ANALYSIS OF NOISE IN CMOS IMAGE SENSOR

I. Brouk*1, A. Nemirovsky2, Y. Nemirovsky1

1Department of Electrical Engineering, Kidron Microelectronics Center, Technion – Israel Institute of Technology, 32000, Haifa, Israel

2Department of Electrical Engineering, Kinneret College on the Sea of Galilee, Jordan Valley, Israel

E-mail: bigor@techunix.technion.ac.il

Introduction CMOS image sensors based on active pixel sensors (APS) are now the preferred technology for most imaging applications. With advanced technology, reduced channel size, novel designs extending the more established pixels based on three transistors (3T design) into four transistors (4T design employing pinned photodiodes), the performance keeps improving [1-2]. Noise sets a limit on image sensor performance, mainly under conditions of low illumination. Analysis of noise in CMOS APS has been reported by several authors (for example, [3-4]). In this paper, we present an analysis of noise due to thermal, 1/f and shot noise sources in two types of APS, known as the 3T [1] and 4T pixel design [2], based on a unified time-dependent approach, using the separation of the system into two parts: time-invariant part (the APS without switching) and a time-variant part (taking into consideration the switching process). We suggest that the conventional noise analysis based on the frequency domain [4], usually used for noise calculations of APS's cannot be strictly applied, because the switched APS circuitry under study cannot be represented as a linear time-invariant system. To calculate explicit noise expressions for noise performance we, therefore, resort to time dependent circuit models and perform time-domain noise analysis, taking into account the stationary nature of the various noise processes. The main advantage of the present method is that it is mathematically correct and avoids a basic flaw underlining the widely-used conventional methods (that freely use time-invariant methods for time-dependent systems). Although for many practical applications the resulting error is small, or even negligible, yet there may be situations where the resulting error may be considerable, not to mention the tutorial value of the correct method presented here.

The Operation Principles and Noise Sources in 3T and 4T APS

In the 3T design (Fig.1) each pixel consists of one photodiode and three transistors: transistor M4 performing the reset of photodiode, transistor M1 operating as a source follower, and transistor M2 operating as an analog

selection switch. The APS can be designed on the base of NMOS transistors, PMOS transistors, or both NMOS and PMOS transistors [5]. The photo-signal is integrated on the floating diffusion (FD) capacitance Cd, which is compromised of the photodiode junction capacitance in parallel with the gate capacitance of transistor M1 and the junction capacitance (source or drain) of transistor M4. In addition to the pixel elements, there are several elements, which are common within each row of APS: transistor M3, providing current for the source follower and transistors M5 and M6 operating as a pass-gate.

M3

VDD D1

CL

Output

“FD”

VDD

Read Row

Read Row

Read Column

Vb

Reset M1

M2 M4

M6

M5

Pixel

Row Bus

Cd

The 4T design [2] (Fig.2), in turn, introduces two novel features: the regular photodiode is replaced by a pinned photodiode (PPD) (D1), which is separated from the output node by the transfer gate TX (transistor M7) similar to the photogate version of APS [1]. It should be noted that the transfer gate TX is not a regular transistor: both the transfer gate TX and PPD are carefully optimized to remove all free electrons from the PPD to the FD. As shown in Fig.2, the source of the TX transistor is the N-side region of the PPD, where the N-region is floating underneath a heavy p+ doping pinning layer (see, for example, [6]). The drain side of TX transistor is the FD node, to which the electrons are transferred and where they are converted into voltage signal. When the transfer gate TX is turned off, the photodiode is isolated from the readout FD node, thus the integration of the photo-generated charge happens at the capacitance Cph of the photodiode. However, if the transfer gate TX is turned on, the accumulated charge is redistributed to capacitance Cd (of the FD), which is compromised of the gate capacitance of transistor M1 in parallel with the source junction capacitance of transistor M4. The rest of the pixel components perform the same functions as in 3T design: transistor M4 performs the reset of capacitance Cd, transistor M1 operates as a source follower, performing read out of the voltage at FD node, and transistor M2 operates as an analog selection switch. The additional elements, such as transistor M3, providing current for the source follower and transistors M5-M6, operating as a pass-gate, are common for each row of both 3T and 4T APS.

Figure 1. APS: 3T design.

The additional transistor TX introduces the following advantages: the FD provides an in-pixel memory cell, allowing the reset of the FD and the first sampling to be performed “in parallel” with the signal integration, thus enabling true correlated double sampling (CDS) and reduced kTC noise. These aspects are clarified by the timing diagram (Fig.3). The timing diagram of the 4T pixel is shown in Fig.3 and presents the sequences for three control signals: “Reset”, “TX” and “Select”, where “Select” = “Read Column” ∧ “Read Row”. The operation of 4T pixel includes six phases: charging, reset, integration, charge transfer and sampling (twice). The first phase of 4T pixel operation is the charging of capacitances Cph and Cd. During this phase both the switch “Reset” and transfer gate TX are turned on, capacitance Cd is charged to the mean voltage defined by (VDD-VDS,M4), while the PPD node (connected to the transfer gate TX) is charged to the fixed voltage, defined by the fully depleted PPD. At time t1 (reset phase) the transfer gate TX is turned off and the signal charge generated by incident light begins to be collected on the photodiode capacitance Cph. The potential of the n-region of the photodiode is decreased as photo-generated charge is accumulated. At the same time, the FD capacitance Cd remains to be connected to VDD through the reset transistor M4 and therefore it does not accumulate the photo-carriers. At time t2, before the first sampling, the “Reset” control is turned off, causing the capacitance Cd to be floating. As a result of this operation, after time t2, the voltage on capacitance Cd is defined by: (1) the voltage accumulated on capacitance Cd till time t2 (including a contribution of the reset noise), (2) the DC-contribution of dark- and photo-current through the p-n junction of the FD, (3) the shot noise defined by this current, and (4) the charge transferred from PPD D1 during the charge transfer phase (see below). It is clear that the DC-contribution of dark- and photo-current can be reduced by decrease of the time interval (t5-t2). During the first sampling, which begins at time t3 turning on “Select” control, the voltage on capacitance Cd (at FD node) is read out. Before the second sampling takes place, “TX” is turned on at time t4, transferring all charge accumulated on the photodiode capacitance Cph to the floating capacitance Cd. After this step, at time t5 “Select” control is turned on, performing the second sampling of the voltage at FD node, containing the signal and the same contribution of reset noise, which was read out during the first sampling. Subtracting the results of two samples by means of CDS circuit (out of pixel) and assuming that the contribution of the dark- and photo- currents flowing through p-n junction at FD node is negligible relatively the reset noise at FD node, reset noise can be fully eliminated at the output of CDS circuit. The last requirement is very important from the point of true CDS function.

CL

M3

VDD

D1

VDD

Read Row

Read Row

Read Column

Vb

Reset M1

M2 M4

M6

M5

Pixel

Row Bus

TX

M7

Cph

Cd

“FD”

Output

The total noise related to the whole system is the RMS fluctuations of the output signal VOUT; these fluctuations are contributed by several different noise sources, including: - Shot noise of the dark and signal current; - MOS transistor thermal and 1/f noise.

Figure 2. APS: 4T design.

Figure 3. Timing diagram for 4T design.

A Novel Unified Time-Dependent Approach for Noise Analysis in APS

Analysis of stationary noise in time-invariant, analog (linear) systems is usually performed by using power spectral density (PSD) of the noise under consideration [4]. This approach is very convenient because the noise components generated in the various elements (such as resistors, transistors, photodiodes) are usually characterized in the form of PSD. However, this approach is not valid when the noise cannot be modeled as a stationary random process, or if the system is not linear or is not time-invariant. A system comprising an APS operating periodically as determined by its controlling switches cannot be modeled as a time-invariant system, since its time-response does depend on the actual phase of the period. Nevertheless, it is still rather common to use PSD for noise analysis in such systems. To overcome this difficulty, the analysis is performed in this study in the time domain and consists of the following steps: a) The noise component under consideration (i.e., thermal, shot or 1/f) is

represented as a sample function defined over a probability space; b) The system is separated into a time-invariant part (the APS without

switching) and a time-variant part (i.e., the switches); c) The time-variant part is formulated using unit-step functions and then

attributed to the sample function representation of the noise process. The result is a time-domain noise representation, in which the noise is no longer stationary, but is equal to the original stationary process multiplied by a deterministic time-dependent function that represents the time-variant (switch/switches) effect;

d) A convolution technique is applied to explicitly calculate the variance of the noise at the output of the system. The result is obviously time dependent owing to the time-variant part of the system;

e) Each phase is calculated separately (Table 1).

Noise contribution by each phase

3T APS 4T APS

Reset √ Cancelled Charging - - Integration √ √ Charge Transfer - √ Sampling √ √ (twice)

Total Noise in APS: Simulations vs. Measurement Results

The total noise at the output of APS matrix is defined as a superposition of the noise contributions during the different phases of APS operation. Taking into account that all noise sources are not correlated and that the reset noise is cancelled in the case of 4T pixel, the total noise at the pixel output is given by:

Table 1. Comparison between noise contributions within 3T and 4T design.

[ ][ ]

σ+σ+σ

σ+σ+σ=σ

APST4for),t(2H)t()t(

APST3for),t(H)t()t(

adRe22

APSCT2

Int2

adRe22

APSInt2

setRe2

2Output (1)

where HAPS is voltage gain of APS (source follower), tReset, tInt, tRead and tCT are the durations of the reset, integration, reading and charge transfer phases, σ2(tReset), σ2(tInt), σ2(tRead), σ2(tCT) are the variances of the voltage contributed during the reset phase, integration phase, reading phase and charge transfer phase, correspondingly [7]. The terms σ2(tReset) and σ2(tRead) are given by:

σ+σ

σ+σ+σ=σ

APST4for),t()t(

APST3for),t()t()t()t(

setRe2

f/1setRe2Th

setRe2SNsetRe

2f/1setRe

2Th

setRe2 (2)

σ

σ+σ=σ

APST4for),t(

APST3for),t()t()t(

adRe2Th

adRe2

f/1adRe2Th

adRe2 (3)

where indexes “Th”, “1/f” and “SN” correspond to the contributions of the thermal noise, 1/f noise and shot noise. The detailed analysis of the contribution of each noise source is presented in [7].

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

1 10 100 1000 10000 100000

Input Signal, [electrons]

Inpu

t Ref

erre

d R

MS

Noi

se, [

elec

tron

s]

3T APS (Simulated)

4T APS (Simulated)

4T APS [8], (Measured)

Main design parameters of the simulated APS:- 3T APS: Cd=3 fF, CL=2 pF, Conversion Gain=45.3 uV/e;- 4T APS: Cd=2.2 fF, CL=2 pF, Conversion Gain=61.8 uV/e.

Fig.4 [7] shows the simulated total input referred noise in 3T APS, implemented by N-type transistors and the simulated total input referred noise in 4T APS (provided that the reset noise and 1/f noise contribution of the

Figure 4. Total noise in: - 3T APS and 4T APS (simulated in accordance with 0.18 µm specialized CIS process of Tower Semiconductor Ltd. [9]), - 4T APS [8] (measured, for 4T APS, which were fabricated in 0.18 µm specialized CIS process of Tower Semiconductor Ltd. [9]).

reading phase are absolutely cancelled), calculated in accordance with Eq.(1). Fig.4 also exhibits the measured total input referred noise for 4T APS [8], while the pixels were simulated/fabricated in 0.18 µm specialized CIS process provided by [9]. A summary of the main sensor characteristics is provided in Table 2. One can see that 4T APS exhibits significantly lower noise than 3T APS.

3T APS (Simulated)

4T APS (Simulated)

4T APS [8] (Measured)

Technology 0.18 µm specialized CIS process of Tower Semiconductor Ltd. [9]

0.18 µm specialized CIS process of Tower Semiconductor Ltd. [9]

0.18 µm specialized CIS process of Tower Semiconductor Ltd. [9]

Transistors per pixel

3 (N-type) 4 (N-type) 4 (N-type)

FD capacitance

See “Integration capacitance”

2.2 fF 1.5 fF − 8 fF (depending on the pixel design)

Integration capacitance

3 fF 2.2 fF 1.5 fF − 8 fF (depending on the pixel design)

Saturation charge

~ 19 ke ~14 ke 10 ke − 60 ke (depending on the pixel size)

Minimum pixel input referred noise

~ 25.5 e ~ 3 e 3 − 6 e (depending on the pixel design)

Photodiode type

N-well / P-sub. Pinned Pinned

Conclusion

This paper exhibits the noise analysis within APS, which has been done using a unified time-dependent approach allowing analysis of the switched circuits with time-varying sources. In accordance with this approach, analytic expressions have been obtained for each source of the noise as a function of time. The simulation results are in excellent agreement with the measurements, demonstrating that 4T APS exhibits significantly lower noise than 3T APS (Fig.4) due to the reset noise cancellation and the unique features introduced by the PPD and the transfer gate TX. It should be noted that analysis of noise in APS in the time domain was already performed in [3], using a time-varying circuit model. However, the approach presented here is more fundamental and more complete. Moreover, the result first reported in [3] of reset noise of kT/2Cd is obtained here

Table 2. Main parameters of APS corresponding to Fig.4.

rigorously for contribution of N-type reset switch, while a P-type switch still exhibits kT/Cd. However, once we consider also the contribution of the photodiode, the overall reset noise is still kT/Cd both for N-type and P-type reset switch. For the sake of strictness, it should be noted that the analysis of noise in APS in the time domain was performed in [3] for different operation conditions. According to [3] the settling time of the reset operation was larger than the duration of the reset phase, while in our case, as confirmed by simulations, the settling time is negligible relatively to the duration of the reset phase. The main advantage of the rigorous method presented here is that it is mathematically correct and avoids the basic flaw underlining the widely-used conventional methods. The excellent correspondence between measured and simulated noise indicates the validity of the approach. Furthermore, it is obvious that this methodology of noise analysis can be extended and used for more complex architectures.

References

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