POLITECNICO DI MILANO MSC COURSE - MEMS AND MICROSENSORS - 2017/2018 E19 PTC and 4T APS Cristiano Rocco Marra 20/12/2017 In this class we will introduce the photon transfer tecnique, a commonly-used routine to characterize image sensors. We will also analyze differences between 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 in exercise E17 is provided in figure 1. Verify that the calculations you made for the sensor of E17 are correct, extracting also information about the PRNU. What would change on the PTC using the double sampling technique, keeping a 3T architecture? Consider now a camera featuring a 4T CMOS APS, with a pinned diode structure. This specific pixels shows the same maximum full-well-charge and the same PRNU of the 3T case and the pinned implant reduces the dark current by a factor 10. Furthermore, the pixel is readout with the correlated double sampling technique, that reduces the reset noise by a factor 20. Trace the PTC curve in this new situation, evaluating graphically the maximum dynamic range reachable by the sensor. 1
Figure 1: Measured PT curve. PART 1: PHOTON TRANSFER Adapted from J. Janesick, Photon transfer, 1st ed, 2007. Photon transfer (PT) is a valuable testing methodology employed in the design, operation, characterization, optimization, calibration, specification, and application of solid state image sensors and camera systems. Invented in the mid-1970s, today photon transfer is routinely used and continues to evolve. The photon transfer technique is applicable to all imaging disciplines. Detector performance parameters, such as quantum efficiency, noise, charge collection efficiency, sense node capacitance, charge capacity, dynamic 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 box and determine the desired parameters with very little effort. The user needs only to expose the camera to a light source and measure the signal and noise output responses. A functional block diagram for a typical camera system is illustrated in Fig. 2. The system shown is described by the six transfer functions related to the semiconductor, pixel detector, and electronics that process the signal. The gain functions of each box of the figure are difficult to measure individually with good precision, especially those parameters related to the internal workings of the sensor. The PT method provides a solution to find the overall camera transfer function (or gain, or sensitivity) accurately without knowing each individual transfer function. The peculiarity of the PT technique is that it s only fully applicable if a detector s response is shot noise-limited. Fortunately, this is the case for solid state image sensors such as 2
CCD and CMOS matrices. The general PT formula will now be derived. Figure 2: Typical solid state camera system showing internal gain functions and signal and noise parameters. Fig. 3 shows a generic camera block diagram where the input signal exhibits shot noise characteristics, i.e. σ A = A, where A is the mean input signal level, and σ A is the input noise standard deviation. For an image sensor, the only quantities that exhibit this property are photons and electrons (assuming a unity quantum efficiency, η = 1). In fact, σ Nel = 2qi ph 1 2t int t 2 int q = qi ph t int q = Qph q = N ph. Figure 3: Black box camera system with a constant K = B/A used to transfer the input A to the output B. A sensitivity constant defined as K relates the input with the output: and B = K A, σ B = K σ A, where B and σ B are the measured output mean signal level and noise standard deviation, respectively. Units for output B and input A will be different; generally, A is specified in absolute physical units that describe shot noise characteristics (number of photons or electrons), 3
whereas B is specified in relative non-physical units generated by an amplifier or analog-todigital converter (V, LSBs, digital number,... ). Actually, the sensitivity of an image sensor is a function of the wavelength. In this context a linear gain K (instead of an integral law over the visible spectrum) can be precisely defined only if the radiation spectrum is monochromatic. In the exercises, even if the radiation specturm is not monochromatic, we will assume it as characterized by its dominant wavelength - unless differently specified. At this point in the analysis K is unknown. However, by re-arranging the K -equation with proper substitutions we get the PT main result: Hence: K = B A = B σ 2 A = B σ 2 B K 2 = K 2 B σ 2. B K = σ2 B B This is called the PT relation, the equation that is the basis of the PT technique. Note that K is simply found by measuring output statistics (mean and noise variance) without knowledge of neither the individual camera transfer functions nor on the input characteristics (except for its shot-noise requirement). Let s have a look at the typical noises at the output of the sensor. We have (i) shot noise, that increases with the square root of the signal, (ii) PRNU, associated with pixel-to-pixel response differences and whose standard deviation increases linearly with signal, (iii) the so-called read noise, that encompasses all noise sources that are signal independent. These three noise sources can be summed up (quadratically), giving the total output noise σ TOT = σ 2 read + σ2 shot + σ2 PRNU. An ideal photon transfer curve (PTC) response from a camera system exposed to a uniform light source is illustrated in Fig. 4. Noise (rms) is plotted as a function of average output signal. Four distinct noise regimes are identified in a PTC. The first regime, read noise, represents the random noise measured under dark conditions, which includes several different noise contributors; they can be both temporal and FPN: dark shot noise, ktc noise, DSNU,.... As the light illumination is increased, read noise gives way to photon shot noise, which represents the middle region of the curve. Since the plot in Fig. 4 is on log-log coordinates, shot noise is characterized by a line with a slope of 1/2. The third regime is associated with pixel PRNU, which produces a characteristic slope of unity because signal and FPN scale together. The fourth region occurs when the matrix of pixels enters the full-well regime. In this region the noise modulation typically decreases as saturation is approached. The photon transfer curve (PTC) is a commonly used test procedure to characterize digital sensors parameters, i.e. from output data, we can infer a lot of system and pixel parameters of the sensor. This is done without knowing anything of the camera system, i.e. by assuming 4
Figure 4: Ideal total noise PTC illustration showing the four classical noise regimes. the camera as a black box. In fact, given a certain photon flux impinging on the sensor, you can measure the output signal of each pixel. From this data, you can calculate the average output signal, DN, its standard deviation, σ DN, and you can draw your PTC with the average signal on the x-axis and its standard deviation on the y-axis. This can be repeated for different photon fluxes, i.e. for different average output signals, and a complete PT curve is built. In Fig. 5, a measured photon transfer curve is displayed. 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. PTC measurements are usually made (initially) in digital number (DN) units that will be later converted to electron units, if needed. Usually, the light intensity is varied for a PTC sequence, and a low-cost light-emitting diode (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 matrix of pixels being sampled needs to be very high, otherwise FPN measurements will be in error. 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 contribution alone: read, shot and PRNU. This can be easily (and faster) done in a graphical way, by drawing the asymptotic curves, with 0, 1/2 and 1 slopes, respectively (in a log-log plot). Remember the equation of the photon transfer theory: K = σ2 B B. The equation states that one could extract the transfer function of the camera system, by tak- 5
Figure 5: Measured PT curve and extracted parameters. ing the ratio between the output variance and the output signal, assuming that the system is shot noise limited, i.e. if σ A = A. Hence, from measured data, we can immediately infer the transfer function of the system from the number of photons/electrons to the digital output. This is be practically done by simply calculating the ratio between the variance and the average output signal. Things are even easier: K can be found graphically by extending the slope 1/2 shot noise line back to the signal axis. The signal intercept with the 1 DN rms noise line represents the inverse of the transfer function. From Fig. 1: K = [ ] σ 2 B 1 = = 1 = 0.666 DN/electrons. B DN σ B =1 shot 1.5 We can then extrapolate the PRNU of the camera system. As σ PRNU = % PRNU DN, we have % PRNU = σ PRNU DN. The PRNU factor % PRNU can be found from a single data point for the PRNU asymptotic curve; or, as before, we can do it in a graphical way, by denoting that [ σprnu ] 1 % PRNU = =, DN σ PRNU =1 DN PRNU where DN PRNU is the signal where the PRNU line intercepts the 1 DN rms noise. From Fig. 1, we find that % PRNU = 1/25 = 0.04 = 4%. 6
Another parameter that can be extracted from the PT curve is the full-well charge, that corresponds to pixel saturation, which can be found where noise begins to decrease when increasing signal. A 5751 DN full well can be estimated from Fig. 1. Hence, the maximum number of electrons that can be integrated can be estimated as: N sat = DN sat K 5751 DN = = 8635 electrons. 0.666 DN/electrons Read noise can be also extracted: σ read,n = σ read,dn K 5.5 DN = = 8.3 electrons. 0.666 DN/electrons The maximum dynamic range of the sensor can be thus easily determined: DR max = N sat = 8635 σ read,n 8.3 = 1040, that corresponds to 60 db. If you want to find the dynamic range for the given integration time (and not the maximum one), you can find the minimum measurable signal simply finding the point on the graph where the signal is equal to the noise (i.e. SNR = 1). Hint: trace the bisector of the first and third quadrant... The most important thing related with PT is that all these parameters were extrapolated without knowing anything about neither the input light source nor the camera/pixel parameters! 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-detection amplifier located at the end of the matrix so that all signals are read out with the same amplifier. Therefore, any offset is inherently constant for all pixels. On the other hand, each amplifier of each pixel of an active pixel sensor (APS) has its own offset, which results in the generation of fixed pattern noise (FPN). FPN is the spatial variation in pixel 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 considered as offsets within the pixel, are perceived as noise within the whole image, since they are different from one pixel to the other. In general, there are some noise sources that are constant in time, but change between pixel and pixel, due to (i) mismatches in the lithographic process, that lead to variations in capacitance values and transistors dimensions, which reflect on C PD (or on C F D for a 4T pixel, as we will see later) and on the source follower gain, (ii) non-uniformities in dopants 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 acquisition to the following one. Finally, we have temporal noise, given by shot noise of both the photocurrent and the dark current, and ADC quantization noise. 7
The largest sources of in-pixel offsets are reset noise and threshold voltage spread of the source followers. As we learned in previous classes, these noise sources, when considered for each pixel, can be considered as offsets, rather than noises; and we learned that any can be (ideally) eliminated through some calibration and/or post-processing. Therefore, we can try to develop a suppression circuit to get rid of these offsets. The principle of offset suppression for a 3T APS is shown in Fig. 6. First, the pixel output, that contains both the photosignal and the offset, is read out (SHS) and stored in a memory; then, the photodiode is reset, and the pixel output, that now contains only the offset signal, is read out (SHR) and stored in another memory. By subtracting one output from the other, the offset can be canceled. Figure 6: Fixed pattern noise suppression in a 3T active pixel (double sampling technique). In a 3T APS circuit, both threshold voltage variations and ktc noise appear as offsets within the pixel, and thus as FPN within the whole image 1 : V SHS = V DD + σ reset,1 V GS + σ T H Q ph C int + σ temp, V SHR = V DD + σ reset,2 V GS + σ T H. Reset noise has a standard deviation σ reset,q = ktc int. With the previously described FPN suppression operation, the pixel output signal, that contains both the signal and the offset, is 1 N.B.: Here, and in the following equations, noise standard deviations and/or offsets will be linearly summed, as an effective way to show their effects. Of course, total rms noise should be computed by summing the variance of each uncorrelated noise source. 8
readout first, followed by the offset signal readout, after the pixel reset. These signals are then subtracted to obtain the signal only. Note that the reset noise components in the two signals (σ reset,1 and σ reset,2 ) are different and uncorrelated, as reset operation for SHS is uncorrelated from the one for SHR. On the other hand, threshold voltage spread, σ T H, is correlated, since the threshold voltage of each specific pixel is constant in time; thus, their effect is completely removed by taking the difference: V = V SHS V SHR = Q ph C int + σ reset,1 + σ reset,2 + σ temp. We were able to remove threshold-voltage FPN, at the cost of increasing ktc noise of a factor 2, with respect to a single acquisition: σ reset,q,3t,ds = 2kTC int. Note that in the 3T topology, as soon as the reset transistor is opened, the integration of signal and dark current starts, so that there is no time to correctly sample the frozen reset noise value without interfering with the measurement, i.e. without interfering with the photocurrent integration. This is why the reset signal readout (SHR) was performed after the integration, with subsequent increase of reset noise. This operation, in a 3T pixel, is called double sampling. With this technique, we are compensating for threshold voltage spreads, but we are increasing the effects of ktc noise. PART 4: 4T APS AND CORRELATED DOUBLE SAMPLING Two significant challenges exist in conventional pn photodiode pixels: dark current reduction and reset noise reduction. To address these problems, the pinned photodiode structure was introduced and has become very popular in most recent CMOS image sensors. The basic pinned photodiode pixel configuration is shown in Fig. 7a. The pixel consists of a pinned photodiode and four transistors that include a transfer gate (MTX), a reset transistor (MRS), an amplifier transistor (MRD), and a select transistor (MSEL). Thus, the pixel structure is often called a four-transistor (4T) pixel in contrast to the conventional 3T one. The time diagram of the image acquisition in a 4T pixel is illustrated in Fig. 7b. At the beginning of the pixel readout, the floating diffusion (FD) node is reset at the supply voltage 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 offsets and reset noise at the FD node. Next, the transfer gate (MTX) turns on so that the accumulated charge in the pinned photodiode is transferred completely to the FD node. Because of the complete charge transfer, no reset noise is generated during the transfer operation. The transferred charge drops the potential at the FD node, and VPIXOUT decreases. After the transfer operation, VPIXOUT is read out again as VSIG. By subtracting VRST from VSIG, pixel FPN and reset noise are removed, resulting in a reduced overall noise. Since noises (both FPN and ktc) in VRST and VSIG signals are correlated, this operation is called correlated double sampling (CDS). Which is the capacitance seen by the integration node (FD) to ground? In principle, we have the parallel of the physical diffusion capacitance and the input capacitance of the MRD transistor: C int = C F D + C in,mrd. On the contrary with respect to a standard 3T pixel, with a 9
Figure 7: Pinned photodiode pixel (4T pixel): (a) pixel structure and (b) timing diagram. pinned photodiode topology, the physical diffusion capacitance can be made very small. As it is not responsible of photons collection, there is no need to make it wide. Assuming a floating diffusion area corresponding to minimum-size transistors, A di f f = W min L min, and assuming a depletion width of 1 µm, we get a physical floating diffusion capacitance of C F D = ɛ 0ɛ r W L x dep = 6.8 af, while the input capacitance of MRD transistor can be estimated as C in,mrd = C ox W L = 0.5 ff, which is much higher than the physical diffusion one. With 4T pixel, it is a common property that the integration capacitance is dominated by the input capacitance of the source follower, 10
MRD. This leads to huge benefits in terms of linearity of the pixel, as the 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 benefit obtained from the adoption of the pinned photodiode (with respect to standard pn photodiodes) is the lower dark current. Since the surface of the pinned photodiode is shielded by a p + layer, dark current is highly reduced, from around 10 na/cm 2, typical of pn photodiodes, to less than 1 na/cm 2. In order to trace the Photon Transfer Curve in this new situation, we can re-calculate some noise contributions: The dark current is lowered by the pinned implant: from 0.2f A of the 3T APS of exercise E17 we reached 0.02f A in the 4T architecture. Consequently, we can quantify the dark shot noise improvement as follows: σ dark,n = qid,4t t int q = 1.1electr ons (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 figure 7) ideally cancels the KTC noise term, sampling the reset just before the transfer gate 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 spurious effects. One can trace the PTC curve noting that: 1. for the sake of simplicity, we can assume that the whole systyem is somehow adjusted in 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 flat portion of the curve given by the reset and dark noise, will be shifted downwards reaching a value of: DN read = (σ 2 dark,n + σ2 ) K = 0.75DN (2) K TC The PTC obtained in this new situation is plotted in figure 8, compared with the 3T APS curve. The maximum dynamic range its evidently increased: 5751 DR = 20log 10 = 77.7dB (3) 0.75 Some final remarks: the correlated double sampling nulls the source follower transistor voltage spread (as in the 3T case). Any other out-of-pixel electronic stage can introduce its own 11
Figure 8: PTC for the 4T APS with CDS. threshold spread, but can be realized with bigger MOS since the fill factor depends only on in-pixel transistors. So, their voltage spread will be lower, given the Pelgrom relation: σ Vt = const ant (W L) (4) Furthermore, the exercise told us to consider an unchanged PRNU for the 4T pixel. In a real case, the situation can be a little more tricky: the integration capacitance (that determines the photo-response of our pixel) is now dominated by the gate capacitance of a minimumsize MOS. An additive contribution to PRNU is showing up, related to the gate capacitance spread... 12