Design and Characterization of Nano-Displacement Sensor with High-Frequency Oscillators

The circuitry of a capacitive nanometer displacement sensor using the ring oscillator has been analyzed and characterized. We focus on the sensitivity of the sensor to detect the nanometer displacement or strain. The displaced target object must be conductive and the medium around the target object must be an insulator or a vacuum. The sensitivity in the range of L < 1 μm is enhanced with decreases in the size of the sensor electrode, and using a higher free-running oscillation frequency can increase sensitivity. The proposed sensor, which converts the displacement of the target object to the oscillation frequency, was fabricated with CMOS 350 nm technology, and the sensitivity was estimated at 8.16 kHz/nm. The results of our study indicated that the presented sensor has enough sensitivity to detect the nanometer displacement of the target object at a distance within 1 μm from the surface of the sensor electrode.


Introduction
Proximity sensors and tactile sensors working in the very narrow nominal range can be used to detect microparticles and micromotion of the objects.Furthermore, the integrated proximity sensors have a wide range of applications, such as measurement of the texture, analysis of fingerprints [1], measurement of the tactile or strain distribution [2], and use in touch screens [3].The proximity sensors and the sensitive displacement sensors in previous studies have been implemented on the basis of various principles of measurement, for example, a capacitive coupling method and some variations with a 30 nm resolution [4,5], an Eddy current method [6], a millimeter-wave reflection method with a 10 μm resolution of [7], and an integrated Michelson interferometry with a 20 nm resolution [8].In particular, the capacitive proximity sensors based on an RC oscillation [9] and a delta-sigma modulation [10] offer technical advantages, that is, a higher sensitivity and higher sampling speed because of the higher operating frequency of the electronic circuit as the semiconductor technology is scaled down.The capacitive sensor based on the RC oscillation can be implemented in a very small area, and it is possible to be implanted in the structural element of buildings, machines, and living organisms.
In this paper, we present the circuit analysis of a nanometer displacement sensor, that is, a very high sensitive capacitive proximity sensor, and characterization results of the proposed sensor chip.We focus on the sensitivity of the sensor to detect displacement or strain at the nanometer scale.

Circuitry and Sensitivity Analysis
A cross-sectional view of the sensor chip is shown in Figure 1.The top metal is dedicated to the ground electrode and the sensor electrode.The target object forms capacitances C g and C s against the sensor electrode and ground electrode.The C f is a parasitic capacitance between the two electrodes.The capacitances C g and C s depend on the distance between each electrode and target object while the capacitance C f is determined by the geometry of the ground and sensor electrodes.On the assumption that the conductive object has a flat surface, the total capacitance C A between the electrodes is shown in: where n is a ratio of C s and C g , L is a distance between the bottom of the target object and top surface of the ground or sensor electrodes, S is an area of the sensor electrode, and ε r and ε 0 are a relative permittivity of the ambient and an electric constant, respectively.If a round-headed tip with the curvature radius R is used as a target object, C A is replaced by C AR shown in (1c), given that the conductive object is grounded and R is sufficiently smaller than the sensor electrode: A schematic diagram of the circuit detecting a capacitance change of C A is shown in Figure 2. The sensing ring oscillator is connected to the sensor electrode, and the oscillation frequency f S changes depending on the value of the capacitance C A .On the other hand, the reference ring oscillator is connected to the reference capacitance C R .The oscillation frequency f R of the reference ring oscillator is fixed by the capacitance C R .These ring oscillators are adjacently placed each other with a matching layout technique to cancel the difference of electronic characteristics of the transistors.It is difficult to count the oscillation frequency of the ring oscillators because the oscillation frequency of the ring oscillator is very high.The output signals from two oscillators are mixed with each other, and the output frequency of the mixer circuit is converted to | f S ± f R |.The RC low-pass filter (LPF) passes the down-converted signal at | f S − f R |, selectively.The frequency of the down-converted signal is counted by the 28-bit counter.The counting period is controlled by the pulse width of the "Enable" signal, and the bit width of the output value depends on the period of the enable signal.The precision of the frequency measurement is thus inversely proportional to the sampling frequency of the counter output.
The free-running frequency f osc of the 3-stage ring oscillator is determined by the parasitic capacitance C L in each inverter, transconductance parameter β of MOSFETs (metaloxide-semiconductor field effect transistor), and power supply voltage V DD according to the following equations [11]: ) where value t d0 is the delay time of the inverters.The extra load capacitance C A is then added to the sensing ring oscillator, and the frequency f S of the sensing ring oscillator is estimated as follows: f S = 1 6t d0 + 2Δt d , ( From (1a), (2a), and (3), Equation ( 4) is derived: The sensitivity of the sensor for the displacement of the target object K d is found by using (4): ( The parameters f osc and C L depend on the fabrication technology, and C A is a function of the distance L. The freerunning oscillation frequency f osc and the sensitivity of the sensor increase with the advancement of technology node.By using (5) with the assumption that n = 1, ε r = 1 (in vacuum), the sensitivity of the sensor at distance L was estimated by using the typical values of f osc ∼ 55 GHz and C L ∼ 0.3 fF in the CMOS (complementary metal-oxidesemiconductor) 32 nm technology [12].The L dependence of sensitivity for the size of the sensor electrode is shown in Figure 3.The sensitivity in the range of L < 1 μm is enhanced by using a smaller sensor electrode.On the other hand, the sensitivity in the range of L > 1 μm decreases with smaller sensor electrode.The displacement of the target in the nanometer scale is detected as a change of the oscillation frequency in the MHz band.
For a round-headed object, the sensitivity for the displacement of the target object is derived based on (1c): The L dependence of sensitivity for the round-headed object is similar to the calculation result shown in Figure 3, and the sensitivity is increased with the smaller curvature radius of the object.However, the maximum sensitivity becomes 10 times lower than that for an object which has a flat surface.

Results
The sensor circuit presented in Figure 2 was fabricated by using CMOS 350 nm technology.The chip photograph is shown in Figure 4.This chip includes three discrete sensors and an array of 120 sensors.The discrete sensors were used to characterize the shift of the oscillation frequency, and the sensor in the center of the array was used to observe the counter output.With the exception of the active one at the center, all sensor electrodes were connected to the ground by the control signal to switch between the sensor circuit and the ground.The size of the sensor electrode was 39 μm × 39 μm, and the space between the active sensor electrode and the grounded electrode was 10 μm.The size and space of the sensor electrode was not optimized for high sensitivity, but the sensitivity of the sensor with larger electrodes was less affected by the process variation of the chip.The spectra of the output signal of the sensing ring oscillator are shown in Figure 5.A round-headed tungsten probe   with a 60 μm curvature radius was employed as a target object.The capacitance between the tungsten probe and the sensor electrode can be approximated by using the parallelplates model shown as (1a) because the curvature radius of the target object is larger than the sensor electrode.The oscillation frequencies f S for L = 10 μm and 1 μm were 266.6225MHz and 348.2000MHz, respectively.The sensitivity is estimated at 8.16 kHz/nm.Higher sensitivity is expected in the range of L < 1 μm, but the passivation film on the chip obstructed the measurement.The curve of oscillation frequency versus distance will be shown elsewhere after a reattempt to control distance by using an improved chip and an accurate mechanism.The value of the sensitivity is equivalent to that where a 1 nm displacement is measured with precision of 8 bit within 31 ms if there is no phase noise and no fluctuation of the oscillation frequency.The ring oscillator does not have good noise performance.However, the deterioration of the measurement accuracy caused by the influence of the noise can be controlled by the frequency count of the long period.The output value of the counter versus time is shown in Figure 6.The output period is 12.8 μs.These responses are observed with no target object on the sensor chip and in the condition that the surface mount device of the EIA 0603 standard is placed on the sensor surface, respectively.The output value at 1 s implies the frequency of the down-converted signal.The weak nonlinearity of the counter output-time characteristics was observed at 90 ms after the start of measurement.This nonlinearity could be regarded as a result of the temperature drift of the ring oscillator by self-heating.

Conclusions
The circuitry of capacitive nanometer displacement sensor using the ring oscillator has been characterized.The sensitivity in the range of L < 1 μm is enhanced with decreases in the size of the sensor electrode, and using a higher free-running oscillation frequency increases sensitivity.The proposed sensor was fabricated using CMOS 350 nm technology, and the sensitivity was estimated at 8.16 kHz/nm.It has been shown that the presented sensor has enough sensitivity to detect the nanometer displacement of the target object that is within 1 μm from the surface of the sensor electrode.

Figure 3 :
Figure 3: Sensitivity for displacement at L. The curves are calculated assuming CMOS 32 nm technology.

Figure 5 :
Figure 5: Spectra of sensing ring oscillator.(a) Distance from target object was (a) 1 μm and (b) 10 μm.Target object was round-headed tungsten probe with curvature radius of 60 μm.

Figure 6 :
Figure 6: Output value of counter versus time.Output period is 12.8 μs.Output value at 1 s implies the frequency of down-converted signal.