Vacuum 64 (2002) 307–313

Electrical simulation of a p–i–n image sensor

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

Electronics and Communications Department, ISEL, Rua Conselheiro Em!ııdio Navarro 1, 1949-014 Lisbon, Portugal

Abstract

We have modelled a p–i–n image sensor under local illumination through a two-dimensional non-linear circuit. The

sensor is described as an array of photodiodes interconnected through lateral resistors, which model the sheet resistance

of the doped layers. Under small-signal analysis, each photodiode is modelled by a current-controlled resistor

proportional to the inverse of the photocurrent. A SPICE based simulator is used to analyse the sensor output

characteristics.

Several configurations and contact geometries are analysed for the image transducer. The image responsivity, the

spatial resolution and the image distortion are modelled by changing the ratio between the transversal and the lateral

resistors or the acquisition points. Results show that the geometry and location of the contacts affect the distortion of

the restored image. The conductivity of the doped layers and the light flux illumination influences the image resolution

and accuracy. The simulated and experimental results were found in a good agreement. r 2002 Elsevier Science Ltd.

All rights reserved.

Keywords: Semiconductor device modelling; Electrical modelling of p–i–n devices; Electrical simulation; Optical sensors; Image

acquisition and representation

1. Introduction

An electrical model for a device comes first

from the simple theory of the device, trying to

capture its basic operation features. Subsequently,

the model is enhanced from the feedback of

experimental results. At the same time, some

of the sensor characteristics may be improved

using the insight obtained from simulation

results.

SPICE [1] is the de facto industrial standard

for computer-aided circuit analysis, including

models of semiconductor devices: p–n junct-

ion diode, bipolar junction transistor, field

effect transistor, etc. Usually, a general-purpose

circuit simulator using SPICE performs three

main types of analysis: non-linear dc, non-

linear transient, and linear small-signal ac

analysis.

Electrical simulation is a helpful tool to get

insight into the physical model of a semiconductor

imager. An electrical simulation based on SPICE

program was used to describe and analyse the

image sensor performance. Several configurations

of the sensor were analysed: contact geometry,

n-layer conductivity, and image intensity levels.

Results from simulation are supported by experi-

mental results.

*Corresponding author. Tel.: +351-21-8317289; fax: +351-

21-8317114.

E-mail address: joao.martins@isel.pt (J. Martins).

0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 3 0 6 - 2

2. Sensor structure and simulation model

2.1. Sensor configuration and operation

Large area image transducers in the assembly

glass/ZnO : Al//pS a-Si : H//iS a-Si : H//nS a-

SixC1�x : H/Al [2] are modelled and studied by

means of an electrical simulation. The sensor is a

two dimensional structure composed of a p–i–n

photodiode (the active element) and front and

back contacts that are used as electrical interface.

In Fig. 1 the geometrical configuration as well as

the electrical model proposed are depicted.

The p–i–n experimental transducers were de-

posited by plasma enhanced chemical vapour

deposition at a 13.56 MHz radio frequency and

the contacts deposited by thermal evaporation.

Deposition conditions, experimental details and

sensor performance are described elsewhere [2,3].

A focused image, constituted by a steady-state

light, is projected onto a fixed location in the

photosensitive surface, through the transparent

contact. For image acquisition, a low-power

chopped laser spot scans the sensor in the frame

mode. The read-out of the injected carriers is

achieved by measuring the ac component of the

short circuit current, Isc: It was shown that the

output signal depends on the photocurrent pro-

duced by the image, Idc; as much as by the one

produced by the scanner, Iac [4].

The methodology used for image representation

is explained through a modulation of the potential

barrier due to the local steady-state illumination of

the junction. Here, due to the higher conductivity

of the doped layer, the photogenerated minority

carriers build up across all the active surface, while

the majority carriers are accumulated in the

illuminated region, beyond the depletion layer

edge, causing a reduction in the band bending

across this region [5]. If, in addition, a weak light

spot is scanning the device, in the dark regions the

carriers generated by the scanner are separated by

the junction electric field and collected (high ac

component of the current). Those generated inside

the illuminated regions can drift in the lateral

direction, due to the local lowering of the potential

barrier, and recombine inside the amorphous bulk

(low ac component of the current). So, illuminated

regions are ascribed to low ac components of the

photocurrent, and dark regions to high ac photo-

current values.

All the image acquisition process is performed

by storing the current values as a two dimensional

array of discrete values, Im;n; each one representing

the photocurrent induced by the chopped light at

the selected m� n position. The image intensity is

obtained by subtracting the input matrix Im;n (with

image) from the background, bm;n (without image)

and inverting the results.

2.2. Electrical model

In operation, a photodiode can be represented

by a photogenerated current source feeding into an

ideal diode, and its internal characteristics are best

modelled by the introduction of a shunt resistor, a

shunt capacitor and a series resistor [6]. For large

signal or dc mode, the photodiode is modelled as a

non-linear current source, ID; that depends on the

photocurrent, Iph; and on the voltage across the

diode, VD; through ID ¼ IS½expðVD=ZVT Þ � 1Þ� �Iph; with IS the saturation current, Z the ideality

factor of the diode, and VT the thermal voltage.

However, under small-signal conditions, the

photodiode is a non-linear photocurrent-con-

trolled resistor (rd), which represents an incre-

mental resistance, around the quiescent operating

point and is expressed in terms of Iph as 1=rd ¼@ID=@VDEIph=ZVT :

The electrical model for the p–i–n image sensor

can be an array of photodiodes intercon-

nected through lateral resistors [7] (see Fig. 1).

Each photodiode is replaced by its incrementalFig. 1. Sensor configuration and electrical model.

J. Martins et al. / Vacuum 64 (2002) 307–313308

resistance and connected to its four neighbours, in

a row-line matrix, by resistors: RLn and RLp that

model the sheet resistance of the n- and p-doped

layers, respectively. The contacts may have differ-

ent configurations and establish the points for

transversal measurements. The image pattern is

reconstructed from the photovoltage readout in

the same way as described in Section 2.1.

2.3. Simulation analysis

Simulation results were obtained using a

SPICE-based simulator. Fig. 2 shows a fraction

of the electrical circuit, being part of the non-

planar structure used for simulation. One can

depict the diodes (D), the lateral (RL) and

transversal (rd) resistors, the scanner source (Is),and a point of voltage measurement (V).

The scanner is a sine-wave current source

(0.1 mA, 10 Hz) applied from each top node of

the circuit to the ground or reference point. Those

nodes are the diode anodes, corresponding to the

m� n points for voltage read-out.

Different contact geometry configurations can

be used: strips at the structure borders or large

area contacts covering the entire active surface. In

the simulation circuit the contact shaping is

achieved by choosing the points for voltage read-

out: the measurement point (V) and the ground or

reference point. For the case where the contacts

are localised at the structure borders, the measure-

ment and ground points are fixed at circuit nodes

representing the contact regions where the lateral

resistors (RL) are short-circuited. For large area

contacts, the voltage measurement points change

for each m� n value read-out, as is shown in

Fig. 2.

Several p–i–n sensors with different n-layer

conductivity were also simulated. This was

achieved by changing RL for the whole circuit,

accordingly. Higher conductivities correspond to

lower values of RL: Also, different image intensity

levels were analysed, changing rd on points

allocated to the image area.

2.4. Simulation procedure

The simulation procedure has two phases, the

circuit construction and the simulation process.

The first phase has three steps. In the first step, the

array dimension is chosen. The number of lines

and rows in the circuit of Fig. 2 depend on the

image shape, and their number is chosen in order

to have enough nodes to include the image area

and a surrounding dark region. This region is

made large enough to accommodate the contact

regions and suppress the influence from the

structure border. The second step is to choose

the points of measurement, accordingly the con-

tact geometry. In the third step the circuit nodes

are allocated to image positions and the values for

rd ;RLn and RLp are chosen.

In the second phase, a voltage distribution

composed of a matrix of m� n values is obtained.

Each simulation run corresponds to a different

assigned node where the scanner source is applied.

The stored values are the amplitudes of the

sinusoidal small signals taken in each simulation

process step. The image intensity matrix is

obtained as described in Section 2.2.

3. Results and discussion

3.1. Contact geometry versus blurring effect

The contact geometry is an important parameter

to define accurately the image. Several contact

geometry configurations were analysed [8].Fig. 2. Electrical circuit for simulation.

J. Martins et al. / Vacuum 64 (2002) 307–313 309

Fig. 3 shows the simulated image intensity of a

rectangle (4� 3) using: (a) strip contacts around

the border and (b) a large area contact covering

the active surface. The values of rd ;RLn and RLpwere kept constant during the simulation process,

with rd=RLn ¼ 10�2: The grey level image repre-

sentation is also depicted.

The results show that contact area and location

play an important role in image representation,

since its location influences the carrier path before

collection [2]. As the contact area increases from

the border strips to cover contacts, a decrease on

the blurring effect is detected. In the configuration

with border strips, the carriers after generation are

diverted in the lateral direction (across RLn;p)towards the contact. The ac component of the

photocurrent decreases in the dark region mainly

near the image border, giving rise to a blurring

effect as shown in Fig. 3a. However, if the contact

area extends all over the active surface, the lateral

path is short-circuited and the carriers are

collected at the generated points. The image

intensity increases and the blurring effect is

minimised (Fig. 3b). Large area contacts all

over the active surface will be used for further

simulations.

3.2. Doped layer resistivities versus spatialresolution

Fig. 4 depicts 3D graphics of the simulated

image intensity and grey levels image representa-

tion outputs from the sensor, obtained under

illumination with two half-circles for two different

ratios: (a) rd=RLn ¼ 10�1 and (b) rd=RLn ¼ 10�2:The rd=RLp ratio was kept constant (10�2) during

the simulation process. For comparison, Fig. 4

shows the experimental results for two sensors

with n-layer conductivities of 2.6� 10�4 and

3.1� 10�5 1/O cm, respectively.

The simulated and experimental results are in

good agreement. The observed difference in both

images depends on the ratio between rd (image

intensity) and RLn (n-layer resistivity) for a

constant value of RLp (p-layer resistivity). As

rd=RLn increases the image intensity smoothes

and it presents some blur at the edges.

Fig. 3. Simulation outputs for: (a) strips border contacts, and (b) large area contacts.

J. Martins et al. / Vacuum 64 (2002) 307–313310

For the sensor having the most resistive layer

(Fig. 4b) the carriers injected near the gap borders by

the ac current source (the scanner) are diverted to the

less resistive path (the image, rd5RLn) and do not

contribute to the ac component of the photocurrent.

If RL;n lowers (Fig. 4a), the border carriers will drift

also in the lateral direction (rdoRLn) toward the

image, increasing the ac component of the current

inside the image and decreasing it outside.

Experimental details support the simulated

results. They show that by using a low conductiv-

ity n-layer (n-SixC1�x : H) a good image represen-

tation is achieved (Fig. 4b), with sharp edges and

almost no blur. However, if the n-layer conductiv-

ity is higher (Fig. 4a) the image intensity repre-

sentation is deteriorated, the edges are blurred and

the wide gap could not be clearly identified. In this

case, some restoring algorithms should be used to

sharpen the edges in blurred image [9].

3.3. Image intensity

Fig. 5(a) shows the outputs from the sensor

obtained under a donut illumination for two

different values of rd=RLn : 10�2 (left plots); 10�1

(right plots). RLn and RLp were kept constant

during the simulation process.

For comparison, a 7.5 mm donut having an

inner hole of 2.5 mm diameter was projected onto

the sensor having the most resistive n-layer. The

scanner intensity (FS) was kept constant while the

light source flux (FL) used for mapping the donut

into the sensor was changed. Fig. 5(b) displays the

experimentally acquired images, at FL ¼ 5 mW/

cm2 (left plot) and FL ¼ 0:5 mW/cm2 (right plot)

keeping the scanner flux FS ¼ 2:5 � 10�2 mW/cm2.

A good contrast between the illuminated (low rdvalues) and the dark regions (high rd values) is

observed. As rd decreases, the image intensity

increases. Under full contact collection the carriers

injected by the ac current source flow in the

transversal direction. The potential drop inside the

dark regions is high (high rd) and decreases inside

the illuminated regions, as rd decreases (FL

increases). Again, a good agreement between

simulated (Fig. 5(a)) and experimental (Fig. 5(b))

results is found.

4. Conclusions

A physical model supported by an electrical

simulation was presented. A SPICE based simu-

lator was used to infer the output characteristics.

Fig. 4. Simulation and experimental outputs for: (a) lower n-layer resistivity, (b) higher n-layer resistivity.

J. Martins et al. / Vacuum 64 (2002) 307–313 311

Simulated results are in good agreement with the

experimental findings, showing that contact geo-

metry, sensor configuration and image intensity

influence the sensor output characteristics. A

trade-off between the lateral resistance, that

models the resistivity of the doped layers, and

the transversal one, that models the brightness of

the image, is needed for a correct read-out.

Further improvements must be introduced to

complete the electrical model, in order to suggest

additional changes to the transducer configuration

and to the experimental readout process of the

image acquisition procedure.

Acknowledgements

We would like to thank Prof. Reinhard Schwarz

for helpful discussions. This work has been

financially supported by PRAXIS/P/EEI/12183/

1998.

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Fig. 5. Higher (left plots) and lower (right plots) image intensity from: (a) simulation outputs, (b) experimental outputs.

J. Martins et al. / Vacuum 64 (2002) 307–313312

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