1. Introduction
Smart integrated temperature sensors and circuits are the main building blocks in all analog and mixed-signal applications, as well as in high-performance systems-on-chip (SoCs). Since the design complexity and density of VLSI circuits are increasing day by day continuous thermal monitoring is necessary to reduce thermal damage, increase reliability and avoid thermal runaway scenarios that can cause irreversible damage, i.e., overheating. The temperature across the chip should be monitored continuously, and the system operation should be adjusted accordingly. For example, in multicore SoCs, temperature information is being leveraged to maximize performance. The workload is shuffled between different cores before the temperature rises to a dangerous level. Alternatively, the clock rate is dynamically adjusted to boost system performance within a certain thermal budget [
1,
2,
3].
To implement a comprehensive thermal monitoring system multiple temperature sensors should be used. The desired number of sensors, their exact location, and accuracy depend greatly on system-level requirements, integrated circuits (IC) packaging, and cooling system (if any). Sensor accuracy and operation range are two key system-level considerations. Typically, a less accurate sensor consumes less silicon area and power compared to a highly accurate sensor. A narrower temperature detection dynamic range relaxes the linearity requirements, which further saves area and power. It is challenging to generalize this problem, but it is widely known that the design tradeoffs are largely driven by exact application and system-level architecture. Therefore, the temperature sensors, which are used for temperature monitoring in VLSI chips should meet the following requirements: compatibility with the target process, a reasonable silicon area, low power consumption, require no additional fabrication (CMOS-SOI compatibility), low cost, high accuracy and sensor linearity in the desired temperature range.
Following these requirements, various on-chip temperature-sensing circuit have been reported in the literature. In CMOS technology, the most widely used approach takes advantage of the proportional-to-absolute temperature (PTAT) property of the voltage difference between two forward-biased diodes or bipolar junction transistors (BJT) with different currents or areas [
4,
5]. The accuracy of BJT-based sensors depends on the diode ideality factor and accuracy of the current ratio used to bias them. Diode ideality factor is a process-dependent parameter. Careful and meticulous layout for good matching alone cannot guarantee the required matching between the individual current mirrors to achieve the desired level of accuracy. Therefore, on-chip dynamic element matching, trimming, and post fabrication calibration techniques are used in this type of sensor to improve accuracy. As a result, thermal diodes that enable accurate temperature measurement are large and power consuming, renders them suboptimal for the whole chip thermal profiling applications where placement of a large number of sensors is necessary.
For temperature sensors operating above 500 K or uncooled thermal sensors [
6] CMOS-SOI process is usually adopted due to its reduced leakage currents compared to bulk CMOS, low power consumption and availability of commercial process. Most of the CMOS based temperature sensors are not compatible with CMOS-SOI technology due to the thin device layer. The two most commonly used elements for temperature sensing available in CMOS-SOI technology are: lateral diodes [
7,
8,
9,
10,
11,
12] and standard MOSFET transistors [
13]. The SOI-based diode is an attractive choice for a temperature sensor because it is compact in size, gives linear response up to ultra-high temperature [
11] and is simpler to integrate with on-chip, sensor drive and readout circuitry. While SOI diode temperature sensors have been utilize for temperature monitoring in different application [
7,
8,
9,
10,
11,
12] the effect of device mismatches and consequently calibration needs are rarely discussed. One of these [
8], describes a work that uses a SOI lateral PIN diode for temperature sensing from 100 K to 400 K and suggests to improve the diodes accuracy by reducing the temperature range of the diode. In other study [
12], a smart CMOS-SOI temperature sensor has been described that uses a self-discharging SOI diode for temperature sensing and an error of ±1.95C (3ϭ) has been achieved after two-point calibration.
In this paper, we address the aforementioned challenges by demonstrating the design and successful implementation of a small, low-power, and accurate on chip temperature sensing circuit based on “Threshold Voltage Thermometry” [
14], namely a threshold voltage (
Vt) extractor circuit. The performance of the
Vt extractor circuit is compared to a standard circuit used for temperature sensing, i.e., PTAT circuit, in terms of sensitivity, linearity, speed, accuracy, calibration needs, area and sensor power consumption. Both circuits were designed using 1 µm PD CMOS-SOI technology [
15] and their performance has been experimentally verified by comparing simulated and measured results.
For 1 µm CMOS-SOI process, this 80 × 100 (µm2) sensor consumes ~30 μW using a 5-V supply. Our thermal measurements using multiple chips show only ±1.5 K inaccuracy between the 300 K and 500 K temperature range.
2. Proportional to Absolute Temperature (PTAT) Circuit
Proportional to absolute temperature circuits are widely used to generate temperature independent current/voltage sources, band-gap reference circuits and temperature sensors in many digital, analog and mix-signal systems. Typical CMOS based PTAT circuits are shown in
Figure 1a,b [
16]. The first circuit is based on the exponential dependence of the vertical PN diode forward voltage upon temperature and the second one is based on the dependence of resistors and channel mobility to generate an output voltage/current proportional to the chip local temperature.
2.1. Principle of Operation
The sensing principle of a PTAT temperature sensor is depicted in
Figure 1a. The sensor’s core consists of a pair of matched vertical PN diodes biased by two identical current sources (
Ipn) while diode D2 consists of n parallel connected diodes with the same device area [
7]. The voltage drop on each diode is given by [
14]:
where
Ipn is the diode current,
q is the electron charge,
kB is Boltzmann’s constant,
Vpn is the voltage across the diode,
T is the absolute temperature,
I0 is the temperature-dependent reverse saturation current.
By choosing the upper transistors so that the current in both branches is similar (
IM1 =
IM1 =
Ipn), and by neglecting channel length modulation and bulk effect the circuit output voltage can be calculated:
where
n is the number of parallel connected diodes,
Iout is the circuit output current,
Rout and
Rs are the output and series resistors respectively. Usually, the resistors
Rout and
Rs are from the same type so their temperature coefficient will balance each other and improve the circuit performance.
Figure 1b illustrates another PTAT implementation which uses the dependence of mobility and resistors upon temperature to generate the output voltage. The upper
p-type transistors (M1 and M2) have the same current (
IM1 =
IM2 =
Id) because they have identical dimensions. Hence, we can calculate the NMOS gate voltage:
where
Vgs is the transistor gate-source voltage and
Id is the transistor drain current.
By neglecting body effect we can determine the circuit output voltage:
where
µn is the electron mobility,
K is transistors M4 and M5 size ratio,
W and
L are the transistor width and length respectively and
Cox is the oxide capacitance.
As seen from Equation (4), the output voltage is inversely proportional to the channel mobility creating a proportional to absolute temperature output voltage. It is important to emphasize that since each diode-connected device feeds from a current source this design is relatively independent of Vdd.
2.2. Implementation
In CMOS-SOI technology it is impossible to manufacture a vertical diode due to the thin body layer; hence, in order to implement a diode based circuit (
Figure 1a), a forward-biased diode is built with a lateral structure based on the device layer, forming a source/drain PIN junction. The diode based circuit was implemented using 25 N+/P-well/P+ non-gated diodes (24 are finger diodes interdigitated in parallel) with width of 16 µm and length of 0.25 µm, as presented in
Figure 2. The PMOS and NMOS dimensions are (
W/
L)
P = 6 µm/2 µm/(
W/
L)
N = 6 µm/3 µm for the diode based design and (
W/
L)
P = 24 µm/2 µm/(
W/
L)
N = 6 µm/3 µm for the resistor based design. The size ratio between transistors M4 and M5, i.e.,
K, in the resistor based PTAT (
Figure 1b) is 2.
Both architectures are realized in a standard 1 µm PD CMOS-SOI process [
15]. The maximum operating voltage is 5 V. The buried oxide (BOX) thickness is 1 μm, the gate oxide thickness is 25 nm, and the active silicon thickness is 250 nm. The circuits chip areas are 178 × 150 µm
2 and 85 × 100 µm
2 for the diode based design and the resistor based design, respectively. The resistors in both circuits are implemented using high resistivity Polysilicon.
Although the SOI lateral diode is modeled as an ideal diode, it should be noted that the saturation current exhibits perimeter dependence rather than area dependence, as in regular planar bulk diodes, due to the thin body layer. Contrary to CMOS bulk diodes, where surface effects may be neglected, the thin device layer in SOI technology requires a model where the current is primarily dependent on surface effects, i.e., I0 = JSW(T) × Perimeter.
As a result, the saturation current is strongly affected by the surface, determined by the device periphery. This significantly increases the mismatch between diodes and affects the diode’s performance as a temperature sensor, as reported in [
14] for lateral diodes fabricated in two different SOI processes.
2.3. Measurements and Simulations
The output voltage of both designs is sampled by using a DMM4040 Digital Precision Multimeter (Tektronix, Beaverton, OR, USA) while the circuit’s temperature is determined with a variable temperature micro probe system from MMR Technologies (San Jose, CA, USA), which features a temperature control accuracy of ±0.01 K. All transistors (M1–M5) are biased and their current measured using a B1500A semiconductor parameter analyzer (Agilent, Santa Clara, California, USA). Three samples from each design were characterized in temperature ranging from 300 K to 500 K and the measured output voltage is shown in
Figure 3. These results are compared to
Vout vs.
T curves obtained from electrical simulations in the SPICE simulator based on BSIM4 MOSFET models [
17], also presented in
Figure 3.
The temperature sensing circuits’ performance is also analyzed using process corner simulations. A four-corner model file provided by the foundry is used for the corner-based analysis. In
Figure 3 only the corners with worst case variations are shown—Fast NMOS Fast PMOS (FF) and Slow NMOS Slow PMOS (SS).
In this analysis, the coefficient of determination, R
2 [
18] has been used to evaluate the linearity of the sensor, through the agreement between the experimental data and their best linear fit.
Figure 3 shows that the resistor based design exhibits linear dependence upon temperature in the entire temperature range (R
2 = 0.9988 in the worst case sample) and minimal variations between the measured samples. The diode based design is also linear as a function of temperature (R
2 = 0.9985 in the worst case sample), but has larger variations between the different samples. The measured temperature sensitivity of the output voltage after a linear curve fit is 9.8 mV/K for the resistor based PTAT design and it is close to that obtained from the simulation. The sensitivity of the diode based design is 4.7 mV/K for a bias current of 3.3 µA, which is higher than that reported for SOI lateral PIN diodes, which is in the order of 1.1 mV/K for a bias current of 2 µA [
7,
8,
9].
As illustrated in
Figure 3, for the diode based design there is a DC shift between the measured and simulated results for all measured samples (maximum value of DC shift is 32 mV) due to the dependence of the saturation current in the diode dimensions. This dependency of the saturation current causes a large mismatch between lateral diodes that should be identical, as reported by us in [
14]. As a result, the accuracy of the diode based PTAT circuit decreases.
In addition, the corner analysis shows that the worst case maximum temperature error occurs at the FF corner and caused combined offset of 100 mV and 150 mV for the resistor and diode based PTAT designs. It is important to note that this offset includes large mismatches in polysilicon resistance value and can be improved by matched layout. The shifts and variations between the different measured samples for the diode based design results in large temperature measurement errors and require precise calibration process.
The error in the temperature measurement (Δ
T) has been obtained by calculating the difference, Δ
Vout, between the measured and simulated
Vout vs.
T, which is then converted into temperature using the circuit sensitivity.
Figure 4 shows the error in temperature measurement as a function of applied temperature for both designs in the measured samples presented in
Figure 3. Accordingly, the sensor’s inaccuracy is estimated:
From the extracted error curves presented in
Figure 4 one can observe a maximum error of ±6.5 K for the diode based PTAT circuit and an error of ±1.5 K when using the temperature dependence of polysilicon resistors, without any additional calibration. These results show that the resistor based PTAT circuit is a good temperature sensor for temperatures ranging from 300 K till 500 K, though it is power consuming. The circuit measured power consumption at room temperature is 0.25 mW for the resistor based design and 45 µW for the diode based design. Errors similar to the errors calculated for the resistor based design, in order of 2 K, have been presented in [
12] after two-point calibration for temperature sensing from 278 K up to 373 K using fully depleted single lateral SOI diode consuming 100 µW.
2.4. Time Response
In addition to the steady-state on-chip temperature distribution, the sensor’s thermal transient response can also be of interest for various applications. For instance, in dynamic thermal/leakage management, the dynamic variation of on-chip temperature is used to adjust the operation of the chip such that the leakage power and the peak chip temperature can be properly controlled [
19].
The time response of a temperature sensor is defined as the time it takes the sensor output to achieve 63% of its final value after a step change in temperature is impressed on its surface. To perform thermal transient analysis, a numerical integration method such as the backward Euler is required [
20]. To solve the thermal transient analysis problem, one can model the thermal system as an equivalent RC circuit. Then, a SPICE-like simulation technique can be applied to the equivalent RC circuit to provide the thermal transient response [
20,
21]. In this study the PTAT time response was simulated using SPICE circuit simulator with BSIM4 MOSFET models [
17]. The standard MOSFET models were changed to include a parameter describing each device specific temperature rise above the simulated ambient temperature, i.e.,
trise. Then, in order to simulate a local temperature, only trise of the MOSFETs composing the temperature sensing circuit were changed externally and the PTAT output voltage was sampled. The transient simulation results are presented in
Figure 5 for both PTAT designs and two temperature profiles: a graduate and a step temperature change.
Figure 5a,c show the PTAT response to a graduate temperature change; from
t = 10 µs to
t = 30 µs the circuit local temperature increases from 295 K to 330 K (
trise = 35 K) and then it starts to cool down to room temperature. This is a lifelike scenario for most CMOS-SOI applications were the thermal time constants are long [
22]. It can be easily concluded that both PTAT designs follow the temperature changes accurately and without delay, meaning that the time response of the circuit is much smaller than chip thermal time constants.
The time response of each design is obtained by simulating a step change in the sensor local temperature and the results are presented in
Figure 5b,d. Time constants of 170 ns and 165 ns were calculated for the resistor and diode based designs, respectively.