Politecnico di MilanoMSc Course - MEMS and Microsensors - 2020/2021

E18

PTC and 4T APS

Paolo Frigerio

10/12/2020

In this class we will introduce the photon transfer tecnique, a commonly-used

routine to characterize image sensors. We will also analyze di�erences be-

tween photon transfer curves in 3T and 4T APS topology, using the correlated

double sampling technique.

Problem

The PTC (Photon Transfer Curve) of the 3T CMOS active pixel sensor analyzed inexercise E17 is provided in �gure 1.

• Verify that the calculations you made for the sensor of E17 are correct, extractingalso information about the PRNU.

• What would change on the PTC using the double sampling technique, keeping a3T architecture?

Consider now a camera featuring a 4T CMOS APS, with a pinned diode structure. Thisspeci�c pixels shows the same maximum full-well-charge and the same PRNU of the 3Tcase and the pinned implant reduces the dark current by a factor 10. Furthermore, thepixel is readout with the correlated double sampling technique, that reduces the resetnoise by a factor 20.

• Trace the PTC curve in this new situation, evaluating graphically the maximumdynamic range reachable by the sensor.

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Figure 1: Measured PT curve.

Part 1: Photon transfer

Photon transfer (PT) is a valuable testing methodology employed in the design, oper-ation, characterization, optimization, calibration, speci�cation, and application of solidstate image sensors and camera systems. Invented in the mid-1970s, today photon trans-fer is routinely used and continues to evolve. The photon transfer technique is appli-cable to all imaging disciplines. Detector performance parameters, such as quantume�ciency, noise, charge collection e�ciency, sense node capacitance, charge capacity, dy-namic range, non-linearity, pixel responsivity, . . . , depend on photon transfer results.Photon transfer can treat a camera system, no matter how complex it is, as a black boxand determine the desired parameters with very little e�ort. The user needs only toexpose the camera to a light source and measure the signal and noise output responses.Fig. 2 shows a generic camera block diagram where the input signal exhibits Poisson shotnoise characteristics, i.e.

σA =√A,

where A is the mean input signal level, and σA is the input noise standard deviation.For an image sensor, the only quantities that exhibit this property are photoelectrons.In fact,

σNel=

√2qiph

1

2tint· t2int

q=

√qiphtint

q=

√Qphq

=√Nel.

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Figure 2: Black box camera system with a constant K = B/A used to transfer the inputA to the output B.

A sensitivity constant de�ned as K relates the input with the output:

B = KA,

andσB = KσA + σadd,

where B and σB are the measured output mean signal level and noise standard deviation,respectively, and σadd is the standard deviation of all the other noise contributions dueto the non-idealities of a real image sensor.Actually, the sensitivity of an image sensor is a function of the wavelength. In thiscontext a linear gain K (instead of an integral law over the visible spectrum) can beprecisely de�ned only if the radiation spectrum is monochromatic. In the exercises, evenif the radiation specturm is not monochromatic, we will assume it as characterized by itsdominant wavelength - unless di�erently speci�ed.At this point in the analysis K is unknown. However, assuming to �nd a operationregion where the term σA is dominant (and thus σadd is negligible), by re-arranging theK-equation with proper substitutions we get the result:

K =B

A=

B

σ2A=

B

σ2BK2

=K2B

σ2B.

Hence:

K =σ2BB

This is called the PT relation, the equation that is the basis of the PT technique. Notethat K is simply found by measuring output statistics (mean and noise variance) withoutknowledge of neither the individual camera transfer functions nor on the input character-istics (except for the requirement to measure the output in a shot-noise limited workingregion).

Let's have a look at the typical noises at the output of the sensor. We have (i) shotnoise, that increases with the square root of the signal, (ii) PRNU, associated with

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pixel-to-pixel response di�erences and whose standard deviation increases linearly withsignal, (iii) the so-called read noise, that encompasses all noise sources that are signalindependent. These three noise sources can be summed up (quadratically), giving thetotal output noise

σTOT =√σ2read + σ2shot + σ2PRNU .

An ideal photon transfer curve (PTC) response from a camera system exposed to auniform light source is illustrated in Fig. 3. Noise (rms) is plotted as a function ofaverage output signal. Four distinct noise regimes are identi�ed in a PTC. The �rstregime, read noise, represents the random noise measured under dark conditions, whichincludes several di�erent noise contributors; they can be both temporal and FPN: darkshot noise, kTC noise, DSNU, . . . . As the light illumination is increased, read noise givesway to photon shot noise, which represents the middle region of the curve. Since the plotin Fig. 3 is on log-log coordinates, shot noise is characterized by a line with a slope of1/2. The third regime is associated with pixel PRNU, which produces a characteristicslope of unity because signal and FPN scale together. The fourth region occurs when thematrix of pixels enters the full-well regime. In this region the noise modulation typicallydecreases as saturation is approached.

Figure 3: Ideal total noise PTC illustration showing the four classical noise regimes.

The photon transfer curve (PTC) is a commonly used test procedure to characterizedigital sensors parameters, i.e. from output data, we can infer a lot of system and pixelparameters of the sensor. This is done without knowing anything of the camera system,i.e. by assuming the camera as a black box. In fact, given a certain photon �ux impinging

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on the sensor, you can measure the output signal of each pixel. From this data, you cancalculate the average output signal, DN , its standard deviation, σDN , and you can drawyour PTC with the average signal on the x -axis and its standard deviation on the y-axis. This can be repeated for di�erent photon �uxes, i.e. for di�erent average outputsignals, and a complete PT curve is built. In Fig. 4, a measured photon transfer curve isdisplayed. On the x -axis we have the digital output number corresponding to the signal,while on the y-axis we have the output rms noise expressed in rms digital number. PTCmeasurements are usually made (initially) in digital number (DN) units that will be laterconverted to electron units, if needed.

Figure 4: Measured PT curve and extracted parameters.

Usually, the light intensity is varied for a PTC sequence, and a low-cost light-emittingdiode (LED) is often utilized. The color of the LED is not critical for PTC work; however,FPN typically shows some wavelength dependence. Light uniformity across the matrixof pixels being sampled needs to be very high, otherwise FPN measurements will be inerror.For each light level, one can plot the data extracted from the measurement, as in Fig. 1.

There exist a precise mathematical routine that helps you to calculate each noise contri-bution alone: read, shot and PRNU. This can be easily (and faster) done in a graphicalway, by drawing the asymptotic curves, with 0, 1/2 and 1 slopes, respectively (in a log-logplot).

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Remember the equation of the photon transfer theory:

K =σ2BB.

The equation states that one could extract the transfer function of the camera system,by taking the ratio between the output variance and the output signal, assuming thatthe system is shot noise limited, i.e. if σA =

√A. Hence, from measured data, we can im-

mediately infer the transfer function of the system from the number of photons/electronsto the digital output. This is be practically done by simply calculating the ratio betweenthe variance and the average output signal. Things are even easier: K can be foundgraphically by extending the slope 1/2 shot noise line back to the signal axis. The signalintercept with the 1 DN rms noise line represents the inverse of the transfer function.From Fig. 1:

K =

[σ2BB

]σB=1

=1

DNshot=

1

1.5= 0.666 DN/electrons.

We can then extrapolate the PRNU of the camera system. As σPRNU = %PRNU ·DN ,we have

%PRNU =σPRNUDN

.

The PRNU factor %PRNU can be found from a single data point for the PRNU asymptoticcurve; or, as before, we can do it in a graphical way, by denoting that

%PRNU =[σPRNUDN

]σPRNU=1

=1

DNPRNU,

where DNPRNU is the signal where the PRNU line intercepts the 1 DN rms noise. FromFig. 1, we �nd that %PRNU = 1/25 = 0.04 = 4%.Another parameter that can be extracted from the PT curve is the full-well charge, thatcorresponds to pixel saturation, which can be found where noise begins to decrease whenincreasing signal. A 5751 DN full well can be estimated from Fig. 1. Hence, the maximumnumber of electrons that can be integrated can be estimated as:

Nsat =DNsat

K=

5400 DN

0.666 DN/electrons= 8108 electrons.

Read noise can be also extracted:

σread,N =σread,DN

K=

6 DN

0.666 DN/electrons= 9 electrons.

The dynamic range of the sensor corresponding to the integration time used to acquirethe PTC can be thus easily determined:

DR =Nsat

σread,N=

8108

9= 900,

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that corresponds to 59 dB. These numbers are, with a reasonable error due to the ex-trapolating procedure, the same that we obtained during the last exercise class.Note that from the PTC you can also extract the minimum measurable signal includingthe e�ect of the photocurrent shot noise by �nding the point on the PTC where signaland noise are equal (i.e. SNR = 1). Hint: trace the bisector of the �rst and thirdquadrant...The most important thing related with PT is that all these parameters were extrapo-lated without knowing anything about neither the input light source nor the camera/pixelparameters! This is the greatest strength of the photon transfer technique.

Part 2: Double sampling technique in 3T pixel

Passive pixel sensors (PPSs) transfer photogenerated charge to a unique charge-detectionampli�er located at the end of the matrix so that all signals are read out with the sameampli�er. Therefore, any o�set is inherently constant for all pixels. On the other hand,each ampli�er of each pixel of an active pixel sensor (APS) has its own o�set, whichresults in the generation of �xed pattern noise (FPN). FPN is the spatial variation inpixel output values under uniform illumination due to parameter variations (mismatches)across the sensor.Remember that some `signals', e.g. sampling-induced kTC noise, that might be consideredas o�sets within the pixel, are perceived as noise within the whole image, since they aredi�erent from one pixel to the other.In general, there are some noise sources that are constant in time, but change betweenpixel and pixel, due to (i) mismatches in the lithographic process, that lead to variationsin capacitance values and transistors' dimensions, which re�ect on CPD (or on CFD fora 4T pixel, as we will see later) and on the source follower gain, (ii) non-uniformities indopants concentration, that lead to a spread of the threshold voltage of the transistors.There is reset (kTC) noise, that changes both from pixel to pixel and from one acquisitionto the following one. Finally, we have temporal noise, given by shot noise of both thephotocurrent and the dark current, and ADC quantization noise.The largest sources of in-pixel o�sets are reset noise and threshold voltage spread of thesource followers. As we learned in previous classes, these noise sources, when consideredfor each pixel, can be considered as o�sets, rather than noises; and we learned that anycan be (ideally) eliminated through some calibration and/or post-processing. Therefore,we can try to develop a suppression circuit to get rid of these o�sets.

The principle of o�set suppression for a 3T APS is shown in Fig. 5. First, the pixeloutput, that contains both the photosignal and the o�set, is read out (SHS) and storedin a memory; then, the photodiode is reset, and the pixel output, that now contains onlythe o�set signal, is read out (SHR) and stored in another memory. By subtracting oneoutput from the other, the o�set can be canceled.In a 3T APS circuit, both threshold voltage variations and kTC noise appear as o�sets

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Figure 5: Fixed pattern noise suppression in a 3T active pixel (double sampling tech-nique).

within the pixel, and thus as FPN within the whole image1:

VSHS = VDD + σreset,1 − VGS + σTH −QphCint

+ σtemp,

VSHR = VDD + σreset,2 − VGS + σTH .

Reset noise has a standard deviation σreset,Q =√kTCint. With the previously described

FPN suppression operation, the pixel output signal, that contains both the signal andthe o�set, is readout �rst, followed by the o�set signal readout, after the pixel reset.These signals are then subtracted to obtain the signal only. Note that the reset noisecomponents in the two signals (σreset,1 and σreset,2) are di�erent and uncorrelated, as resetoperation for SHS is uncorrelated from the one for SHR. On the other hand, thresholdvoltage spread, σTH , is correlated, since the threshold voltage of each speci�c pixel isconstant in time; thus, their e�ect is completely removed by taking the di�erence:

∆V = VSHS − VSHR = −QphCint

+ σreset,1 + σreset,2 + σtemp.

We were able to remove threshold-voltage FPN, at the cost of increasing kTC noise of afactor

√2, with respect to a single acquisition:

σreset,Q,3T,DS =√

2kTCint.

1N.B.: Here, and in the following equations, noise standard deviations and/or o�sets will be linearlysummed, as an e�ective way to show their e�ects. Of course, total rms noise should be computed bysumming the variance of each uncorrelated noise source.

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Note that in the 3T topology, as soon as the reset transistor is opened, the integrationof signal and dark current starts, so that there is no time to correctly sample the frozenreset noise value without interfering with the measurement, i.e. without interfering withthe photocurrent integration. This is why the reset signal readout (SHR) was performedafter the integration, with subsequent increase of reset noise.This operation, in a 3T pixel, is called double sampling. With this technique, we arecompensating for threshold voltage spreads, but we are increasing the e�ects of kTCnoise.

Part 4: 4T APS and correlated double sampling

Two signi�cant challenges exist in conventional pn photodiode pixels: dark current re-duction and reset noise reduction. To address these problems, the pinned photodiodestructure was introduced and has become very popular in most recent CMOS image sen-sors. The basic pinned photodiode pixel con�guration is shown in Fig. 6a. The pixelconsists of a pinned photodiode and four transistors that include a transfer gate (MTX),a reset transistor (MRS), an ampli�er transistor (MRD), and a select transistor (MSEL).Thus, the pixel structure is often called a four-transistor (4T) pixel in contrast to theconventional 3T one.The time diagram of the image acquisition in a 4T pixel is illustrated in Fig. 6b. At thebeginning of the pixel readout, the �oating di�usion (FD) node is reset at the supply volt-age by the reset transistor (MRS). Then the pixel output (VPIXOUT) is read out once,as a reset signal (VRST), and stored. VRST includes both inherent pixel o�sets and resetnoise at the FD node. Next, the transfer gate (MTX) turns on so that the accumulatedcharge in the pinned photodiode is transferred completely to the FD node. Because of thecomplete charge transfer, no reset noise is generated during the transfer operation. Thetransferred charge drops the potential at the FD node, and VPIXOUT decreases. Afterthe transfer operation, VPIXOUT is read out again as VSIG. By subtracting VRST fromVSIG, pixel FPN and reset noise are removed, resulting in a reduced overall noise. Sincenoises (both FPN and kTC) in VRST and VSIG signals are correlated, this operation iscalled correlated double sampling (CDS).Which is the capacitance seen by the integration node (FD) to ground? In principle, wehave the parallel of the physical di�usion capacitance and the input capacitance of theMRD transistor: Cint = CFD + Cin,MRD. On the contrary with respect to a standard3T pixel, with a pinned photodiode topology, the physical di�usion capacitance can bemade very small. As it is not responsible of photons collection, there is no need to makeit wide. Assuming a �oating di�usion area corresponding to minimum-size transistors,Adiff = WminLmin, and assuming a depletion width of 1 µm, we get a physical �oatingdi�usion capacitance of

CFD =ε0εrWL

xdep= 6.8 aF,

while the input capacitance of MRD transistor can be estimated as

Cin,MRD = C ′oxWL = 0.5 fF,

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Figure 6: Pinned photodiode pixel (4T pixel): (a) pixel structure and (b) timing diagram.

which is much higher than the physical di�usion one. With 4T pixel, it is a commonproperty that the integration capacitance is dominated by the input capacitance of thesource follower, MRD. This leads to huge bene�ts in terms of linearity of the pixel, asthe integration capacitance is now independent from a physical depletion capacitance,whose value, as we learned in previous classes, depends on the signal itself.Another important bene�t obtained from the adoption of the pinned photodiode (withrespect to standard pn photodiodes) is the lower dark current. Since the surface of thepinned photodiode is shielded by a p+ layer, dark current is highly reduced, from around10 nA/cm2, typical of pn photodiodes, to less than 1 nA/cm2.In order to trace the Photon Transfer Curve in this new situation, we can re-calculatesome noise contributions:

• The dark current is lowered by the pinned implant: from 0.2 fA of the 3T APSof exercise E17 we reached 0.02 fA in the 4T architecture. Consequently, we can

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quantify the dark shot noise improvement as follows:

σdark,N =

√qid,4T tint

q= 1.1 electrons (1)

• The KTC rms value is improved by a factor 20, resulting in a 0.4 electrons noise.The correlated double sampling (performed following the timing scheme of �gure6) ideally cancels the KTC noise term, sampling the reset just before the transfergate opening. Anyway, in a real situation, a residual contribution is always present,e.g. given by a discharge of the sample & hold capacitance or by other spuriouse�ects.

One can trace the PTC curve noting that:

1. for the sake of simplicity, we can assume that the whole system is somehow adjustedin order to obtain the same K gain of the 3T topology;

2. the full-well-charge is unchanged with respect to the 3T analyzed topology;

3. also the PRNU and the photocurrent shot noise will not change;

4. the only PTC improvement happens at the low-end. Indeed, the �at portion of thecurve given by the reset and dark noise, will be shifted downwards reaching a valueof:

DNread =√

(σ2dark,n + σ2KTC) ·K = 0.75DN (2)

The PTC obtained in this new situation is plotted in �gure 7, compared with the3T APS curve.

The maximum dynamic range its evidently increased:

DR = 20 · log10

(5751

0.75

)= 77.7dB (3)

Some �nal remarks: the correlated double sampling nulls the source follower transistorvoltage spread (as in the 3T case). Any other out-of-pixel electronic stage can introduceits own threshold spread, but can be realized with bigger MOS since the �ll factor dependsonly on in-pixel transistors. So, their voltage spread will be lower, given the Pelgromrelation:

σVt =const.√WL

(4)

Furthermore, the exercise told us to consider an unchanged PRNU for the 4T pixel. Ina real case, the situation can be a little more tricky: the integration capacitance (thatdetermines the photo-response of our pixel) is now dominated by the gate capacitance ofa minimum-size MOS. An additive contribution to PRNU is showing up, related to thegate capacitance spread...

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Figure 7: PTC for the 4T APS with CDS.

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