Complementary metal-oxide-semiconductor (CMOS) image sensors offer many advantages over CCDs’, such as system-on-chip, low power consumption and possibly lower cost of camera systems [1,2]. The pinned photodiode technology introduced to CMOS image sensors in mid-90s effectively reduces the dark current and cancels the kTC noise of pixels, and attains high conversion gain [3]. As a result, the noise level of recent CMOS image sensors is becoming even better than CCD image sensors, especially for applications that high frame-rate is required. Low-noise high-gain column readout circuits used for pixel noise cancelling and signal sampling are greatly contributing to the reduction of the readout random noise [4–7]. This high-gain column amplifier reduces the noise of wideband amplifiers at the output of image sensors by a factor of the gain, and if the amplifier reset noise is cancelled, the thermal noise due to the pixel source follow (SF) amplifier can be reduced by a factor of square root of the gain [7]. Nevertheless, for next-generation low-noise CMOS image sensors, advanced noise reduction techniques are needed in order to more effectively reduce the pixel SF amplifier noises, especially 1/f and random telegraph signal (RTS) noises and maintain the signal dynamic range.

In this paper, the noise reduction effects of another type of column-parallel high-gain signal readout circuits, correlated multiple sampling (CMS) circuits, for CMOS image sensors are discussed. In the CMS, both reset and signal levels of pixel outputs are sampled for multiple times and summed up, and the difference of the average of the two levels is calculated for pixel-related noise cancelling. Two types of the CMS circuits are proposed. One is with a simple integration and the other is with a folding integration. In the folding integrator, the signal swing of the integrator output is suppressed by a negative feedback using a comparator (one-bit analog-to-digital converter (ADC)) and a one-bit digital-to-analog converter (DAC). This allows us to reduce the readout noise while maintaining the signal dynamic range. A prototype 1Mpixel CMOS image sensor with pinned photodiodes and the column-parallel CMS circuits has been implemented. The noise measurement results show an interesting behavior for low-noise pixels and noisy pixels. The noise behavior in low-noise pixels due to thermal and 1/f noises and noisy pixels due to RTS and RTS-like noises is discussed with a noise analysis using a transfer function of the CMS.

The noise reduction effect of the CMS circuits for thermal, 1/f and RTS noises can be calculated in frequency domain if the noise power spectrum and transfer function of the CMS operation are known. The transfer function of the CMS circuits as a discrete time system can be obtained from Equation (5). The interval of the two multiple samples T_g influences to the 1/f noise reduction effect. For simplicity, T_g is supposed to be integer multiple of the sampling time T₀. Therefore, T_g is given by M_gT₀, where M_g is an integer. The final output of the CMS circuits as a function of discrete time, ΔV_SC(nT₀) is written as (11) Δ V SC ( n T 0 ) = ∑ k = 0 M − 1 { V P ( ( n − k ) T 0 ) − V P ( ( n − k − M − M g + 1 ) T 0 ) }where T₀ is the sampling period, V_P ((n − k) T₀) and V_P ((n − k − M − M_g + 1) T₀) are reset and signal levels of pixel outputs of the k-th sample, respectively. The transfer function of the CMS is obtained with z-transform, and is expressed in the z domain as (12) H CMS ( z ) = ( 1 − z − M )     ( 1 − z − ( M + M g − 1 ) ) 1 − z − 1 .

If M_g = 1, then it is simplified to (13) H CMS ( z ) = ( 1 − z − M ) 2 1 − z − 1 .

The output noise power, υ n , CMS 2 ¯ after the CMS process is calculated as (14) υ n , CMS 2 ¯ = ∫ 0 ∞ S n ( f ) 1 1 + ( ω / ω c ) 2 | H CMS ( e j ω T 0 ) | 2 dfwhere S_n (f) is a noise spectrum of the pixel source follower and ω_c is the cut-off angular frequency of the sampling circuits in the CMS. The noise power spectrum of the pixel source follower is given by (15) S n ( f ) = S nt + k f f + k RTS ⋅ τ RTS 1 + ( 2 π   f τ RTS ) 2where S_nt is the power spectrum density of the thermal noise, k_f is the flicker noise coefficient, and k_RTS and τ_RTS are the RTS noise coefficient and relaxation time, respectively, of the RTS noise. The RTS noise due to a single trap has a Lorentzian-type spectrum as given by the third term of Equation (15), and τ_RTS is given by (16) 1 τ RTS = 1 τ c + 1 τ ewhere τ_c and τ_e are mean time that the trap in the gate oxide captures and emits an electron, respectively [7].

The thermal noise with the CMS operation can be calculated without performing the integration of Equation (14) as (17) υ nt , CMS 2 ¯ = S nt ω CMS 2if ω_CMS ≪ ω_c, where ω_CMS is the bandwidth (cuf-off angular frequency) of the CMS circuits given by (18) ω CMS = 2 T 0 sin − 1 ( 2 M ) ≅ 2 T 0 2 M         ( f o r   M ≫   1 ) .Therefore the thermal noise power is reduced in inverse proportion to M as shown in Figure 6 due to bandwidth limitation effect.

From Equation (12) with z = exp(jωT₀), the noise power transfer function for the CMS is given by (19) | H CMS ( e j ω T 0 ) | 2 = 4 sin 2 ( ω M T 0 / 2 ) sin 2 { ω   ( M + M g − 1 )   T 0 / 2 } sin 2 ( ω T 0 / 2 )   .

The 1/f noise power with the CMS operation can be calculated by Equation (14) and (19). The result as a function of ω_cT₀ is shown in Figure 7(a) for M_g = 1 [10]. The noise power is normalized with 2M²k_f. In the case of M = 1, the CMS is operating as the correlatd double sampling (CDS) [9]. For M = ∞, it approaches 1.39 which corresponds to a differential averager using continuous integration [7]. The noise power as a function of M_g is shown in Figure 7(b). The noise power has a tendency to increase as M_g increases. For effective noise reduction, M_g should be minimized.

From Equation (14) and the third term of Equation (15), the normalized noise power with k_RTS is given by (20) υ n , RTS 2 ¯ = ∫ 0 ∞ k RTS / ω RTS 1 + ( ω / ω RTS ) 2 1 1 + ( ω / ω c ) 2 | H CMS ( e j ω T 0 ) | 2 d fwhere ω_RTS = 1/τ_RTS. The calculated RTS noise after the CMS process is shown in Figure 8. It shows the noise amplitude normalized by k_RTS as a function of the number of samplings. Three curves for ω_RTS/ω_C = 0.07, 0.1 and 0.13 are plotted. If the bandwidth of the CMS, ω_CMS determined by M is smaller than ω_RTS, the noise reduction effect becomes efficient and the gradient of the noise amplitude to M approaches −1/2.

A 1Mpixel CMOS image sensor with column-parallel FI-CMS circuits for the low-noise wide dynamic range readout is implemented with 0.18 μm CMOS technology with pinned photodiodes. The chip photomicrograph is shown in Figure 9. In this chip, the operation of the SI-CMS is also possible by disabling the function of folding. The pixel type is a 4-Tr pinned photodiode active pixel. The specifications of the CMOS image sensor are summarized in Table 1. The number of effective pixels is 1,024(H) × 1,024(V), the pixel size is 7.5 μm × 7.5 μm, and the conversion gain is 35 μV/e⁻. Chip outputs are come out by 4 channel output buffers, and are comprised of analog residue signals and counter output codes.

Figure 10(a) shows measurement results of the linearity of the implemented CMOS image sensor operating in the SI-CMS mode. Though the linearity is degraded at large output swing for M = 1, the gain of the signal in the linear region almost exactly follows the number of samplings. The dark noise distribution of the 1Mpixel CMOS image sensor is shown in Figure 10(b). The noise electron at the peak of distribution is about 15.6 e⁻ when the sampling number is 1. The noise electron is reduced to smaller than 2 e⁻ for the sampling number of 16. The noise distribution is entirely shifted to the lower noise as increasing the number of samplings.

Using the noise distribution shown in Figure 10(b), a cumulative probability (C.P.) P(y) of the temporal noise as a function of noise electrons given by (21) P ( y ) = ∑ x = y ∞ h ( x ) ∑ x = 0 ∞ h ( x )is calculated as shown in Figure 11, where h(x) is the distribution as a function of the noise electrons (x). The pixel noise sources are mainly thermal and 1/f noises of the source follower amplifier. However, some pixels have a large noise due to RTS and RTS-like noises. The tailing part of distribution of the cumulative probability (< 10⁻⁴) is due to the RTS- and RTS-like noise. Therefore, pixels are roughly classified into two types, low noise (C.P. > 10⁻⁴), and noisy pixels (C.P. < 10⁻⁴). In low noise region, the dominant noise components are the thermal and 1/f noises. In large noise region, the noisy pixels are mainly due to RTS or RTS-like noises [11]. The results of Figure 11 show that the CMS has a noise reduction effect of RTS and RTS-like noises if the number of samplings is increased.

Figure 12 shows behaviors of the low-noise and noisy pixels when the number of samplings is increased. Two plots show the values of noise electrons for low-noise and noisy pixels at 90 and 0.01% of cumulative probabilities, respectively. In the low-noise pixels, the noise amplitude is in inverse proportion to M, for M ≤ 4. This means that the dominant noise comes from the circuits and systems connected at the back of the CMS integrator such as output buffers and external ADCs. For M > 4, the CMS has a tendency of noise reduction in inverse proportion to square root of M. In this region, the dominant noise is due to thermal noise of the pixel source follower as predicted by Equations (17) and (18). Though it is not clearly shown in Figure 12, the noise reduction effect of the CMS is limited by the 1/f noise of the pixel source follower if the number of samplings is increased to larger than 16 as predicted by results of Figure 7(a). In the noisy pixels, the noise reduction effect of the CMS is very small for M ≤ 4, and the noise reduction factor ( Δ υ n ¯ / Δ M) seems to approach to −1/2 for M > 4. This result could be explained by the results of Figure 8 if the dominant noise is the RTS noise and 0.001% of the pixels (noisy pixels) takes ω_RTS/ω_C of around 0.1. However, further detailed measurements and analysis are necessary to conclude it.

Figure 13(a) and 13(b) show characteristics of the linearity and the dark noise distribution with the 1Mpixel CMOS image sensor using the column-parallel FI-CMS, respectively. In the linearity, the equivalent output signal M × ( V PR ¯ − V PS ¯ ) is calculated in digital domain using the value of (N_S − N_R), and ΔV_SC of Equation (10). The gain of the signal in the linear region follows the number of samplings. An important difference compared with the linear measurement results of SI-CMS (Figure 10(a)) is that the equivalent output is not limited to the maximum output swing of the integrator even though the number of samplings is increased to 16 while the output of the SI-CMS is limited to the maximum output swing of about 1 V. The maximum equivalent output swing of the FI-CMS is 6.94 V using M = 16 and the power supply voltage of 3.3 V. This shows the effectiveness for the wide dynamic range of the FI-CMS.

The problem of the FI-CMS of the present design when compared with that of the SI-CMS is the degradation of linearity and longer tailing of the dark noise distribution, as shown in Figure 13. A possible reason of the degradation is a coupling of digital signal lines running along sensitive analog circuit nodes in the column. In the SI-CMS mode, these digital lines are always fixed to “0”. As shown in the noise distribution of Figure 13(b), the FI-CMS has a noise reduction effect of the multiple sampling similar to that of the SI-CMS. Theoretically, the FI-CMS has the same noise reduction effect as that of the SI-CMS. Since the pixel outputs have large offset deviations, the influence of the coupling noise depends on the pixel source follower offsets. In most of the pixels, the influence of the digital signal coupling noise is cancelled out by the CDS operation if the reset and signal samplings have the same operation. However, in some pixels, the CDS does not completely cancel the coupling noise due to the FI-CMS operation, and population of noisy pixel increases. Therefore, the tailing of the distribution in Figure 13(b) is due to large digital signal coupling noises. The majority of the noise distribution around the peak has a behavior similar to that of the SI-CMS. The mean value of the distribution is 2.2 electrons, which corresponds to the input-referred noise of 77 μV_rms.

Table 2 shows a summary of measurement results of noise and dynamic range. In the case of the simple integration, the noise is reduced to smaller than 2 electrons while sacrificing the dynamic range to be 59.4 dB. On the other hand, in the case of the folding integration, the dynamic range of 75.0 dB (= 6.94 V/ (16 × 77 μV)) is attained while reducing the noise to 2.2 electrons.

In this paper, column-parallel correlated multiple sampling (CMS) circuits and their noise reduction effects have been investigated with an implemented 1Mpixel pinned photodiode CMOS image sensor. A simple integration CMS (SI-CMS) shows the effectiveness of system, thermal and RTS noise reductions. A very low noise level of less than 2 electrons is attained for sampling 16 times. A folding integraion CMS (FI-CMS) allows us to realize low-noise wide dynamic range CMOS image sensors. The dynamic range of 75 dB and noise level of 2.2 electrons have been achieved simultaneously. In the present design, the linearity and noise characteristics of the SI-CMS are better than those of the FI-CMS. Also, the SI-CMS which is simplified from the FI-CMS can be implemented in a smaller area at the column. Therefore the SI-CMS is useful if the dynamic range is not a great concern. To attain full advantage of the FI-CMS, improvements of the FI-CMS are necessary for further increasing dynamic range, improving the linearity, and reducing the noise level by redesigning the column readout circuits. A technique for reducing digital coupling noise proposed in [12] is useful.