Sensor Systems PDF - Electronics Engineering

SENSOR SYSTEMS From Prof. F. Villa Lectures Electronics Engineering Politecnico di Milano  Sensor Systems Electronics Engineering Lenzi Francesco, Donato Carlo Giorgio Politecnico di Milano Academic Year 2022-2023 Released und...

SENSOR SYSTEMS From Prof. F. Villa Lectures Electronics Engineering Politecnico di Milano  Sensor Systems Electronics Engineering Lenzi Francesco, Donato Carlo Giorgio Politecnico di Milano Academic Year 2022-2023 Released under Creative Commons license BY-NC-SA 4.0 1 From prof. Federica Villa lectures of Sensor Systems free copy Contents 1 Sensors systems basics 3 1.1 Definitions........................................ 3 1.2 Sensor Calibrations................................... 5 2 Light Sensors 6 2.1 Photodiode....................................... 7 2.2 Other photodiode architectures............................ 14 2.3 Light Dependent Resistor (LDR)........................... 15 3 Image Sensors 16 3.1 Charge Coupled Devices................................ 16 3.2 CMOS active pixel sensors............................... 23 4 Temperature Sensors 26 4.1 Resistance Temperature Detector (RTD)....................... 26 4.2 Thermistors....................................... 33 4.3 Thermocouple...................................... 35 4.4 RTDs, thermistors and thermocouples: a comparative table............ 39 4.5 Diode and bandgap temperature sensors....................... 39 4.6 Infrared thermometer.................................. 41 5 Magnetic Field Sensors 46 5.1 Hall Sensors....................................... 46 5.2 Magneto-Resistive sensors............................... 47 6 Strain and Force Sensors 52 6.1 Resistive Strain Gauge................................. 52 6.2 Piezoelectric Force Sensors............................... 54 7 Displacement and Distance Sensors 57 7.1 Potentiometer...................................... 57 7.2 Capacitive sensors................................... 58 7.3 Inductive sensors.................................... 62 7.4 Acoustic sensors.................................... 65 7.5 Optical sensors..................................... 68 7.6 Displacement Encoders................................. 70 7.7 Magnetic Sensors.................................... 71 8 Microphones 72 8.1 Microphones Classification............................... 73 8.2 Microphones dimensions................................ 75 8.3 Microphone capsules.................................. 76 8.4 Mechanic Contribution................................. 77 8.5 Dynamic Microphones................................. 78 written by Francesco Lenzi & Donato Carlo Giorgio Page 2 From prof. Federica Villa lectures of Sensor Systems free copy 1 Sensors systems basics A sensor system is composed of a sensing part and a processing part. Indeed, multiple sen- sors interact with a processor (a Micro-Controller Unit, MCU), which allows access to the sensors ensemble through a single access interface. The sensors acquire the signals that describe the physical phenomena in our scope with some readout electronics and send the information to the micro-controller. If a sensor embeds an Analog-to-Digital converter and a small processing unit that can communicate through simple communication protocols, it is called a Smart Sensor. 1.1 Definitions Transducer: a device which transforms energy from one type to another, even if both energy types are in the same domain. – Typical domains are mechanical, electrical, chemical, magnetic, optical and thermal. Transducers can be further divided into Sensors and Actuators. Sensor: a device which monitors a parameter of a system, hopefully without disturbing that parameter. (Other domains to electrical domain). Actuator: component of machines which is responsible for moving or controlling a mech- anism or system. (Electrical to any domain). An example of a system is the Sensor-Electronics-Actuator chain, in which a physical quantity is sensed and the signal is processed by electronics to control an actuator. This chain can work in a loop (we sense the physical quantity that we control through the actuator) or not. Sensors classifications Sensors can be classified by the physical phenomena that they measure or by the used measuring mechanism. Those classification overlap. For example, a resistive sensor can measure stress (strain gauges), temperature (thermistors) etc... 1.1.1 Sensor characterization Sensitivity It is the ratio between the change in the output signal to a small change in the input physical signal. It can be interpreted as the slope of the input-output fit line: ∂Out ∆Out S= ≃ → ∆Out = S · ∆In ∂In ∆In Resolution (LSB) It is the smallest increment of measure that a device can make. If we have a smart sensor (embedded ADC) it is represented by the Least Significant Bit. Full Scale Range (FSR) It is the maximum measurable interval, after it the measure satu- rates. It can be limited both by the electronics or by the sensor. written by Francesco Lenzi & Donato Carlo Giorgio Page 3 From prof. Federica Villa lectures of Sensor Systems free copy Number of bits (n) In sensors that have a digital output 2n is the number of levels in which the FSR is divided: F SR 2n = LSB Accuracy It is the error between the result of a measurement and the true value. Precision (or Repeatability) It is the sensor’s ability to output the same value for the same input over several trials. Linearity It is the deviation of the output from a best-fit straight line for a given range of the sensor. The more a sensor is linear, the more the approximation to finite variations (with ∆) of the sensitivity equation done above is correct. There are two kinds of non-linearity: Differential Non-Linearity (DNL) and Integral Non-Linearity (INL). The former is the difference between the ideal range of values represented by a bit code and the ac- tual one (e.g. the code 00101011 represents a value that ideally is in an LSB interval), the latter is the distance between the ideal measured value and the actual one. i X DN L(i) = ∆in(i) − LSB IN L(i) = DN L(k) k=1 Transfer Function (frequency response) It is the relationship between the physical input signal and the electrical output signal, which may constitute a complete description of the sensor characteristics as a function of frequency. It is generally represented by Magnitude and Phase Bode Diagrams. Bandwidth It is the frequency range between the lower and upper cutoff frequencies (i.e. the frequencies in which we have a -3dB attenuation from the flat region), within which the sensor transfer function is constant gain or linear. written by Francesco Lenzi & Donato Carlo Giorgio Page 4 From prof. Federica Villa lectures of Sensor Systems free copy Noise It is the random fluctuation in the measured value. It can assume different frequency behaviours (e.g. white noise is flat in frequency, 1/f noise is infinite in DC, etc... ). It is quantified with its RMS (root mean square) value and limits the minimum acquirable signal. Dynamic Range It is the ratio of maximum measurable input amplitude (limited by the FSR) to minimum input amplitude (limited by LSB or the noise): INmax DR|dB = 20log( ) INmin 1.1.2 Sensors readout To readout the acquired signal there is a need for an Analog-to-Digital converter and some signal processing elements. The simplest one is the ADC and micro-controller configuration, which employs a micro-controller to process the signal. Most micro-controller units have an embedded ADC ready to use. Another kind of readout is done through Data Acquisition Cards (DAQ) connected to a personal computer with USB interface. Those cards have analog and digital I/Os and can interface through LabVIEW or user-generated code. Smart sensors, which have some pre-built-in processing and communication electronics, have their own digital outputs that make use of communication protocols. Those can be either parallel (not easy to manage and so not actually used) or serial (1 bit at a time). Serial I/O interfaces can be either: Synchronous: they have at least a clock and a data wire. They must match byte format, stop/start bits, parity check, etc... – Serial Peripheral Interface (SPI) which has 3 signals: clock, bidirectional data and chip select; – Inter-Integrated Circuit (I2 C) which has 2 signals: clock and data; Asynchronous: they don’t make use of a clock. They must match the baud rate and bit width, transmission protocol, etc... – UART: setting a baud rate, we can send the data following the protocol; – Frequency Encoded: measures pulse width and frequency (e.g.: PWM). 1.2 Sensor Calibrations Some non-ideal behaviours of the sensor can be corrected in post-processing, i.e. by calibrating the sensor’s electronics readout. Those non-idealities are offsets, for which the measured output has a constant difference with the real value, non-linearities, which can be corrected if known, and cross-parameter sensi- tivities, which is an output variation due to the variation of a physical quantity that we don’t want to measure (e.g. temperature drifts). To calibrate the sensors we can use analog signal conditioning (e.g. differential readouts), look-up tables and digital, post-processing calibrations. written by Francesco Lenzi & Donato Carlo Giorgio Page 5 From prof. Federica Villa lectures of Sensor Systems free copy 2 Light Sensors Light sensors are devices that can sense light by measuring its intensity or just its presence. The physical principle on which they rely is the light-assisted electron-hole couplet generation. Basics Semiconductors have their molecules organized in reticular structures in which the molecules are bonded together by sharing electrons. Those electrons, if excited with the right amount of energy can jump out of the bond and travel along the material. When the electron jumps out of the bond, not only a negative free charge is generated, but also a positive one, because the molecule without an electron is left with a positive charge. This phenomenon is an electron-hole couplet generation. The creation of free charge makes the creation of current easier: the conductivity rises (the resistivity lowers). Moreover, we can make the semiconductor have an excess of charge per se by introducing in the reticular structure some atoms which have a different number of electrons: doping. If we add atoms with less electrons (more positive charges in the semiconductor), we call it p doping, and vice versa if we add atoms with more electrons we call it n doping. The diode If we put in contact a p-doped and an n-doped semiconductor, the electrons near the interface of the n-type material will diffuse across the junction to fill the holes in the p-type material. This diffusion process creates a region of negative ions in the p-type material and a region of positive ions in the n-type material, those two regions are depleted from free carriers and are therefore called depletion region. The depletion region is a region where no free charge carriers exist, and therefore it acts as an insulator (no current). Moreover, since there is some fixed charge, there is an intrinsic voltage difference across the junction, which is called Built-in voltage ϕbi. However, if a voltage is applied to the diode in the for- ward direction (positive terminal connected to the p-type material and negative terminal connected to the n-type material), the electric field created by the applied voltage will reduce the width of the depletion region. If the voltage is high enough to overcome the potential barrier created by the depletion region, i.e. the built-in voltage, electrons and holes will be free to flow from the n-type material to the p-type material, creating a for- ward current through the diode. This is called forward operation. On the other hand, if a voltage is applied to the diode in the reverse direction, the depletion region widens, and the applied voltage increases the potential barrier, preventing electrons from flowing across the junction. Therefore, a reverse current in a diode is very small, and it acts as an insulator. This is called reverse operation. written by Francesco Lenzi & Donato Carlo Giorgio Page 6 From prof. Federica Villa lectures of Sensor Systems free copy If however, the reverse voltage is too high, the electric field can be so high that more electron-hole couplets are generated and the diode becomes highly conductive again. This is called breakdown operation and the reverse voltage threshold to the breakdown is called breakdown voltage. 2.1 Photodiode 2.1.1 Photodiode physics (a) The photodiode operation. (b) The photodiode characteristics. Figure 1 The photodiode operates by light-assisted electron-hole pair generation. Indeed, light is a wave that has an energy that can excite the electron and generate the couplet. To make the photodiode work, we bias it with a reverse voltage VR less than the breakdown voltage, to make the depleted region as large as possible. The couplets generated in the depleted region from the light’s energy will be accelerated to the contacts, as shown in 1a, generating a photocurrent. The pairs generated in the P and in the N regions will recombine, i.e. will encounter some other free carriers that have the opposite charge and nullify each other.1 The photocurrent has a reverse current direction (goes from negative to positive contacts) and in- creases as shown in 1b along with the light intensity (optical power). In the figure we note that there is a current I0 even when there is no light impinging on the photodiode, this is called dark current and is due to couplets thermally generated. 1 Physically, when a free electron and a free hole encounter, the electron goes in the place of the hole and re-establishes the molecular bonding. written by Francesco Lenzi & Donato Carlo Giorgio Page 7 From prof. Federica Villa lectures of Sensor Systems free copy Figure 2: left: PN photodiode right: PIN photodiode Some typical structures of photodiodes are the ones shown in figure 2. In particular, one widely used structure is the PIN structure, where an intrinsic2 region is placed in between the two highly doped regions. In this way we have two advantages: in the first place we have more depleted region, since the whole intrinsic region will be depleted, and secondly, we will have a lower capacitance due to the diode. In fact, in the reverse-biased diode we have a situation much similar to the capacitance model: we have two conductive plates and an insulating layer that stores some electric field (the depleted region). Using the capacitance model, being dins the distance between the plates, Apd the surface area of the photodiode, and εins the dielectric constant in the insulator: Apd C = εins dins Therefore, the more the depleted region deep, the lower is the capacitance, and this accelerates our electrical readout time. Another important parameter to take into ac- count is the light penetration depth. The light penetration depth in silicon is the dis- tance that light can penetrate a silicon mate- rial before it is absorbed. It is dependent on the impinging wavelength, as shown in figure 3. It is defined as the depth at which the in- tensity of the radiation inside the material falls to 1/e (about 37%) of its original value at the surface. Since the light impinges on the photodiode from up to down and we want the light to be Figure 3: Si penetration depth. absorbed in the depleted region, every photo- diode geometry can detect some wavelengths. For example, if we want to measure the presence of green light (λ = 500nm), the penetration depth will be (D ≃ 1µm) and therefore we want a small P region (wP ≪ 1µm), and a depleted region of at least 1µm. It is worth noting that we have a cut-off at about 1000nm for the penetration depth in silicon because larger wavelengths don’t have the energy to generate the couplet, and therefore we would need to use another material. 2 Not doped, or lightly doped semiconductor. written by Francesco Lenzi & Donato Carlo Giorgio Page 8 From prof. Federica Villa lectures of Sensor Systems free copy 2.1.2 Photodiode sensitivity and electrical model Sensitivity The sensitivity of a photodiode is calculated as the ratio between generated photocurrent and the optical power density impinging on the sensor itself, this is called Responsivity. Iph Rλ = Popt The responsivity depends on a variety of parameters, like the incident light wavelength, the applied reverse voltage and the temperature. For what matters the temperature, it affects a variety of parameters of the sensor and therefore, the temperature coefficient varies with the wavelength. We can thus write that: Rλ ∝ λ, VR , T (λ) Figure 4: Photodiode responsivity Electrical model We model the photodiode with the circuit in figure 5 in which we have the following parameters: Iph : Photo-generated current Id : Dark current, thermally generated Cj : Junction capacitance εsi AP D Cj = wdep RSH : Shunt resistance:3 the I/V slope at 0V in the PD characteristics Figure 5: Photodiode electrical model. Rs : Series resistance: the sum of the re- sistance of the contacts and the neutral regions.4,5 (wtot − wdep ) · ρ Rs = + Rc A 3 In the depleted region there are some free carriers, that can conduct current, but since they are few, the resistance is huge. 4 The neutral regions are the doped regions that are not depleted. Since they have a lot of free carriers they have low resistance. 5 ρ is the resistivity and is the inverse of the conductivity. written by Francesco Lenzi & Donato Carlo Giorgio Page 9 From prof. Federica Villa lectures of Sensor Systems free copy 2.1.3 Photodiode noise model and readout circuits Some basics about noise: Noise is a statistical variation of the value we want to measure and it is due to a variety of environmental and device-related h 2i factors. It is represented by its frequency spectrum, which has a dimensionality of Hz , with x physical variable dimension x h 2i (e.g. Hz V if we have voltage noise). To properly use the noise in our calculations, we use the rms (root mean square) value of it, which represents the physical variable’s variance. It is the square root of the integral of the frequency noise spectrum over the whole spectral bandwidth, and it has the dimension of the physical variable of the considered noise (e.g. a voltage noise rms value will be σ = [V ]) Noise models For what matters diodes, we can find two kinds of noise: Thermal (Johnson) noise, due to the Brownian mo- tion of the free charges6,7  2 4kT A2   V SV = 4kT · R SI = Hz R Hz Shot noise, due to the finite charge of the carriers8 SI = 2q · I Since those noises do not depend on the frequency (i.e. are white noises), we can integrate them over our bandwidth of interest as we are calculating a rectangular area: Figure 6: p p Up: Johnson noise Vn = SV · ∆f , In = SI · ∆f Down: Shot noise When we are doing our calculation with power spectral densities, all the transfers have to be squared. Let’s see it by passing from the voltage (Thevenin) model to the current (Norton) model for Johnson noise: SV 4kT R 4kT SI = 2 = 2 = R R R 6 Carriers that move around due to thermal energy can be modeled as a random current or a random voltage. The two models in figure 6 are equivalent. 7 k is the Boltzmann constant. 8 The elementary charge is not infinitesimal: it is quantized as a multiple of the elementary charge, but in our models, we treat the current as a continuous function. This kind of noise takes this model mismatch into account. written by Francesco Lenzi & Donato Carlo Giorgio Page 10 From prof. Federica Villa lectures of Sensor Systems free copy Photodiode noise model Now we can apply those noise models to the electrical model of the photodiode. In this model, we find two current generators, a capacitance and two resistances. Since the capacitance is a dynamic component, we can consider its contribution separately, when we will compute the equivalent bandwidth9. Hence, we will compute the output noise power density in DC (capacitances are open circuits). We have two main contributions to the output noise: Shot noise (from current generators) q Isn = 2q(Iph + Id ) · ∆f Johnson noise (from the resistances) s s 2 Rsh 4kT 4kT Ijn ,Rsh = 2 ∆f ≈ ∆f Rsh (Rsh + Rs ) Rsh s s r 4kT Rs2 4kT Rs Rs Ijn ,Rs = ∆f ≈ ∆f ≃ Ijn ,Rsh · Rs (Rsh + Rs )2 Rsh Rsh Rsh In particular, note that, since Rs ≪ Rsh , the shot noise current from the generators will mostly go in the series resistance than in the shunt resistance. This is explicitly shown in the resistance thermal noise contribution, where the current dividers are approximated. Note that we have not calculated ∆f , and this value can show a frequency dependence in our final readout noise calculations. Noise Equivalent Power (NEP) In some datasheets, the noise contributions are not shown one by one, but another engineering parameter is given: the Noise Equivalent Power. It is defined as the amount of optical power impinging on a photodetector to generate a current larger than the noise current, i.e. to have a signal-to-noise ratio bigger than one. It is strictly related to the responsivity Rλ. I In In Rλ = = =⇒ N EP = P N EP Rλ Photodiode basic readout circuits Datasheets also provide some simple circuits that we can use to readout the current signal generated by the photodiode. Those are based on operational amplifiers. We will see three basic readout circuits: Non-inverting configuration Transimpedance Amplifier configuration Charge Amplifier configuration (light integrator) 9 To avoid doing integrals, when possible, we compute an equivalent bandwidth so that we can compute the rms noise as the area of a rectangle for every bandwidth. written by Francesco Lenzi & Donato Carlo Giorgio Page 11 From prof. Federica Villa lectures of Sensor Systems free copy Non-inverting configuration In the non-inverting configuration, the photodiode current Isc flows into RL creating a voltage that is amplified by the OP-AMP with the typical non- inverting transfer function, therefore:   Rf Vo = Isc · RL · 1 + R The disadvantage of this configuration is that the voltage across the diode, which is its reverse voltage, changes, and therefore also the responsivity Rλ changes. In particular, the responsivity is reduced while the photocurrent rise. We want a fixed reverse voltage across the photodiode. Transimpedance Amplifier configuration To solve this problem, an inverting configuration can be used. Indeed the voltage across the photo- diode is fixed by the loop (v+ = v− = 0V ). The photocurrent will flow through the feedback and we can compute the output voltage thanks to the virtual ground at the negative terminal: Vo = Isc · Rf The problem of this configuration is stability because the junction capacitance Cj of the photo- diode modifies the frequency response of the circuit and can create some oscillations in the step response. To avoid this problem, a possible solution is to put a compensation capacitance Cc in parallel to Rf in the feedback that low-pass filters the input signal (we gain stability at the cost of reduced bandwidth). Light Integration (Charge Amplifier configuration) The light integrator can give the integral of the photocurrent at its output. It is composed of a capacitance that integrates the current and a reset switch that discharges the capacitance when the reset signal is on. We can easily demonstrate the integral behaviour of the capacitance: dQ dV Q = C · V =⇒ =I=C dT dt dV ∆V ≈ =⇒ ∆V = · ∆T dt ∆T C < Isc > Vo = ∆T C written by Francesco Lenzi & Donato Carlo Giorgio Page 12 From prof. Federica Villa lectures of Sensor Systems free copy 2.1.4 Photodiode applications Photodiodes are widespread in a vast variety of applications, some of those are: Cameras: Light meters, Auto-focus, Automatic shutter control... Medical: X-ray detection, Pulse oximeters, Blood particle analyzers... Safety equipment: Smoke detectors, Flame monitors, Security systems... Automotive: Twilight detectors, Climate control (sunlight detectors)... Industry: Bar code scanners, Brightness controls, Rotary encoders, Position sensors... Communications: Fiber optic links, Optical communications... For example, in our board, we have an infrared re- ceiver module that can be use for optical commu- nication. The signal is created by flashing a Light Emitting Diode (LED) of our board, modulating its pulses at the right frequency. The receiver module is a smart sensor that has a photodiode covered with a black colour filter so that the responsivity peaks only in the Near Infra- Red (NIR), i.e. 950nm. The readout electronics consists of an Automatic Gain Control (AGC) cir- Figure 7: Infra-Red receiver module. cuit, a Band-pass filter and a demodulator, that ensure the acquisition of only the communication signal. (a) Responsivity. (b) Sensitivity with respect to the angle Figure 8: Some characteristics of our Infra-Red (IR) receiver module. written by Francesco Lenzi & Donato Carlo Giorgio Page 13 From prof. Federica Villa lectures of Sensor Systems free copy 2.2 Other photodiode architectures (a) Avalanche Photodiode (b) Single-Photon Avalanche Photodiode Avalanche photodiode The Avalanche Photodiode (APD) is a kind of photodiode where the disposition of the doped regions and the applied reverse voltage (which is near, but below the breakdown voltage) makes possible the avalanche effect. The avalanche effect verifies when the field in the depleted region is so high that the free carriers generate electron-hole couplets by hitting the diode atoms. The generated couple is likewise accelerated by the high field and can generate another couplet and so on. This makes the APDs have an internal gain, i.e. a single photon can generate a lot of carriers. These character- istics make the APD a good choice when we have a very low signal and we want to achieve a better signal-to-noise ratio against the electronic noise of the readout. For what matter the structure, in the APD we have an absorption region where the first couplets are generated, and a multiplication region where the high field grants ionization by impact. Single-Photon Avalanche Photodiode The Single-Photon Avalanche Photodiode SPAD is an APD where the applied reverse voltage is well above the breakdown voltage. In this way, just a single photon makes the photodiode start generating a lot of current. The output of the SPAD is thus digital (ON or OFF), we can’t distinguish if we have one photon or more. After the detection of one photon, a quenching circuit makes the diode current turn off to bring it into the reset state, ready to detect another photon. written by Francesco Lenzi & Donato Carlo Giorgio Page 14 From prof. Federica Villa lectures of Sensor Systems free copy Silicon Photo-Multiplier If we put more SPADs in parallel in an array, we can create a sil- icon photo-multiplier (SiPM): in this way we have a discrete output, proportional to the number of impinging photons. 2.3 Light Dependent Resistor (LDR) A Light Dependent Resistor (LDR) is a type of resistor that changes its resistance in response to changes in light intensity. It is also known as a photo-resistor or photocell. The working principle of an LDR is based on the photo-conductivity effect, where the resistance of a semiconductor material changes when exposed to light: the energy of the photons is absorbed by the material, which causes an increase in the number of free charge carriers in the material. The presence of free charge carriers increases the material conductivity, i.e. reduces the resistance of the LDR. The resistance of an LDR is measured in Ohms [Ω] and its sensitivity is low, strongly non-linear, material dependent and strongly temperature dependent. For this reason, the LDRs are often used as cheap light ON/OFF detectors. Figure 10: Light-Dependent Resistor characteristic example. written by Francesco Lenzi & Donato Carlo Giorgio Page 15 From prof. Federica Villa lectures of Sensor Systems free copy 3 Image Sensors Image sensors are, in general, a system composed of a multitude of sensors, called pixels, so that they can capture a scene and convert it in a series of electrical signals. There are two kinds of image sensors: Charge Coupled Devices (CCDs); CMOS active pixel image sensors. 3.1 Charge Coupled Devices 3.1.1 CCD physics Those kind of devices have pixels based on the MOS capacitor, which is composed of a PN junction and an insulator at the cathode (n doped contact). Figure 11: CCD structure and the equivalent model Because of its structure, we can model the CCD pixel like a photodiode with a capacitance10 in series at the cathode. In this way, by biasing the photodiode with reverse voltage, as shown in figure 11, when the light impinges on the depleted region, the generated free charge collects on the capacitance plates instead of creating a current.11 The result is that a voltage drop is created across the insulator and, the higher the voltage, the higher the charge and thus the optical intensity. Note that the CCD has more than one electrode and only the central one is biased when collecting the photogenerated charge. 10 Recall: a capacitance is composed of two conductive plates and an insulator in between. 11 The carriers cannot cross the insulator. written by Francesco Lenzi & Donato Carlo Giorgio Page 16 From prof. Federica Villa lectures of Sensor Systems free copy 3.1.2 CCD pixel architecture, structure and readout Figure 12: CCD architectures: front side illuminated vs. back side illuminated There are two possible architectures of the CCD pixel which are differentiated from the side from which they detect light. The front-side illuminated architecture is the standard one, where the n type doped silicon is grown on a thick p type substrate and then the insulator and the electrodes are placed on top. The problem here is that the electrode has to be transparent because if they absorb light, the responsivity drops. The back side illuminated architecture is more laborious to make. Indeed, after the standard fabrication process, the wafer is flipped and the substrate is thinned. In this way, since the thinned substrate is strongly planar, an Anti-Reflective (AR) coating is put on top of the wafer, so that almost all the light is absorbed. Moreover, having the electrodes on the bottom, we can easily reach the contacts without covering the pixel with wires (reducing the absorbed light). (a) CCD structure. (b) CCD readout scheme. Figure 13 written by Francesco Lenzi & Donato Carlo Giorgio Page 17 From prof. Federica Villa lectures of Sensor Systems free copy Structure The CCD structure is shown in figure 13a, where the pixels are in columns are connected (they share the same structural parts), and they are distinguished only by the active pads (the central one is biased to collect the photogenerated charge). The rows instead are divided by channel stops, that are highly doped semiconductors that avoid the passage of charge between rows. Therefore each column has one biased and two unbiased electrode, in an alternate way. Thus, every row that collects charge is surrounded by two unbiased electrodes: we have a grid of "Charge Wells". Readout The readout operation is shown in figure 13b: first, the charge is transferred verti- cally, by biasing the alternative electrodes, and then the charge is transferred horizontally. In this way, we read the charge one pixel at a time, column by column and row by row. Note that if we want to read one pixel we need to make the charge travel along the whole vertical-horizontal path, therefore some pixels are readout faster than others. The charge transfer process is shown below in figure 14. Figure 14: CCD charge transfer process. Note that we need three electrodes and not only two because during the charge-sharing phases of the charge transfer (i.e. steps 2, 4 and 5 in figure 14) we need to have at least one unbiased electrode to avoid the charge relative to one pixel mixes with the one relative to the adjacent ones. written by Francesco Lenzi & Donato Carlo Giorgio Page 18 From prof. Federica Villa lectures of Sensor Systems free copy 3.1.3 CCD characterization and performance We can subdivide the characterization of charge-coupled devices into four quality parameters: charge generation, charge collection, charge transfer and charge readout. Charge generation Sensitivity: quantum efficiency The charge generation is the ability of the charge-coupled device to collect photons in order to generate charge. This capability is expressed by the Quan- tum Efficiency (QE), which varies with the impinging light wavelength. The quantum efficiency is the probability that an electron is released for each incident photon:12 detected photons #e− QE = = incident photons #ph As for responsivity,13 the mechanisms that hamper the photon collection (i.e. the quantum efficiency) are: surface light reflection, light absorption in non-active areas and transmission from active areas to elsewhere. Fixed pattern noise The quantum efficiency is not the same for all the pixels of the CCD camera because of process non- uniformities: differences in thickness, electrode area, doping and bias. Those non-uniformities create the so-called Fixed Pattern Noise. Fortunately, since those are deterministic for a particular device, they can be calibrated by taking a picture of a uniformly illuminated flat surface and adjusting the bias of every single pixel to get a uniform image. Dark Current As for all devices that make use of semiconductors, there is some current which is being generated from the thermal effect: the thermal energy excites the molecular structure of the device generating electron-hole couplets. Obviously, this phenomenon is temperature dependent. The majority of dark current is created near the interface between the Si and the SiO2 insulator, where the interface quantum states, which are at an energy level between the valence and conduction bands, act as a stepping stone for electrons. Charge collection Well Capacity and Saturation The charge collection capability of a charge-coupled device pixel is defined by its Well Capacity. This is the maximum amount of charge that can be held e− in a pixel and typically is around 10000 µm 2 , i.e. few hundred electrons per pixel. If the amount of charge exceeds the well capacity, we incur Saturation. As a rule of thumb: if we are at 80% of well capacity, we get a non-linear response, while if we are at 100% of well capacity, we incur in blooming. 12 The QE is a probability: we can assume it as a percentage value. Iph 13 #e− J q hc QE and responsivity are strictly related, in fact: QE = #ph = Φph = Popt =⇒ QE = Rλ · qλ hc λ written by Francesco Lenzi & Donato Carlo Giorgio Page 19 From prof. Federica Villa lectures of Sensor Systems free copy (a) Unwanted charge sharing. (b) Blooming image of stars. Figure 15 Blooming It occurs when the pixel’s charge exceeds the well capacity and thus the photogen- erated charge spills over other pixels as shown in figure 15a. The charge bleed occurs mainly among columns and lightly on rows, because of channel stoppers. Charge transfer Charge Transfer Efficiency The ability to transfer charge from one pixel to the other during the readout phase is defined by the Charge Transfer Efficiency (CTE). It is the fraction of transferred electrons from one pixel to the next one and it is typically 99.99% ÷ 99.9999%. Since those numbers are not so manageable, it is often used the Charge Transfer Inefficiency (CTI), defined as the fraction of electron deferred by one pixel, i.e. CT I = 1 − CT E. One of the factors that cause inefficiency is the presence of defects in the silicon crystal lattice that capture (trap) the free charges. Note that, because of this phenomenon, the last read pixel is the most inef- ficient one. E.g. with CT E = 0.99999 and 12M pixels, i.e. about 3500x3500 pixels (7000 transfers in the worst case): CT I = 1 − 0.999997000 = 6.7%. Since this phenomenon is deterministic, it can be calibrated. Charge transfer defects Some other defects are Dark Columns, due to some pixels that don’t collect charge (e.g. broken electrodes) and so "trap" all the charge from the pixels higher than it (they can’t transfer), creating a dark column. Another kind of defect due to "trap" pixels is Bright Columns, due to the inability of some pixels to transfer charge (e.g. broken electrodes). At some points, this charge leaks out of the pixel, going to the adjacent ones and creating a bright column. Lastly, there are Hot Spots, which are small white areas in the image created by pixels that have a higher than normal dark current. Those increase with the increase of the charge integration time we select. In the extreme case, the current is so high in some pixels that they start emitting light by themselves and this light is sensed by the adjacent ones (light emitting defects). Note that all those defects can be eliminated in the final image with calibrations such as pixel interpolation (interpolation among adjacent pixels) because those defects are deterministic. written by Francesco Lenzi & Donato Carlo Giorgio Page 20 From prof. Federica Villa lectures of Sensor Systems free copy Charge readout The last step for the acquisition of an image from a charge coupled device camera is the electronic readout. In figure 16a it is shown a simple readout circuit composed of a MOS transistor in source follower configuration. The charge coming from the pixels, one by one, is integrated in the integration capacitance and the corresponding voltage reading is given at the source follower output. (a) CCD simple readout circuit. (b) CCD readout electrons rms. Figure 16 Readout noise The limiting factor in the readout is definitely the amplifier noise. Since it is fixed by the amplifier manufacturer, the only ways to reduce it are: √reducing the circuit bandwidth and increasing the integration time. In fact, since σn = Sv · ∆f , a decrease in ∆f corresponds in a decrement in the rms noise. This corresponds also to reducing the sampling frequency, in fact, as shown in figure 16b, the noise ramps up when the frequency increases. From the image we can see that the noise in rms electrons: it is very low for frequencies below 500khz (i.e. 2µs). However, this corresponds to a large acquisition time, in fact, assuming a 12 Mpixel camera: Tread = 2µs · 12 · 106 = 24s which is unbearably high for most applications. Reset noise For the configuration shown in figure 16a, we have a reset noise due to the so- called KTC noise. This noise appears every time we have an RC network. In fact, considering the voltage noise of a resistance SR = 4kT R, the equivalent bandwidth14 is ∆f = 4RC 1 , therefore: √ r r 1 kT Q=C·V σv,n = 4kT R = =====⇒ σq,n = C · σv,n = kT C 4RC C The reset noise is noise due to the voltage fluctuation due to KTC noise that makes us start the integration over the capacitance with a non-zero voltage baseline. To avoid it we use the Correlated Double Sampling, for which we sample the output both before and after the integration, so that we can remove the baseline. 14 As said in section 2.1.3 in footnote 9, the equivalent bandwidth can be computed by equating the integral of the Lorentzian function (i.e. the transform of the negative exponential, the time response of the RC low pass R +∞ 2 1 filter) to a rectangle area: Sw · ∆f = −∞ Sw 1+s·RC ds written by Francesco Lenzi & Donato Carlo Giorgio Page 21 From prof. Federica Villa lectures of Sensor Systems free copy 3.1.4 Colour filtering The light has a colour that depends on its wavelength, hence on its energy (E = hc λ ), but the photogenerated charge doesn’t have a colour. For this reason, to discriminate colours we put optical filters (colour filters) on the image sensors. Those filters make every pixel absorb just one colour component of the light impinging on the pixel itself, and therefore have the colour information related to just one colour. To "fill in" the missing colour information, a Demosaicing algorithm, consisting in some kind of interpolation, is used in signal post- processing. Note that the colour filter array (CFA) used in figure is composed of mostly (66%) green tiles. This kind of CFA is called Bayer array and takes into account that the human eye is more sensitive to the green wavelength. 3.1.5 Types of CCDs The functioning principle of the charge coupled device cameras makes it so that during the integration phase the pixels have to not absorb any light to avoid altering the previous image. To this aim, there are several types of CCD cameras, as shown in figure 17. Figure 17: Types of CCD sensors. The first one (from left to right) is the Full Frame one, where the entire chip is exposed to the light and covered by a mechanical shutter during the readout phase. The second one is the Frame Transfer architecture, where there is an image array that collects the charge and stores it in a covered storage array in a fast way, and the readout is done slowly (as usual) from the storage array. It has the advantage of exploiting a kind of pipeline operation so that it can almost continuously acquire the image and also no shutter is needed. However, this architecture suffers from halved resolution (only half the chip is used to acquire the image). The last one is the Interline Transfer architecture, where, similarly to the frame transfer one, half of the pixels are used just for the readout, but they are organized in columns. In this way, the transfer is faster, but the fill factor (ratio between the active are and the total one) is halved. To solve the fill factor problem, one solution is the usage of optical microlenses that focus the light just on the photon-absorbing pixels. written by Francesco Lenzi & Donato Carlo Giorgio Page 22 From prof. Federica Villa lectures of Sensor Systems free copy 3.1.6 CCD cameras applications The functioning principle and the structure of the charge coupled device cameras makes that they have the advantage of having a very high Fill Factor: since there is no readout electronics in situ for every pixel, the photon-absorption area can be almost the whole sensor area. However, this comes at a cost: for the same reason indeed the readout relies on slow charge- sharing transients that make those devices suitable for few applications, mostly industrial or scientific. Some of them are: Microscopy and biology; Astronomy and astro-photography; Infrared photography (e.g. for VLSI testing)... 3.2 CMOS active pixel sensors 3.2.1 3T active pixel structure and electrical model The CMOS active pixel sensor is an image sensor based on the standard photodiode that performs the photo-generated charge-to-voltage conversion directly in every pixel. For this reason, the CMOS active pixel is composed of the photodiode and at least three readout transistors. (a) CMOS pixel cross-section. (b) CMOS pixel electrical model. Figure 18 As we can see in figure 18b, the structure of a 3T APS is composed of a photodiode that generates a charge that will be integrated into the stray capacitance15 at the gate node of the buffer transistor M2, creating a voltage proportional to the charge at its gate equal to the one at it’s source. Then, there are: the row select transistor M3 which enables a row-by-row readout of the whole image sensor, and the reset transistor, which activates to refresh the charge on the integration capacitance right before the image acquisition. Note that, by decoupling the acquisition and the readout, now we have a much higher readout speed, at the cost of the Fill Factor (microlenses are used, as shown in figure 18a). 15 This capacitance is formed by the contributions of the diode capacitance, the gate capacitance of M2 and the gate-source capacitance of M1. written by Francesco Lenzi & Donato Carlo Giorgio Page 23 From prof. Federica Villa lectures of Sensor Systems free copy 3.2.2 CMOS APS Noise For what matters the noise, the 3T active pixel sensor suffers from all the noises we have studied for what matters photodiodes and CCD sensors: Fixed Pattern Noise (FPN) caused by process variations: photodiodes and buffer tran- sistor performance mismatches among the pixels; Since it’s fixed for every sensor, it is corrigible by flat field correction: on-chip subtrac- tion of an image with constant illuminant; Reset noise i.e. KTC noise Amplifier noise, dependent on the frequency with a 1/f trend; Shot noise as for every photodiode application. 3.2.3 CMOS sensor structure and readout Sensor structure The great advantage of CMOS sensors with respect to CCDs is the usage of CMOS process. Indeed, it is hugely simpler to integrate faster electronics within the sensor, and make a sensor-electronics co- design, thus smart sensors. In addition, the backside- illuminated technology is still available for this kind of sensor. In figure, you can see an example of an integrated CMOS smart sensor provided with in situ image pro- cessing. Readout modes For what matter the readout of the image, there are two possible solutions: Rolling shutter: Each frame is captured by scanning the rows across the scene rapidly: not all parts of the image of the scene are recorded at the same instant. This produces predictable distortions when acquiring fast-moving objects or rapid flashes of light. Global shutter: The entire frame is captured at the same instant. This grants better results for moving images, but it’s overall slower and a lot of electronics is involved. Moreover, since the readout is done at the pixel site, the user can choose to readout only a part of the pixel to achieve higher frame rates. In fact, we can use a smaller window of interest (a subset of adjacent pixels) or a window subsampling (a subset of non-adjacent pixels) to readout faster at the cost of less resolution. written by Francesco Lenzi & Donato Carlo Giorgio Page 24 From prof. Federica Villa lectures of Sensor Systems free copy 3.2.4 CMOS APS applications The higher speed with respect to the CCD cameras makes the CMOS cameras suitable for a wider range of applications, from consumer to medical and industrial. Some possible applications are: High volume imagers for consumer applications (e.g. phone cameras and webcams); Imagers for machine vision; High speed motion capture cameras; Digital radiography; Endoscopy... 3.2.5 CCD vs. CMOS image sensors In conclusion, comparing the CCD and the CMOS image sensors we can find that: The advantages of CCD image sensors are uniformity, the highest fill factor and higher near- infra-red sensitivity. The advantages of CMOS image sensors are the faster readout, the selectable active window (for higher frame rate), the already digital output, the fewer electronics outside the sensor and the less power consumption. All in all, we can say that the CCD image sensors are more suitable for a custom imager, while the CMOS ones are the right choice for large scale economy applications. Figure 19: Charge coupled device and CMOS image sensors written by Francesco Lenzi & Donato Carlo Giorgio Page 25 From prof. Federica Villa lectures of Sensor Systems free copy 4 Temperature Sensors Temperature sensors are a variety of sensors that can measure the temperature of an object. We will study the following ones: Resistance Temperature Detectors (RTDs); Thermistors; Thermocouples; Diode and bandgap temperature sensors; Infrared thermometers. 4.1 Resistance Temperature Detector (RTD) An RTD is a device which contains a metallic electrical resistance (referred to as a “sensing element” or “bulb”) that changes resistance value depending on its temperature. The resistance change produced by the temperature variation can be measured and used to determine the temperature of a material. Those sensors are characterized by the nominal resistance R0 at the nominal temperature T0 and by the material, which defines its resistivity temperature dependence. Some typical values are: Resistances: 100Ω, 200Ω, 500Ω, 1000Ω(±0.05% ÷ 0.1%) Materials: Platinum, Nickel, Copper, Silver, Gold, Iron Temperature range: −200℃ ÷ 800℃ Reference temperature: 0℃ (R0 ) or 25℃ (R25 ) Figure 20: Resistance temperature detector components written by Francesco Lenzi & Donato Carlo Giorgio Page 26 From prof. Federica Villa lectures of Sensor Systems free copy 4.1.1 RTD structures The are two sensing structures for the RTDs: the film pattern and the wire wound, which can come with a coiled design or an outer wound design. Wire wound The wire wound structure consists of a metallic wire wound around a mandrel and, as shown in figure 21, they can come in two designs: the coiled and the outer wound design. In the coiled design, the metal is wound into a coil and packaged inside the ceramic mandrel, whereas, in the outer wound design, the metal is wound around the outside of the ceramic mandrel and coated with an insulating material. Since the metal is coiled, an inductive effect is unavoidable for both designs. Figure 21: Resistance temperature detector wire wound structures Film pattern The film pattern RTDs are fabricated start- ing from a ceramic structure coated with metal that is selectively removed through pho- tolithography in order to create a pattern that acts as a long, flat conductor which provides electrical resistance. Then, lead wires are bonded to the metal-coated substrate. Those wires are held in place using a bead of epoxy or glass. For this structure we do not have an inductive effect, but, since we have a very thin metal, there is the danger of self-heating (the current flowing in the resistance heats it). written by Francesco Lenzi & Donato Carlo Giorgio Page 27 From prof. Federica Villa lectures of Sensor Systems free copy 4.1.2 RTD characterization The sensitivity for resistance temperature detectors is defined as the variation of the resistance over the variation of temperature. A parameter which is strictly related to the sensitivity is the Temperature Coefficient α which is the normalized resistance variation with respect to the temperature variation of 100℃.     ∆R Ω 1 ∆R S 1 R100 − R0 1 S= α= = = ∆T ℃ R0 ∆T R0 R0 100℃ ℃ RTDs typically have a Positive Temperature Coefficient (PTC) and are quite linear, as shown in figure 22. Indeed, the characteristic equation of the RTD resistance is: RRT D = R0 (1 + α∆T ) = R0 + ∆R ← ∆R = αR0 ∆T Figure 22: Temperature coefficients. Platinum R/T plot (blue) vs. linear plot (red). 4.1.3 Resistance Variation Readout Circuits To readout the resistance variation we have two possible setups: we can either make some known current flow in the resistance and measure the resulting voltage difference (taking into account the possible wiring resistances) or apply a known voltage to some resistance networks called bridges and measure the voltage difference between some nodes. Current controlled readout circuits: 2 lead wires readout, 3 lead wires readout or 4 lead wires readout. Voltage controlled readout circuits: Wheatstone bridge, 3-wire bridge. Note that those circuits are used to readout every kind of resistance, not only RTDs. written by Francesco Lenzi & Donato Carlo Giorgio Page 28 From prof. Federica Villa lectures of Sensor Systems free copy Current controlled readout circuits Simple readout A simple current readout for the RTD can be made by using a PMOS as a current generator and an operational amplifier in a non-inverting configuration. Since we know the current coming from the transistor (we select its gate voltage), we can compute the resistance value by read- ing the OP-AMP output voltage. Note that is important to use a non-inverting configuration because we want that all our current flows in the RTD (high impedance at the amplifier connection node). This readout is usable only if the temperature we want to measure is not high, otherwise, the circuit could incur to permanent damages, since it is near the hot object. To monitor high temperatures, we want to protect our readout circuit. To do so, we need to connect the RTD to long wires, which show a not negligible resistance value. 2 lead wires setup It is the least accurate since there is no way of eliminating the lead wire resistance from the sensor measurement, therefore it can be used either when we do not need good accuracy or we have short (low resistance) wires. Rmeas = RL1 + RRT D + RL2 3 lead wires setup In this case we can reject the wire contribution by adding a third wire and injecting two cur- rents (first IA , then IB ) to readout two voltages. In fact, if RL1 = RL2 = RL3 (reasonable, if we use the same wires): RA = RL1 + RRT D + RL2 RB = RL2 + RL3 Rmeas = RA − RB = RRT D The good accuracy and simplicity of this readout setup make it the most used in industrial applications. Indeed, when long distances exist between the sensor and the measurement instrument, significant savings can be made by using this instead of a four-wire cable. written by Francesco Lenzi & Donato Carlo Giorgio Page 29 From prof. Federica Villa lectures of Sensor Systems free copy 4 lead wires setup In this case we use two wires for the current injection and two wires for the readout. The read- out wires have to be connected to a high impedance (such as an Instrumentation Amplifier, INA) to avoid the current flows into them (no voltage across them). In this way, the measured resistance is exactly the RTD resistance. Rmeas = RRT D It is the most accurate setup and it is used primarily for laboratory purposes. Moreover, this readout method can be used when we are not sure that we can connect directly to the resistance that we want to measure. Voltage controlled readout circuits Wheatstone Bridge (a) Wheatstone bridge configuration. (b) Nodal analysis scheme. Figure 23 In this case we have a bridge of four resistors, where one of these is the one we want to measure and we readout the voltage between the two branches of the bridge. The big advantage is that, since the readout is intrinsically differential, we read and amplify just the voltage variation due to the resistance variation (thus avoiding saturation). Let’s compute the resistance considering the circuit in figure 23b when Vout = 0: R x0 ( ( Rx = Rx0 V+ = R1 +R x 0 V+ = V− R3 V− = R2 +R3 Rx0 R3 1 1 R1 R2 =⇒ = =⇒ R = R =⇒ = R1 + Rx0 R2 + R3 1 + Rx 1 1 + R3 2 Rx0 R3 0 Therefore, we need to put R1 = R2 and R3 = Rx0 to have a null output at standard conditions. written by Francesco Lenzi & Donato Carlo Giorgio Page 30 From prof. Federica Villa lectures of Sensor Systems free copy Considering now the perturbed conditions, we can repeat the computation considering Rx = Rx0 + ∆R and performing the algebra:   V+ = R1R+Rx x  R V− = R2 +R3 3   V+ = Rx0 +∆R   R1 +Rx0 +∆R R1 = R2 =⇒ Rx0 Vout = V+ − V−   V − = R1 +Rx0 R3 = Rx0      Rx = Rx0 + ∆R    Rx0 + ∆R Rx0 Vout = Vs · − = R1 + Rx0 + ∆R R1 + Rx0 Rx0 (R1 + Rx0 ) + ∆RR1 + ∆RRx0 − Rx0 (R1 + Rx0 ) − ∆RRx0 = Vs · = (R1 + Rx0 )2 + ∆R(R1 + Rx0 ) ∆RR1 R1 ∆R = Vs ·  = Vs · · 1 + R ∆R  2 (R + R )2 · 1 + ∆R (R1 + Rx0 ) +R 1 x0 R1 +Rx0 1 x0 It is reasonable to assume that ∆R ≪ R1 + Rx0 =⇒ ∆R 1+ R ∆R ≈ ∆R, and therefore: 1 +R x0 R1 ∆R=αR ∆T R1 Vout ≈ Vs · · ∆R −−−−−−0−−→ Vout = Vs · · αR0 ∆T (R1 + Rx0 )2 (R1 + Rx0 )2 Choosing R1 = R2 = R3 = Rx0 provides the maximum sensitivity ∆T : Vout Vout 1 ∆R = · Vs 4 Rx0 To achieve high sensitivities we need to provide a higher power supply voltage Vs , this is a com- mon trade-off in electronics. However, this configuration has the same problem as the two lead wires current readout setup: the resistance of the wires with which we probe the RTD resistor can be not negligible. 2-wire vs. 3-wire Wheatstone bridge Figure 24: Two wire and three wire Wheatstone bridges. written by Francesco Lenzi & Donato Carlo Giorgio Page 31 From prof. Federica Villa lectures of Sensor Systems free copy Considering the results obtained before, we can put R1 = R2 = R3 = Rx0 = R an compute Vout = V+ − V− : R + ∆R 1 Vout = Vs · ( + ) when RL = 0 2R + ∆R 2 Considering RL1 = RL2 = RL3 for the sake of simplicity, we obtain the following equations for the absolute error. Note that in the three wires configuration, since we have a high impedance readout (no current in branch C of figure 24) the upper RL doesn’t contribute to the read voltage: 2-wires setup 3-wires setup     R + ∆R + 2RL 1 R + ∆R + RL 1 Vout,2W = Vs · − Vout,3W = Vs · − 2R + ∆R + 2RL 2 2R + ∆R + 2RL 2 ε2W = Vout,2W − Vout = ε3W = Vout,2W − Vout = 2RRL −RRL = Vs ·   = Vs ·   2RL 2RL (2R + ∆R)2 1 + 2R+∆R (2R + ∆R)2 1 + 2R+∆R Considering ∆R ≪ R and practising some al- Considering ∆R ≪ R and practicing some al- gebra, we obtain: gebra, we obtain: RL RL ∆R ε2W ≈ Vs · ε3W ≈ −Vs · · 2(R + RL ) 2(R + RL ) 2R Observing the absolute error, we notice that the 3-wires configuration is multiplied by a factor 2R and, since ∆R ≪ R we have a much smaller error. ∆R Note, in conclusion, that there isn’t any 4-wire configuration for the resistance bridge readout. Self-heating Since RTDs are resistors, they will produce heat when a current is passed through them. This heat alters the RTD resistance value, therefore a maximum current limit is needed. The normal current limit for industrial RTDs is 1 mA. As discussed previously, thin film RTDs are more susceptible to self-heating, while wire-wound configurations can withstand even more than 1 mA (however, they are still subject to self-heating). The self-heating phenomenon is however exploited as an advantage in some applications. 4.1.4 RTD applications The Resistive Temperature Detectors have various advantages. First of all, the huge linearity (they are the most linear temperature detector), then they benefits of great stability, accuracy and repeatability. The disadvantages are however the narrow measuring range and the requirement of an ex- ternal power source as well as a quite slow response time. written by Francesco Lenzi & Donato Carlo Giorgio Page 32 From prof. Federica Villa lectures of Sensor Systems free copy The characteristics of the RTDs make them suitable for all applications that benefit from high accuracy in a quite narrow temperature range: Air conditioning; Food processing, stoves, grills; Plastic processing; Microelectronics... Moreover, an application that exploits self-heating is the current limiter since the resistance increases when the current increases. 4.2 Thermistors The thermistors are thermally sensitive resistors that show a resistance variation along with temperature changes. The main difference with the RTDs is the material with which they are made. The thermistors are indeed not made of metal and they are categorized through their material: NTC thermistors: made with ceramic semiconductors (transition metal oxides), that have a negative temperature coefficient; PTC thermistors: made with polycrystalline ceramic materials, that have a positive temperature coefficient. Another difference with RTDs is the fact that thermistors have a strongly non-linear charac- teristic. Only the most recent PTC thermistors can achieve a somewhat linear behaviour. 4.2.1 NTC thermistors characterization Figure 25: Thermistor components from bigger to smaller (left to right). NTC thermistors are made with metal oxides (manganese, nickel, cobalt, iron, copper and aluminium) and come in three possible shapes, as shown in figure 25. The disk structure in particular can be used to exploit self-heating since they have a larger temperature capacitance. Note that the nonlinear characteristic translates into more processing time from the microcon- troller. written by Francesco Lenzi & Donato Carlo Giorgio Page 33 From prof. Federica Villa lectures of Sensor Systems free copy NTC thermistor characteristic The characteristic of the NTC thermistor is nonlinear, in fact it is exponential. Being R25 the resistance at 25℃, β the thermistor con- stant (which depends on the material), having the temperatures expressed in Kelvin, it is:   1 β − T1 R(T ) = R25 · e T 25 4.2.2 PTC thermistors characterization PTC thermistors are made with polycrystalline ceramic (composed of oxalate or carbonate with added dopant materials). PTC thermistor characteristic The characteristic of the PTC thermistor has a strongly nonlinearity, in fact it is also non-monotone: it exhibits a slight negative resistance variation until a "switching point" is reached, where the resistance shows a huge in- crease with temperature. For this reason, PTC thermistors are usually used as temperature switches: open switch when tempera- ture exceeds a threshold. The threshold Tc is called Curie temperature and it is defined as the tempera- ture at which R(Tc ) = 2 · Rmin 4.2.3 Thermistors applications Thermistors have the advantage of being cheap, robust and high sensitivity (higher than RTDs) temperature sensors. The disadvantage is the very narrow measuring range (lower than RTDs), strong nonlin- earity, low stability and somewhat medium accuracy and response time. NTC applications For their characteristics, NTC thermistors are suitable for: cheap tem- perature measurements (cost less than RTDs, which are made with platinum), temperature compensation circuits and inrush current limiters: limit the current spikes at circuit startup exploiting self-heating and negative temperature coefficient, making the current ramp up (resis- tance ramp down) slowly as the circuit "warms up". PTC applications PTC thermistors are instead mostly used as thermal switches, i.e. re- versible fuses, (polyfuse) for overcurrent protection. For some cheap and old applications they were also used to passively control the charge of batteries (when the battery is charge it warms up and the PTC thermistors blocks the current). written by Francesco Lenzi & Donato Carlo Giorgio Page 34 From prof. Federica Villa lectures of Sensor Systems free copy 4.3 Thermocouple Thermocouples are temperature sensors that are commonly used to measure temperature in a wide range of environments. They consist of two different metals joined together at one end, and when there is a temperature difference between the two ends, a voltage is generated that is proportional to the temperature difference. 4.3.1 Thermocouple physics: Seebeck effect The functioning principle of thermocouples is the Seebeck effect. Figure 26: Seebeck effect. Let us consider a conductive material which is subject to a temperature gradient. In the hot part, the electrons will absorb the thermal energy to reach higher quantum levels, leaving free the lower energy levels. Those high energy electrons will diffuse towards the cold side, creating a charge gradient, i.e. a voltage difference. Since the low energy levels are free in the hot side, the low energy electrons of the cold side will tend to diffuse as well, but towards the hot side, decreasing the charge gradient. However, this effect is minor, because high energy electrons are characterized by high mobility and therefore diffuse more.16 Seebeck coefficient It describes the sen- sitivity of the conductor (semiconductor) dT. It is defined as the potential of the S(T ) = dV cold side with respect to the hot side: typically it is negative for n-doped semiconductors and metals (Cu is an exception) and positive for p-doped semiconductors. Furthermore, it is not constant with temperature, we can either compute it only within a range (linearization) or integrate it to get the resulting voltage. Figure 27: Some materials Seebeck coefficients. Z T ∆V = S(T )dT T0 16 This qualitative result is mathematically derived using the Mott formula. written by Francesco Lenzi & Donato Carlo Giorgio Page 35 From prof. Federica Villa lectures of Sensor Systems free copy 4.3.2 Thermocouple structure and readout The working principle of the thermocouple makes mandatory the choice of building them using different materials that have different Seebeck coefficients. This is shown in figure 28. Figure 28: Thermocouple Seebeck effect readout voltage and materials. Left: all wires made in aluminium; Right: wires in nickel and aluminium. Indeed, if we perform a Kirchhoff voltage law (KVL) along the whole sensing mesh and calculate the voltage differences with the integral on the single material (figure 28, left) setup, we get that: Z TH Z TH Z TC ∆VX = ∆VM − ∆VH + ∆VC =⇒ ∆VX = SAl (T )dT − SAl (T )dT + SAl (T )dT TC TX TX Z TH Z TH Z TX Z TH Z TH ∆VX = SAl (T )dT − SAl (T )dT − SAl (T )dT = SAl (T )dT − SAl (T )dT = 0 TC TX TC TC TC The integrals elide each other and the measured voltage is zero. This doesn’t happen if we use two different materials, since the Seebeck coefficients would be different. Doing the same calculation for the circuit on the right in figure 28 we get in fact: Z TH Z TH ∆VX = SAl (T )dT − SN i (T )dT ̸= 0 TC TC The structure of the thermocouple is therefore formed by the two different metals in contact in the tip which is is contact with the object of measure, a reference junction that is a part at a known temperature at which the two met- als are attached, and the two wires (that have to be of the same length and have to have the same thermal gradient so that they cancel out in the KVL) that reach the operational amplifier readout circuit. Z TM ∆Vmeas = ∆Vlead + ∆VB − ∆VA − ∆Vlead = ∆VB − ∆VA = (SB (T ) − SA (T )) dT TR Z TM ∆Vmeas = SAB (T )dT SAB = SB (T ) − SA (T ) TR written by Francesco Lenzi & Donato Carlo Giorgio Page 36 From prof. Federica Villa lectures of Sensor Systems free copy There is a big variety of thermocouples, each of those with its materials and temperature ranges. Some examples are the type J (-210 to 1200 °C), type K (-270 to 1372 °C), type T (-270 to 400 °C) and the tungsten ones, type G*,C* and D* (0 to 2320 °C). It is clear that the thermocouples have the advantage to have a wide temperature measure- ment range. Linearity Since the Seebeck coefficient is dependent on temperature, thermocouples are quite non-linear and thus need some pro- cessing to compute an accurate measure- ment, which translates into microcontroller’s operations. From the chart on the side, we can note that the K-type thermocou- ple is somewhat more linear in the 0 to 1000 °C range and thus can be used to make faster measurements (paying in accu- racy). Reference junction It is a point of the thermocouple wires which is at a known temperature. For accurate scientific measurement, some structures are involved as the ice-bath junction: the wires go in a thermal tank, such as an ice-bath, at a known temperature before going to the read- out amplifier. For less accurate applications a second thermal sensor (an RTD, a thermistor, or others) is used instead to know the temperature of the metals at the desired distance.17 Tips and grounding options There are three kinds of tips grounding options, which embed or not a cap: Insulated: the cap and the metals are sepa- rated, so the common mode voltage of the tip is unknown (only differential readout). We need to provide a common mode grounding one terminal of the readout OP-AMP. Grounded: the cap and the metals are in con- tact, so we have a common mode voltage (com- mon mode + differential voltages). The common mode voltage has to be in the OP-AMP operat- ing voltage range. Exposed: no cap is used (useful for fast read- outs). Electrically it’s equivalent to the grounded configuration. 17 We do not directly use the other sensor because the thermocouple may be used for high-range measurement for which the other sensors would fail. written by Francesco Lenzi & Donato Carlo Giorgio Page 37 From prof. Federica Villa lectures of Sensor Systems free copy A functioning readout configuration if the tip type is unknown is to put a highly resistive path to grout at one terminal, so that we have a ground common mode in the insulated configuration and we avoid high currents in the grounded and exposed configuration (which can have a high common mode voltage that could lead to high currents if we use a small resistance). Readout circuit examples In figure 29 are depicted two examples of readout circuits for the thermocouple. (a) INA based readout. (b) Integrated solution. Figure 29 The one in figure 29a is based on an instrumentation amplifier (INA) in which the leads are grounded and low-passed before being amplified and then low-passed again. In particular, note that the 10nF capacitor between the input terminals interacts only in differential mode (in com- mon mode it is at a fixed voltage), where also the 1nF capacitors give their contributions to low-pass. The result is that the common mode pole is far, while the differential one is nearer. This is fine since the differential disturbances are located in lower frequency ranges. Furthermore, we have a narrow low-pass at the output to avoid the 50 and 60 Hz disturbances that come from the power supply.   It is important to underline that the common mode rejection ratio CM RR = G GCM dif f is not infinite and has to be checked in the datasheet when we use such configurations. In figure 29b, instead, it is depicted a more integrated solution provided by Analog Devices, that makes use of an INA along with a Σ-∆ analog to digital converter and a temperature sensor for the reference junction, both connectable to a microcontroller through SPI protocol. 4.3.3 Thermocouple applications Thermocouples have the great advantage to achieve huge measuring ranges, which makes them suitable for all kinds of industrial and consumer applications. Moreover, they have a fast response time, moderate price, no self-heating, robustness to mechanical stress and a tiny measuring point (the tip). The main drawback of the thermocouple is the need for a second sensor as a reference junction: we can measure only relative temperature, not the absolute one. Less disruptive drawbacks are: the low sensitivity and slightly low linearity, the somewhat medium accuracy and the susceptibility to electromagnetic interferences. written by Francesco Lenzi & Donato Carlo Giorgio Page 38 From prof. Federica Villa lectures of Sensor Systems free copy 4.4 RTDs, thermistors and thermocouples: a comparative table To sum up, now that we have seen the advantages and disadvantages of RTDs, thermistors and thermocouples, we can compare them and choose them for the right application. Figure 30 4.5 Diode and bandgap temperature sensors The bandgap temperature sensor and the thermal diode, with respect to the other temperature sensors we have seen, have the advantage to be easily integrated in CMOS technology. Diode Since the diode current has the feature of being dependent on the temperature, it is quite immediate to utilize it as a temperature sensor. In fact, being k the Boltzmann constant, m a constant parameter dependent on technology and IS the reverse saturation current, a parameter dependent on technology and slightly on temperature, we have that the diode current is:  qV  I = IS · e mkT − 1 Providing a fixed current I, we can derive the diode sensitivity on temperature by performing the logarithm of both sides of the previous equation:     kT I ∆V k I V =m · ln + 1 =⇒ = m · ln +1 q IS ∆T q IS This equation shows that the sensitivity is quite linear with the temperature, except for the slight temperature dependence of the reverse saturation current IS. Fortunately, however, the dependence can be elided through a differential readout: the bandgap temperature sensor. written by Francesco Lenzi & Donato Carlo Giorgio Page 39 From prof. Federica Villa lectures of Sensor Systems free copy Bandgap temperature sensor In the figure aside is depicted a bandgap temperature sensor. We can see two current generator that make the currents I1 and I2 flow through two p-n-p BJT transistors18 in transdiode configuration. The transdiode configuration makes the BJT transistors behave like diodes with the p-side on the emitter side. The advantage of using those instead of normal diodes is that in this case we have the technology constant m ≃ 1. Considering the emitter to base voltage VEB as the forward voltage of the equivalent diode, the reverse saturation current as the product of the electron flux by the diode area (BJT emit- ter) IS = JS · A, and the generators’ current much larger than the reverse saturation current I ≫ IS =⇒ IIS ≫ 1 to remove the constant in the logarithm, we can compute the differential voltage at the amplifier input terminals using the diode equation:       kT I1 kT I2 kT I 1 A2 VEB1 − VEB2 ≈ · ln − · ln = · ln q A1 JS q A2 JS q I 2 A1 Now the voltage-to-temperature function is linear. We can call the ratio A2 A1 = r and put I1 = I2 so that we get the linear sensitivity: ∆V k = · ln(r) ∆T q Note that some unbalance has to be put either between currents or between areas to avoid getting a zero sensitivity (logarithm of 1). Our board temperature sensor In our board an integrated band- gap smart sensor is provided. It is embedded with an ADC, an oscil- lator and various registers. Among those registers, we have the tempera- ture register, which saves a value de- pendent on the temperature, a con- figuration register, and some more. 18 BJT transistors are like the MOSFETs. They have three terminals: the emitter, similar to the source (where there is the arrow), the base, similar to the gate, and the collector, similar to the drain. written by Francesco Lenzi & Donato Carlo Giorgio Page 40 From prof. Federica Villa lectures of Sensor Systems free copy 4.6 Infrared thermometer Infrared thermometers are temperature sensors that make use of optics to perform the measure- ment. They can work either as spot temperature sensors, i.e. measure the temperature of a single point, or as thermal image sensors, i.e. a sensor that does not image light, but temperature. 4.6.1 IR thermometer physics Every object at a non-null temperature emits optical radiations. To discuss the physics of this phenomenon, it is necessary to define the following parameters: Absorption A: the effectiveness of an object to absorb optical power. 0 ≤ A ≤ 1 Emissivity ε: the effectiveness of an object to emit optical power. 0 ≤ ε ≤ 1 Transmissivity T: the effectiveness of an object to transmit optical power through itself. 0≤T ≤1 Reflectivity R: the effectiveness of an object to reflect (back-scatter) optical power. 0≤R≤1 For every object at equilibrium, the absorption is equal to the emissivity A = ε and the sum of absorption, transmission and reflection is unitary A + R + T = 1. (a) Black body emission graph. (b) Generic body emission graphs. Figure 31: Optical power emitted per square centimeter with respect to the wavelength. The black body A black body is an object for which A = ε = 1 and R = T = 0. For this kind of object two physical laws are defined: Stefan-Boltzmann law: PA = σ · ε · T 4 2K4. where σ is the Stefan-Boltzmann constant and σ = 5.67 · 10−8 mW Connects the optical power emitted by an object to its temperature. Wien displacement law: λmax · T = 2898µm · K Connects the maximum emitted wavelength of an object to its temperature. written by Francesco Lenzi & Donato Carlo Giorgio Page 41 From prof. Federica Villa lectures of Sensor Systems free copy Analyzing those laws we obtain the curves shown in figure 31a, where we can appreciate the increase of the emitted spectrum and the reduction of the peak emitted wavelength with respect to the temperature. In particular, we have a 10µm wavelength emitted at room temperature. A body for which A = ε < 1 is called a grey Body, in particular, if R + ε = 1 and T = 0 it is called solid grey body (either reflects or absorbs the light). Their emission s