the emission from wider surfaces . Finite element analysis of the electric fields and the investigation of electron emission from the
substrate could lead to a better understanding of the physical mechanisms on
the sensor chip. Overall, it could be shown that the development of the
sensor chip led to an amplification of the pressure-dependent measuring
signals, which exceeded expectations. It is very likely that simple
multimeters or integrated readout circuits are sufficient to measure the
signals. This would mean a significant reduction of the measuring effort.