Mixed-Mode Simulation of Optical-Based Systems: PSD Application

Ricardo Doldán, Eduardo Peralías, Alberto Yúfera and Adoración RuedaInstituto de Microelectrónica de Sevilla (IMSE), Centro Nacional de Microelectrónica (CNM)

Av. Reina Mercedes s/n. Edificio CICA. 41012. Sevilla. SPAINphone: +34 -955056666. fax: +34-955056686

emails: rdoldan, peralias, yufera, rueda@imse.cnm.es

ABSTRACT

This paper reports a new model for electrical simulation of photodetector cells, that includes its complete dynamics, andenables full system characterization, both optical and electrical parts by using the same simulation environment (Spectrein our case). The modelling of the optical parts presented in this work allows the designer to change parameters such asincident spot position and optical power, speed in spot position, photodevices responsivity, pixel fill-factor, etc. The paperpresents the design and the simulation-based verification of a Position Sensing Detection (PSD) system for applicationswith resolutions in the micrometer range and with spot movement tracking operation originated in a DNA sensing process.

Keywords: Spectre-HDL, PSD, Photodetectors, DNA sensors.

1. INTRODUCCION

Low-cost CMOS technology is rapidly developing and becoming the mainstay in the IC market. The possibility ofimplementing photoelectronic conversion devices as photodiodes and phototransistors in CMOS takes designers to leavenon-standard technologies and develop their imaging applications in CMOS where they can integrate in one chipphotosensors and its signal processing circuitry. Therefore, there is a need for compact models for these photosensors inthe IC designers community. These models should be implemented in the standard CAD applications so that they can beeasily used. Several SPICE models have been already presented [1-3]. But most of them limit themselves to the electricalpart of the photodiode without having the possibility of modelling the light distribution in an array of photodetectors, asusually is required in photosensing applications.

Analog Hardware Description Languages such as Spectre-HDL give designers the possibility of integrating differentdisciplines in one model. In this work, Spectre-HDL is used to build a complete photodetector cell model for electricalsimulations. The cell consists of an array of photodiodes which is lighted by a moving spot which is modelated like agaussian power distribution. The optical detection system will be employed to measure changes on the position of a lightspot emitted by a VCSEL cell. The changes in spot positions are driven by the deflection of cantilever nano-structuresemployed to sense the hybridisation process of biological material (DNA) for gene identification. A simplified set-up isshown in Fig. 1. Each photodiode gets the corresponding amount of light power according to its position in the array andto the parameters defined for the cell instance. The model is used to design a PSD application based on a proposeddetection algorithm in which the position resolution required is less than the pixel size (sub-pixel resolution). Although anew electrical photodiode model is also introduced and used in our application, it is not the objective of this paper to showthe actual accuracy of this model, but mainly to prove the advantages of an hierarchical modelling approach regarding itstuning and reconfiguration capabilities. The provided photodetector cell model can be configured to use any electricalphotodiode model chosen by the designer and also to include other light power distribution functions which better suit theparticular application. Moreover, as far as we know, it is the first Spectre-HDL photodetector model which integrateselectrical photodiode model and dynamics of light movement over the cell. Section 2 describes the photodiode electricalmodel. Section 3 shows how the model was implemented in Spectre-HDL and how the photodetector cell was modelled

and implemented. In section 4 the PSD algorithm is described. In Section 5 the application where the cell model was usedis explained including the signal processing circuits. Section 7 summarizes the conclusions of this work.

2. PHOTODIODE MODEL

The photoelectric effect appears in every lighted pn diode. The amount of generated photocurrent depends on the quantityof photons arriving at the depletion region. The relationship between the light power absorbed Popt and the generatedphotocurrent Iph is a function of the wave length (λ) and can be expressed as

(1)

where η = η (λ) is the quantum efficiency, defined as the ratio between the number of generated electron-hole pairs andthe number of photons that hit the semiconductor surface, h is the Planck constant, q is the electron charge and c is thespeed of light in vacuum. The electric model of the photodiode used can be seen in Fig. 2. There, Iph is the photocurrentgenerated by the incident light, and the diode ID characteristic is given by the known expression

(2)

where VD is the diode voltage and Is represents the leakage currents of the reverse bias diode, that in the case ofphotodiodes are also called dark currents [4] as they are the only currents that pass through the device in the absence oflight (zero input response). This leakage currents are a function of the area and perimeter of the junction, minority carrierconcentrations and the minority carrier diffusion length and lifetime. In the technology process data sheet an expressionfor Is is given as

Cantilever

Spot

Photodetector Array

VCSEL

2Rx ≈ 40µm

2Ry ≈ 400µm

d 1

Nc

. . .

12

Nr

. . .

rowscolumns

Fig.1: Illustrating the DNA sensing process: when gene detection appears, the cantilever deflection (d) goes from the initial value(d0) to the actual one (d1), provoking a displacement on the Spot Center (SC) form the initial location (SC0) to the actual one (SC1).

d0

d1

SC0

SC1

Iph

qηλPopthc

----------------------=

ID Is e

qVDkT

------------

1–

=

(3)

where Js y Jsw are the leakage currents density per drawn area (area) and per drawn perimeter (perim), respectively. Thephotodiode presents a junction capacitance given by

(4)

where φ is the junction potential, Cj and Cjsw are the junction capacitance for VD = 0 per drawn area and per drawnperimeter, respectively, and Mj y Mjsw are the area and sidewall junction grading coefficient, respectively. Finallyresistances RD1 and RD2 model second order effects. RD1 models the dependence of the photocurrents with the reverse biasvoltage. RD2 models the potential drop in the diode connections. Typical values for these parameters are 109Ω and higherfor RD1, and a few ohms for RD2.

3. PHOTODIODE-SPOT MODEL IN SPECTRE-HDL

Spectre-HDL ([6]) lets designers of analog systems and integrated circuits create and use modules that encapsulate high-level behavioural descriptions of systems and components. The behaviour of each module is described mathematically interms of its terminals and external parameters applied to the module. These behavioural descriptions can be used in manydisciplines (electrical, mechanical, fluid and so on). Using this language a photodiode and a photodetector cell aremodeled. For the models a hierarchical design is followed, so after the photodiode model, a pixel model is implementedand from there a Nr x Nc pixel photocell is modelled.

The Spectre-HDL photodiode-spot model is done with a behavioural description of the device. We assume a rectangularshape for the pixels and photodiodes. The input parameters are: size of the pixel (Lxcell, Lycell), size of the photodiode(lx, ly), photodiode position in the respective pixel (dx,dy), coordinates of the SC (xc, yc), dimensions of the spot (Rx,Ry), number of rows and columns of the array (Nr, Nc), wave length (λ) and power of the incident light beam (Popt) andquantum efficiency for that wave length (ceff). The model has 4 nodes, two for the optic circuit, xc and yc, and two forthe electric ones, A and K. The flow into the optic input is defined as the total light power hitting the junction surface, andusing (1) we can estimate the generated photocurrent. The incident optical power over each pixel can be calculated byintegrating the optical power density equation (1) over the intersection of the spot and each particular pixel surface,because of every pixel “knows” where the center spot is thanks the coordinates xc and yc. Equation (2) and (3) is then usedto calculate the current through the diode. Current through RD1 and voltage drop in RD2 are then calculated completing theelectrical circuit. Figure 3 shows how is performed the mixed-mode operation both optical and electrical parts of thephotodiode in the Spectre-HDL implementation.

The Light Spot Movement Implementation, in mixed-signal simulations, results of interest to enable simulations ofincident light of a spot moving through the cell. Therefore, spot movement is implemented by passing the spot centreposition argument through a function that defines this position for each simulation time slot. To do so it uses twoparameters. In every time, each pixel knows where is the SC (xc and yc coordinates), and evaluates the incident Pspotcorresponding to itself. DC and transient simulations can be performed by programming the movement of the SC bymeans of an independent sources to drive xc and yc changes.

Is area Js⋅ perim Jssw⋅+=

CDarea Cj⋅

1VD

φ------–

Mj

--------------------------perim Cjsw⋅

1VD

φ------–

Mjsw

------------------------------+=

Fig.2: Photodiode macromodel.

RD2

RD1CDID

Iph

D

+

-VD

A

K

Popt,λ

4. PSD ALGORITHM

The simulation of the optical system is intended to evaluate and design an opto-electronic system for Position DetectionSensing (PSD). The system must track the path the centre of a spot follows, with circular or elliptic shape, along aphototetection surface. This tracking is representative of a sensing process, and is placed in the range from sub-micrometers up to some decens of micrometers. This means that, for some standard pixel sizes, the spot centre could bealways inside a pixel. With this in mind, we propose an algorithm for PSD of the centre divided in two steps. Let ussuppose the ideal case for the photodetector cell shown in Fig. 4. The photodetector cell consists of an array of Nr x Ncpixels where every pixel is totally a photosensor and every pixel “touches” its neighbour. In general, the pixel shape couldbe not be squared.

Step1: We call Iij the current generated at the (i,j) pixel on the array, obtained from the incident optical power, Pij, over itsphotodetection surface. Each Iij pixel current will generate a voltage, Vij, as a consecuence of a linear integration. Finalresult for step 1 is that a two dimension array of pixel voltages (frame) has been generated. In this moment, we could knowin which pixel the spot is, having a resolution of the spot centre position equal to the pixel size, or equivalently, a pixelresolution system. We want to obtain more resolution, because of typical pixel sizes are in the order of some micrometers.

Spot

PowerSize

Wavelength

Photo-diode

SizeWavelengthQuantum efficiency

Center positionNumber of rows and columns

Pixel position inthe array

Independent Voltage Sourcesfor simulate the spot center evolution

Fig.3: Photodiode model implemented using Spectre-AHDL.

AHDL Spectre

Pixel Array

(transistor level)

Spectre-HDL

module DIODE(K,A,xc,yc,ixcell,Ncol,Nrow,Lxcell,Lycell,dx,dy,lx,ly,Rx,Ry,P0,ceff,lmbda)node [V, I] K, A;node [V, I] xc, yc;

1 2 ... Nc

1

2

Nr

..

.

rows Lh

Lv

Fig.4 Basic configuration for the array of photosensors Nr x Nc.

Ih1

Ih2

Ihr

.

Iv1 Iv2 Ivc. . .

.

. pixel

columns

Step2: To increase the accuracy of the measured, we calculate the baricenter of the acquired voltage distribution (Vij). Thiscan be done by the following process. For the one dimension case: let us consider a gaussian optical power distributionalong the x-axis,

(5)

being A a constant. and xc and sigma the statistical parameters associated to it. We define the Baricenter function B,associated to this power distribution as,

(6)

that, for simetrical functions, it would be the goemetrical center of the gaussian distribution, or mean value.

For the discrete case, the i-th pixel will be placed at xj = jL, being L the pixel size, Figure 5. For the interval Zj = [xj-1,xj],we define the function,

(7)

and the baricenter function for the discrete case is,

. (8)

For small values of L, is true the following approximation,

p x( )A

σ 2π------------e

x xc–( )2

2σ2--------------------–

=

B xc σ,( )

xp x( ) xd∞–

∞

∫

p x( ) xd∞

∞

∫

-----------------------1

σ 2π------------- xe

x xc–( )2

2σ2--------------------–

xd∞–

∞

∫xc

σ 2π------------- e

x xc–( )2

2σ2--------------------–

xd∞–

∞

∫ xc= = = =

x

p(x)

0 L 2L ... xj-1 xj ... xc

Ij

Fig.5: Discrete case: Baricenter definition.

Ij p x( ) xdxj 1–

xj

∫=

B xc σ,( )

xjIjj ∞–=

j ∞=

∑

Ijj ∞

j ∞=

∑

--------------------=

(9)

and then,

(10)

In the particular discrete case, the number of pixel is finite, and they will be inside a D domain. In a general case, wecan select an interval , considering a subset of N, with intervarls of lenght L, as it is shown in Figure 6.

We define the subset S of D as,

(11)

in such a way that the intervarls Zj in S are simmetrical around xc. To define the baricenter at D, we take out the non-simetrical intervarls. Once measured the Vij voltage in the pixel array, we start in the following way to calculate thebaricenter.

5. PSD SYSTEM IMPLEMENTATION

Figure 7 showns the basic circuit blocks employed to implement a Nr x Nc pixel array system for PSD. It is composed bya pixel array, digital circuit for control and I/O decoding, analog circuits for output buffer implementation, etc. The systemhas been simulated and designed in a AMS 0.35µm tecnology. In the next, it will be described briefly these circuit blocks.

Píxel. We use the well known structure Active Pixel Sensor (APS), shown in Fig. 8. It performes two basic operations: forMres on, Vpixel is update to Vinipix, while for Mres off, the photocurrents is integrated at the parasitic capacitance onnode Vpixel, where the capacitance is aproximately Cph, th ephotodiode capacitor. Transitor Mseg works as a voltagefollower and Msw allows to connect/disconnect the pixel to the vertical bus (for columns) connecting all pixels in acolumn. The layout of the pixel a 0.35µm technology is shown in Fig. 9.

xe

x xc–( )2

2σ2--------------------–

x xje

xj xc–( )2

2σ2---------------------–

L xjIj≈≈dxj 1–

xj

∫

B xc σ,( )L 0→

lim xc→

0 x T≤ ≤ NL=

x

p(x)

0 L 2L ... NLxc

T

T-xc T-xc

set D

sub-set S

Fig.6: Baricenter function fo rthe discrete case and finite domain.

S

0 2xc, ifxc T 2⁄<,

or

2xc T T,– if xc T 2⁄>,

=

Fila<1>

Fila<128>

Fila<i>

Col<1> . . . Col<16>Col<j> . . .

CDS

Multiplexor

PHOTOSENSORs

128 x 16

Sv

ShRow Select

Sv

PAD

PAD

Colunm Select

BUFFER

BUFFERVoutS

VoutR

Fig.7 PSD system block diagram.

DIGITAL

BLOCK

Ipixel

Res

Vinipix ≅ 0.9 V

Vdd = 3.3 V

Row<i>

Fig.8 (a) Circuit schematic for the APS. (b) Transient of voltage Vpixel while the photocurrent is being integrated.

Vertical BusBvj

Vpixel

Vij Vinipix

Vpixel

Res

(a) (b)Mres

Mseg

Msw

0.4/0.35

0.4/0.35

0.4/0.35

0 T

ly = 6 µm

lx = 8 µm

Ly = 12 µm

Lx = 12 µm

Fig.9 Pixel layout corresponding to the APS in Fig. 8.

To correct the influence of the main sources of noise in APS based system on the integration process, it is used theCorrelated Double Sampling (CDS) tecnique [ ]. which is based on sampling two times the APS output: the first, whenMres is switched off, and the second, at the end of the integration interval. The difference will calcel the noise and also,will eliminate the non-zero substated effect of Mres threshold voltage. The shematic in Fig. 10 shows the CDS circuitsused. The branch controlled by SHR takes samples of the signals inmediately after the reset signal is activated, and thebranch controlled by SHS does it at the end of the integration interval.

6. RESULTS

An example was chosen and simulated with the implemented photodetector, in order to evaluate the proposed spectre-AHDL model using the PSD algorithm before described. In this example, we consider that the SC moves following a trackfrom P0 to P1 in Fig 11. The dimension of the pixel matrix is 8x32 pixels, being each pixel of 12µm x 12µm. The spotsize has a elliptic shape, with a minor radius of 20µm (x-axis) and a major radius of 100µm (y-axis). The total incidentoptical power is 1µW, with a gaussian distribution in both axis. Fig. 11 illustrates the simulation process in the pixel wherethe movement is located. The SC path goes from P0 to P1, taking steps of 0.2µm in both coordinates. Once the center spotis defined (xc, yc), the current generated on each photodiode is evaluated, using both contributions: electrical and optical.Table I summarize the input conditions and the results obtained. The theoretical inputs are xc,yc and the obtained bysimulation, xc’ and yc’. From each point to the inmediatelly before in the list, we found delta_xc and delta_yc increments.

SHSCol<j>

Vbias2 ≅ 2.4 V

Vdd

BufferVoutS_PAD

Vbias1 ≅ 0.7 V

Bv<j>

Fig.10 CDS circuit schematic.

SHR

- Incorporar resultados de simulacion. Un ejemplo de aplicacion del modelo.

Table 1: Mixed-Mode simulation. All measures in [µm]

xc yc xc’ yc’ Delta_xc’ delta_yc’

66.2100 243,6900 68,1835 243,9243 - -66.4100 243,8900 68,2622 244,0036 0,0787 0.079366.6100 243,0900 68,3408 244,0828 0,0786 0.082766.8100 244,2900 68,4170 244,1645 0,0762 0.081767.0100 244,4900 68,4770 244,4920 0,0600 0.327567.2100 244,6900 68,5960 244,4920 0,1190 0.000067.4100 244,8900 68,6548 244,4038 0,0588 -0.088267.6100 245,0900 68,7341 244,4835 0,0793 0.0797

Fig.11 Basic configuration for the array of photosensors Nr x Nc.

(60um,240um)

(60um,252um)

(72um,240um)

(72um,252um)

P0(66.21um,243.69um)

P1(67.61um,245.09um)

pixel

7. CONCLUSIONS

A mixed-signal model of a photodetector cell for electrical simulation has been presented including the complete dynamicmodel for a photodiode. The novelty of the work lies on the integration of both an electrical photodiode model and thedynamics of light movement over the cell. A PSD algorithm has been also proposed for spot center movement detection.Its CMOS implementation has been validated using the Spectre-HDL photodiode model.

ACKNOWLEDGEMENT

This work is in part supported by the European Project OPTONANOGEN: IST-2001-37239, and the Spanish ProjectTIC2002-10473-E.

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