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Journal of Non-Crystalline Solids 352 (2006) 1813–1817

Spice model for a laser scanned photodiode tricolor image sensor

J. Martins *, M. Fernandes, A. Fantoni, M. Vieira

Electronics, Telecommunications, and Computer Engineering Department, ISEL, 1950-062 Lisboa, Portugal

Available online 27 March 2006

Abstract

A SPICE model of the three color a-SiC:H/a-Si:H p–i–n/p–i–n detector operation is presented. The equivalent electric circuit able todescribe the behavior of the multilayer structure under non-uniform illumination is composed of two series connected diodes, represent-ing the p–i–n structures, with two non-linear current sources in parallel, representing the photogeneration for different steady-state RGBillumination, with their values depending on the light penetration depth and intensity of the impinging light. This device represents the1D model of the Laser Scanned Photodiode and may be interconnected in a 2D array trough resistors, modeling the high resistivity of thea-SiC:H layers. Electrical simulations were performed for different illumination conditions, and they are compared with the experimentaldata. The influence of the electrical model parameters on sensor characteristics is analyzed. A physical model supported by the electricalsimulation gives insight into the methodology used for image representation and color discrimination.� 2006 Elsevier B.V. All rights reserved.

PACS: 85.30.De; 85.60.Bt; 85.60.Gz; 78.66.Jg

Keywords: Amorphous semiconductors; Devices; Electrical and electronic properties; Modeling and simulation; Optical properties

1. Introduction

Efforts have been devoted towards the development of anew kind of color sensor, the so-called laser scanned pho-todiode (LSP) [1]. This sensor allows simultaneous imageand color detection by combining the wavelength filteringproperty of silicon with the sensor responsivity dependenceon the applied voltage. The LSP image sensor is based onone single sensing element, and uses a modulated low-power beam of laser light to scan the active area directly.The main advantage is the simplicity of the structure; nei-ther special photolithography techniques for patterningnor high voltage requirements and bulky design areneeded.

Early work on characterization and modeling of imagesensors electrical behavior [2] gave some insight into thedevelopment of the current design. Then, the large-areap–i–n structures used for pattern detection of a B/W imagewere modeled by a consistent non-planar array of photo-

0022-3093/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.jnoncrysol.2006.01.052

* Corresponding author.E-mail address: jfmartins@deetc.isel.ipl.pt (J. Martins).

diodes. Now, the results from different light wavelengthsof the image to be detected are the main concern. Bothmodels will be merged in order to achieve both image pat-tern and color detection. The circuit includes elements try-ing to capture several aspects of the sensor structure andthe observed data: diodes for p–i–n structures; currentsources discriminating light wavelength cases of study;capacitors showing charge and phase dependencies; extraparallel and series resistors; and current dependent currentsources for some transmission and feedback aspects.Adjusting the values of some model parameters, semicon-ductor parameters and common electrical components,and selecting the type of simulation analysis (DC, AC,and transient-time domain), it was possible to explain someof the observed singularities of the sensor, aiming toexplain color detection. The scanner beam can be modeledthrough a current source, DC or sine-wave signal, in paral-lel with one of the diodes. The current measured at the elec-trical contacts has a steady-state and a sinusoidalcomponent, the former due to the diode currents and thesteady-state photocurrent, and the later due to the scannerinduced photogeneration.

Applied Voltage (V)-1.0 -0.5 0.0 0.5 1.0

Cur

rent

(A

)

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

IPH1 (< IPH2) IPH2 (< IPH3) IPH3

-6

a

1814 J. Martins et al. / Journal of Non-Crystalline Solids 352 (2006) 1813–1817

2. Experimental details

The sensing element consists of a 1000 nm thickp(SiC:H)/i(SiC:H)/n(SiC:H)/p(SiC:H)/i(Si:H)/n(Si:H) mul-tilayer device deposited by PECVD and two transparentconductive contacts.

In this configuration, full color detection is attemptedbased on spatially separated absorption of different wave-lengths. The blue sensitivity and the red transmittance wereoptimized respectively through a thin a-SiC:H front absor-ber with an optical gap of 2.1 eV and a thick a-SiH backabsorber with an optical gap around 1.8 eV. Their thick-nesses are a trade-off between the full absorption of theblue light into the front diode, and the green light acrossboth. To decrease the lateral currents that could lead toimage smearing and to enhance the blue sensitivity, thedoped layers (20 nm thick) are based on a-SiC:H [3]. Thedevices were characterized through the analysis of the pho-tocurrent and the spectral response under different steady-state optical bias (kL = 450, 550, 650 nm) and appliedvoltages (�6 V < V < 6 V).

The image to acquire is optically mapped onto the frontphotodiode and a low-power light spot scans the devicefrom the opposite side, a steady or chopped light source.The photocurrent generated by the moving spot is recordedas the electronic image signal, and its magnitude and phasedepend on the pattern localization, wavelength and inten-sity of the light.

3. Results

Fig. 1 illustrates the DC electrical model for a p–i–namorphous photodiode comprising a regular diode D1

and a current source IPH1 for illumination biasing pur-poses. The diode has the usual model parameters availablein SPICE specifications [4,5] (e.g. saturation currents, emis-sion coefficients, series-parasitic resistance and shuntcapacitances) and a few more trying to model the photodi-ode. In order to attain the common current–voltage (I–V)characteristics for amorphous photodiodes under illumina-tion, the saturation current IS for the diode in the model is

Vsweep

IPH1{D1_IPH}

I

0

0

Vdc0VdcD1

PARAM ET ERS:

D1_NR = 1

D1_VJ = 2

D1_IS = {({D1_IPH}+{D1_IScan})/(exp({D1_VOC}/({D1_N}*{D1_VT}))-2)}

D1_N = 4

D1_ISR = 0

D1_RS = 4

D1_CJ0 = 1n

D1_VOC = 0.5

D1_IPH = 1m

D1_IScan = 0

D1_VT = 0.0259

Vsweep

Fig. 1. Electrical model for a p–i–n amorphous photodiode.

made dependent on the photocurrent and computedaccording to Eq. (1):

IS ¼IPH

expðV OC=gV TÞ � 1. ð1Þ

This assumption allows the diode D1 to forward current inthe opposite direction and with the same magnitude of thephotocurrent modeled by IPH1 source at the open-circuitvoltage VOC.

Fig. 2(a) shows three I–V curves obtained by simulationwith the above model corresponding to three intensities ofthe photocurrent IPH1. In Fig. 2(b) the measured I–V

curves of the back diode are shown for comparison. Theused spice model does not account for the s-shape effectin those experimental curves which is due to carbon incor-poration in the doped layers, but this does not invalidatethe interpretation of the sensor characteristics. One mayobserve the photocurrent values under reverse bias; theVOC value approximately the same for the three cases;and the steepest increase in current for higher photocurrentvalues under forward bias.

Fig. 3 illustrates the model for the p–i–n/p–i–n structure,connecting in series two photodiodes with the aboveexplained model. IPH1 and IPH2 current sources also allow

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-4.0x10-6

-3.0x10-6

-2.0x10-6

-1.0x10-6

0.0

1.0x10-6

2.0x10-6

3.0x10-6

4.0x10

IPH1 (< IPH2)IPH2 (< IPH3) IPH3

Cur

rent

den

sity

(A

.cm

-2)

Applied Voltage (V)b

Fig. 2. I–V curves for the p–i–n photodiode: (a) simulated and (b)measured.

Vsweep

D2 IScanner{D2_IScan}

IPH2{D2_IPH}

D1 IPH1{D1_IPH}

0

Fig. 3. Electrical model for the p–i–n/p–i–n structure.

-8

-4

0

4Red

-8

-4

0

4Blue

-8

-4

0

4Green

Applied Voltage (V)-6 -4 -2 0 2 4 6

-4

0

4

Dark

VD1VD2

________ _ _ _ _

VD

1, V

D2

(V)

Fig. 4. DC voltage across cell diodes under different RGB illuminationconditions for a range of applied voltages.

J. Martins et al. / Journal of Non-Crystalline Solids 352 (2006) 1813–1817 1815

for the specification of different light penetration depths.The current source Iscanner in parallel with diode D2 modelsthe scanner light effect for the LSP measurement technique[6], allowing a scanning of the tandem structure for imagepattern recognition. The image is assumed to be projectedon the front cell D1 and the scanner beam is projected onthe back cell D2.

The light is absorbed in a different way and asymmetri-cally in the front and back cells, depending on the wave-length of the image projected onto the image sensor. Theblue light is absorbed exclusively into the front diode(IPH1 5 0, IPH2 = 0), which is transparent to the red lightthat is absorbed in the back diode (IPH2 5 0, IPH1 = 0).The levels of green light absorption are not uniform in bothdiodes and depend on the structure of both cells (IPH2 5 0,IPH1 5 0). In order to study the effect of the steady illumi-nation, Fig. 4 shows the simulated DC voltage valuesacross diodes D1 and D2 (Fig. 3) under red/blue/green/dark light illumination conditions for applied voltagesfrom �6 V to 6 V. Iscanner = 0 and VOC2 = 0.6 V is slightlyhigher than VOC1 = 0.5 V due to the sensor configuration.For the red light case IPH2 = 1 mA and IPH1 = 0, and forthe blue light case IPH1 = 1 mA and IPH2 = 0. For the greenlight case were chosen values of uniform absorption acrossboth diodes (IPH1 = IPH2 = 0.5 mA).

4. Discussion

The comprehension of available experimental andnumerical material simulation results for several a-Si tan-dem structures is important to achieve good model param-eter values. From Fig. 4 it is shown that in the red and bluelight cases, VD1

and VD2curves intersect at a potential

slightly higher than the sum of the VOC values. For nega-tive applied voltages it is observed that the forward biaseddiode is the one that is assigned to light absorption. Forpositive applied voltages the other diode has a higher volt-age drop value due to higher current imposition. In thegreen case, VD1

is slightly negative for negative applied

voltages and slightly lower than VD2for positive applied

voltages, because D1 has a smaller VOC value. However,and particularly for the green case, the diodes behaviorsomehow depends on the values of VOC and IPH, and con-sequently on the cells structure. Depending on which diodeis assigned a VOC and/or IPH higher magnitude, the charac-teristic behavior of each diode may interchange.

Fig. 5 depicts the sensor simulated DC I–V curves wherefor each case of light wavelength the assumptions describedabove are valid, and for the scanner current source waschosen a DC value somewhat lower (one tenth) than themagnitude of the photocurrents. These normalized I–V

curves are computed according to Eq. (2):

I ¼ ðI imageþscanner � I imageÞ. ð2ÞThe graph on the left ranges for applied voltages �6 to1.5 V, and the graph on the right for applied voltages1.5–6 V. For reverse applied voltages one may clearly dis-tinguish the blue curve; the red curve is approximately zeroas in the dark case; and the green case values change fromvalues near red to blue depending on the cells structure.For the green light case a photocurrent value that is equalin both diodes and half of the value used in the other twocolor cases was used. For forward biasing the curves havealso a distinguishable behavior. Further, values of voltage

Applied Voltage (V)-6 -4 -2 0

Cur

rent

(A

)

-1.5e-6

-1.0e-6

-5.0e-7

0.0

5.0e-7

RED BLUE GREEN DARK

2 3 4 5 6-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

RED BLUE GREEN DARK

Fig. 5. Sensor DC I–V curves under different RGB illumination conditions.

1816 J. Martins et al. / Journal of Non-Crystalline Solids 352 (2006) 1813–1817

where blue/red/green curves intersect the dark one may beused to help the light color separation.

An additional simulation for AC values was performedusing a sine-wave signal for the scanner current sourceIscanner, a chopped laser beam in experimental procedures.An intermediate RC (100 X, 1 lF) parallel circuit betweenthe two photodiode cells was introduced in the model.With a time-domain analysis type, the magnitude of thealternate component of the output current gives supple-mentary information to the discrimination of colors. Thephase difference of the output signal to the scanner signalalso assumes dissimilar behavior depending on the colorcase and applied voltage as can be observed in Fig. 6.

Results show that the following observations control thesensor behavior (Figs. 4–6): the shallow penetration of theblue photons into the front diode; the deep penetration ofthe red photons exclusively into the back diode; or thedecay of the green absorption across both. Both the frontand the back diodes are optically and electrically in series.Since light traverses through the sequence and is absorbedaccording to its wavelength and since the diodes are electri-cally in series, both diodes should ensure that they eachgive the same current. Any diode whose current is below

Phase

Applied Voltage (V)0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ang

le (

degr

ees)

50

100

150

200

250

300

350

400

RED imageBLUE image

a b

Fig. 6. Output AC signals: (a) phas

the other would have to reduce its bucking current andconsequently its voltage to try to catch up. This diodemay even have to reverse bias itself in its efforts to get inline with the other. This effect is what we call the self-biaseffect.

To sustain the net current across the device the backdiode current has to be adjusted through an increase ofthe electrical field and thus it becomes reverse biased(Fig. 4), even under short circuit conditions. Simulatedresults show that the application of an external electricalbias (forward or reverse) mainly influences potential distri-bution within the less photoexcited sub-cell (Fig. 4). Whencompared with the potential profile under thermo-dynam-ical equilibrium (IPH1,2 = 0), the voltage drop under illumi-nation conditions remains constant in the most absorbingcell (IPH 5 0), while the less absorbing one (IPH = 0) reactsby assuming a reverse bias configuration. Hence, an oppo-site behavior is observed under red and blue light.

The deep penetration of the red photons uniformly andexclusively into the back diode, and the transparency of thefront diode to this wavelength push the electrical field up inthe front diode (self-reverse effect) and down into the backone (self-forward effect) as seen in Fig. 4. In the green range

AC amplitude

Applied Voltage (V)0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cur

rent

(A

)

0.000

0.002

0.004

0.006

0.008

0.010

RED imageBLUE image

e difference and (b) amplitude.

J. Martins et al. / Journal of Non-Crystalline Solids 352 (2006) 1813–1817 1817

both reverse and forward self-bias effects coexist. Here, theself-reverse effect due to the front absorption is balanced bythe self-forward effect due to the back absorption.

5. Conclusions

A SPICE model of the three color a-SiC:H/a-Si:H p–i–n/p–i–n detector operation was presented.

The equivalent electric circuit is based on two series con-nected diodes, representing the p–i–n structures, with twonon-linear current sources in parallel, representing thephotogeneration for different steady-state red, green andblue irradiation, with their values depending on the built-in potential of the diodes.

The main readout characteristics were recognized inorder to demonstrate that the presented tandem structure

is capable of color discrimination. Some future work com-prises the further exploration of AC characteristics, andsimultaneous image pattern and color recognition.

References

[1] M. Vieira, M. Fernandes, P. Louro, R. Schwarz, M. Schubert, J. Non-Cryst. Solids 299–302 (2002) 1245.

[2] J. Martins, M. Fernandes, M. Vieira, Vacuum 64 (2002) 307.[3] M. Vieira, M. Fernandes, P. Louro, A. Fantoni, R. Schwarz, J. Non-

Cryst. Solids 338–340 (2004) 754.[4] Semiconductor Device Modeling with SPICE, Giuseppe Massobrio e

Paolo Antognetti, McGraw-Hill, 1998.[5] C. Protogeropoulos, B.J. Brinkworth, R.H. Marshall, B.M. Cross, in:

Eur. Photovoltaic Sol. Energ. Conf., 1991, p. 412.[6] M. Vieira, M. Fernandes, J. Martins, P. Louro, A. Macarico, R.

Schwarz, M. Schubert, IEEE Sensor J. 1 (2) (2001) 158.