5. Silicon Pressure Sensors
5.1 Background on Piezoresistive Effect
The roots of silicon micromachining technology date back to Bell Laboratories. The research team developing the basics of semiconductor technology discovered a piezoresistive effect in silicon and germanium. The piezoresistive effect creates a resistance change in the semiconductor material in response to stress. This change was approximately two orders of magnitude larger than the equivalent resistance change of metals (used previously for strain gauge applications), promising an attractive option for sensors. The high sensitivity, or gauge factor, is perhaps 100 times that of wire strain gauges. Piezoresistors are implanted into a homogeneous single crystalline silicon medium. The implanted resistors thus are integrated into the silicon force sensing member. Typically, other types of strain gauges are bonded to force sensing members of dissimilar material, resulting in thermo-elastic strain and complex fabrication processes.
Most strain gauges are inherently unstable due to degradation of the bond, as well as temperature sensitivity and hysteresis caused by the thermoelastic strain.
Silicon is an ideal material for receiving the applied force because it’s a perfect crystal and does not become permanently stretched. After being strained, it returns to the original shape. Silicon wafers are better than metal for pressure sensing diaphragms, as silicon has extremely good elasticity within its operating range.
Silicon diaphragms normally fail only by rupturing.
5.2 Piezoresistive Effect-Based Pressure Sensor Basics
FIG. 21 Four-element bridge used in a piezoresistive pressure sensor.
FIG. 22 Sensor equivalent circuit.
The most popular silicon pressure sensors are piezoresistive bridges that produce a differential output voltage in response to pressure applied to a thin silicon diaphragm. The sensing element of a typical solid-state pressure sensor consists of four nearly equal piezoresistors buried in the surface of a thin circular silicon diaphragm (see FIG. 21). A pressure or force causes the thin diaphragm to flex, inducing a stress or strain in the diaphragm and the buried resistors. The resistor values will change, depending on the amount of strain they undergo, which depends on the amount of pressure or force applied to the diaphragm. Therefore, a change in pressure (mechanical input) is converted to a change in resistance (electrical output). The resistors can be connected in either a half-bridge or a full-Whetstone-bridge arrangement. For a pressure or force applied to the diaphragm using a full-bridge arrangement, the resistors can be approximated theoretically as shown in FIG. 21 (nonamplified units). Here, R -t-AR and R-AR represent the actual resistor values at the applied pressure or force. R represents the resistor value for the undeflected diaphragm (pressure is zero) where all four resistors are nearly equal in value. And AR represents the change in resistance due to an applied pressure or force. All four resistors will change by approximately the same value. Note that two resistors increase and two decrease depending on their orientation with respect to the crystalline direction of the silicon material. The signal voltage generated by the full-bridge arrangement is proportional to the amount of supply voltage (Vcc) and the amount of pressure or force applied that generates the resistance change, AR. In a practical pressure sensor such as the Motorola MPX2100, the Whetstone bridge as shown in FIG. 22 is used.
Bridge resistors RP1, RP2, RV1, and RV2 are arranged on a thin silicon diaphragm such that when pressure is applied RP1 and RP2 increase in value while RV1 and RV2 decrease a similar amount. Pressure on the diaphragm, therefore, unbalances the bridge and produces a differential output signal. A fundamental property of this structure is that the differential output voltage is directly proportional to bias voltage, B+. This characteristic implies that the accuracy of the pressure measurement depends directly on the tolerance of the bias supply. It also provides a convenient means for temperature compensation. The bridge resistors are silicon resistors that have positive temperature coefficients.
Therefore, when they are placed in series with zero Tc temperature compensation resistors, RC1 and RC2, the amount of voltage applied to the bridge increases with temperature. This increase in voltage produces an increase in electrical sensitivity, which offsets and compensates for the negative temperature coefficient associated with piezoresistance.
Since RC1 and RC2 are approximately equal, the output voltage common mode is very nearly fixed at 1/2B+. In a typical MPX2100 sensor, the bridge resistors are nominally 425 r; RC1 and RC2 are nominally 680 f2. With these values and 10 V applied to B+, a AR of 1.8 f2 at full-scale pressure produces 40 mV of differential output voltage.
5.3 Pressure Sensor Types
Most pressure sensor manufacturers support three types of pressure measurements: absolute pressure, differential pressure, and gauge pressure. These are illustrated in FIG. 23.
Absolute pressure is measured with respect to a vacuum reference, an example of which is the measurement of barometer pressure. In absolute devices, the P2 port is sealed with a vacuum representing a fixed reference. The difference in pressure between the vacuum reference and the measured amount applied at the P1 port causes the deflection of the diaphragm, producing the output voltage change ( FIG. 23(a)). Differential pressure is the difference between two pressures. For instance, the measurement of pressure dropped across an orifice or venturi used to compute the flow rate. In differential devices, measurements are applied to both ports ( FIG. 23(b)). Gauge pressure is a form of differential pressure measurement in which atmospheric pressure is used as the reference. Measurement of auto tire pressure, where a pressure above atmosphere is needed to maintain tire performance characteristics, is an example. In gauge devices, the P1 port is vented to atmospheric pressure and the measured amount is applied to the P2 port ( FIG. 23(c)).
5.4 Errors and Sensor Performance
FIG. 23 Different pressure measurements: (a) absolute, (b) differential,
(c) gauge. (Microswitch, Honeywell, Inc., USA.)
In practical applications, when calculating the total error of a pressure sensor, several defined errors should be used. To determine the degree of specific errors for the pressure sensor selected, it’s necessary to refer to the sensor's specification sheets. In specific customer applications, some of the published specifications can be reduced or eliminated. For example, if a sensor is used over half the specified temperature range, then the specific temperature error can be reduced by half. If an auto-zeroing technique is used, the null offset and null shift errors can be eliminated. The major factor affecting high-performance applications is the temperature dependence of the pressure characteristics. Some of the error parameters are these.
• Null offset. Null offset is the electrical output present when the pressure or force on both sides of the diaphragm is equal.
• Span. Span is the algebraic difference between the output end points. Normally, the end points are null and full scale.
• Null temperature shift. Null temperature shift is the change in null resulting from a change in temperature. Null shift is not a predictable error because it can shift up or down from unit to unit. A change in temperature will cause the entire output curve to shift up or down along the voltage axis ( FIG. 24(a)).
• Sensitivity temperature shift. Sensitivity temperature shift is the change in sensitivity due to a change in temperature. A change in temperature will cause a change in the slope of the sensor output curve ( FIG. 24(b)).
• Linearity error. Linearity error is the deviation of the sensor output curve from a specified straight line over a desired pressure range. One method of computing linearity error is least squares, which mathematically provide a best fit straight line to the data points ( FIG. 24(c)). Another method is terminal-base linearity or end point linearity, which is determined by drawing a straight line (L1) between the end data points on the output curve. Next a perpendicular line is drawn from line L1 to a data point on the output curve. The data point is chosen to achieve the maximum length of the perpendicular line. The length of the perpendicular line represents terminal-base linearity error ( FIG. 24(d)).
• Repeatability error. Repeatability error is the deviation in output readings for successive applications of any given input pressure or force with other conditions remaining constant ( FIG. 24(e)).
• Hysteresis error. Hysteresis error usually is expressed as a combination of mechanical hysteresis and temperature hysteresis. Some manufacturers, such as Microswitch, express hysteresis as a combination of the two effects ( FIG. 24(f)). Mechanical hysteresis is the output deviation at a certain input pressure or force when that input is approached first with increasing pressure or force and then with decreasing pressure or force. Temperature hysteresis is the output deviation at a certain input, before and after a temperature cycle.
• Ratiometricity error. Ratiometricity implies the sensor output is proportional to the supply voltage with other conditions remaining constant. Ratiometricity error is the change in this proportion and usually is expressed as a percent of span.
When choosing a pressure or force sensor, the total error contribution is important. Two methods take into account the individual errors and the unit-to-unit interchangeability errors: the root sum squared using maximum values and the worst-case error. The root sum squared method gives the most realistic value for accuracy. With the worst-case error method, the chances of one sensor having all errors at the maximum are very remote.
5.5 Practical Components
FIG. 24 Typical error curves for pressure sensors: (a) null shift error,
(b) sensitivity error, (c) best-fit straight-line linearity, (d) terminal-base
linearity, (e) repeatability, (f) hysteresis.
Pressure sensing is one of the most established and well-developed areas of sensor technology. One reason for its popularity is that it can be used to measure various real-world phenomena, like flow, fluid level, and acoustic intensities, in addition to pressure. In the automotive industry alone, For example, pressure sensors have been identified for use in ten different applications. In guidance control and industrial control systems, pressure sensors long have been used for a number of precision pressure measurement.
Practical components available from manufacturers could be basically divided into several categories: basic uncompensated types, calibrated and temperature compensated types, and signal conditioned types.
The standard pressure ranges, from manufacturers such as Motorola, Honeywell, and IC Sensors, vary between none to a few psi up to 0-5000 psi.
5.5.1 Basic Uncompensated Sensors
Most of the basic uncompensated pressure sensor devices are silicon piezoresistive strain gauge designs. Some examples of these devices are listed in Table 3.
These uncompensated basic sensors contain a basic transducer structure as shown in FIG. 25. FIG. 25 illustrates the top view of the pressure sensor silicon chip, showing the strain-gauge resistor diagonally placed on the edge of the diaphragm. Voltage is applied across pins 1 and 3, while the taps that sense the voltage differential transversely across the pressure-sensitive resistor are connected to terminals 2 and 4. An external series resistor is used to provide temperature compensation while reducing the voltage impressed on the sensor to within its rated value.
The recommended voltage drive is 3 V DC and should not exceed 6 V under any operating condition. The differential voltage output of the sensor, appearing between terminals 2 and 4, will be positive when the pressure applied to the "pressure" side of the sensor is greater than the pressure applied to the "vacuum" side. Nominal full-scale span of the transducer is 60 mV when driven by a 3 V constant voltage source.
When no pressure is applied to the sensor there will be some output voltage, called zero pressure offset. For the MPX700 sensor this voltage is guaranteed to be within the range of 0-35 mV. The zero pressure offset output voltage easily is nulled out by a suitable instrumentation amplifier. The output voltage of the sensor will vary in a linear manner with applied pressure. FIG. 26 illustrates output voltage vs. pressure differential applied to the sensor, when driven by a 3 V source.
(coming soon) TABLE 3 Uncompensated pressure sensors. (of Motorola Inc.)
FIG. 25 Sensor construction as applied to Motorola MPX series showing
electrical connections. (of Motorola Inc.)
FIG. 26 Characteristics of the MPX700 series devices: (a)output vs. pressure
differential, (b)linearity specification comparison. (of Motorola Inc.)
FIG. 27 Schematic diagram of a digital pressure gauge using the MPX700
series.
5.5.1.1 Temperature Compensation
Because this strain gauge is an integral part of the silicon diaphragm, there are no temperature effects due to differences in the thermal expansion of the strain gauge and the diaphragm, as often are encountered in bonded strain gauge pressure sensors. However, the properties of the strain gauge itself are temperature dependent, requiring that the device be temperature compensated if it’s to be used over an extensive temperature range. Temperature compensation and offset calibration can be achieved rather simply with additional resistive components. Several approaches to external temperature compensation over both -40 to +125°C and 0 to +80°C ranges are presented in Motorola Applications Note AN 840 (Schwartz, Derrington, and Gragg, ooo). FIG. 27 shows a practical circuit for a digital pressure gauge.
The simplest method of temperature compensation, placing a resistance (R19 and R20) in series with the sensor driving voltage, is utilized in FIG. 27. This provides good results over a temperature span of 0-80°C, yielding a 0.5% full-scale span-compensated device. Since the desired bridge driving voltage is about 3 V, placing the temperature compensating resistor in series with the bridge circuit has the additional advantage of reducing the power supply voltage, 15 V, to the desired 3 V level. Note that the 15 V power source must be held to within a tight tolerance, since the output voltage of the transducer is ratiometric with the supply voltage. In most applications, an ordinary fixed 15 V regulator chip can be used to provide the required stable supply voltage.
The series method of compensation requires a series resistor which is equal to 3.577 times the bridge input resistance at 25°C. The range of transducer resistance is between 400 and 550 f2, so the compensating network will be 1431-1967 f2. If a temperature compensated span of greater than 4-0.5% is satisfactory or the operating temperature range of the circuit is less than 80°C, one value of compensating resistance can be used for any sensor resistance over the range 400-550 f2. In the circuit of FIG. 27, the temperature compensating network is composed of two resistors to allow the quiescent voltage of the sensor at pins 2 and 4 to be near the center level (2.5 V) of the analog and digital circuit that follows.
5.5.1.2 Signal Amplification
To amplify the transducer output (60 mV at 100 psi) to a useful level that can drive subsequent circuitry, common opamps such as LM324 could be used.
The circuit in FIG. 27 shows the application, which allows means to null out the DC offset output voltage of the transducer when no pressure is applied. The high input impedance of the IC1 ensures that the circuit does not load the basic transducer. In the practical circuit of FIG. 27, the differential output of the instrumentation amplifier is fed to the ADC (IC2), to provide a digital readout of the pressure difference impressed on the transducer. (Motorola Application Note AN-1105).
5.5.1.3 Signal Conditioning for Uncompensated Pressure Sensors
Today's unamplified solid-state sensors typically have an output voltage of tens of millivolts (Motorola's basic 10 kPa pressure sensor, MPX10, has a typical full-scale output of 58 mV, when powered with a 5 V supply). Therefore, a gain stage is needed to obtain a signal large enough for additional processing. This additional processing may include digitization by a microcontroller's analog-to-digital converter, input to a comparator, and the like.
An instrumentation amplifier for pressure sensors should have a high input impedance, a low output impedance, differential to single-ended conversion of the pressure-related voltage output, and high gain capability. In addition, it will be useful to have the gain adjustment without compromising common mode rejection and both positive and negative DC-level shifts of the zero pressure offset.
Varying the gain and offset is desirable since full-scale span and zero pressure offset voltages of pressure sensors will vary somewhat from unit to unit.
Therefore, a variable gain is desirable to fine tune the sensor's full-scale span, and a positive or negative DC-level shift (offset adjustment) of the pressure sensor signal is needed to translate the pressure sensor's signal-conditioned output span to a specific level (e.g., with the high and low reference voltages of an ADC). Pressure sensor interface circuits may require either a positive or a negative DC-level shift to adjust the zero pressure offset voltage. As described previously, if the signal-conditioned pressure sensor voltage is an input to an ADC, the sensor's output dynamic range must be positioned within the high and low reference voltages of the ADC; that is, the zero pressure offset voltage must be greater than (or equal to) the low reference voltage and the full-scale pressure voltage must be less than (or equal to) the high reference voltage (see FIG. 28(a)). Otherwise, voltages above the high reference will be digitally converted as 255 decimal (for an 8-bit ADC), and voltages below the low reference will be converted as 0. This creates nonlinearity in the analog-to-digital conversion.
FIG. 28 Sensor signal conditioning: (a) positioning the sensor's full-scale
span within the ADC's or amplifier's dynamic range, (b) a suitable two
amp signal conditioning stage
A similar requirement that warrants the use of a DC-level shift is to prevent the pressure sensor's voltage from extending into the saturation regions of the operational amplifiers. This also would cause nonlinearity in the sensor output measurements. For example, if an opamp powered with a single-ended 5 V supply saturates near the low rail of the supply at 0.2 V, a positive DC-level shift may be required to position the zero pressure offset voltage at or above 0.2 V. Likewise, if the same opamp saturates near the high rail of the supply at 4.8 V, a negative DC-level shift may be required to position the full-scale pressure voltage at or below 4.8 V. It should be obvious that, if the gain of the amplifiers is too large, the span may be too large to be positioned within the 4.6 V window (regardless of ability to level shift the DC offset). In such a case, the gain must be decreased to reduce the span.
FIG. 28(b) shows a suitable two-amplifier signal conditioning state with variable gain and a negative DC-level shift capability (Jacobsen and Baum, Motorola Application Note AN-1525). Complete analysis of the circuit is beyond the scope of the section. For further details, Jacobsen and Baum (AN-1525, 1995) and Jacobsen (1996).
5.5.2 Calibrated and Temperature Compensated Pressure Sensors
To provide precise span, offset calibration, and temperature compensation, basic sensor elements such as Motorola's transducer could be supplemented with special circuitry within the sensor package. An example of such a device family is the MPX2000 series pressure transducers from Motorola. The MPX2000 series sensors are available both as unported elements and as ported assemblies suitable for pressure, vacuum, and differential pressure measurements in the range 10-200 kPa.
FIG. 29 The MPX2000 series: (a) sensor block diagram, (b) arrangement
of thermistors and laser-trimmed resistor sensors. (Motorola Inc.)
FIG. 29 is a block diagram of the MPX2000 series sensors, showing the arrangement of seven laser-trimmed resistors and two thermistors used for calibration of the sensor for offset, span, symmetry, and temperature compensation.
5.5.3 Signal-Conditioned Pressure Sensors
In this category of sensors, additional circuitry is added for signal conditioning (amplification), temperature compensation, calibration, and the like, so that the user needs fewer additional components. An example of such a sensor family from Motorola is the MPX5000. These sensors are available in full-scale pressure ranges of 50 kPa (7.3 psi) and 100 kPa (14.7 psi). With the recommended 5.0 V supply, the MPX5000 series produces an output of 0.5 V at no pressure to 4.5 V at full-scale pressure. (See Table 4 for the MPX5100DP's electrical characteristics.)
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TABLE 4 MPX5100DP electrical characteristics
Characteristics Symbol Minimum Typical Maximum
Pressure range (kPa) Pop 0 --100 Supply voltage (V) V s --5.0 6.0 Full-scale span (V) VFSS 3.9 4.0 4.1 Zero pressure offset (V) Vow 0.4 0.5 0.6 Sensitivity (mV/kPa) S m 40 Linearity (%FSS) ---0.5 --0.5 Temperature effect on span (%FSS) m -1.0 m 1.0 Temperature effect on offset (mV) ---50 0.2 50
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FIG. 30 A fully integrated pressure sensor.
These sensors integrate on-chip bipolar op-amp circuitry and thin-film resistor networks to provide high-level analog output signal and temperature compensation. The small form factor and high reliability of on-chip integration make these devices suitable for automotive applications such as manifold absolute pressure sensing. FIG. 30 is a schematic of the fully integrated pressure sensor.
To explain the advantage of signal conditioning on chip, refer to FIG. 31.
FIG. 31(a) is a schematic of the circuitry to be coupled with an MPX2000 series (which is compensated for temperature and calibrated for offset) to achieve ground referenced output with amplification.
Some devices similar to the MPX5100 go one step further by adding the differential-to-ground referenced conversion and the amplification circuitry on chip. This reduces the 18-component circuit in FIG. 31 (a) to a 1-signal conditioned sensor, as shown in FIG. 31 (b). FIG. 32 is a schematic of a fully integrated pressure sensor such as the MPX5100.
FIG. 31 Simplification of external circuitry by internal signal conditioning:
(a) high-level ground referenced output using an MPX2000 series transducer,
(b) similar output-integrated device. (Motorola Inc.)
FIG. 32 A fully integrated pressure sensor.
5.5.4 Interface Between Pressure Sensors and Microprocessors or ADCs
In many practical situations, designers face the need to provide an interface between pressure sensors and microprocessors or microcontroller-based systems.
In such cases, the designer should consider the level of on-chip signal conditioning or on-chip temperature compensation/calibration available in designing the system. In sensors with on-chip calibration and temperature compensation, the basic block diagram of a system could be depicted as in FIG. 33.
FIG. 33 A basic block diagram for the interface between a compensated
sensor and an ADC and microprocessor unit (MPU). (Motorola Inc.)
When on-chip calibration and temperature compensation are not available, the gain stages shown need be designed to take care of such needs. While processor techniques are similar to other applications, such as temperature sensors, there are many advanced techniques for higher resolution or compensating for the offset and temperature. For such examples, see Schultz (Motorola AN-1318), Burri (Motorola AN-1097), Lucus (Motorola AN-1305), and Winkler (Motorola AN-1326). When configuring silicon pressure sensors with ADCs or microcontrollers with built-in ADCs, the ratiometric function of both the ADC and sensor could be used to minimize the need for additional components such as voltage reference sources. The ratiometric function of these elements makes all voltage variations from power supply rejected by the system.
The many advance techniques of using microcontroller-based sensor systems are beyond the scope of this section. Four Motorola application notes above describe such practical and useful techniques.