Advanced course on ELECTICAL CHAACTEISATION OF NANOSCALE SAMPLES & BIO-CHEMICAL INTEFACES: methods and electronic instrumentation. MEASUING SMALL CUENTS basic considerations Marco Sampietro HOW to MEASUE SMALL CUENTS I V Directly INTEGATE the incoming CHAGE on a Capacitance (internal or external) I X 0 Send CUENT to a circuit or AMPLIFICATION in a controlled way Most common output: V out = I or I out =A I
Bit (j) DIECT INTEGATION o Current into the CMOS image sensors mainly implement this approach Word (i) PPS Pixel I in C «Triple role» o the pixel Photon-to-charge Memory Charge-to-voltage Fujimori et al., ISSCC (2000) Non linear DIECT INTEGATION o Current into the + Compact - Limited accuracy: Only part o the charge stays in I + - Measuring instrument adds troubles! - Interesting when capacitance is small : V =Q/C 00e - on C=F gives 6mV - Discrete-time measurement: Time evolution o the current is lost V out Wiring current integration sampling signal V out Voltage ampliier reset - Bandwidth depending on, on wiring and on ampliier T s time 2
eal-time CUENT to VOLTAGE CONVETE eal-time voltage reading on V Meas + I - 4kT S I ( ) - Larger is beneicial to S/N : S I N 4kT Ideal Instrumentation ampliier Z in = I in =0 Measuring instrument adds troubles! i too big, it is again an integration! eal-time CUENT to VOLTAGE CONVETE V I C TOT Disadvantages : Direct voltage reading on V Meas + - Ideal Instrumentation ampliier Z in = I in =0 - Voltage across the (V ) changes (pa, =GV meas =mv) Disturbs the experiment Modiy the measured current - Limited bandwidth : with C TOT =pf =ms (60Hz) - Limited accuracy : V Meas = I 3
CUENT BUFFE Current GAIN = BUFFE Direct voltage reading on I C V e V Meas C STAY V EE + - Z in >> - Source impedance is high at low currents (no bias) I =pa gm k I : i k=25 A/V 2 00M g m Subthreshold : g m =I /kt/q 25 G g m - Unidirectional Simple FET BUFFE not easable FEEDBACK CUENT BUFFE () Current GAIN = V Meas - I C + V EE V e Bandwidth Advantages : - educed input impedance (less dependent on I ) I I =pa gm Zin Gloop - C is less limiting the bandwidth Disadvantages : - Higher power consumption, larger occupied area 4
Application : ELECTOCHEMICAL DETECTO AAY S.Ayer et al., IEEE Trans. On Circuits & Systems, V.54, n.4, 736-744 (2007) TOWAD the TANSIMPEDANCE AMPLIFIE - V Meas I C + V e I C - + V Meas V e 5
The ideal TANSIMPEDANCE AMPLIFIE i i ( t ) C TOT A V o (t)=-i i (t). Low output impedance Input impedance not dependent on I sensitivity large precision stable Example : to measure pa = G V o =mv A=0 5 V = 0nV independent o and C TOT FONT-END o most INSTUMENTS i i ( t ) Z V IN V BIAS V o (t) = - i i (t). Z C TOT V BIAS 6
FEQUENCY ESPONSE : ideal case i ( t ) C i Unavoidable parasitic capacitance V out C TOT (-) Limited bandwidth (+) but independent o setup 2 C i =G, C i =pf = ms (60Hz) STABILITY CONSIDEATIONS C G loop (w) A(s) C important or stability C TOT C TOT A(s) V out -20 db/dec w G loop A (s) 0 s opamp s(c sc CTOT ) 7
NOISE ANALYSIS - PAALLEL NOISE S i 4kT I C TOT OA S I v o ( t ) S input () Feedback resistor may have / noise High is beneicial 4kT S OA I VOLTAGE NOISE in AMPLIFIES ELECTONS are NOT FLOWING in a EGIMENTAL WAY (only on the average) Gate So does the Gate VOLTAGE V GS Drain Source Standing current has MICOFLUCTUATIONS Thermal noise Johnson noise Flicker noise 8
I C TOT Current Noise VOLTAGE NOISE in AMPLIFIES : series noise.. that mixes with signal! dv in Voltage dt luctuations.. Z V o (t) V GS.. produce an additional luctuating current.. SEIES NOISE : INPUT CAPACITANCE and FEQUENCY I nois I noise dv C dt G C e V G V e + - Increases with CAPACITANCE Keep ALL capacitances small! Increases with requency HIGH Frequency measurements may be less resolved 9
Which capacitance should be small? C Au Signal Area Noise rms C Au Area S N Constant with area IF YOU USE ALL THE SENSING AEA NO POBLEMS. with parasitics Signal Area C Au C stray Noise rms C TOT C Au + C stray S N Area Au k Area C Au stray Does not scale with area Can be very BAD! 0
For exceptional measurements : parasitics should go nano C Au C stray C stray SENSING AEA MICOFLUDIC PDMS CHANNEL SUBSTATE CONNECTIONS INSTUMENT-ON-CHIP so ELECTONICS should go nano LOW-NOISE FONT-END LOCK-IN ΣΔ ADC C Au 3mm Measuring instrument as close as possible to the (no parasitics along the way) NOISE ANALYSIS : practical case 250M AD823 I 8pF S V =(2nV) 2 /Hz S I =(3A) 2 /Hz Current noise[a/sqrt(hz)] p 00 0 BW I 4kT theoretical prediction 00 k 0k 00k M Frequency [Hz]
BIG instrument vs CHIP instrument MICOFLUDIC PDMS CHANNEL SENSING AEA SUBSTATE Axopatch 200B Vs CONNECTIONS INSTUMENT-ON-CHIP LOW-NOISE LOCK-IN FONT-END ΣΔ ADC 3mm POLIMI Pe7 No need o external reset Instrumental Noise [A/sqrt(Hz)] 0 Our chip Axopatch 200B 00a 0 00 k 0k 00k M Frequency [Hz] Better perormance on ast measurements NOISE ANALYSIS: a deeper insight I C TOT 4kT A Sv 2 g m v o ( t ) S Itot () C 2 TOT 2
NOISE ANALYSIS (2) I C TOT 4kT A Sv 2 g m v o ( t ) S Itot () C 2 TOT C TOT NOISE ANALYSIS (2) I C TOT 4kT A Sv 2 g m v o ( t ) S Itot () C 2 TOT C TOT 3
NOISE ANALYSIS (2) I C TOT 4kT A Sv 2 g m v o ( t ) S Itot () C 2 TOT / C TOT COMPAISON btwn SCHEMES I C V EE V e I C TOT Advantages : - Bidirectional - Easy bias - Low output impedance 4
Noise S() Noise S() TIME plots vs FEQUENCY plots Oscilloscope T t BW NOISE MS BW S( ) d 0 Large bandwidth Large rms noise Area esolution vs Bandwidth NOISE BANDWIDTH vs SIGNAL Signal bandwidth (Physical limits o the sensor) Ampliier bandwidth (sets the noise level) NEVE USE MOE BANDWIDTH THAN EQUIED by the SIGNAL 5
apacitance [af] 205.50 205.50 s af af 0. ms rise time af 205.50 s A af af = 80mV = 00kHz A = 80mV af 0. s BW = 3Hz Time rise [s] time A = = 80mV 00kHz = 00kHz 205.50 BW = 3Hz 205.50 0 00 200 205.50 300 BW = 3Hz 400 500 600 205.50 0 00 200 300 400 500 600 af I BW = 0 khz pacitance [af] noise = pa af af 0 00 200 300 400 500 600 205.50 0 00 200 300 400 500 600 A = 80mV = 00kHz BW = 3Hz I BW = 0 Hz 0 00 200 300 400 500 600 af 0 00 200 300 400 500 600 BW = 3Hz = 00kHz 80mV = A A = 80mV = 00kHz BW = 3Hz 205.50 A = 80mV A = 80mV af = 00kHz = 00kHz BW = 3Hz BW = 3Hz Current noise[a/sqrt(hz)] 0 p 00 0 00 200 300 400 500 600 0 theoretical prediction 00 k 0k 00k M Frequency [Hz] 7.25 7.00.25 6.75.00 6.50.75 af af 6.25.50 af af 6.00.25 A = 80mV 5.75.00 = 00kHzA = 80mV 5.50 A = 80mV.75 BW = 3Hz = 00kHz A = 80mV 205.50 = 00kHzBW = 3Hz = 00kHz.50 0 00 200 205.50300 400BW 500 = 3Hz 600 BW = 3Hz 0 00 200 300 400 500 600 0 00 200 300 0 00 400 Time 200 500 [s] 300 600 400 500 600 Beneits in reducing the bandwidth af noise = 30 A 0 00 200 300 400 500 600 A = 80mV = 00kHz 205.50 BW = 3Hz A = 80mV 300 = 00kHz 400 500 600 0 00 200 BW = 3Hz BW = 3Hz = 00kHz 80mV = A af af BW = 3Hz = 00kHz 80mV = A Drawings not to scale Not too low in requency It is usually beneicial to average longer but Electronic noise increases at low requency (traps, mobility luctuations, Mechanical vibrations Thermal luctuations Noise (pa/sqrt(hz)) 00 0 0 00 k 0k 00k M Frequency (Hz) Bio-physical instability Example : Current noise rom glass nanopores Physical origin: intrinsic, nanobubbles, mobile charges on the surace o nanopore? 6
sometimes HIGH FEQUENCIES AE NECESSAY! Example : nanopore sequencing Ionic current blockage At 20mV, DNA is translocated at a rate o 0µs per nucleotide MHz bandwidth Space resolution limited by physical dimension o the pore -hemolysin protein pore in a lipid bilayer membrane pa resolution NOT possible Fast sequencing diicult! Conclusion () ead currents with a TANSIMPEDANCE AMPLIFIE i i ( t ) V o (t)=-i i (t). C TOT Low output impedance sensitivity large precision stable 7
Noise S() Current Noise Conclusion (2) Be aware o input capacitance KEEP C in SMALL I noise dv C dt G Z C in Increases with requency Conclusion (3) Don t use more bandwidth than dictated by the signal Signal bandwidth (Physical limits o the sensor) Ampliier bandwidth (sets the noise level) 8
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