Dark Current and Signal-to-Noise Ratio in BDJ Image Sensors

1892 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 6, DECEMBER 2006

Dark Current and Signal-to-Noise Ratio inBDJ Image Sensors

Sylvain Feruglio, Member, IEEE, Victor Fouad Hanna, Fellow, IEEE, Georges Alquie, Member, IEEE,and Gabriel Vasilescu, Senior Member, IEEE

Abstract—In this paper, analytical expressions of dark currentsand equivalent noise generators of a CMOS color image sensorare presented, and the signal-to-noise ratio (SNR) at both outputsis evaluated. Static measurements and simulations on AustriaMicro Systems 0.35-µm CMOS test structures yield guidelines toincrease the SNR of the buried double junction photodetector.

Index Terms—Active pixel sensor (APS), buried double junction(BDJ), CMOS, dark current, noise, photodetector, signal-to-noiseratio (SNR).

I. INTRODUCTION

DURING the last decade, for low power dissipation and lowcost applications, CMOS active pixel sensors (APSs) have

emerged as alternative solid-state imaging devices to the maturecharge-coupled devices (CCDs). Despite several benefits suchas increased system integration on chip, high resolution, andrandom addressing, CMOS APSs have not yet reached the CCDperformance in terms of minimum detectable signal, mainlydue to their high dark current and significant noise level.

This paper is organized in five sections. Following the in-troduction, Section II describes the structure, its principle ofoperation, and the Simulation Program with Integrated CircuitEmphasis (SPICE) model of the CMOS buried double junction(BDJ) photodetector. Section III presents the physical mecha-nisms implied in dark current generation. Then, in Section IV,the experimental results with a 0.35-µm CMOS test chip arepresented, and several parameters are extracted. Finally, a noiseanalysis is carried out in Section V, followed by conclusions inthe last section.

II. BDJ PHOTODETECTOR

A. Principle and Operation

Generally, an APS can be defined as a simple photodetec-tor (photodiode or photoMOS) associated with some CMOStransistors (usually between two and five) to provide intrapixelamplification and nondestructive readout. When applied tothe BDJ photodetector, a typical configuration is shown inFig. 1 [19].

The photodetector, which is fabricated in a standard CMOSprocess, consists of two buried p-n junctions (i.e., J1: p+-

Manuscript received August 15, 2005; revised July 24, 2006.The authors are with the Laboratoire des Instruments et Systèmes Ile de

France, Pierre and Marie Curie University–Paris VI, 94200 Ivry sur Seine,France (e-mail: [email protected]).

Color versions of all figures are available online at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIM.2006.884291

Fig. 1. CMOS BDJ APS.

Fig. 2. Simplified cross section of the BDJ photodetector.

diffusion/n-well and J2: p-substrate/n-well), vertically stackedand supplying at the outputs two currents I1 and I2 (Fig. 2)such that

I1 = Iph1 + Idc1 (1a)

I2 = Iph1 + Idc1 + Iph2 + Idc2

= I1 + I3 (1b)

where Iph1 and Iph2 represent the photocurrents, and Idc1 andIdc2 are the dark currents flowing through each junction.

The device operation is based on the silicon propertyof absorbing each radiation wavelength at a different depth[1]–[11]. Under reverse-biased conditions, in addition to thedark current, each junction collects the photo-generated carriersat its depth. Hence, two spectral responses are available from

0018-9456/$20.00 © 2006 IEEE

FERUGLIO et al.: DARK CURRENT AND SIGNAL-TO-NOISE RATIO IN BDJ IMAGE SENSORS 1893

Fig. 3. Spectral response of each photodetector junction J1 and J2 versus theincident wavelength.

Fig. 4. Photocurrents ratio I3/I1 versus the incident wavelength.

the same pixel, and they look like two bandpass plots centeredon two different wavelengths (Fig. 3). Furthermore, as depictedin Fig. 4, the output current ratio I3/I1 shows a monotonicallyincreasing function with the wavelength λ. Thus, no opticalfilters or prisms are needed for color applications; consequently,we expect a more efficient light acquisition and a less expensivedevice.

These properties make this device particularly attractive forcolor detection, light intensity measurement, and monochro-matic light wavelength measurement. Many biomedical andchemical applications have been developed, including a fluo-rescence detector [4], an autocalibrated pH-meter [5], and aniron concentration meter [6]. For color image sensors dedicatedto imagery, an alternative approach has been proposed byFindlater et al. [7]–[9] by adding two suitable filters in orderto obtain an equal sampling of all colors in the space domain.Moreover, with this kind of sensor, the crosstalk betweenneighbor pixels is reduced below the value obtained whenusing conventional CMOS image sensors. Finally, it will bepointed out that this detector can operate up to a few hundredmegahertz [10], [11], which opens the field of applications tocommunication systems.

Fig. 5. Proposed large-signal equivalent circuit of the BDJ photodetector inreverse bias.

B. SPICE Large-Signal Model

As the device is actually a p+-n-p structure with a relativelythin middle layer (less than 1 µm), it can be modeled asa bipolar transistor, operating in the cutoff region, with twoadditional photocurrent sources. A mutual coupling betweenjunctions exists, and consequently, an interdependency of diffu-sion currents flowing through junctions is expected. Thus, likein any traditional Ebers–Moll model, two current-controlledcurrent sources α1ID2 and α2ID1 are associated with ID1 andID2, respectively.

When using two ideal diodes, the dark current includes onlyone component [10]. To improve the accuracy, we proposethe equivalent circuit in Fig. 5, where various mechanisms ofgenerating the dark current can be considered. The followingnotations have been adopted:

1) Iph1 and Iph2: photocurrent sources, whose expressionsare given in Appendix A;

2) R1,R2, andR3: parasitic series resistances, whose valuesdepend on the BDJ active area;

3) Ig1, Ig2, ID1, ID2, α2ID1, α1ID2, and It1: dark currentcomponents due to various mechanisms;

4) Cj1 and Cj2: junction capacitances. In reverse and lowforward bias, each junction capacitance value depends onthe surface and sidewall depletion layer width. Accordingto [12], they are globally evaluated using the followingexpression:

Cj =AjCjS0(

1 − VVbi

)MjS+

PjCjSW0(1 − V

Vbi

)MjSW

=Cj0(

1 − VVbiEFF

)Mj

≡ Ajε0εrWEFF

(2)

where V corresponds to the voltage bias applied to theconsidered junction [i.e., (V ′

2 − V ′1) for J1 and (V ′

2 − V ′3)

for J2], Aj and Pj are the junction area and perime-ter, respectively, Vbi is the built-in potential, CjS0,CjSW0, and Cj0 denote the zero-bias junction area ca-pacitance, sidewall capacitance, and effective junctioncapacitance, respectively, MjS, MjSW, and Mj are di-mensionless technological parameters, ε0εr is the siliconpermittivity, and WEFF represents the effective depletionlayer width.


III. DARK (LEAKAGE) CURRENT

Without illumination, the leakage current flowing through areverse-biased p-n junction is called dark current. This currentdepends on the junction characteristics, and it superposes onthat due to the carriers generated by light. Since noise is definedas any fluctuation superposing on the useful signal and tendingto obscure its information content [20], the dark current will beconsidered as one of the noise components. The value of thiscurrent imposes a physical limit on the two critical benchmarksof any photodetector, namely the optical detection range andthe noise floor.

The particular value of the dark current varies from sample tosample and depends on temperature, fabrication quality, dopinglevel, voltage bias, sensor design (layout), etc. It is assumed tobe mainly due to thermally generated carriers, but it can alsobe seriously increased due to the defects of the semiconductorlattice, dislocations, and unwanted contamination with impuri-ties during fabrication, etc. Thus, exactly like the 1/f noise, thedark current can be used as a diagnostic tool for quality andreliability of CMOS detectors.

Furthermore, for the image sensors integrated in a retina, thedark current may exhibit large variation from pixel to pixel. If,for two adjacent sensors, the forward current–voltage (I–V )characteristics are almost similar, the reverse characteristicsmay result fairly different. Not only the values of the currentat a certain voltage and a certain temperature differ by severalorders of magnitude from pixel to pixel, but the shape of thecharacteristic can also be different. This dark current nonuni-formity increases the fixed pattern noise and the dark signalnonuniformity.

A general description of the dark current includes edge,surface, and bulk effects, which are expressed as the sum ofsurface-dependent and sidewall-dependent components. Thecommon expression is

Idc = AjJs + PjJp = AjJEFF (3)

where Js is the surface contribution, Jp is the sidewall part, andJEFF represents the effective junction density current.

Many physical processes are involved in the generation ofthe carriers, which sustain the dark current. The most im-portant among them are thermal generation of carriers, band-to-band tunneling (BBT), trap-assisted tunneling (TAT), andimpact ionization [3], [12]–[17]. These carriers move either bydiffusion (as it happens for the thermally generated carriersin the bulk p or n regions) or by drift (as for the thermallygenerated carriers in the depleted region). Traditionally, theformer is designated as the diffusion component, and the latteras the generation–recombination (GR) component. Note thattunneling and impact ionization both occur in the depletedregion, where generated carriers move by drift.

Considering a BDJ sensor, both of the output dark currentscan be expressed as

Idc1 =Aj1(Jg1 + Jd1 + Jt1) (4a)

Idc2 =Aj2(Jg2 + Jd2) (4b)

where Aj1 and Aj2 are the areas of both junctions, Jg1 andJg2 represent the surface density of the GR current of J1 andJ2, respectively, Jd1 and Jd2 are the surface densities due todiffusion process, and Jt1 is the BBT surface density of currentfor J1.

A. Diffusion Contribution

For a junction temperature slightly higher than the ambienttemperature, low doping (typically less than 1018 cm−3), anda small reverse voltage bias, an important contribution arisesfrom the diffusion of thermally generated minority carriers,moving from both neutral regions of a p-n junction to itsdepletion layer, where they recombine.

In the case of the BDJ sensor, two diffusion currents Id1

and Id2, flowing in the bulk toward the shallow junction J1

and toward the deep junction J2, respectively, contribute to thedark current. Both Id1 and Id2 have an electron and a holecomponent. Solving the minority carriers’ diffusion equationwith a proper set of boundary conditions [3], [4], [10] and underthe stationary-state assumption, the diffusion current densitiesfor J1 and J2 have been analytically deduced as

Jd1 =

[JD1

(exp

(qV ′

1 − V ′2

kT

)− 1)

− α1JD2

(exp

(qV ′

3 − V ′2

kT

)− 1)]

(5a)

Jd2 =

[JD2

(exp

(qV3′ − V ′

2

kT

)− 1)

− α2JD1

(exp

(qV ′

1 − V ′2

kT

)− 1)]

(5b)

where

α1JD2 =α2JD1

≈ q Dpn2i

LpND

[sh

(x2n − x1n

Lp

)]−1

(6)

JD1 ≈ q

Dn1n

2i

Ln1NA1

ch(

x1pLn1

)+ Dn1

Sr1Ln1sh(

x1pLn1

)sh(

x1pLn1

)+ Dn1

Sr1Ln1ch(

x1pLn1

)

+Dpn

2i

LpND

[th

(x2n − x1n

Lp

)]−1

(7)

JD2 ≈ qn2i

(Dn2

Ln2NA2+

Dp

LpND

[th

(x2n − x1n

Lp

)]−1)

(8)

where q is the elementary electron charge, V ′1, V ′

2, and V ′3 are

the intrinsic potentials at diode terminals (Fig. 5), and Ln1, Lp,and Ln2 are the minority carrier diffusion lengths in the p+-diffusion, n-well, and p-substrate regions, respectively, NA1,


Fig. 6. Simplified diagram of the BDJ characterization.

ND, and NA2 are the doping concentrations of these layers,Dn1, Dp, and Dn2 denote the minority carrier diffusion con-stants, Sr1 is the surface recombination velocity, ni representsthe intrinsic carrier concentration, k is the Boltzmann constant,and T is the photodetector temperature. Various geometricalparameters are given in Fig. 2.

B. GR Contribution

The thermal GR is generally a well-balanced process every-where, except into regions where a strong internal electricalfield rapidly separates the newly created carriers, avoidingrecombination. As a general rule, image sensors operate underreverse bias. Consequently, the carriers generated inside thedepleted regions (where high internal field exists) contribute tothe dark current. The opposite process (recombination) occursin the neutral p and n regions close to the depletion layer.It is mainly the trap-assisted type and can be explained bythe Shockley–Read–Hall (SRH) model [17]. The GR currentdensity Jg is obtained by summing the maximum SRH GR netrateU(x) over the depletion region widthW [3], [12]–[17], i.e.,

Jg = q

∫W

U(x)dx. (9)

Under a reverse bias greater than kT/q, U(x) is given by

U(x) ≈ ni

[2√τnτp cosh

(Et − Ei

kT+

12

ln(τpτn

))]−1

(10)

where Et is the trap level, and Ei = EG/2 in which EG is thesilicon band gap.

Assuming that the effective GR lifetime for electrons andholes are equal (τn = τp = τg) and for Et = Ei, we obtainafter some algebra

Jg ≈ qni

2W

τg. (11)

The contribution of this process is generally dominantat ambient temperature for moderate reverse voltage bias(i.e., 1–5 V) and weakly doped junctions. However, for doping

concentrations higher than 1018 cm−3 and breakdown voltagegreater than 6 V, (5) and (11) cannot explain the observed largedark current. It can be explained by the fact that the tunnelingeffect has been neglected.

C. Tunneling Effect Contribution

This effect appears when the electrical field is relatively highbut not strong enough to break up a covalent bond, as it happensduring the ionization impact process.

Tunneling is mainly observed for reverse-biased p-n junc-tions with highly doping profile and thin depletion layers. Thisprocess states that a nonzero probability of electron and holetransitions between valence and conduction bands exists due tothe strong electrical field in the depletion layer [13]–[15]. Fora direct transition (i.e., BBT), the contribution to the junctioncurrent can be modeled as a generation of Dirac functions in theregion where the electrical field is at a maximum. The adoptedexpression corresponds to the conventional Zener tunnelingequation, where the local maximal electrical field EMAX isemployed instead of the mean electrical field [13], [15], i.e.,

Jt ≈ qV CbbtE3/2MAX exp (−E0/EMAX) . (12)

Note that Cbbt and E0 are constants that depend on the devicematerial.

D. Other Dark Current Contributions

Other phenomena can equally increase the dark current.First, the TAT mechanism appears in the bulk when the

electrical field is typically higher than 105 V/cm. Basically,TAT refers to the indirect carrier transition between conductionand valence energy bands, where traps states in the band gapact as stepping stones for carriers [13], [14]. This significantlyincreases the net recombination rate.

In addition to the previous process, at the Si−SiO2 interface(mainly at the border of the depletion region), a surface GRSHR mechanism yields another component of the dark current.As it depends on several parameters such as surface-statedensity, density of traps, and, equally, the state of the surface(accumulated, depleted, or inversed), this process cannot be


Fig. 7. Capacitance–voltage (C–V ) characterization of both junctions forthree different areas.

explicitly accounted in the expression of Jg. Instead, its con-tribution is considered by means of the effective carrier lifetimeτg [16]. However, as it is strongly dependent on the surfacestate, the effective carrier lifetime can be quite different fortwo neighboring junctions. This explains the large spread of themeasured values for τg.

Finally, at high reverse voltage, impact ionization mechanismbecomes dominant and highly dependent on the internal elec-trical field and on the critical electrical field. It overtakes thetunneling effect [13].

The previous points have been applied to the investigatedBDJ structure. The resulting analytical expressions (given inAppendix A) have been implemented in a MATLAB programin order to evaluate each contribution and to determine the keyparameters fitting the experimental data.

IV. EXPERIMENTAL RESULTS

Semiautomatic Kelvin measurements have been performedwith on-wafer probe station on an Austria Micro Systems(AMS) 0.35-µm CMOS test chip incorporating BDJ structuresof different sizes (active area Aj of 10 × 10, 20 × 20, and 50 ×50 µm2) at ambient temperature and in dark room conditions.C–V and I–V plots have been obtained using the CV-meterHP 4280A and the modular dc source/monitor HP 4142B,respectively (Figs. 6 and 7). In order to minimize interferences,the device under test (DUT) is enclosed in a Faraday cage andtriaxial cables, with lengths up to 1.5 m, and are used to connectthe DUT sample to measurement devices. Moreover, each datapoint of this Kelvin measurement is an ensemble mean valueof 100 (or more) samples, with a maximum integration time(i.e., 10 ms), which is controlled via Agilent IC-CAP software.

A. C–V Measurement

On-wafer C–V characterization has been done in two steps.First, as some n-well/p-substrate junctions have been also sepa-rately fabricated, the C–V plot of the isolated deepest junction(J2) has been delivered. Applying a single least square fit, theparameters of (2) have been extracted. Then, the C–V plotof the BDJ sensor in different configurations has been deter-

TABLE IMEASURED BDJ PARAMETERS AT T = 300 K

Fig. 8. Measured and simulated I–V characteristics of both junctions of a10 × 10 µm2 area under dark condition.

mined. Combining these results with the previous computedparameters of J2, the fitted parameters of the shallow junctionJ1 can be deduced. Note that in contrast to the first junction, thesidewall capacitances for the deep junction cannot be ignoredwhen evaluating the total capacitance.

Assimilating the junction capacitance to a parallel-platestructure [as suggested by the last term on the right-handside of (2)], the effective depletion layer widths WEFF1 andWEFF2 and their maximum effective electrical fields EMAX1

andEMAX2 versus the reverse voltage bias can be deduced from(2) [13], i.e.,

EMAX ≡ VbiEFF

WEFF(1 −Mj)

(1 − V

VbiEFF

)1−Mj

. (13)

Due to the inherent heterogeneous doping, the electrical fieldis not really constant along the junction area. As all leakagecurrent components are sensitive functions of this field, thesecurrents are strongly confined into the area where the electricalfield is the highest. For both J1 and J2, this means that theeffective junction area is not equal to the real junction surface.Consequently, all fitted parameters refer to an effective area.


Fig. 9. Influence of the mutual coupling between the 50 × 50 µm2 BDJ active area with a zoom of the dark current ratio I3/I1 versus V2.

Fig. 10. Measured and simulated I–V plots of the J1 and J2 junctions in darkfor a 50 × 50 µm2 BDJ.

B. I–V Measurement

I–V measurements under forward and reverse bias have alsobeen performed. In Table I, Js and Jp represent the surface andthe sidewall current density at a reverse bias of 3 V, respectively.It is to be noticed that for small-size junctions, the sidewallcomponents represent a significant part of the total current ofeach junction.

The I–V plots under dark condition are useful to de-tect an eventual voltage dependency of the leakage current(Figs. 8–11).

It can be seen that below a reverse bias of 0.5 V, the behaviorof both junction leakage currents indicates that both diffusionand SRH GR processes are present. According to (5)–(8),the diffusion components and the mutual coupling betweenjunctions are significant when at least one of the two junctionsis forward-biased. Fig. 9 illustrates this statement: We haveapplied V1 = 1 V to the p+-diffusion, whereas V2 (the n-wellbias) varies between 0 and 4 V, and V3 is kept constant at0 V. Thus, the first junction (delivering I1) is initially forward-biased, and then it is reverse-biased. Concerning the second

Fig. 11. Measured I–V plots of J1 in the dark for three different areas.

junction (delivering I3), it operates always under reverse bias.Like any bipolar transistor, we obtain a current ratioα2 = I3/I1between 0 and 1 for V2 < 1 V. For V2 > 1 V, other leakagecurrent components are dominant, and there is no correlationbetween I3 and I1. A similar statement applies to a1.

We note that in the context of a reverse bias in the range[0.5 V, 3.5 V] applied to J2 and a bias between 0.5 and1.5 V applied to J1 (Fig. 10), a voltage dependency of the darkcurrent in V Mj is observed, which is typical to the SRH process.From (11), the effective carrier lifetimes τg can be computed.As previously explained, a large spreading of measured datafor similar samples of BDJ sensor is expected.

It can also be seen also above 1.5 V, due to tunnelingmechanism, the current of junction J1 shows a fast exponentialvariation with the increasing reverse voltage (see Figs. 8, 10,and 11). For the weakly doped deep junction J2, this effectis not noticed. The Cbbt and E0 parameters of (12) are thenextracted by a single least-square fit.

Finally, we notice that the breakdown voltage Vbr, whichcorresponds to the avalanche process activation, is obtained at0.1 A · cm−2. For J1, we have Vbr1 = 8 V and Vbr2 = 27 Vfor J2.

All key parameters deduced from these measurements aresummarized in Table I.


Fig. 12. Proposed equivalent noise circuit of the BDJ photodetector.

V. NOISE ANALYSIS

Physically, noise is associated with the fluctuations in thephotocurrent and also in the dark current. Many processescontribute to the generation of these fluctuations. In practice,for each kind of current, one process (not necessary the same)can override the others in establishing the final value.

Mathematically speaking, the dark current can be viewed asthe superposition of a constant quantity to a fluctuating one,the latter quantity eventually resulting from a stochastic processhaving a Gaussian distribution. For sensors fabricated in pairs,we dispose differential (or ratiometric) techniques to cancel bysubtraction (or by division) the constant part [20]; however, forthe fluctuating term, nothing can be done, except to design (oroperate) the sensor in such a way to lower this fluctuating term.

A. BDJ Intrinsic Noise

Based on the equivalent circuit shown in Fig. 5, a generalequivalent noise circuit of the BDJ photodetector is proposedin Fig. 12. The following new elements appear:

1) g11and g22, which are dynamic conductances defined asfollows: g11 = ∂I1/∂(V ′

2 − V ′1) and g22 = ∂I3/∂(V ′

2 −V ′

3);2) g12 and g21, which are transconductances expressed as

follows: g12 = ∂I1/∂(V ′2 − V ′

3) and g21 = ∂I3/∂(V ′2 −

V ′1);

3) vnR1, vnR2, and vnR3, which are thermal noise voltagegenerators. They take into account the thermal fluctu-ations arising in the parasitic (bulk) resistances. Theirpower spectral densities (PSDs) are calculated using thefollowing general equation:

SvnR (f) =v2nR

∆f= 4kTR. (14)

4) in1 and in2, which represent equivalent current noisesources. They lump the effect of shot, GR, and 1/f noisemechanisms. Consequently, their PSDs are computed asfollows:

Sin(f) =i2in∆f

= Sin_SH + Sin_GR + Sin_1/f . (15)

Since both junctions are reverse-biased, the thermal noiseof serial bulk resistances is usually neglected [2], [3], [19].

Consequently, the shot noise is the dominant white noise sourceacross each junction.

In any photodetector, two uncorrelated current componentscontribute to shot noise, namely 1) the dark current Idc and2) the carriers generated by light Iph. Hence, the resulting PSDis computed as

Sin_SH (f) = 2q(Iph + Idc). (16)

Various bulk and interface effects are still present in differentproportions. At medium frequency and/or in regions wheredoping is weak, the GR noise contribution is significant, es-pecially for low-quality materials or when the SRH mechanismbecomes dominant. At low frequencies, the 1/f noise becomesan important source of random fluctuation. It is mainly due tosurface recombination as well as bulk mobility fluctuation ofcarriers. In practical situations, the Hooge’s approach [19]–[23]is adopted. The GR and 1/f noise PSDs of a p-n junction aredescribed by the following general equations:

Sin_GR(f) =4qG(Iph + Idc)1 + (2πfτr)2

(17)

Sin_1/f(f) =CfIσ

fκ(18)

where τr corresponds to the effective relaxation lifetime oftraps in the considered junction, G is the photoconductive gain,and σ, κ, and Cf are device-dependent constants obtained byfitting measured data. The parameter κ is close to unity andis an increasing function of dark current (0.5 < κ < 1.5) [22];σ = 2 for reverse-biased dark current and is lower at forwardbias and high illumination (0.5 < σ ≤ 2). In addition, theflicker parameter Cf is not constant, as predicted by Hooge’slaw. It depends strongly on the operating point of the sensor(illuminated or not in reverse or forward bias). Thus, for ap-i-n diode, Blecher et al. [23] noticed that the measured flickernoise PSD of the photocurrent is several orders of magnitudelower than that of the dark current. Consequently, the flickernoise component due to the photocarriers must be distinguishedfrom the flicker noise contribution of the dark current.

B. Signal-to-Noise Ratio (SNR)

The SNR is one of the most important benchmarks of anyimage sensor, since it gives a global indication on the quality ofthe device.

Traditionally, the SNR is defined, at any point and at aspecified frequency, as the ratio of the useful signal powerPsignal to the noise power Pnoise [20] and is expressed indecibels, i.e.,

SNR = 10 log10

(Psignal

Pnoise

). (19)

Under steady-state conditions, we have performed a noiseanalysis on the equivalent circuit in Fig. 12, with both outputsshort-circuited to the ground. The equivalent noise current


TABLE IIBDJ PARAMETERS ADOPTED FOR SIMULATION, WITH θ,

θ′ = 1, 2 AND θ �= θ′

Fig. 13. SNR versus useful signal Iph1 and Iph1 + Iph2, respectively, forIph2 = 2Iph1, f = 10 Hz, and ∆f = 1 Hz. “Ideal SNR” refers only to theshot noise of photocurrents, whereas “Real SNR” means (B1) and “SNR*”corresponds to (B2).

at each output can be computed, and the output SNRs areevaluated as

SNRIout1 = 10 log10

(I2ph1

i2n1

)(20a)

SNRIout2 = 10 log10

(I2ph1 + I2ph2

i2n1 + i2n2

). (20b)

By means of the equations proposed in Appendix B, togetherwith the parameters of Table II, the plots in Fig. 13 are obtained.At low illumination and under the conditions imposed either by(B1) (SNR*) or by (B2) (Real SNR), a slope of 20 dB/dec forboth SNRs versus the signal magnitude can be put in evidence.Note that a slope of 10 dB/dec also exists for the “Ideal SNR.” Itsimply denotes that noise is a direct consequence of the photonarrival statistics (i.e., Iphθ Idcθ, with θ = 1, 2).

C. Discussion

To optimize the SNR value, many important points must beconsidered.

First, in the case of wideband systems, and if the bandwidthof the circuits processing the signal delivered by the BDJ isexcessively large, the global SNR can be seriously degraded.Thus, a good strategy is to strictly limit the bandwidth to thatrequired by the useful signal.

Second, for a digital imager in an integration mode [19],the benefit is that the integration process reduces the noisecomponents having a frequency of the same order of magni-tude (or higher) as the reciprocal integration time. However,large leakage currents diminish the integration period, and thisinversely affects the dynamic range.

Concerning the isolated BDJ, optimum performance can beobtained by positioning the depleted layer of each junction at adepth correlated to the wavelength to be detected.

Efforts are needed to reduce stress inside the device structureand its associated surface states. Do not place sensors at theedges of the retina and employ guard rings, if possible. Further-more, minimize the perimeter-to-area ratio.

Moreover, the dark currents Idc1 and Idc2 must be loweredto improve the minimum detectable signal. Since conductancesand spectral sensitivities are parameters that depend on theadopted technology, only cooling the device can still increasethe SNRs.

It is to be noticed that each junction must also be properlybiased to deactivate certain processes such as BBT and, thus,to lower the level of the dark current. Furthermore, the powerbudget must be controlled as well in order to avoid a localincrease in the junction temperature.

Despite careful photodetector layout, some factors inducedduring manufacturing such as stress and etching damages causea proliferation of recombination centers, mainly for the shallowjunction J1. Therefore, the employed CMOS technology mustbe carefully selected. For instance, the use of deuterium anneal-ing instead of the conventional gas annealing process showsgood perspectives [18].

As far as the deeper junction J2 is concerned, a highly dopedepitaxial layer could be also associated with the p-substrate.Thus, the parasitic bulk resistance R3 will be lowered, and theunwanted substrate noise will be mitigated. In addition, notethat a metal employed as an optical mask to stop radiationoutside the photodetector area (as shown in Fig. 1) is highlyrecommended.

It is to be noticed also that when operating at very lowillumination (i.e., Iph ≤ Idc), we must reduce the 1/f noisecontribution. It can be seen from (15) and (16) that the PSDvalue of both shot and GR noises increases with the junctioncurrent, whereas the flicker noise depends on the square ofthe junction current (17). Thus, supposing that shot (or GR)noise dominates due to its low rate of increase with the junctioncurrent, the SNR will be improved as the incident light intensitystrengthens. Moreover, it is well known that for a zero-voltagebias, the 1/f noise contribution vanishes. However, with zerobias, the photodetector is rather in photovoltaic mode, which isnot appropriate. Kleinpenning et al. [21] stated that the 1/f noiseis proportional to the carriers’ lifetime, which, in turn, dependson the doping (N−1/2, for an abrupt junction). Thus, thecorner frequency between the shot noise and the flicker noisedecreases with the increasing lifetime. If we could decrease


the doping of the p+-diffusion, the depletion layer width willbe increased, and the built-in electrical field will be lowered.Thus, the tunneling effect will be minimized. By contrast,the GR process will be little stimulated, but fortunately, anoverall improvement is expected. Nevertheless, this possibilityis contrary to the actual tendency of continual downscaling ofthe standard CMOS technologies, where p-n junctions at verysmall depths require increasing the doping, and this yields ahigh internal electrical field.

Finally, it is interesting to mention that Lu et al. [2] proposethe following SNR definition of the current ratio I3/I1:

SNR−1I3/I1

∝ ∆(Iph2/Iph1)Iph2/Iph1

≈ I2ph1

i2n1

+I2ph2

i2n2

. (21)

They noted that the values obtained using (21) cannot be higherthan those of the photocurrents [previously established with(20)]. However, when the noise of the incident light sourceis dominant, with a simultaneous sampling of both outputcurrents, the common fluctuation part can be canceled. Con-sequently, the SNR will be improved.

VI. CONCLUSION

From our developed analytical expressions for the dark cur-rents as well as our proposed expressions of the BDJ equivalentnoise sources, the SNR is deduced at both outputs. C–V andI–V static measurements performed on AMS 0.35-µm CMOStest structures show good agreement with our proposed model.Some key parameters are obtained by fitting experimental data.Finally, several solutions are proposed in order to increase theSNR of the isolated BDJ color sensor.

APPENDIX ABDJ CURRENTS

I1 = Iph1 + Idc1 (A1)

I2 = I1 + I3 (A2)

I3 = Iph2 + Idc2. (A3)

Analytical Expressions of Photocurrents

Both photocurrents Iph1 and Iph2 are the sum ofthree photo-generated components: two diffusion components(i.e., IphN1 and IphP1 for J1 and IphN2 and IphP2 for J2) andone drift component (i.e., IphDR1 for J1 and IphDR2 for J2)[1], [2]. In the following expressions, α is the silicon absorptioncoefficient, and φt is the monochromatic light flow penetratinginside the device.Shallow Junction J1:

Iph1 = IphDR1 + IphN1 + IphP1 (A4)

where IphDR1, IphN1, and IphP1 are defined as in (A5)–(A7),shown at the bottom of the page.Deep Junction J2:

Iph2 = IphDR2 + IphP2 + IphN2 (A8)

where

IphDR2 = qAj2φt exp [−α(xn2 − xp2)] (A9)

IphP2 = − qAj2φtαLp

1 − α2L2p

exp(−αx2n)

×[−

exp(−α(x2n−x1n))−ch(

x2n−x1nLp

)sh(

x2n−x1nLp

) +αLp

]

(A10)

IphN2 = qAj2φtαLn2

1 + αLn2exp(−αx2p). (A11)

Analytical Expressions of Dark Currents

Shallow Junction J1:

Idc1 = Id1 + Ig1 + It1 (A12)

IphDR1 = qAj1φt exp [−α(x1n − x1p)] (A5)

IphN1 = qAj1φtαLn1

1 − α2L2n1

−αLn1 exp(−αx1p) +

[1 + αDn1

Sr1

]− exp(−αx1p)

(ch(

x1pLn1

)+ Dn1

Sr1Ln1sh(

x1pLn1

))sh(

x1pLn1

)+ Dn1

Sr1Ln1ch(

x1pLn1

)(A6)

IphP1 = qAj1φtαLp

1 − α2L2p

exp(−αx1n)

−ch

(x2n−x1n

Lp

)− exp (−α(x2n − x1n))

sh(

x2n−x1nLp

) + αLp

(A7)


where

Id1 = qn2i

Aj1

[Dn1

Ln1NA1

ch(

x1pLn1

)+ Dn1

Sr1Ln1sh(

x1pLn1

)sh(

x1pLn1

)+ Dn1

Sr1Ln1ch(

x1pLn1

)

+Dpn

2i

LpND

[th

(x2n − x1n

Lp

)]−1]

×(

exp(qV ′

1 − V ′2

kT

)− 1)

−Aj2Dp

LpND

[sh

(x2n − x1n

Lp

)]−1

×(

exp(qV ′

3 − V ′2

kT

)− 1) (A13)

Ig1 = qAj1ni

2WEFF1

τg1(A14)

It1 = qAj1 (V ′2 − V ′

1)CbbtE3/2MAX exp (−E0/EMAX) .

(A15)

Deep Junction J2:

Idc2 = Ig2 + Id2 (A16)

where

Id2 = qn2i

[Aj2

(Dn2

Ln2NA2

+Dp

LpND

[th

(x2n − x1n

Lp

)]−1)

×(

exp(qV ′

3 − V ′2

kT

)− 1)

−Aj1Dp

LpND

[sh

(x2n − x1n

Lp

)]−1

×(

exp(qV ′

1 − V ′2

kT

)− 1)]

(A17)

Ig2 = qAj2ni

2WEFF2

τg2. (A18)

APPENDIX BANALYTICAL EXPRESSIONS OF THE SNRS

In spite of the evidence that the coefficients of the 1/f noisedependency are not the same for the photocurrent and for thedark current, in the following, they will be assumed to be equal.

In addition, as the dark current is superposed on the usefulsignal, its rms value can be considered as a deterministicnoise. Consequently, we have taken it into account in the SNRexpression (B1a) and (B1b), shown at the bottom of the page.After subtraction of the deterministic part of the dark current(for instance, by means of an uncorrelated double sampling),the stochastic part is now twice its original value, and the SNRsbecome (B2a) and (B2b), shown at the bottom of the page.

SNRIout1 = 10 log10

(I2ph1

/I2dc1+2q

[I1

(1+

2G1

1+(2πfτr1)2

)]∆f+Cf1

Iσ11

fκ1∆f)

(B1a)

SNRIout2 = 10 log10

I2ph1+I2ph2

I2dc1+I2dc2+2q[I1

(1+ 2G1

1+(2πfτr1)2

)+I3

(1+ 2G2

1+(2πfτr2)2

)]∆f+Cf1

Iσ11

fκ1 ∆f+Cf2I

σ23

fκ2 ∆f

(B1b)

SNRIout1 =10 log10

(I2ph1

/2q[(I1+Idc1)

(1+

2G1

1+(2πfτr1)2

)]∆f+Cf1

Iσ11 +Iσ1

dc1

fκ1∆f)

(B2a)

SNRIout2 =10 log10

I2ph1+I2ph2(

2q[(I1+Idc1)

(1+ 2G1

1+(2πfτr1)2

)+(I3+Idc2)

(1+ 2G2

1+(2πfτr2)2

)]+Cf1

Iσ11 +I

σ1dc1

fκ1 +Cf2I

σ13 +I

σ2dc2

fκ2

)∆f

(B2b)


REFERENCES

[1] G. N. Lu, M. B. Chouikha, M. Sedjil, G. Sou, and G. Alquie, “In-vestigation of the buried double p-n junctions implanted in CMOStechnology for wavelength-sensitive detection,” Int. J. Electr., vol. 83,no. 3, 1997.

[2] G. N. Lu, G. Sou, F. Devigny, and G. Guillaud, “Design and testing ofa CMOS BDJ detector for integrated micro-analysis,” Microelectron. J.,vol. 32, no. 3, pp. 227–234, 2001.

[3] S. Feruglio, F. Haned, G. Vasilescu, M. B. Chouikha, G. Sou,V. Fouad Hanna, and G. Alquie, “A general model of the CMOSburied double junction photo-detector,” in Proc. IEEE IST, Stresa, Italy,May 2004.

[4] G. N. Lu, G. Guillaud, G. Sou, F. Devigny, M. Pitaval, andP. Morin, “Investigation of CMOS BDJ detector for fluorescence de-tection in microarray analysis,” in Proc. IEEE EMBS—Special TopicConf. Microtechnologies Medecine and Biology, Lyon, France, Oct. 2000,pp. 381–386.

[5] M. Sedjil and G. N. Lu, “A seawater pH determination method usinga BDJ detector,” Meas. Sci. Technol., vol. 9, no. 9, pp. 1587–1592,Sep. 1998.

[6] G. N. Lu, “A dual-wavelength method using the BDJ detector and itsapplications to iron concentration measurement,” Meas. Sci. Technol.,vol. 10, no. 4, pp. 312–315, Apr. 1999.

[7] K. M. Findlater, “A CMOS camera employing a double junc-tion active pixel,” Ph.D. dissertation, Univ. Edinburgh, Edinburgh, U.K.,2001.

[8] K. M. Findlater, P. B. Denyer, J. E. D. Hurwitz, J. M. Raynor, andD. Renshaw, “Buried double junction pixel using green and magentafilters,” in Proc. IEEE CCDs and AIS, 1999, pp. 6.1–6.4.

[9] K. M. Findlater, D. Renshaw, J. E. D. Hurwitz, R. K. Henderson, T. E. R.Bailey, S. G. Smith, M. D. Purcell, and J. M. Raynor, “A CMOS imagesensor employing a double junction photodiode,” in Proc. IEEE CCDsand AIS, 2001, pp. 60–63.

[10] M. Sedjil, “Modélisation de capteurs de couleur intégrés et développe-ment d’application,” Ph.D. dissertation, Univ. D. Diderot, Paris-VII, Paris,France, 1999.

[11] P. Lalanne and J.-C. Rodier, “CMOS photodiode based on vertical p-n-pjunctions,” in Proc. WOCS, 1997.

[12] H. Aharoni and T. Ohmi, “Analysis of n+p silicon junctionswith varying substrate doping concentrations made under ultra cleanprocessing technology,” J. Appl. Phys., vol. 81, no. 3, pp. 1270–1288,Feb. 1997.

[13] G. A. M. Hurkx, D. B. M. Klaassen, and M. P. G. Knuvers, “A new modelfor device simulation including tunneling,” IEEE Trans. Electron Devices,vol. 39, no. 2, pp. 331–338, Feb. 1992.

[14] E. Hackbarth and D. D.-L. Tang, “Inherent and stress-induced leakage inheavily doped silicon junctions,” IEEE Trans. Electron Devices, vol. 35,no. 12, pp. 2108–2118, Dec. 1988.

[15] J. Furlan, Z. Gorup, F. Smole, and M. Topic, “Modellingtunnelling-assisted recombination rate in space-charge region ofPN A-Si:H junction,” J. Modelling Simul. Microsyst., vol. 1, no. 2,1999.

[16] D. K. Schroder, “Carrier lifetimes in silicon,” IEEE Trans. ElectronDevices, vol. 44, no. 1, pp. 160–170, Jan. 1997.

[17] R. S. Muller, T. I. Kamins, and M. Chan, Device Electronics for IntegratedCircuits, 3rd ed. Hoboken, NJ: Wiley, 2003.

[18] H. I. Kwon, O. J. Kwon, H. Shin, B.-G. Park, S. S. Park, and J. D. Lee,“The effects of deuterium annealing on the reduction of dark currents inthe CMOS APS,” IEEE Trans. Electron Devices, vol. 51, no. 8, pp. 1346–1349, Aug. 2004.

[19] S. Feruglio, V. Fouad Hanna, G. Alquie, and G. Vasilescu, “Exact noiseanalysis of a CMOS BDJ APS,” in Proc. IEEE ISCAS, May 2005,pp. 2337–2340.

[20] G. Vasilescu, Electronic Noise and Interfering Signals: Principles andApplications. Heidelberg, Germany: Springer-Verlag, 2005.

[21] T. G. M. Kleinpenning, “1/f noise in p-n junction diodes,” J. Vac.Sci. Technol. A, Vac. Surf. Films, vol. 3, no. 1, pp. 176–182,Jan./Feb. 1985.

[22] R. H. Hamstra and P. Wendland, “Noise and frequency response of siliconphotodiode operational amplifier combination,” Appl. Opt., vol. 11, no. 7,pp. 1539–1547, Jul. 1972.

[23] F. Blecher, K. Seibel, and M. Böhm, “Photo- and dark current noise ina-Si:H pin diodes at forward and reverse bias,” in Proc. MRS SpringMeeting, San Francisco, CA, Apr. 1998.

[24] S. Feruglio, “Etude du bruit dans les capteurs d’images integrés, typeAPS,” Ph.D. dissertation, Univ. Pierre and Marie Curie, Paris, France,2005. (Paris 6).

Sylvain Feruglio (M’06) was born in Le Raincy,France, on April 29, 1977. He received the B.Sc. andM.Sc. degrees in electronic, electrotechnique, andautomatism and the master’s degree (with honors)in electronics, option instrumentation, and systemsfrom the Pierre and Marie Curie University (UPMC)-Paris VI, Ivry sur Seine, France, in 1999, 2000, and2001, respectively, and the Ph.D. degree in noisecomputation in integrated active pixel image sensorsfrom the Laboratoire des Instruments et Systèmes Ilede France, UPMC-Paris VI, Paris, France, in 2005.

He continues his activities through a postdoctoral position with the Insti-tut de Microélectronique, Electromagnétisme et Photonique, Institut NationalPolytechnique de Grenoble, Grenoble, France, which concerns the study of45-nm CMOS technologies. He is currently with the Laboratoire des In-struments et Systèmes Ile de France, Pierre and Marie Curie University-Paris VI. His research interests mainly include the micro- and nanoelectronicson silicon, noise computation, and simulation in integrated CMOS devices andimage sensors.

Victor Fouad Hanna (SM’87–F’96) was born inCairo, Egypt, on November 1, 1944. He receivedthe B.Sc. degree (honours) in electronic engineer-ing from Cairo University in 1965 and the M.Sc.degree in microwave engineering from AlexandriaUniversity, Alexandria, Egypt, in 1969. He receivedthe D.Sc. degree [Doctorat-Sciences Physiques (doc-torat d’Etat)] from l’Institut National Polytechique(I.N.P.), Toulouse, France, in 1975.

He was a Research Assistant in the National Re-search Center, Cairo, and the microwave laboratory

of the I.N.P., Toulouse, from 1965–1970 and 1970–1975, respectively. From1975 to 1979, he was a Researcher in the Electrical and Electronics EngineeringLaboratory, National Research Center, Cairo, engaged in research in the fieldof microwave theory and techniques and microwave solid-state devices. From1979 to 1997, he was in the Centre National d’Etudes des Télécommunications,France, where he was expert in microwave theory and techniques and wasresponsible for the group Application of Electromagnetic theory in microwaveand millimeter circuits in its Satellite Telecommunications Systems Division.Since 1997, he has been a Professor at the University Pierre et Marie Curie(University of Paris 6), Paris, France, in the Electronic Department. His currentresearch interests deal with electromagnetic theory, numerical methods forsolving field problems, characterization of microstrip-like transmission lines,millimeter-wave transmission lines, and bio-electromagnetism. He is an authorand co-author of more than 300 articles.

Dr. Hanna was selected as recipient of the IEEE Third Millenium medal.He was the chairman of the Commission B of the URSI IN France from 2001to March 2004. He was the President of the IEEE France Section from 2002to 2005. He is Emeritus Member of the French Society for Electrical andElectronic Engineers and Chair of its International Relations Committee sinceJune 2005. He has been the Chair of the Région 8 IEEE Educational ActivitiesCommittee since January 2004.


Georges Alquie (M’95) received the Master ofSciences degree in physics from the University ofMontpellier, Montpellier, France, the Ph.D. degreefrom the University of Orsay, Orsay, France, and thehigh level Doctorate from the University Pierre andMarie Curie, Ivry-sur-Seine, France, in 1977.

He is currently Professor in electrical engineeringat the University of Pierre et Marie Curie, mainlyinvolved in microwave techniques and electromag-netism. His research activity, which concerns themicrowave and millimeter domain, is performed at

the Laboratoire des Instruments et Systèmes d’Ile de France (LISIF). He isinvolved in the design and modelling of integrated passive circuits, integratedlow noise active microwave devices (MMICs), and microwave photonicsdevices for telecommunications and defense applications. In the LISIF, hehas also been in charge of the research management of the Microelectronics,Instrumentation, Microwave, and Electromagnetism group.

Gabriel Vasilescu (M’85–SM’03) received theDipl.Ing. and Dr.Ing. degrees in electronics fromthe Bucharest Polytechnic Institute, Bucharest,Romania, in 1965 and 1974 respectively, and thePh.D. degree from the University Pierre and MarieCurie–Paris VI, Paris, France, in 1994.

In 1966, he joined the Bucharest PolytechnicInstitute as Assistant to Prof. P. Reinhard, in elec-tronic devices and circuits. From 1977 to 1982, heworked at the Institute of Telecommunications, Oran,Algeria, as an Associated Professor of electronic

circuits. In 1983, he moved to the University of Limoges, France, where hesuccessively held positions of Associate Assistant, Associate Junior Lecturer,and Associate Senior Lecturer of CAD of microwave circuits. Since 1987, hehas been a Senior Lecturer at the University Pierre and Marie Curie, Paris,France, where he is currently involved with noise and interfering signalsin electronic circuits. His research interests include sensitivity analysis ofelectronic circuits, noise computation in electronic circuits and APS imagesensors, crosstalk analysis, SPICE simulation of biological processes, and noisein biological systems.

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Dark Current and Signal-to-Noise Ratio in BDJ Image Sensors

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