High resolution measurements The differential approach

Transcription

1 Electrical characterisation of nanoscale samples & biochemical interfaces: methods and electronic instrumentation High resolution measurements The differential approach Giorgio Ferrari Dipartimento di elettronica, informazione e bioingegneria Politecnico di Milano Milano, November OUTLOOK of the LESSON Difficulties of high resolution measurements Linear noise sources Non-linear noise sources Differential approach Examples 2 1

2 Definitions 3 Sensor + electronics response: Given by sensor and electronics V out V max V noise S min Minimum detectable signal (limit of detection): S min Maximum signal (saturation sensor or electronics) : S max Dynamic range: S max /S min Sensor S max Interface electronics S A. D Amico and C. Di Natale, A contribution on some basic definitions of sensors properties, IEEE Sens. J., vol. 1, no. 3, pp , Definitions V out V max V x V x V noise S x S min S x S max S Resolution: minimum measurable S x Relative resolution: S x /S x (sensitivity: V x / S x ) 4 2

3 The problem of the lesson Assuming an ideal sensor (linear, no noise) V out Sensor Interface electronics V max V x V noise V x S x S min S x S max S Is S x = S min for any S x? (resolution indep. of S x ) Is relative resolution = S min /S max (1/ dynamic range)? 5 Ex.: -based capacitance meas. sensor C F C x C p e n Main noise source Ex. : = 1V, C p =1pF, C F =0.1pF, BW= 1Hz 2, V out,max = 2V C x,min = 2 zf, C x,max = 0.2pF DR= 10 8, resolution = 10 ppb 6 3

4 High resolution meas. require: Low-noise, wide-bandwidth circuits and a full control of the setup, for example: - Noise of the waveform generator - Gain fluctuations - Temperature effects - 1/f noise - Dielectric noise - 7 Noise of the stimulus signal Example: sine waveform Power spectral density Amplitude and phase noise Additive noise f 0 frequency 8 4

5 Stimulus: additive noise C F e wg C x C p e n e wg >> e n (x 10) but C p could be >> C x Set the maximum resolution Resolution still better than 1 ppm Minimize e wg at the frequency of the measurement 9 A voltage divider can be beneficial if e wg is independent of Stimulus: additive noise C pp C F e wg C x C p e n e wg >> e n (x10) but C p could be >> C x Set the maximum resolution 10 Pay attention to the stray parallel capacitance C pp : Increase the total noise Limit max (saturation of the amplifiers) 5

6 Stimulus: amplitude and phase noise Power spectral density Amplitude and phase noise Additive noise f 0 frequency 1 sin 2 11 Phase noise modulation It is NOT important for high resolution meas.: Phasor notation: ϕ rms y x The measured amplitude is not affected

7 Phase noise modulation It is IMPORTANT in the case of signal + large spurious shifted of 90 : Phasor notation: V spurious ϕ rms S min V spurious sin(ϕ rms ) x V good signal S min V spurious ϕ rms Example: -100dBc/Hz at 100Hz offset (BW=100Hz) S min /V spurious > 100 ppm 13 Amplitude noise modulation It is IMPORTANT for high resolution meas. sin( nt) digital sine V REF D A C V REF sin( t) V REF sin( t) S Vref Power spectral density of V REF V REF f The demodulated amplitude has the SAME noise of V REF 1/f noise at the output of the! 14 7

8 Amplitude noise modulation Example: White noise: 5 /, noise corner: 100Hz Noise spectral density [V 2 /Hz] k 10k Frequency [Hz] rms noise [V] 600n 500n 400n 300n 200n 100n (f min = 0.1mHz) white + 1/f noise white noise 0 100m k 10k Bandwidth [Hz] High resolution requires narrow BW 1/f noise of AM set a limit! 15 Ex.: -based capacitance meas. C F C x C p e n Front end amplifier and conditioning stages: e n other? 16 8

9 Temperature fluctuations C F V C out = C x /C F x V AC C p A fluctuation of the gain changes the output (as AM) Temperature coeff. of a C0G cap. («0 drift») is up C/C= 30 ppm/ C 1 ppm requires a temperature stability better than 0.03 C (worst case) 17 Gain set by a resistor R F V C out = C x R F x V AC C p Temperature coeff. of standard R is 50 ppm/ C ( 100ppm/ C for high value resistors) 1 ppm requires a temperature stability better than 0.02 C or resistors with low temp. coef. (down to 1 ppm/ C) 1/f noise of a resistor is often a resistivity fluctuation 1 ppm requires low 1/f noise resistors (metal thin film) 18 9

10 Temperature effect Output [V] SR830 lock-in: 840nV rms Custom lock-in, standard R (50 ppm/ C): 240nV rms (4 ppm) Custom lock-in, LTC R (5 ppm/ C): 45 nv rms (0.7 ppm) Low temp. coef. components along the signal path! 19 Noise from the input capacitance R V ac C x C p1 e n Is the capacitance a true noiseless component? What is the role of the substrate? M. Sampietro Conductive or insulating substrate 20 10

11 Ex.: -based capacitance meas. C F C x C p Digital : Analog stages DAC cos -sin DDS Digital processing V IN Analog stages A.A. filter ADC cos Filters Outputs x jy -sin 21 ADC: amplitude noise modulation V R,ADC [1+n R,ADC (t)], ADC, 1, S Vr,adc Power spectral density of V R,ADC Unavoidable slow fluctuations of the ADC gain Unavoidable fluctuations of the output! f 22 11

12 Resolution limits of s out in f = 1 MHz Output Spectral analysis Zurich Instruments, HF2LI Output noise spectral density [Hz] 100µ V IN = 1 V V IN = 300 mv 10µ 1µ 100n V IN = 100 mv V IN = 30 mv V IN = 0 V V IN = 1 V (quad: 40 mv) k 10k 100k Frequency [Hz] Resolution [ppm] 1k m 1 khz BW (ideal) 1 khz BW 10 Hz BW (ideal) 10 Hz BW 1m 10m 100m 1 Signal amplitude [V] How to improve the resolution? The limiting factor is the gain fluctuations of voltage source, amplifiers, ADC OUT = (G+δG(t)) S δout(t) = δg(t) S The additional noise is proportional to the signal only keep the useful signal! 24 12

13 The differential approach S = baseline + S S S-Ref baseline Ref t t Gain fluctuations prop. to S S baseline 25 t The differential approach S = baseline + S S S-Ref baseline Ref 26 baseline t t t Gain fluctuations prop. to S S Ref must share the gain fluctuations of the stimulus The subtraction should be implemented as soon as possible (no digital domain!) 13

14 Ex 1: Wheastone bridge V OUT A DIFF - A DUT AREF + V IN fluctuations reduced by the CMRR (balanced case) 27 Amplifier and input operate on A DIFF Z 1,Z 2,Z 3,Z DUT should be placed near to experience the same temperature fluctuations Ex 1: Wheastone bridge MEMS piezoresistive sensors (pressures, acceleration, ) Proceedings of the IEEE 2009, , DOI: /JPROC Sensors 2009, 9(8), ; doi: /s

15 Ex 2: Ratiometric Half bridge V OUT Z REF Z DUT /2 + - V IN No compensation of fluctuations Large signal processed by amplifiers and 29 Ex 2: Ratiometric Half bridge V OUT Z REF Balun - Z DUT A DIFF + - V IN Balanced structure Balun or inverting amplifier (requires a stable gain!) Z REF adjacent to Z DUT 30 15

16 Ex 2: Ratiometric Half bridge MEMS capacitive sensors (pressures, acceleration, ) Microsystem Technologies, 2013, pp , DOI: /s z 31 e/gyroscope.html Ex 3: Current sensing V OUT Z REF Balun - Z DUT 0V - + V IN Balanced structure Balun or inverting amplifier (requires a stable gain!) Z REF adjacent to Z DUT 32 16

17 Cap. detection of the surface coverage dust deposition, cell growth, C el (t) C el time M. Carminati, Capacitive detection of micrometric airborne particulate matter for solid-state personal air quality monitors, Sensors Actuators A 219, Interdigitated Electrodes Large sensitive area implies large total capacitance Ex.: area 1 mm 2 gap 1 m length 500 m resolution: 30 ppm C total = 15pF C min = 450 af Minimum particle size > 50 m 34 17

18 Differential electrodes architecture Differential structure Common mode rejection Generator Environment 35 Realized Chip Prototype 1 mm 2 collection area 5µm 2mm Noise: 450 af (single structure) Noise: 65 zf (differential structure) C el = 1.7aF 36 18

19 Ex 4: Current-Sensing AFM (CS-AFM) A voltage bias is applied between a conductive tip and the sample on a conductive substrate. The current flowing through the sample is measured while the tip is maintained in contact under force feedback control. conductive probe I DC R sample current detector force feedback X,Y,Z piezo V DC Advantages compared to STM: 1) conducting and insulating samples 2) independent topography and electrical image topography I DC 37 Nanoscale Impedance Microscopy Conductive probe C R AC piezo Topography controls sample VDC topography + v AC (t) Lock-in amplifier AFM controller I DC C R AC I DC +i AC (t) I-V Z( f ) Noise Current amplifier with BW=1MHz: Capacitance and dielectric maps Impedance measurements (100Hz 1MHz) Noise spectroscopy (proof of the concept, ICNF 2005) Current transient on a s scale G. Gomila (IBEC), L. Fumagalli (University of Manchester) Fumagalli L et al, Nanotechnology 2006 Fumagalli L., Ph. D. Thesis 38 19

20 Dielectric measurements ε r is an intrinsic property of matter given by chemical composition, structure, density, Measured by capacitance meas. + theoretical interpretation avoiding topography artifacts analytical formula and/or simulations z R r h long-range contributions from the full tip and probe extremely small signal to detect ~ 1:1 million ratio L. Fumagalli et al. Nanotechnology 2006 L. Fumagalli et al. Nano Letters 2009 L. Fumagalli et. al. Nature Mater apex ~ 1 attofarad stray contribution ~ 1picoFarad Compensation path No (reasonable) differential setup I stray C F C stray C c -1 C c = C stray C stray is not fixed, a calibration is required 40 20

21 Compensation path A more practical configuration C F C stray C c D A C - n/2 14 nc c /2 14 = C stray 14 bit AD5446: 14-bit multiplying DAC, BW= 12MHz, gain temp. coef. <20 ppm / C 41 Summary Resolution could be limited by gain fluctuations: Signal source (DAC, optical source, ) Amplifiers (C, R, ) A/D converters Differential approach Remove large baseline: gain fluctuations prop. to the signal Reference path generated from the same signal source Differential sensor Circuit with a calibrated component (+ variable gain and/or phase shifter) Reference path with S whenever possible (e.g. MEMS) 42 21