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

Mixed-Mode Simulation of Optical-Based Systems: PSD Application Ricardo Doldán, Eduardo Peralías, Alberto Yúfera and Adoración Rueda Instituto de Microelectrónica de Sevilla (IMSE), Centro Nacional de Microelectrónica (CNM) Av. Reina Mercedes s/n. Edificio CICA. 41012. Sevilla. SPAIN phone: +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, and enables full system characterization, both optical and electrical parts by using the same simulation environment (Spectre in our case). The modelling of the optical parts presented in this work allows the designer to change parameters such as incident spot position and optical power, speed in spot position, photodevices responsivity, pixel fill-factor, etc. The paper presents the design and the simulation-based verification of a Position Sensing Detection (PSD) system for applications with 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 of implementing photoelectronic conversion devices as photodiodes and phototransistors in CMOS takes designers to leave non-standard technologies and develop their imaging applications in CMOS where they can integrate in one chip photosensors and its signal processing circuitry. Therefore, there is a need for compact models for these photosensors in the IC designers community. These models should be implemented in the standard CAD applications so that they can be easily used. Several SPICE models have been already presented [1-3]. But most of them limit themselves to the electrical part of the photodiode without having the possibility of modelling the light distribution in an array of photodetectors, as usually is required in photosensing applications. Analog Hardware Description Languages such as Spectre-HDL give designers the possibility of integrating different disciplines in one model. In this work, Spectre-HDL is used to build a complete photodetector cell model for electrical simulations. The cell consists of an array of photodiodes which is lighted by a moving spot which is modelated like a gaussian power distribution. The optical detection system will be employed to measure changes on the position of a light spot emitted by a VCSEL cell. The changes in spot positions are driven by the deflection of cantilever nano-structures employed to sense the hybridisation process of biological material (DNA) for gene identification. A simplified set-up is shown in Fig. 1. Each photodiode gets the corresponding amount of light power according to its position in the array and to the parameters defined for the cell instance. The model is used to design a PSD application based on a proposed detection algorithm in which the position resolution required is less than the pixel size (sub-pixel resolution). Although a new electrical photodiode model is also introduced and used in our application, it is not the objective of this paper to show the actual accuracy of this model, but mainly to prove the advantages of an hierarchical modelling approach regarding its tuning and reconfiguration capabilities. The provided photodetector cell model can be configured to use any electrical photodiode model chosen by the designer and also to include other light power distribution functions which better suit the particular application. Moreover, as far as we know, it is the first Spectre-HDL photodetector model which integrates electrical photodiode model and dynamics of light movement over the cell. Section 2 describes the photodiode electrical model. 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 used is explained including the signal processing circuits. Section 7 summarizes the conclusions of this work.

Cantilever

d1 d0

d

rows

Photodetector Array 2

1

1

Spot . .

Nr

2R

x

VCSEL

≈

columns

.

Nc

SC1

.

..

SC0 2R y

40 µm

µm 00 ≈4

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).

2. PHOTODIODE MODEL The photoelectric effect appears in every lighted pn diode. The amount of generated photocurrent depends on the quantity of photons arriving at the depletion region. The relationship between the light power absorbed Popt and the generated photocurrent Iph is a function of the wave length (λ) and can be expressed as qηλP opt I ph = --------------------hc

(1)

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

D ---------- kT – 1 ID = Is  e  

(2)

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

I s = area ⋅ J s + perim ⋅ J ssw

(3)

where Js y Jsw are the leakage currents density per drawn area (area) and per drawn perimeter (perim), respectively. The photodiode presents a junction capacitance given by perim ⋅ C jsw area ⋅ C C D = -------------------------j- + ----------------------------M j V D V D M jsw  1 – ----- 1 – -----  φ φ

(4)

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

Popt,λ}

A RD2

+

}

Iph

VD -

ID

CD

RD1 K

Fig.2: Photodiode macromodel.

3. PHOTODIODE-SPOT MODEL IN SPECTRE-HDL Spectre-HDL ([6]) lets designers of analog systems and integrated circuits create and use modules that encapsulate highlevel behavioural descriptions of systems and components. The behaviour of each module is described mathematically in terms of its terminals and external parameters applied to the module. These behavioural descriptions can be used in many disciplines (electrical, mechanical, fluid and so on). Using this language a photodiode and a photodetector cell are modeled. For the models a hierarchical design is followed, so after the photodiode model, a pixel model is implemented and 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 rectangular shape 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) and quantum efficiency for that wave length (ceff). The model has 4 nodes, two for the optic circuit, xc and yc, and two for the electric ones, A and K. The flow into the optic input is defined as the total light power hitting the junction surface, and using (1) we can estimate the generated photocurrent. The incident optical power over each pixel can be calculated by integrating 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 used to calculate the current through the diode. Current through RD1 and voltage drop in RD2 are then calculated completing the electrical circuit. Figure 3 shows how is performed the mixed-mode operation both optical and electrical parts of the photodiode in the Spectre-HDL implementation. The Light Spot Movement Implementation, in mixed-signal simulations, results of interest to enable simulations of incident light of a spot moving through the cell. Therefore, spot movement is implemented by passing the spot centre position argument through a function that defines this position for each simulation time slot. To do so it uses two parameters. In every time, each pixel knows where is the SC (xc and yc coordinates), and evaluates the incident Pspot corresponding to itself. DC and transient simulations can be performed by programming the movement of the SC by means of an independent sources to drive xc and yc changes.

AHDL

Spectre Photo-diode

Spot Power Size Wavelength Center position

Size Wavelength Quantum efficiency Number of rows and columns

Pixel Array (transistor level)

Pixel position in the array

Independent Voltage Sources for simulate the spot center evolution 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;

Spectre-HDL

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

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

1

2

...

Nc

1 rows

Ih1 Ih2

2

. . .

. . .

Lh Lv pixel

Ihr

Nr Iv1

Iv2

. . .

Ivc

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

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

Step2: To increase the accuracy of the measured, we calculate the baricenter of the acquired voltage distribution (Vij). This can be done by the following process. For the one dimension case: let us consider a gaussian optical power distribution along the x-axis, 2

A = ------------ e

p(x)

σ

( x – xc ) – ------------------2 2σ

(5)

2π

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, ∞

∫ xp ( x ) dx

B ( x c, σ )

1 ∞ -----------= –---------------------= ∞

∫ xe 2π

σ

∫ p ( x ) dx

2

∞

( x – xc ) – ------------------2 2σ

x

c dx = ------------

σ 2π

–∞

∞

∫e

2

( x – xc ) – ------------------2 2σ

dx = x c

(6)

–∞

∞

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

Ij

0 L 2L ...

xj-1 xj ...

xc

x

Fig.5: Discrete case: Baricenter definition.

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, xj

Ij

=

∫

p ( x ) dx

(7)

xj – 1

and the baricenter function for the discrete case is, j=∞

∑ B ( x c, σ )

xj Ij

= –∞ = j------------------j=∞

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

j

∞

Ij

.

(8)

2

xj

∫

xe

( x – xc ) – ------------------2 2σ

2

dx ≈ x j e

( xj – xc ) – -------------------2 2σ

L ≈ xj Ij

(9)

xj – 1

and then, lim B ( x c, σ ) L→0

→ xc

(10)

In the particular discrete case, the number of pixel is finite, and they will be inside a D domain. In a general case, we can select an interval 0 ≤ x ≤ T = NL , considering a subset of N, with intervarls of lenght L, as it is shown in Figure 6. p(x) sub-set S

T-xc

T-xc

xc

0 L 2L ...

NL

T

x

set D

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

We define the subset S of D as,

S

   =    

0, 2x c

, ifx c < T ⁄ 2 or

2x c – T, T

(11)

, if x c > T ⁄ 2

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

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 by a pixel array, digital circuit for control and I/O decoding, analog circuits for output buffer implementation, etc. The system has 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: for Mres on, Vpixel is update to Vinipix, while for Mres off, the photocurrents is integrated at the parasitic capacitance on node Vpixel, where the capacitance is aproximately Cph, th ephotodiode capacitor. Transitor Mseg works as a voltage follower and Msw allows to connect/disconnect the pixel to the vertical bus (for columns) connecting all pixels in a column. The layout of the pixel a 0.35µm technology is shown in Fig. 9.

Sv

Colunm Select

Col . . .

Col . . .

Col

Fila

Fila

DIGITAL Row Select

BLOCK

PHOTOSENSORs 128 x 16

Sh

Fila

VoutS Sv

PAD

BUFFER

CDS

PAD

VoutR BUFFER

Multiplexor

Fig.7

PSD system block diagram. Vdd = 3.3 V

Res Ipixel Vpixel

(a)

Row

Mseg 0.4/0.35

Vpixel

Msw

(b)

Mres 0.4/0.35

Res

Vij

Vinipix

0.4/0.35

0 Vinipix ≅ 0.9 V

Fig.8

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

lx = 8 µm

ly = 6 µm

Ly = 12 µm

Lx = 12 µm

Fig.9

T

Vertical BusBvj

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 the Correlated Double Sampling (CDS) tecnique [ ]. which is based on sampling two times the APS output: the first, when Mres 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 circuits used. The branch controlled by SHR takes samples of the signals inmediately after the reset signal is activated, and the branch controlled by SHS does it at the end of the integration interval. Vdd

Vbias2 ≅ 2.4 V Buffer

Bv

SHS

VoutS_PAD

Col

SHR

Vbias1 ≅ 0.7 V

Fig.10

CDS circuit schematic.

6. RESULTS An example was chosen and simulated with the implemented photodetector, in order to evaluate the proposed spectreAHDL model using the PSD algorithm before described. In this example, we consider that the SC moves following a track from P0 to P1 in Fig 11. The dimension of the pixel matrix is 8x32 pixels, being each pixel of 12µm x 12µm. The spot size has a elliptic shape, with a minor radius of 20µm (x-axis) and a major radius of 100µm (y-axis). The total incident optical power is 1µW, with a gaussian distribution in both axis. Fig. 11 illustrates the simulation process in the pixel where the movement is located. The SC path goes from P0 to P1, taking steps of 0.2µm in both coordinates. Once the center spot is 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 by simulation, xc’ and yc’. From each point to the inmediatelly before in the list, we found delta_xc and delta_yc increments.

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

0.0793

66.6100

243,0900

68,3408

244,0828

0,0786

0.0827

66.8100

244,2900

68,4170

244,1645

0,0762

0.0817

67.0100

244,4900

68,4770

244,4920

0,0600

0.3275

67.2100

244,6900

68,5960

244,4920

0,1190

0.0000

67.4100

244,8900

68,6548

244,4038

0,0588

-0.0882

67.6100

245,0900

68,7341

244,4835

0,0793

0.0797

pixel

(60um,240um)

(72um,240um)

P0(66.21um,243.69um)

P1(67.61um,245.09um)

(60um,252um)

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

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

(72um,252um)

7. CONCLUSIONS A mixed-signal model of a photodetector cell for electrical simulation has been presented including the complete dynamic model for a photodiode. The novelty of the work lies on the integration of both an electrical photodiode model and the dynamics 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 Project TIC2002-10473-E.

REFERENCES 1. 2. 3. 4. 5. 6.

7. 8. 9.

R.J.Perry and K.arora: “Using PSPICE to simulate the photoresponse of ideal CMOS integrated circuit photodiodes”. In Proc. IEEE Southeastcon96 Bringing Together Education, Science and Technology. pp: 374–380, Apr. 1996. T.N.Swe and K.S.Yeo: “An accurate photodiode model for DC and high frequency SPICE circuit simulation”. In Proc. Modelling and Simulation of Microsystems, 2001. Alfredo Arnaud: “Optical based sensors and their signal conditioning”. Master’s thesis, Fac. de Ingeniería. Universidad de la República. Uruguay, May 2000. A.G. Andreou Z.K. Kalayjian: “ Mismatch in photo-diode and phototransistor arrays”. IEEE Int. Symposium on Circuits and Systems, IV:121–124, May 28-31 2000. CADENCE Design Systems Inc. www.cadence.com. P. Aguirre, A. Yúfera, A Rueda: “SpectreHDL Model of a Photodetector Cell for Electrical Simulation and its Application in a WTA Based Light Spot Center Location Circuit”. IEEE Proc. of the Midwest 2003. Cairo (Egypt) Dec. 2003. R. Doldán, E. Peralias, A. Yúfera and A. Rueda: “Design and Simulation of Mixed-Mode Optical System for PSD Applications”. XIX Conference on Design of Circuits and Integrated Systems. Bordeaux. France. Nov. 2004. J.Lazzaro et al.: “Winner-Take-All networks of O(N) complexity”. In Proc. Neural Information Processing Systems (NIPS), page 703, 1989. Referencias CDS.