Manuela A Vieira

Paula Louro

Alessandro Fantoni

Manuel Barata

Vitor Silva

SiC Multilayer Photonic Structures with Self Optical Bias Amplification

Keywords: A-SiC:H Pi'n/Pin Optical Filters, Self Amplification, Photodetection, Electrical Model, Optoelectronic Logic Programming, MUX/DEMUX Device

Characteristics of tunable wavelength pi'n/pin filters based on a-SiC:H multilayered stacked cells are studied both experimental and theoretically. Results show that the device combines the demultiplexing operation with the simultaneous photodetection and self amplification of the signal. An algorithm to decode the multiplex signal is established. A capacitive active band-pass filter model is presented and supported by an electrical simulation of the state variable filter circuit. Experimental and simulated results show that the device acts as a state variable filter. It combines the properties of active high-pass and low-pass filter sections into a capacitive active band-pass filter using a changing photo capacitance to control the power delivered to the load.

Introduction

An optical filter comprises a material that has nonlinear, i.e., amplitude-dependent, response to each incident light wave. This nonlinearity provides the possibility for selectively removing or adding wavelengths and can compensate for coupling losses and be used to boost signal before demultiplexing.

In the WDM signal transmission, three channels (red, green and blue) are demultiplexed using wavelength selective channel filters. Background light can be changed to select different wavelength channels. By superimposing background illumination to the pulsed channel the device behaves as a filter, producing signal attenuation, or as an amplifier, producing signal gain, depending on the channel/background wavelength combination. This effect [START_REF] Vieira | Light-activated amplification in Si-C tandem devices: A capacitive active filter model[END_REF] can be described in terms of a wavelength controlled photo-capacitance.

Optical filters were produced and optimized for a fine tuning of a specific wavelength. Depending on the wavelength of the external background, the monolithic device acts either as a short-or a long-pass band filter or as a band-stop filter.

Contribution to Value Creation

Systems that transmit, receive, and/or process intelligence require some form of modulation, which is the deliberate distortion of a carrier to impress intelligence (data) upon it that allows the subsequent recovery of the information. Data transmission can be improved using the well known wavelength division multiplexing-demultiplexing technique. The plastic optical fiber is a suitable, promising solution as transmission medium for short range communications. Besides it is more resilient to damage than glass due to its intrinsic material characteristics. It is easier to terminate, polish, and connect as well, which can reduce the cost of installation and maintenance. So, the conception of new devices based on new materials for signal (de)multiplexing in the visible spectrum is a demand in the direction of an increased potential for value creation. Such technological innovation can influence economic transformation, create value in the society and ultimately improve individuals' lives. Therefore, the theoretical approach presented in this research is useful in examining a particular aspect of value creation, configuring firm activities (automotive industry, aerospace, medical and housing sectors) to create value combining unique resources and capabilities, devices based on new materials for signal (de)multiplexing in the visible spectrum, in the direction of an increased potential for value creation.

Device Configuration and Operation

The tunable optical devices were produced by PECVD and optimized for a proper fine tuning of a specific wavelength. The active device consists of a p-i'(a-SiC:H)-n/pi(a-Si:H)-n heterostructure with low conductivity doped layers.

Fig. 1. Device configuration

The thicknesses and optical gap of the thin í'-(200nm; 2.1 eV) and thick i-(1000nm; 1.8eV) layers are optimized for light absorption in the blue and red ranges, respectively [START_REF] Vieira | pinpín and pinpii'n multilayer devices with voltage controlled optical readout[END_REF]. As a result, both front and back pin structures act as optical filters confining, respectively, the blue and the red optical carriers. Device configuration is depicted in Fig. 1.

The manipulation of the magnitude is achieved by changing the wavelength (color channels) of the modulated lights and its frequency. By providing a complex illumination of the device combining radiations with different and complementary penetration depths it is possible to control the spectral response of the device. In the WDM signal transmission, three channels (red, green and blue) are demultiplexed using wavelength selective channel filters. Background light can be changed to select different wavelength channels. By superimposing background illumination to the pulsed channel the device behaves as a filter, producing signal attenuation, or as an amplifier, producing signal gain, depending on the channel/background wavelength combination. This effect is reported and fully discussed elsewhere [START_REF] Vieira | Light-activated amplification in Si-C tandem devices: A capacitive active filter model[END_REF].

Voltage Controlled Sensitivity

To test the sensitivity of the device under different applied voltage and optical bias three modulated monochromatic lights channels: red (R: 626 nm), green (G: 524 nm) and blue (B: 470nm) and their polychromatic combinations (multiplexed signal) illuminated separately the device and the generated photocurrent was measured under positive and negative voltages, with and without steady state red, green and blue optical bias. The light modulation frequency of each channel was chosen to be multiple of the others to ensure a synchronous relation of ON-OFF states along each cycle and the optical powers were adjusted to give different signal magnitudes at -8V. Results show that the red input signal remains constant, the green decreases and the blue almost disappears as the voltage changes from negative to positive. The output multiplexed signal, obtained with the combination of the three optical sources, depends on both the applied voltage and on the ON-OFF state of each input optical channel. Under negative bias, there are eight separate levels (2 3 level encoding) while under positive bias they were reduced to one half (2 2 level encoding). The highest level appears when all the channels are ON and the lowest if they are OFF. Furthermore, the levels ascribed to the mixture of three or two input channels are higher than the ones due to the presence of only one (R, G, B).

Optical Bias Controlled Sensitivity

In Fig. 3, at -8V, the same red, green and blue monochromatic input channels (a) and their polychromatic combination but with different bit sequences (b), without (φ=0) and with red steady state optical bias (624 nm, φ=73mWcm-2) are displayed at a bit rate of 6000bps. The bit sequences to drive the channels are shown in the top of the figure to guide the eyes. Results show that under steady state irradiation the red background enhances the light-to-dark sensitivity in the short wavelength range and quenches it in the long wavelength range. Since, under red illumination, the electrical field increases locally at least absorbing cell [3], the front diode (self optical amplification) the collection due to the carriers generated by the blue channel (absorbed in the front diode) is enhanced (Fig. 3a). The channel gain, defined as the ratio between the channel signal with and without steady state optical bias becomes higher than one (α B >>1, see arrows). In the back diode the electric field is reduced (self optical quench) so, the collection of the carrier generated by the red channel is reduced. Here, the gain becomes lower than one (α R <<1). The green channel is mostly absorbed across the back diode due to its higher thickness, so its gain is also lower than one (α G <1) but higher than α R due to the front carrier collection.

When the polychromatic combination of the different pulsed channels impinges on the device, under red steady state additional optical bias, the output signal has a strong nonlinear dependence on the light absorption profile in a mode that induces a nonlinear wavelength bias dependent gain. This gain depends on the background wavelength that controls the input signals (Fig. 3a).

To recover the transmitted information (6000bps, 8 bit per wavelength channel) the output waveforms under red irradiation and without it were used. Both multiplexed signals, during a complete cycle (T), were divided into eight time slots (∆=133 µs), each one with a bandwidth of 7.5 KHz corresponding to one bit where the independent optical signals can be ON [START_REF] Vieira | Light-activated amplification in Si-C tandem devices: A capacitive active filter model[END_REF] or OFF (0). In Fig. 3 all the possible combination of the three input channels are present, so, the waveform of the output without optical bias is, as in Fig. 2b, an 8-level encoding (2 3 ) to which it corresponds 8 different photocurrent thresholds. Taking into account Fig. 3, under red background the red channel is strongly quenched and the blue enhanced. So, the output waveform becomes a main 4-level encoding (2 2 ). Here, the higher level corresponds to both blue and green ON (_11) and the lower to the absence of both (_00). The other two intermediate levels are ascribed, the upper level to the ON state of the blue (_01) channel and the lower to the green channel ON (_10). To decode the red channel, similar time slots with red background have to be compared with the ones without it, being higher the ones with the red channel ON. Using this simple algorithm the independent red, green and blue bit sequences were decoded as: B [01010101], G [00110011] and R [00001111].

Photo Capacitive Active Band Pass Filter Model

Based on the experimental results and device configuration an optoelectronic model supported by the complete dynamical large signal Ebers-Moll model with series resistors and capacitors was developed [START_REF] Vieira | Voltage Controlled Amorphous Si/SiC Phototransistors and Photodiodes as Wavelength Selective Devices: Theoretical and Electrical Approaches[END_REF][START_REF] Vieira | Double pin Photodiodes with two Optical Gate Connections for Light Triggering: A capacitive twophototransistor model[END_REF]. The equivalent circuit is displayed in Fig. 4 where α 1 and α 2 coefficients determine how the background affects the state change. In Fig. 5 it is displayed the block diagram of the optoelectronic state model for the pi´npin device under different electrical and optical bias conditions. The input signals, λ 1 , λ 2 , λ 3 model the color channels and i(t) the output signal. R 1 and R 2 are the dynamic internal and back resistances and α 1 and α 2 are the coefficients for the steady state irradiation. Taking into account Fig. 3, under red light background we consider α 1 >1 (α B + α G >1) and α 2 <1(α R + α G <1). The opposite will occur under blue irradiation. Under green background both are balanced. The Kirchhoff's laws give the state-space realization of the equivalent circuit. The time periodic linearized state equations are given by:

) ( 1 1 1 1 1 ) ( 2 , 1 2 2 2 1 2 1 1 1 1 1 2 , 1 2 2 1 1 2 , 1 t v C R C R C R C R C R t i C C dt dv             - - - +             = α α ( ) ( ) t v R t i 2 , 1 2 1 0       = (1)
The operation of this capacitive active circuit is based on the pi'npin device ability to simulate resistors and capacitors, resulting in integrated filters. The lack of external capacitors and inductors reduces the problems associated with those components while adding some interesting new capabilities. The use of amplifying elements (Q 1 , R 1 ( V) Taking into account equation 1, the amplifying elements, α 1 and α 2 , in the control matrix, can provide gain if needed or attenuate unwanted wavelengths (<1) while amplifying (>1) desired ones under suitable optical bias wavelengths. Under optical bias, the control matrix takes into account the enhancement or quenching of the channels (Fig. 3) due to the steady state irradiation. It will be affected by the reverse photo capacitances, (α 1,2 /C 1 . 2 ) that determine how the system input affects the state change.

α 2 I Gpin α 2 I R R 2 Q 2 C 2 α 1 I B Q 1 C 1 α 1 I Gpi ´n
In Fig. 6a it is displayed the electrical field profile [START_REF] Vieira | Light-activated amplification in Si-C tandem devices: A capacitive active filter model[END_REF], at different values of the electric bias, under the effect of the blue channel. In Fig. 6b a red steady state optical bias was superimposed. As expected as the voltage changes from positive to negative the electrical field increases in the less absorbing cell, the back diode. The addition of the red background quenches the field in the back diode where the red photons are absorbed (reverse bias effect) and increases it (reverse bias effect) in the front diode where the blue channel generates the optical carriers. So, the induced variation of the field brings on the blue collection, from which results the observed amplification of the signal (Fig. 3). Under red background light the photogenerated charge accumulations from deep trap levels is maximized for the blue channel and correspond to a photo capacitance

λ 1 λ 3 λ 2 α 1 /C 1 α 2 /C 2 ∑ ∑ -1/R 1 C 1 1/R 2 ∫ dt 1/R 1 C 2 1/R 1 C 1 ∫ dt -1/R 1 C 2 -1/R 2 C 2 ∑ i(t) + i 2 (t) i 1 (t) + + + + + v 1 . . v 2 + v 1 v 2 λ 1 λ 3 λ 2 α 1 /C 1 α 2 /C 2 ∑ ∑ ∑ ∑ -1/R 1 C 1 1/R 2 ∫ dt ∫ dt 1/R 1 C 2 1/R 1 C 1 ∫ dt ∫ dt -1/R 1 C 2 -1/R 2 C 2 ∑ ∑ i(t) + i 2 (t) i 1 (t) + + + + + v 1 . . v 2 + v 1 v 2
behavior of the internal recombination junction (considered as a measure of the density of photogenerated carriers in the space charge region) that combined with the series and parallel resistance of the diodes will result in the explicit definition of cut off wavelengths.

The values and the strategic placement of the resistors in the system matrix determine the basic shape of the output signals (output matrix). Under negative bias applied background the device has low ohmic resistance (low R 1 ) since the base emitter junction of both transistors are reverse polarized and conceived as phototransistors. This results in a charging current gain proportional to the ratio between both collector currents (α 1 C 2 / α 2 C 1 ).

To solve the state equations the four order Runge-Kutta method was applied and MATLAB used as a programming environment. The input parameters were chosen in compliance with the experimental results. In Fig. 7a the simulated current without background (α 1 = α 2 =1) under positive and negative applied voltage is displayed. In Fig. 7b the simulated current under negative bias but under red background is shown. The current sources are also displayed (dash lines).

To simulate the negative and positive electrical bias two values of R 1 were used, a low one under negative bias since the internal junction is forward bias and a high value, under positive bias, due to its reverse state. For the intensity of the current sources the amplitude of the input channel from Fig. 2a were used. To simulate the red background, current sources intensities were multiplied by the on/off ratio between the input channels with and without optical bias (Fig. 3a). To validate the model the experimental multiplexed signals are also shown (solid lines). A good agreement between experimental and simulated data was achieved. The device behaves like an optoelectronic controlled transmission system that stores, amplifies and transports the minority carriers generated by the current pulses, through the capacitors C 1 and C 2. Here, the dc voltage control creates a voltage across one or both capacitors which, when superimposed with an ac pulse, collectively saturates the circuit. Under red background the expected optical amplification in the low wavelength range is observed due to the effect of the active multiple-feedback filter when the back diode is light triggered.

Conclusions

SiC multilayer photonic structures with self optical bias amplification were analyzed. Results show that the light-activated photonic device combines the demultiplexing operation with the simultaneous photodetection and self amplification of an optical signal. The output waveform presents a nonlinear amplitude-dependent response to the wavelengths of the input channels.

A photo capacitive optical filter model was presented and supported by a numerical simulation. An algorithm to decode the multiplexed signals was established.

Fig. 2 Fig. 2 .

 22 Photocurrent (µA)

Fig. 3 .

 3 Photocurrent (µA)

Fig. 4 .

 4 Fig. 4. ac equivalent circuit

Fig. 5 .

 5 Fig. 5. Block diagram of the optoelectronic state model for a pi´n/pin device

Fig. 6 .

 6 Fig. 6. Electrical Field profile using a) the blue channel and b) the blue channel and red optical bias

Fig. 7 .

 7 Photocurrent (µA)

Acknowledgements. This work was supported by FCT (CTS multi annual funding) through the PIDDAC Program funds and PTDC/EEA-ELC/111854/2009.


Asal Kiazadeh

Paulo F Rocha

Qian Chen

Henrique L Gomes

Paulo R Rocha

New Electronic Memory Device Concepts Based on Metal Oxide-Polymer Nanostructures Planer Diodes

Keywords:

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Metal-oxide nanostructured material in a polymeric matrix exhibits different resistivity states. In the previous paper it has shown that the resistive switching will occur through the polymer capped nanostructure silver oxide embedded in a planer diode with two gold electrodes [START_REF] Kiazadeh | Resistive Random Access Memories (RRAMs) Based on Metal Nanoparticles[END_REF]. There are lots of reports showing different mechanisms for resistive switching observation [START_REF] Hickmott | Low-Frequency Negative Resistance in Thin Anodic Oxide Films[END_REF][START_REF] Hickmott | Electron Emission, Electroluminescence, and Voltage-Controlled Negative Resistance in Al-AlO2-Au Diodes[END_REF][START_REF] Barriac | Study of the electrical properties of Al-Al2O3-metal structures[END_REF][START_REF] Simmons | New Conduction and Reversible Memory Phenomena in Thin Insulating Films[END_REF][START_REF] Sutherland | Theory for Negative Resistance and Memory Effects in Thin Insulating Films and Its Application to Au-ZnS-Au Devices[END_REF][START_REF] Ansari | Memory Switching in Thermally Grown Titanium-Oxide Films[END_REF][START_REF] Ma | Nonvolatile electrical bistability of organic/metal-nanocluster/organic system[END_REF][START_REF] Paul | Langmuir-Blodgett film deposition of metallic nanoparticles and their application to electronic memory structures[END_REF].

Up to now, all switching devices prepared with nanoparticles have some functional components in common: (i) Need a polymer network with the nanostructure material which can be metal sulfide, oxide or halide (ii) The initial state of device before switching is a Pristine-state. The pristine device usually needs an Electroforming process. The electroforming process is voltage application sweeping in order to reach to soft breakdown of oxide or halide , the electric field needs to switch for each device is different due to various matrixes chemically in material, work function and physically such as difference in layer thickness. After an electroforming the reproducible on/off system often obtains with a voltage pulse at low resistance state (LRS) voltage region or high resistance (HRS) voltage domain. Lack of an organic matrix, a destructive electrical switching is observed. In fact optimizing the nanostructure matrix is obviously important to observe a reliable switching memory. This report implies some interesting features, which may help better understand the mechanism of electrical switching in metal oxide nanostructure polymeric network. Conceivable mechanism for the resistive switching in this system is following with temperature measurement. In this work it is shown that the XRD pattern after switching appears with different crystalline planes, plus temperature dependent studies reveal that conduction of both on and off states is weak thermal activated. Surprisingly, the carrier transport is the same for both on and off-states. Difference between states comes from the dramatic changes in the carrier density. The main mechanism of charge transport for on-state is tunneling. The charge transport leads to SCLC in higher voltages pulse for the off state. The mechanism will be explained based on percolation concepts. A myriad of conducting percolative paths are created after a soft breakdown in oxide. Some of these paths they switch on-and off leading to the observation of RTS noise.

Contribution to Value Creation

In this work, we utilized the nanostructure silver oxide thin films. Despite of having a sandwich device, the diode is planer in order to explore charge carrier transport within switching phenomena. We reported a memory device, which makes use of thin polymer film hosting a matrix of silver oxide nano structure. With on/off ratio as high as 10 3 , a large retention time and good cycle endurance, the nanoparticles based device is a serious candidate to replace currently available non-volatile memories, and is able to improve all the relevant components as a reliable memory device.

In addition, these planar structures have the active layer directly exposed and can be probed by a number of surface analytical techniques like XRD to identify and characterize structural changes that occur in the devices upon resistive switching.

System Description

The colloidal solution of silver oxide nano structure in PVP was deposited on top of preformed gold microelectrode arrays fabricated on thermal oxidized silicon wafers. The interdigitated gold microelectrode arrays were separated apart 10 µm and 10.000 µm long. Prior to electrical measurements the samples were also pumped in vaccum to remove further any residual solvent. Electrical measurements were carried out using a Keithley 487 picoammeter/voltage source in dark conditions, high vacuum. During all the measurement the conductive silicon substrate is kept grounded to prevent charging of the SiO 2 layer (see inset of Fig. 1(a)).

Current-Voltage Characteristics

Initially, the oxide-polymer matrix is highly insulating and the diodes behave as capacitors. In order to induce bistable resistive states the diode must be submitted to an electric field near to dielectric breakdown. This is known as electroforming and in practice corresponds to a soft-breakdown of the dielectric layer. The details of this breakdown process are still elusive. It is usually assumed that a network of defects is created by the strong electric field. Soft-breakdown is usually distinguished from hard breakdown because the electric power is kept low preventing the propagation of the damage in the dielectric by Joule heating. In practice the voltages required to induce soft breakdown are typically ~48V for a 10 µm channel length between electrodes corresponding to an electric field of 4.8MVm -1 .

After forming the device exhibits the bistable current-voltage characteristics presented in Fig. 1 and already reported in our previous work [START_REF] Kiazadeh | Resistive Random Access Memories (RRAMs) Based on Metal Nanoparticles[END_REF].

Morphological And Structural Characterization

Silver oxide is a complex multiphase material. Silver being multivalent forms by interacting with oxygen various phases such as Ag 2 o, AgO, Ag 3 O 4 and Ag 2 O 3 . The presence of these phases can be identified by using X-ray diffraction (XRD) techniques. Fig. 2 shows a XRD pattern of the diode. In order, to clarify the physical origin of all the different peaks in the spectrum. The XRD was taken for the (a) silicon wafer substrate, (b) for the diode in its pristine state (i.e. right after thin film deposition and (c) in its memory. The first striking observation is that the pristine diode has a crystal structure different from the electroformed diode. This suggests that under the high electric field the silver nanoparticles act as seed and small silver crystals are formed. The peaksin curve (c) of Fig. 2

Voltage Dependence

Fig. 3 shows the I-V characteristics (in a log voltages below the NDR region. In the low field region, both the on follow a power law, i. e. Ohmic conduction) and A is a coefficient which depends on resistance state. At high fields the off-state clearly shows a distinct curve of the off-state show two regions of conduction, viz. (i) nearly bias and (ii) non-ohmic conduction at higher bias.

For lower bias the injected charge carrier density is lower than the generated carrier density and that leads to ohmic behaviour. At slope 2 suggests, the conduction in this region is dominated by trap limited charge limited conduction mechanism [ref].The conduction mechanism in the off state is then governed by defect states. These states act as carrier trapping centres and after trapping the injected charge from electrodes they become charged and Log(I)

A. Kiazadeh et al.

XRD patterns for the substrate (black), Pristine state (blue), Electroformed state Dependence V characteristics (in a log-log scale) of both resistive states for voltages below the NDR region. In the low field region, both the on-and the off follow a power law, i. e. I = AV n where n is an exponent factor (n=1 for perfect Ohmic conduction) and A is a coefficient which depends on resistance state. At high clearly shows a distinct slope with the value of 2. Thus the state show two regions of conduction, viz. (i) nearly ohmic at lower ohmic conduction at higher bias.

Fig. 3. Log (I)-Log (V) for the on and off-states

For lower bias the injected charge carrier density is lower than the generated carrier density and that leads to ohmic behaviour. At higher bias, as the the conduction in this region is dominated by trap limited charge limited conduction mechanism [ref].The conduction mechanism in the off tate is then governed by defect states. These states act as carrier trapping centres and after trapping the injected charge from electrodes they become charged and For lower bias the injected charge carrier density is lower than the thermally higher bias, as the the conduction in this region is dominated by trap limited space charge limited conduction mechanism [ref].The conduction mechanism in the offtate is then governed by defect states. These states act as carrier trapping centres and after trapping the injected charge from electrodes they become charged and thereby expected to build up a space charge. This buildup of space charge by defects then play a key role in determination of SCLC process. At lower bias up to transition voltage (Vt ), the current density (J) governed by the intrinsic free carrier density (n0), in the film can be expressed as here d is the gap between the electrodes n0 is the normal volume generated free carrier density and µ the electron mobility. Using eq. 1 we estimate mobility in the off-state of ~ 1x10 -9 cm 2 /Vs.

J= ݊μܸ ௧ /݀ (1)

Temperature Dependence

To get insight into the charge transport mechanism for both on and off-states we measure the temperature dependence of the current. Fig. 4 shows the Arrhenius plot of the current for an on-state and for two off-states measured with an applied voltage of 3 V. Multiple intermediate off-states are induced by controlling the length of the voltage reset pulse. Longer voltages pulses will induce lower conductance states. Although, the conduction states are separated by almost 5 orders of magnitude in current, it is striking that the activation energy (70 meV) remains identical. This result shows that upon resistive switching the carrier transport mechanism is not changed but the carrier density increases dramatically.

The low value for the activation energy strongly suggests that the carrier transport is by tunneling or variable ranging hooping between shallow localized states.

Conclusions

It is shown that the diode needs an electroforming (soft-breakdown) to become bistable. This process can be considered as a phase-transition from a non-conducting (insulating) to a conducting state. After the soft-breakdown a percolation network of paths is established. The high conductance state is as a result of a myriad of conducting paths within the matrix. For both states the charge transport is via

Log(I) (A)

super off-state off-state on-state tunneling between nanoclusters, but at the off-state the amount of percolative paths are less than on-state. In fact, due to high electric field some of charge carriers being injected into insulator from nanoclusters where there is no compensating charge present in the insulator. Therefore, they cannot participate in conduction nor have a very small contribution in the conduction.

Trapped charges in the insulating matrix at higher electric field might lead to a random offset charge disorder. In the presence of such disorder, charge carriers do not flow uniformly through the nanocomposite film. Because of such kind of disorder, it can exist both off and super off states. The I-V curves show nearly Ohmic behaviour at low bias and SCLC at high bias range.

Fig. 1 .

 1 Fig. 1. (a) Electroforming process (inset: device structure). (b). Current-voltage characteristics showing the high conductance on-state and low conductance off-state

  match with of the presence of the Ag, Ag 2 O and AgO phases.

Fig. 2 .

 2 Fig. 2. XRD patterns for the substrate

,

  Electroformed state (Red) log scale) of both resistive states for and the off-state =1 for perfect Ohmic conduction) and A is a coefficient which depends on resistance state. At high slope with the value of 2. Thus the I-V ohmic at lower

Fig. 4 .

 4 Fig. 4. Arrhenius plot of the current measured at 3V for the one state and for two off-states. The activation energy is 70 meV for all the conduction states

Acknowledgements. We gratefully acknowledge the financial support received from the Dutch Polymer Institute (DPI), project n.º 703, from Fundação para Ciência e Tecnologia (FCT) through the research Unit, Center of Electronics Optoelectronics and Telecommunications (CEOT), REEQ/601/EEI/2005 and the POCI 2010, FEDER and the organic chemistry laboratories in Algarve University.


Q Chen

H L Gomes

D M De Leeuw

S C J Meskers

Electroforming Process in Metal-Oxide-Polymer Resistive Switching Memories

Keywords: Resistive Random Access Memory (RRAM), Electroforming Soft-Breakdown, Non-Volatile Memory

Electroforming of an Al/Al 2 O 3 /polymer/Al resistive switching diode is reported. Electroforming is a dielectric soft-breakdown mechanism leading to hysteretic currentvoltage characteristics and non-volatile memory behavior. Electron trapping occurs at early stages of electroforming. Trapping is physically located at the oxide/polymer interface. The detrapping kinetics is faster under reverse bias and for thicker oxides layers. Thermally detrapping experiments give a trap depth of 0.65 eV and a density of 5x10 17 /cm 2 . It is proposed that the trapped electrons induce a dipole layer across the oxide. The associated electric field triggers breakdown and ultimately dictate the overall memory characteristics.

Introduction

Metal-Insulator-Metal (MIM) structures based on oxides shown resistive switching [1] properties and they are being considered interesting for the resistive random access memories (RRAMs) [START_REF] Akinaga | Proceedings of the IEEE[END_REF]. This simple diode structure, whose resistance can be programmed reversibly to be high or low, offers an interesting opportunity for application in high-density memory arrays, either as a memory [START_REF] Sawa | [END_REF] element in its own right or coupled to CMOS [4] addressing logic. One type offering excellent prospects is the metal-oxide-polymer diode Al/Al 2 O 3 /polymer/metal. Al 2 O 3 [ 5 ] has been studied since 1962, when Hickmott [6] first reported that resistive switching occurs as a result of applied electric field. Studies of post-breakdown conduction in MIS capacitors were also preformed by Srivastaya and Bhattacharyya [ 7 ] using Al/Al 2 O 3 /Cds capacitors. Their sample exhibited bistable switching between two states in the post-breakdown stage, and they conclude that the conduction involved field ionization of traps [8] in both states. Later, Shatzkes, Av-Ron, and Anderson [9] studied the post-breakdown conduction of thick (20-100nm) SiO 2 films in metaloxide-semiconductor (MOS) structures. They used Al/SiO 2 /Si and Cr/SiO 2 /Si capacitors and also obtained a controlled switching between two conduction states, the breakdown [10] being the change from the low to a high conductivity state. More recently, the study of the breakdown and post-breakdown conduction trough thinoxide Cr/SiO 2 /Si capacitors also suggested that the breakdown could be understood as reversible change between two different conduction states. The nature of the defects [11] created during the soft-breakdown remains a matter of debate, for binary oxides such as TiO 2 [12], ZrO 2 [13], and Al 2 O 3 , it is commonly accepted that they are oxygen vacancies [14].

The objective of this study is to get insight into the early stages leading to a softbreakdown or electroforming [ 15 ]. Evidences [ 16 ] are provided showing that breakdown is proceeded by electron trapping [17] at the oxide/polymer interface. The accumulated charge creates an internal electric field that eventually causes the rupture of the dielectric. Understanding the early stage of electroforming may allow us to optimize the electroforming procedure and fabricate resistive switching diodes with better memory characteristics. Furthermore, the role of the polymer layer in controlling the soft-breakdown mechanism [18] may be better understood.

Contribution to Value Creation

This study provides insight into the mechanism than changes a typical insulator material such as Al 2 O 3 into an electrical bistable material interesting for RRAMs. The change in the electrical properties is caused by soft-breakdown process. The polymer layer added in series with Al 2 O 3 plays a crucial role preventing thermal damage caused by Joule heating. Furthermore, it provides trapping sites that promote the establishment of a dipole layer across the oxide. The knowledge gained about the role of this dipole layer in controlling the dielectric breakdown will allow us to optimize the diode structure for non-volatile memory applications.

Device Description

The diode structure shown in Fig. 1 consists of an Al bottom electrode, a sputtered layer of Al 2 O 3 (20 nm), a spirofluorenepolymer (80 nm), and a Ba/Al (5 nm/100 nm) top electrode that forms an Ohmic contact with the polymer. The devices with an active area of 1 and 9 mm 2 were encapsulated to exclude O 2 and H 2 O. In all cases, positive bias voltage refers to the bottom Al electrode being positive with respect to the top Ba electrode. Current-voltage (J-V) curves were obtained using a Keithley 487 picoammeter.

Experimental Results

The pristine devices were turned into programmable resistive switching memories by applying a 12V voltage ramp as will be described in detail below. After this electroforming process, the devices exhibit bistable J-V characteristics and a negative differential resistance (NDR) region in the on-state, as shown in Fig. 2.

Fig. 2. J -V characteristics of the device in the off-and in the on-state

Next we will focus on the electroforming process. Fig. 3 represents the electroforming of the diode. The bias voltage was swept at a ramp rate of 0.1V/s up to 10V and the current density recorded with time. The J-V characteristic shows three distinct regions. In the first stage, region (I), for voltages in the range between 0 and 8V, we observe a pronounced hysteresis in the current-voltage characteristics. In region (II), at bias voltages between 8V and 10V, the current rises exponentially with bias and is due to tunneling of electrons through the oxide. In this regime no hysteresis is observed. Finally in region (III), near 10V, the current rises steeply and becomes noisy which are both typical characteristics of soft breakdown of the oxide. This process is irreversible; the electrical characteristics have changed permanently. The formed device behaves as a non-volatile memory as previously described in Fig. 2. To get insight into the mechanism we need first to understand the behavior in region (I). In the forward scan, the current increases with bias. However, in the backward scan the current is negligible. Actually the current level on the return scan is approximately equal to the displacement current associated with the device geometrical capacitance. The original hysteresis loops can be restored after resting for a few hours or days. These J-V loops are fully reversible. This behavior suggests that the observed hysteresis results from traps that fill in a time scale of seconds but empty slowly, on a time scale of hours. Since this process occurs only when negative bias is applied to the barium electrode, we propose that electrons injected by the barium electrode flow through the polymer layer and they accumulate at the oxide/polymer interface. The electrons must then be compensated by holes located in the aluminum electrode. When the charge build-up is high enough the associated electric field across the oxide layer forces a current (via Fowler-Nordheim or direct tunneling) through the oxide, this current create defects. When a critical defect density is reached the system breaks down and forms a percolation path of defects in the oxide.

Our objective is to get information about the trapped electrons. However, they are too deep to be observed by conventional techniques such as impedance spectroscopy and deep level transient spectroscopy. This is confirmed by the fact that under shortcircuit conditions they take hours to discharge. In order to get insight into the dynamics of these traps, we devise a way to study the temporal dynamics of the forming loops. For a particular J-V loop we defined an onset voltage as the voltage where the current starts to rise. This is illustrated in Fig. 4. The intercept of the dashed line with the voltage axis is assumed to be the onset voltage. First the diodes are brought to a maximum onset voltage of 5 V. When the diode is left resting under short circuited conditions the onset voltage will move slowly with time to towards 0 V. The time dynamics of the onset voltage was monitored as function of time for different oxide thickness. The onset voltage follows an exponential law as function of The thinner the oxide the slower is the recover process. The inset of Fig. 5 shows the relaxation time (τ) for different oxide thickness. It varies from 1 hour for a 20 nm oxide to 0.5 hour for a 50 nm thick oxide. Since the electrons must be neutralized by opposite charges at the aluminum electrode, the thicker the oxide layer the weak is the electric field associated with the dipole layer. This facilitates the trap emptying process.

In order to confirm that the electric field associated with the dipole layer favors the trapping, experiments were carried out under a reverse bias. When a reverse negative bias in the aluminum is applied compensating holes are forced out by the external bias. The accumulated electrons are no longer compensated by holes on the other side of the oxide layer. It is then expected that the emptying process should be faster.

Fig. 6(a) shows the change in onset volt for a reverse field of -5V to fully recover the J-V loop it takes approximately 100 seconds while under zero bias would take days to fully recover. Fig. 6(b) shows the recovery on onset voltage for increasing reverse bias under constant time (100s). The higher the reverse bias the larger is the onset voltage recovers.

In order to obtain the trap signature the detrapping time constant have to be determined for different temperatures. These experiments are current under way. However, one of the simplest methods used to study deep traps in semiconductors was the technique of thermally stimulated conductivity (TSC). In this experiment the traps are filled with the sample at low temperature then, upon heating, the trapped carries are released to the appropriate band and there is an increase in free carries density and hence in the conductivity. The amount of trapped charge is finite, being determined by the number of traps, and as the temperature is increase further all the trapped carriers are eventually released. Since excess carriers in the bands recombine the conductivity eventually falls, so there is a peak in a plot of the conductivity change as a function of temperature. The temperature at which this peak occurs is related to the energy level of the trap and the area under the peak is related to the trap concentration. In this measurement, we pre-formed the sample up to 5 V to fill the electron traps and keep the voltage applied while the device is cooled down to 240 K. Then we measure the short-circuited current while the temperature is rising up to 340 K with a heating rate of 1K/min. The thermal detrapping current is shown in Fig. 7. The curve was fitted using the Cowell and Woods [19] method and the simplified expression [20]:

2 ) exp( 1) exp(

- - + - = θ θ θ B A I (1)
where:

τµν t n A = (2)
n t is the trapped carriers, ν the attempt to escape frequency, τ the trap time constant and µ the carrier mobility.

k E B β υ∆ = (3)
Beta is the heating rate, k is the Boltzmann constant and T the temperature:

kT E ∆ = Θ (4)
The trap concentration is related to the area (A) under the peak by:

Z e A N t β = ( 5
)
where Z is the sample thickness.

From the fit to the TSC curve using expression (1) gives a trap energetic depth of Ea=0.65eV. The area under the curves provides a trap density of 5x10 17 charge/cm 2 . Assuming that they are interface traps.

Conclusions

In summary, we have determined density and energetic location of electron traps in polymer-oxide memories employing a thermal stimulated current method. The trapped charges establish an electric field across the oxide. When the internal field reaches a critical value, soft-breakdown occurs, yielding an active memory diode.

This controlled soft-breakdown mechanism allows for better tuning of the memory characteristics in respect oxide only memories.

Fig. 1 .

 1 Fig. 1. (a) Schematic diagram showing the physical structure of the memory device, (b) photograph of an encapsulated device containing a number of diodes At room temperature, the memory can be switched between off-and on-state by applying voltage pulses with amplitudes corresponding to the top and bottom of the NDR. The device behaves as a non-volatile memory.

  Fig. 3. Typical current-voltage characteristics during electroforming of Al/Al 2 O 3 /polyspirofluorene/Ba/Al diode

  . 5 shows the logarithm of onset voltage as function of time for different oxide thickness.

Fig. 4 .

 4 Fig. 4. Time dependence of the electroforming loops. A device electroformed to 5V will approximately have the onset voltage of 5V (curve (a)). By leaving the device resting in dark, the forming loop (a) will evolve to curve (b) and eventually (c). The onset voltage estimated by the intercept with the voltage axis (dash line) will decrease with time to below 1V

Fig. 5 .

 5 Fig. 5. Semi-log plot of the onset voltage as function of time for different oxide thickness. Inset shows that relaxation time constant (τ) decreases linearly with the oxide thickness

Fig. 6 .

 6 Fig. 6. (a) Change in onset voltage as function of time when a reverse voltage (-5V) is applied; (b) change in onset voltage for increasing reverse bias measured with a fixed time duration (t=100s)

Fig. 7 .

 7 Fig. 7. Thermally stimulated current measured under short-circuited condition. The peak area provides a trap concentration with activation energy of 0.65eV

Acknowledgements. We gratefully acknowledge the financial support received from the Dutch Polymer Institute (DPI), project n.º 703, from Fundação para Ciência e Tecnologia (FCT) through the research Unit, Center of Electronics Optoelectronics and Telecommunications (CEOT), REEQ/601/EEI/2005 and the POCI 2010, FEDER.


Paulo R F Rocha
email: procha@ualg.pt

Asal Kiazadeh
email: akiazadeh@ualg.pt

Qian Chen
email: qchen@ualg.pt

Henrique L Gomes
email: hgomes@ualg.pt

Dynamic Behavior of Resistive Random Access Memories (RRAMS) Based on Plastic Semiconductor

Keywords: Resistive Random Access Memory (RRAM), Switching, Electrical Bistability, Non-Volatile Memory, Negative Differential Resistance (NDR)

Resistive Random Access Memories based on metal-oxide polymer diodes are characterized. The dynamic behavior is studied by recording currentvoltage characteristics with varying voltage ramp speed. It is demonstrated that these organic memory devices have an internal capacitive double-layer structure, which inhibits the switching at high ramp rates (1000 V/s). This behavior is modeled and explained in terms of an equivalent circuit.

Introduction

Organic memory devices are becoming interesting candidates for electronic applications in information technologies [START_REF] Kwork | Moletronics: Future electronics[END_REF]. One emerging candidate is the resistance random access memory (RRAM) based on metal oxides [START_REF] Zhuangl | Novell colossal magnetroresistive thin film nonvolatile resistance random access memory (RRAM)[END_REF][START_REF] Baek | Highly Scalable Non-volatile Resistive Memory using Simple Binary Oxide Driven by Asymmetric Unipolar Voltage Pulses[END_REF] and organic semiconductors [START_REF] Potember | Electrical switching and memory phenomena in Cu-TCNQ thin film[END_REF][START_REF] Müller | CuTCNQ resistive nonvolatile memories with a noble metal bottom electrode[END_REF][START_REF] Ma | Nonvolatile electrical bistability of organic/metal-cluster/organic system[END_REF]. These RRAMs have shown electrically induced resistive switching effects and have been proposed as the basis for future non-volatile memories. They associate the advantages of Flash and DRAM (dynamic random access memories) such as higher packing density, faster switching speed and longer storage life.

Although, several metal-oxides structures exhibited resistive switching properties, the measured switching parameters vary in a wide range, which calls for a more consistent and uniform characterization methodologies. Furthermore, reported switching speeds vary by orders of magnitude [START_REF] Simmons | New Conduction and Reversible Memory Phenomena in Thin Insulating Films[END_REF][START_REF] Verbakel | Switching dynamics in non-volatile polymer memories[END_REF][START_REF] Ma | Organic nonvolatile memory by controlling the dynamic copper-ion concentration within organic layer[END_REF][START_REF] Ma | Organic Reversible Switching Devices for Memory Applications[END_REF][START_REF] Henisch | Switching in organic polymer films[END_REF][START_REF] Jakobsson | On the switching mechanism in Rose Bengal-based memory devices[END_REF][START_REF] Chen | Single-layer organic memory devices based on N,N′-di(naphthalene-l-yl)-N,N′-diphenyl-benzidine[END_REF][START_REF] Mukherjee | Electronically Interacting Composite Systems for Electrical Bistability and Memory Applications[END_REF]. The values range from nanoseconds to milliseconds. The inconsistencies might be due to different semiconductors, device geometries, or measurement procedures. In order to clarify these discrepancies, we characterize the switching speed of a metal-oxide memory device using dynamic measurements and equivalent circuit modeling.

The dynamic characterization of the metal-oxide polymer structure through a double RC circuit provides insight on the switching phenomenon. It is demonstrated the relevance of the oxide layer and its role on limiting the switching speed.

Contribution to Value Creation

Organic based memory devices provide a simplified manufacturing process yielding low-cost, flexible, and light-weight area approaching the nano-scale dimensions. However, the technology development is hampered by the lack of understanding about the switching mechanism.

This study shows that switching is located in the oxide layer. A critical field across this high capacitance oxide layer is therefore needed to switch the memory between on and off states. The associated scan frequency of which the voltage does not exceed the critical field is called the voltage transfer frequency.

The knowledge gain with this study will allow us to optimize the device structure for faster switching speed.

Device Description

The organic memory used consists on a diode structure (Fig. 1) with an Al bottom electrode, a sputtered layer of Al 2 O 3 (20 nm), a spirofluorene polymer (80 nm), and a Ba/Al (5 nm/100 nm) top electrode that forms an Ohmic contact with the polymer. The devices with an active area of 9 and 1 mm 2 were encapsulated to exclude O 2 and H 2 O. The main difference in the device structure between the memory and a bipolar organic light emitting diode (OLED) is the Al bottom contact instead of an ITO contact.

In all cases, positive bias voltage refers to the bottom aluminum electrode being positive with respect to the top Barium electrode. The memories were formed, by applying a sweeping voltage from 0 to 12 V. Quasi-static current-voltage (J-V) curves were obtained using a Keithley 487 picoammeter. The dynamic behavior of the J-V curves was recorded using a signal generator and an oscilloscope combined with a low noise amplifier. The experimental arrangement is shown in Fig. 1. Device modeling was done using Agilent Advanced Design System (ADS).

Experimental Results

The memory device structure and the experimental setup are illustrated in Fig. 1. The current-voltage (J in Fig. 2. The most salient feature of the on negative differential resistance (NDR) region, at a certain threshold voltage (4 Reliable switching is obtained by applying a voltage pulse at the top and at the bottom of the NDR [START_REF] Simmons | New Conduction and Reversible Memory Phenomena in Thin Insulating Films[END_REF][START_REF] Verbakel | Switching dynamics in non-volatile polymer memories[END_REF]. The memory switches to the low resistance on 4 V. A pulse of 7-10 V, corresponding to the end of the NDR regime, sw memory to the high resistance off In order to understand the mechanism which limits the ability of the RRAM to switch, the dynamic behavior of both states was studied as function of the voltage scan rate. The off-state characteristics show a typical behavior. The current increases as the voltage scan rate increases. This is expected due to the effect of increasing displacement current. The off-state behaves as leaky capacitor. Intriguingly the on different behavior. Upon increasing voltage scan rate the current decreases, region becomes less defined and eventually disappears at high voltage scan rates. This behavior is counterintuitive because in similar way as the off at high scan rates is expected. This peculiar behavior of the on the RRAM cannot be programmed on and off at high rates.

We propose that the reason for this counterintuitive characteristics relies on the internal diode structure. The device is a double comprised of a thin oxide layer (20 nm) with a high capacitance, in series with a polymer bulk region (80 nm) with a comparatively small resistance and capacitance. The response of this double modeled by a double RC circui Fig. 4 where C ox and R ox layer. Previously, we have shown that this double frequency response of network when a ramp voltage is applied. state characteristics show a typical behavior. The current increases as the oltage scan rate increases. This is expected due to the effect of increasing displacement state behaves as leaky capacitor. Intriguingly the on-state shows a very different behavior. Upon increasing voltage scan rate the current decreases, region becomes less defined and eventually disappears at high voltage scan rates. This behavior is counterintuitive because in similar way as the off-state an increase in current at high scan rates is expected. This peculiar behavior of the on-state is the reason why the RRAM cannot be programmed on and off at high rates.

We propose that the reason for this counterintuitive behavior of the J characteristics relies on the internal diode structure. The device is a double xide layer (20 nm) with a high capacitance, in series with a polymer bulk region (80 nm) with a comparatively small resistance and capacitance. The response of this double-layer to a high sweeping voltage ramps is conveniently by a double RC circuit. The equivalent circuit model is shown in the inset of ox represent the oxide layer and C poly , R poly represent the polymer layer. Previously, we have shown that this double-layer model adequately describes the frequency response of the diode [START_REF] Gomes | Switching in polymeric resistance random-access memories (RRAMS)[END_REF]. Here, we will describe the behavior of this network when a ramp voltage is applied.

shows the internal voltage across the polymer layer as function of the voltage sweeping speed. Device parameters used were based on typical values estimated by the frequency response [START_REF] Gomes | Switching in polymeric resistance random-access memories (RRAMS)[END_REF]. We use C poly = 3 nF, R poly = 300 kῼ, C . These are in line with the theoretically values estimated on geometrical

Voltage drop across the oxide layer (in %) as a function of the voltage scan rate. through Agilent ADS using the equivalent double RC network in the inset w poly = 3 nF, R poly = 300 kῼ, C oxide = 30 nF, R ox = 80 Mῼ For a low ramp rate most external voltage drop is across the high impedance layer (the oxide) and only a small fraction of the external voltage is dropped across the polymer. When the sweeping frequency increases the oxide capacitance begins to be d and the applied voltage will rapidly increase across the polymer layer. The increase in the voltage sweeping speed has then the effect of moving the voltage drop state characteristics show a typical behavior. The current increases as the oltage scan rate increases. This is expected due to the effect of increasing displacement state shows a very different behavior. Upon increasing voltage scan rate the current decreases, the NDR region becomes less defined and eventually disappears at high voltage scan rates. This state an increase in current te is the reason why of the J-V characteristics relies on the internal diode structure. The device is a double-layer xide layer (20 nm) with a high capacitance, in series with a polymer bulk region (80 nm) with a comparatively small resistance and capacitance.

layer to a high sweeping voltage ramps is conveniently t. The equivalent circuit model is shown in the inset of represent the polymer layer model adequately describes the ]. Here, we will describe the behavior of this shows the internal voltage across the polymer layer as function of the voltage stimated by ῼ, C ox = 30 nF, . These are in line with the theoretically values estimated on geometrical a function of the voltage scan rate. Data using the equivalent double RC network in the inset with the For a low ramp rate most external voltage drop is across the high impedance layer (the oxide) and only a small fraction of the external voltage is dropped across the polymer. When the sweeping frequency increases the oxide capacitance begins to be d and the applied voltage will rapidly increase across the polymer layer. The increase in the voltage sweeping speed has then the effect of moving the voltage drop from the oxide to the polymer layer. Using a simple voltage divider circuit, the fraction of the voltage across the oxide V ox in respect to the total applied voltage V appl is given by: ox poly

poly appl ox Z Z Z 1 V V + - = (1)
Where Z poly and Z ox are the polymer and the oxide impedances respectively. In terms of individual circuit components we can write.

        + + + = poly poly ox ox ox poly ox ox appl ox R C jω 1 R C jω 1 C C C C V V (2)
where j is the imaginary unit and ω the angular frequency. The device internal structure is then basically a voltage divider. However, because the oxide capacitance is much higher that the polymer capacitance, the way the applied external voltage is split between the two layers dependents on the voltage scanning speed or repetition rate. Fig. 4 shows the voltage V ox in percentage of V appl as function of the scan rate. At low frequencies most of the V appl is across the oxide, however as the frequency increases above 20 V/s, V ox decreases rapidly and at 1000 V/s, 55 % of V appl is now across the polymer layer. This underlines the importance of the field across the oxide layer in terms of switching ability, and strongly suggests that increasing the thickness of the oxide layer will speed-up the dynamic response.

Conclusion

The electrical behavior of the memory in both resistive states was dynamically characterized. In the off-state, current increases as the voltage scan rate increases, due to the effect of increasing displacement current. As for the on-state, upon increasing voltage scan rate the current decreases, the NDR region becomes less defined and disappears at high voltage scan rates. This is explained through the device internal structure. Under high repetition rates, the applied voltage moves out from the oxide. This emphasizes the oxide importance in speeding up the dynamic response of the RRAMs.

Fig. 1 .

 1 Fig. 1. On the left it is represented the experimental setup. On the right it is represented the device layout

Fig. 2 .

 2 Fig. 2. J-V characteristicsIn off-state the RRAM exhibit a sharp NDR as shown in the current decreases. The magnitude of the NDR also gradually decreases and vanishes at 1000 V/s.

Fig. 3 .

 3 Fig. 3. On-state J-V characteristics recorded at different scan rates showing the NDR disappearance. The inset shows the In order to understand the mechanism which limits the ability of the RRAM to switch, the dynamic behavior of both states was studied as function of the voltage scan

Fig. 4

 4 shows the internal voltage across the polymer layer as function of the voltage sweeping speed. Device parameters used were based on typical values e modeling the frequency response R ox = 80 Mῼ. These are in line with the theoretically values estimated on geometrical parameters.

Fig. 4 .

 4 Fig. 4. Voltage drop across the oxide layer (in %) as obtained through Agilent ADS following parameters: C poly For a low ramp rate most external voltage drop is across the high impedance layer (the oxide) and only a small fraction of the external voltage is dropped across the polymer. When the sweeping frequency increases the oxide capacitance begins to be shortened and the applied voltage will rapidly increase across the polymer layer. The increase in the voltage sweeping speed has then the effect of moving the voltage drop

Acknowledgments. We gratefully acknowledge the financial support received from the Dutch Polymer Institute (DPI), project n.º 703, from Fundação para Ciência e Tecnologia (FCT) through the research Unit, Center of Electronics Optoelectronics and Telecommunications (CEOT), REEQ/601/EEI/2005 and the POCI 2010, FEDER.


S G Vázquez

N Barreira

M G Penedo
email: mgpenedo@udc.es

M Rodriguez-Blanco

F Gómez-Ulla
email: gomezulla@itogalicia.es

A González
email: ana.gonzalez@udc.es

G Coll De Tuero

Automatic Arteriovenous Ratio Computation: Emulating the Experts

Keywords: arteriovenous ratio computation, retinal imaging, vessel segmentation, vessel classification

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The retinal analysis is a key field for the early diagnosis of several diseases due to retinal blood vessels can be observed directly in a non-invasive way. So, many medical studies explore the relationship between macro-and retinal micro-circulation and associate the width of retinal blood vessels with cardiovascular diseases such as hypertension, strokes, and diabetes [START_REF] Hubbard | Methods for evaluation of retinal microvascular abnormalities associated with hypertension/sclerosis in the atherosclerosis risk in communities studies[END_REF][START_REF] Wong | Retinal microvascular abnormalities and their relationship with hypertension, cardiovascular disease, and mortality[END_REF]. For example, arteriolar narrowing is considered an initial damage in vascular diseases, especially in hypertension. However, the European guidelines for the management of arterial hypertension explicitly exclude arteriolar narrowing to stratify the cardiovascular risk of hypertension due to its subjectivity, imprecision and poor reproducibility. In this sense, some efforts have been made to develop precise and reproducible methods to measure the degree of narrowing in arteries. On this point, an objective way to assess the arteriolar narrowing is the arteriovenous ratio (AVR), this is, the ratio between arteriolar and venular vessel widths. However, the AVR estimation is a difficult task. It involves measuring and classifying the vessels in an area concentric to the optic disc and deciding which ones are appropriate for the calculus. Despite these difficulties, ophthalmologists continue estimating this measure in clinical trials obtaining high correlation values between them although they do not select the same vessel subset.

Several computer-assisted methods have been proposed [START_REF] Hubbard | Methods for evaluation of retinal microvascular abnormalities associated with hypertension/sclerosis in the atherosclerosis risk in communities studies[END_REF][START_REF] Li | Automatic grading of retinal vessel width[END_REF][START_REF] Pose-Reino | Computerized measurement of retinal blood vessel calibre: description, validation and use to determine the influence of ageing and hypertension[END_REF] to achieve an accurate and reproducible measurement. These methods still require user assistance in some phases such as classification of vessels into arteries and veins, the location of the optic nerve or the selection of the suitable vessels for the computation. Recently, some automatic approaches have been presented [START_REF] Tramontan | An improved system for the automatic estimation of the arteriolar-to-venular diameter ratio (avr) in retinal images[END_REF]. However, the validation in large data sets and the testing of its prognosis capacity are currently pending tasks.

We had developed a web-based system [START_REF] Ortega | Sirius: A web-based system for retinal image analysis[END_REF] for retinal image analysis which includes a service to compute the AVR in a semiautomatic way. In that system, once the experts have selected the optic disc position, the system detects the vessels in several circumferences centered at the optic nerve and measures their widths. After that, the experts select the suitable vessels for the AVR computation, classifying them into arteries or veins. Finally, the AVR is calculated as the ratio between the averages of the artery and vein widths. In this paper, we present an improvement to compute the AVR automatically. The new application does not require the user assistance for the optic disc location and the vessel classification tasks so it is fully automatic. In this work, we are mainly concerned on analyzing how different experts select the vessels to achieve a system which emulates the medical experts.

The remaining of the paper is structured as follows. Section 2 explains the proposed methodology to compute the AVR automatically. Section 3 evaluates the system performance. Finally, in Section 4, we provide some concluding remarks.

Method

We propose a methodology to compute the AVR automatically that comprises several stages. First, the optic nerve is located and then the vessels are segmented and measured in several circumferences concentric to the optic disc. After that, the vessel segments obtained are classified as arteries and veins. Finally, the system selects an appropriate set of vessel segments to estimate the AVR.

Optic disc location

The optic nerve location algorithm is based on the Hough transform [START_REF] Blanco | Localization and extraction of the optic disc using the fuzzy circular hough transform[END_REF]. First, the region of interest is delimited using a blob detection method, the Difference of Gaussians operator. In this manner, we convolve the original image with two Gaussians filters at different scales and we obtain the difference between these convolutions. The first approximation of the optic disc center is taken as the maxima of DoG output. The input of this transform is the set of edge pixels computed from the original image. However, only the optic disc edges are necessary. Thus, we combine the Sobel operator and the MLSEC-ST [START_REF] Lopez | Multilocal creaseness based on the level-set extrinsic curvature[END_REF] outputs in order to discard other edges, such as vessel edges. Finally, we extract the optic disc from the remaining edges using the Hough transform.

Measurement of vessel widths

We have proposed a method to measure automatically the vessel widths in several circumferences centered on the optic disc [START_REF] Caderno | Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications[END_REF]. That method is based on snakes. A snake is a contour defined within the image that evolves in order to fit some features of interest. This evolution is governed by external and internal energies in such a way that the model reaches a minimum when it fits the features of interest. In our case, these features are the vessel boundaries. To this end, we initialize a snake in the intersection points of each circumference and the vessel centerlines. The vessel centerlines are detected by means of the MLSEC-ST operator [START_REF] Lopez | Multilocal creaseness based on the level-set extrinsic curvature[END_REF]. Each snake evolves in the direction perpendicular to the centerlines and stops at the vessel contours detected by the Sobel operator. Once the evolution stops, a topological adjustment is performed in order to avoid deviations in the snake contour. Finally, the vessel widths are measured from the snake contours.

Vessel classification into artery and vein

Medical experts use color information to classify arteries and veins. However this task is not straightforward. Although veins are darker than arteries, differences are only visible in main vessels. In the case of secondary vessels, the ophthalmologists have to follow the vessel tree from the optic nerve.

A methodology to classify the retinal vessels has been proposed [START_REF] Vázquez | Improvements in retinal vessel clustering techniques:towards the automatic computation of the arteriovenous ratio[END_REF] and it has been improved in [START_REF] Vázquez | On the automatic computation of the arterio-venous ratio in retinal images: Using minimal paths for the artery/vein classifications[END_REF]. This method involves a local classification to avoid the influence of the lightness variability and the lack of color constancy, and a global integration of local color differences to ensure the decision. First, the multi-scale retinex algorithm is applied to original image to enhance the color constancy. Next, we divide the image into four quadrants centered at the optic disc and we apply a clustering algorithm in each quadrant. Then, the axis is rotated 20° and the classification is performed again in each new quadrant. This process is repeated until it achieves a 180° degree rotation. Finally, the classification results are combined to obtain the final class of a vessel segment. After that, we joint the local classification using a tracking strategy [START_REF] Vázquez | On the automatic computation of the arterio-venous ratio in retinal images: Using minimal paths for the artery/vein classifications[END_REF] which connects the vessel segments which belong to the same vessel in different circumferences.

Vessel selection

In the semiautomatic approach [START_REF] Ortega | Sirius: A web-based system for retinal image analysis[END_REF], once the medical experts had classified the vessels into arteries and veins, the AVR is computed as the ratio between the artery and vein average widths. However, the experts do not take into account all the detected vessels but only a subset of them. They follow some unwritten rules to select the most suitable vessels and, although two experts do not select exactly the same subset, the correlation between them is high [START_REF] Pose-Reino | Estimation of the retinal microvascular calibre in hypertensive patients with the snakes semiautomatic model[END_REF]. This way, we analyze a large data set of images where the AVR was computed by two experts in order to obtain some hypothesis of the selection rules used by experts. Thus, after a knowledge acquisition process and an analysis of the vessel selection made by experts, we have obtained the following hypothesis: H1: Experts rule out the vessels whose width has been over-or sub-estimated. H2: Experts do not take into account vessel segments found over a bifurcation or a crossover.

H3: Experts do not select the same number of arteries and veins at each analysis radius.

H4: Experts select the same global number of arteries and veins. H5: Experts do not take into account thin vessels, either because it is more difficult to know their classes or because it is more probable to overestimate their width.

H6: Experts rule out false positive vessels detected in the background.

We have implemented an algorithm of vessel selection taking into account the above selection hypothesis. The H1 hypothesis has been implemented using the tracking algorithm. To rule out the vessels with over or sub-estimated width, we obtain the median width of each connected segment and we rule out the vessel segments whose width is larger than the double or smaller than the half of the median width. In addition, these extreme vessels can be also detected by means of percentiles, discarding the vessels whose widths are less than the p percentile or larger than the 100-p percentile.

A method which detects bifurcation and crossovers [START_REF] Ortega | Vascular landmark detection in retinal images[END_REF] has been applied to implement the H2 hypothesis. In this case, we have two options, since we can remove the segments before or after the classification procedure. Removing them before the classification can be an advantage in case of crossovers because we avoid altering the mean color value used in the vessel classification procedure since we do not know which vessel is on top of the crossover.

Hypothesis H3 and H4 were carried out excluding the smallest arteries and veins until the number of vessel segments in both classes are the same, globally or in each circumference, respectively.

Hypothesis H5 is performed in three different ways. Two of them consist on ruling out the vessels by percentiles. First, we remove the vessels whose widths are smaller than the p percentile. Another way is computing two different percentiles, one for veins and the other for arteries. The third manner involves detecting fewer vessels, using more restrictive parameters in the MLSEC-ST operator.

We eliminate all the isolated vessel segments which are not connected to any other to carry out the last hypothesis, H6. Moreover, the number of false positives is also reduced when the parameters of the MLSEC-ST operator become more restrictive.

In addition, according to other authors, we try another selection method which just consists of taking into account the six main arteries and six main veins to estimate the AVR. In this case, we only consider the 12 main vessels with the largest median width along the vessel.

AVR Computation

The arteriovenous ratio can be computed of three different ways [START_REF] Hubbard | Methods for evaluation of retinal microvascular abnormalities associated with hypertension/sclerosis in the atherosclerosis risk in communities studies[END_REF][START_REF] Stanton | A method of quantifying retinal microvascular alterations associated with blood pressure and age[END_REF][START_REF] Michael | Revised formulas for summarizing retinal vessel diameters[END_REF]. In our case, we estimate the AVR as the ratio between the average of artery widths and the average of vein widths [START_REF] Pose-Reino | Computerized measurement of retinal blood vessel calibre: description, validation and use to determine the influence of ageing and hypertension[END_REF][START_REF] Stanton | A method of quantifying retinal microvascular alterations associated with blood pressure and age[END_REF].

Results

The proposed methodology has been tested on a set of eighty six color retinal images acquired with a Cannon CR6-45NM non-mydriatic retinal camera at the hospital of Conxo, Santiago de Compostela (Spain). These images have a resolution of 768x576 pixels.

Two ophthalmologists with many years of experience in the study of microvasculature involvement in hypertensive and diabetic retinopathy have estimated the AVR in each fundus image using the automatic system correcting the wrong artery/vein classifications, changing the automatic optic disc location and/or eliminating the vessels that they consider unsuitable for the AVR computation. A Pearson's correlation coefficient of 0.7981, as well as, a non significative hypothesis whose null hypothesis is that the coefficient is different than zero, indicate that there is a high correlation between experts (see Table 1). Moreover, a Welch's t-test was also performed and the p-value achieved reveals that the AVR's estimated by experts are equal in average. If we only take into account the 6 main arteries and veins labeled by experts to estimate the AVR, the correlation increases. The evaluation of the vessel selection algorithm involved testing 649 combinations of hypothesis. Table 1 summarizes the results achieved. It shows the three highest Pearson's correlation coefficients among each expert and the system when the Welch's t-test resulted non significative. Figures 1 and2 show dispersion and boxplot graphs of the AVR estimated by the different experts.

In general, the best options for the vessel selection algorithm are those which implement the H1, H5, and H2 hypothesis. Hypothesis H5 has two different implementations but the correlation results were similar. The best results were obtained eliminating those arteries and veins whose width is smaller than the 10percentiles computed for each class. In addition, if we only take into account the 6 main vessels, the correlation between the each expert and the system is lower.

Conclusions

In this work, we analyze several alternatives for the vessel selection stage in order to develop an automatic AVR computation system. Taking a semi-automatic AVR computation framework as a starting point, the proposed selection procedure provides an estimation of the AVR close to the estimation measured by medical experts in a quite large data set. Therefore, we can say that the automatic system behaves almost like other expert. However, our analysis shows that the selection of vessels has a high influence on the AVR value and that the best selection procedure includes discarding thin vessels, over-and sub-estimated widths as well as segments over bifurcations or crossovers.

Establishing guidelines for the selection of vessels is necessary but it seems a challenge. For that reason, the AVR should be computed using the same subset of vessel segments for each patient in order to use this variable as a reliable prognosis value. This way, future work in this field includes the development of a monitoring methodology using the same vessel points.

Fig. 1 .Fig. 2 .

 12 Fig.1. Dispersion graphs that show the dependence between the AVR measured by different experts.

Table 1 .

 1 Test hypothesis results between experts and/or automatic system.

	Experts	Pearson's correlation	p-value of	p-value of Welch's
		coefficient	Pearson's test	t-test
	Expert1 vs. Expert2	0.7981	< 2.2e-16	0.2496
	Expert1 vs. System H1H5	0.7466	< 2.2e-16	0.8641
	Expert2 vs. System H1H5H2	0.7940	0	0.0138
	Expert2 vs. System H1H5	0.7860	0	0.34
		6 main vessels
	Expert1 vs. Expert2	0.8546	< 2.2e-16	< 2.2e-16
	Expert1 vs. System	0.7472	< 2.2e-16	0.6036
	Expert2 vs. System	0.7161	9.104e-15	0.3464


Arash Sangari
email: sangari@wisc.edu

Adel Ardalan
email: adel.ardalan@gmail.com

Larry Lambe
email: llambe@mssrc.com

Hamid Eghbalnia
email: eghbalhd@ucmail.uc.edu

Amir H Assadi
email: ahassadi@wisc.edu

Mathematical Analysis and Computational Integration of Massive Heterogeneous Data from the Human Retina

Keywords: Retina Vasculature, Image Analysis, Text Analysis, Massive Data, Symbolic Computation

Modern epidemiology integrates knowledge from heterogeneous collections of data consisting of numerical, descriptive and imaging. Largescale epidemiological studies use sophisticated statistical analysis, mathematical models using differential equations and versatile analytic tools that handle numerical data. In contrast, knowledge extraction from images and descriptive information in the form of text and diagrams remain a challenge for most fields, in particular, for diseases of the eye. In this article we provide a roadmap towards extraction of knowledge from text and images with focus on forthcoming applications to epidemiological investigation of retinal diseases, especially from existing massive heterogeneous collections of data distributed around the globe.

Introduction

In epidemiological studies of retinal diseases, one encounters the problem of extracting knowledge from heterogeneous collections of data consisting of numerical, descriptive and imaging. Large scale epidemiological studies use sophisticated statistical analysis, differential equations and related versatile mathematical tools that are developed for numerical data. In contrast, knowledge extraction from retina images and descriptive information in the form of text and diagrams remain scarcely developed. This article provides a roadmap towards epidemiology of diseases of the eye using extraction of knowledge from text, images and numerical data, and heterogeneous data fusion.

In the first part of the article an outline of knowledge extraction from massive text data are discussed. In the second part, we address a general technique for systematic knowledge from very massive retinal image collections. The mathematical tools and concepts are adapted from the PDE based image analysis, which uses advanced numerical and symbolic computation libraries. The algorithms and the ensuing codes are particularly designed for very large industrial-grade projects.

To bring such sophisticated machinery to bear results on retinal image data requires transformation of the raw images into black and white (or gray scale). The simplified images are preprocessed to delineate the anatomical details of the vasculature. Morphometric invariants of the brain structures encountered in such images are, then, extracted in the form of diameter of blood vessels. A weighted graph to capture a combinatorial organization of vessels, branching and notable curvilinear features further a branched tubular surface encodes the endothelial cells that cover the inner part of blood vessels and the whole micro-vessel structures.

The above mentioned data are hierarchically organized to separate distinct phenotypic traits that arise at a particular scale with the appropriate resolution. Finally, the hierarchical graph that encodes combinatorial -quantitative -geometric phenotypic traits could be quantified for massive data analysis using graph theoretic invariants such as the spectrum of Laplace and other operators on graphs. In short, image data provides data structures that quantify morphological traits according to hierarchy resolution and combinatorial features.

Using Information Extraction Techniques to Enhance Systems Biology

As a result of exploding volume of scientific publications which emerge each day, it's becoming more and more intractable to read and consume the knowledge embedded in the scientific community in an integrated, meaningful and efficient manner. Among the main difficulties is the productivity and utilization of the manuscripts and other types of written material, like descriptive data about the disease or the health status of the patient, for professionals in different fields of study who do not want and probably cannot spend a lifetime reading every minor detail of all the disciplines they deal with in interdisciplinary research activities. In order to be able to use the knowledge and also to communicate with the experts in the field, it is essential to be able to have a general overview of the important entities and their relationships. As an example, biological computation specialists need to understand the roles of different genes and their relationships in order to be able to perform meaningful computations and analysis. Another example is to "understand" the notes and descriptions about patients' state of health scribed during physical examinations.

Information extraction (IE) is among the most promising emerging technique which, in the era of supercomputing and computational clouds, enables fast analysis of drastically huge bulks of documents. IE specialists nowadays think of doing complicated machine learning tasks on the whole web [START_REF] Niu | Tuffy: Scaling up Statistical Inference in Markov Logic Networks using an RDBMS[END_REF](the size of the indexed Web is estimated to be about 46 billion pages as of November 2011 [START_REF] Worldwidewebsize | The size of the World Wide Web (The Internet)[END_REF]). This ambitious goal has turned IE techniques into powerful and strong tools which could be utilized to help academic community reducing the time-of-flight for getting into useful and productive research activities. The goal of this phase is to incorporate different largescale, high-throughput, flexible IE techniques to enhance our problem solving skills and leverage our communications with collaborating professionals in genomic sciences, health care and neuroscience to establish fruitful research projects and to contribute in building a framework for translating the extensive amount of knowledge (and wisdom) buried inside scientific publications descriptive healthcare records, even for decades, to be used in action by large number of researchers and students.

IE usually starts with digesting the free text into a structured form using various natural language processing (NLP) methods [START_REF] Sarawagi | Information Extraction[END_REF]. These methods are built upon different sources of information, ranging from linguistic grammatical structures to statistical properties of various types of written and spoken corpora. The main tasks are illustrated in the following figure. A rich literature and set of tools is developed in the area of data integration which tries to unify different data sources in terms of structure and semantic [START_REF] Lenzerini | Data integration[END_REF]. Different machine learning and statistical analysis tools have been tested and turned out to be useful in different contexts. The more general framework of information fusion deals with making decisions based on heterogeneous sources of information, ranging from numerical data to free text to imagery data. Graphical probabilistic models have provided a flexible and powerful framework to fuse data and information. For example, Markov logic networks (MLN) [START_REF] Domingos | Markov Logic: An Interface Layer for Artificial Intelligence[END_REF] have been used successfully to extract information from various sources of textual information. As one of the most basic tools in logic, predicate logic and calculus have played a major role in knowledge representation since their formal introduction. In its simplest form, first-order predicate logic is able to encapsulate knowledge from heterogeneous sources, such as the ones mentioned above, and thanks to new tools that have been developed recently, it is possible to fuse these bodies of knowledge in a solid, powerful and flexible way. MLNs have provided a basic tool to get these together, imposing an arbitrary probability distribution over them and applying rules induced from domain knowledge (by domain experts or extracted automatically) to them to conclude new results.

The Level Set Method

In the image analysis part, we have implemented massively GPU-parallel-distributed CUDA coding of the algorithms to extract the vasculature from "raw" images, to form a "geometric model" made of B&W pixels, and to quantify the morphological traits (see [START_REF] Dashti | Applications of Machine Learning Methods to Quantifying Phenotypic Traits that Distinguish the Wild Type from the Mutant Arabidopsis Thaliana Seedlings during Root Gravitropism[END_REF] and [10]). The outline of the mathematical steps are as follows: Represent the image for one gray-scale frame as :

f J R
→ , and use time-index of images by Greek τ and time-dependence in the image processing algorithms by t . The basic idea is as follows: the typical image :

f J R
→ is written as an outcome of an unknown convolution kernel K with compact support (e.g. a discrete Gaussian), applied to the original image ϕ (or a desirable model that in our case must be suitable for segmentation and midline recovery of the branched structures, and an additive noise ν that we propose to model as a Gaussian white noise K * f ϕ ν = + . The automation algorithm proposes to select the kernel. In epidemiological applications we must confront derivation of a suitable model of noise that will be constructed from the imaging system outputs in lieu of the simplifying assumption above. Begin with the constrained minimization problem with appropriate norms, without further mention for simplicity.

For a class of images according to our protocol, the higher resolution allowed us to select a delta function, and use the simpler form. However, in the case of blurring or temporal loss of the automated focus in large-scale image acquisition, we must adhere to the general form below

Here, c is a scaling constant that is the trade-off between noise and the desired image quality, such as having sharp edges in images of blood vessel branched structures, and arg-min is over all images ϕ , where ϕ is the desired form of the image suitable for algorithms, which use an iterative regularization to recover finer scales.

An intermediate problem that we propose to solve is GPU-massive parallel implementation of methods based on the following simplified ideas (also variously appear in independent publications loccit). Start with Chan-Wong-Kaveh-Osher et al [START_REF] Osher | An iterative regularization method for total variation-based image restoration[END_REF] proposal for constrained optimization with ( , )

F K ϕ as a function of joint variables ( , ) K ϕ : 2 2 1 2 , 1 ( , ) arg min{ ( , ) : || || || || || || } 2 L BV BV K K F K K f c c K ϕ ϕ ϕ ϕ ϕ = = * - + + (2)
When we view F as a one-variable functional depending only on K or only ϕ , by fixing one, then F is convex, while ( , )

F K ϕ fails to be jointly convex. To overcome this difficulty, we follow Osher et al and propose to solve the two Euler-Lagrange equations (below, where L 2 -conjugates are given by the "hat" decoration) alternatively:

2 2 1 2 , 1 ( , ) arg min{ ( , ) : || || || || || || } 2 L BV BV K K F K K f c c K ϕ ϕ ϕ ϕ ϕ = = * - + + (3) 1 2 ( , ) ( ) . 0 | | ( , ) ( ) . 0 | | K F K K K f c K F K K f c K ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ∇ = * * --∇ = ∇ ∇ = * * --∇ = ∇ ) ) (4)
Fixing K first, solves for ϕ from the first equation and then switch the roles of K and ϕ , also the two equations, respectively.

In our 2010 article [START_REF] Dashti | Applications of Machine Learning Methods to Quantifying Phenotypic Traits that Distinguish the Wild Type from the Mutant Arabidopsis Thaliana Seedlings during Root Gravitropism[END_REF] and subsequent developments, we have developed a set of new algorithms and their object-oriented C-code for massively parallel-distributed hardware. In this ameliorated version, our research benefits from design of advanced numerical and symbolic computation algorithms by Lambe et al, and we have gained speed and efficiency that are orders of magnitude better, thus several practical challenges and bottlenecks of past approaches are overcome. Further, we have developed the codes for massively parallel-distributed platforms using the codegeneration capabilities.

The Symbolic Active Contour Method

In classical implementations of the active contour algorithms by level set method, the contours around objects approximated as a zero level of the function which is the numerical solution of equation ( 2) [START_REF] Chan | Active contours without edges[END_REF], [9].

It is possible to replace these numerical methods by deriving an analytic model of the active contour and obtain analytic expressions for their gradients using symbolic computation.

Specifically, we use Gaussian process regression (GPR) ([10],[11]) to fit analytic functions oversubsets of original image and ExprLib ([12], [START_REF] Camberos | Hybrid Symbolic-Numeric Methodology for Fluid Dynamics Simulations[END_REF]) to do the update step of "Level Set Function" LSF by symbolic calculation of gradients. Furthermore, ExprLib has the capability to generate source code that represents these calculations. Thus we have updated our method of level sets by:

• Interpolating the image using GPR and generating C code for the model using the relevant data that was generated using ExprLib's code generating facilities, • Using the analytic expressions generated above in ExprLib to obtain the gradients symbolically and then generating C code for those gradients, • Incorporating the code for the contours and gradients into our procedure. This hybrid approach, interpolating image pieces and doing symbolic computation, has following benefits in analysis of retina images:

• The accuracy of active contour segmentation would be improved because of precise calculation of derivatives. • Measuring contour deformation in time-lapse images with analytic form of contours would be more robust and informative. We can also take the derivatives of contour deformation respect to time to find out the dynamics of the retinal vessel deformation.

Total Effective Resistance Using Weighted Laplacians

The spectral theory of graphs has been well studied over the last few decades. While the original body of research spectral graph theory examined adjacency matrices, more recent work has focused on the spectrum associated to the Laplacian of a graph. The Laplacian of a graph, denoted by L, forms the discrete analog of the Laplace-Beltrami operator of spectral geometry. For a simple graph G = (V, E) with |V | = n and the vertices of G labeled as {1,2,...,n}, The Laplacian L is the difference ∆ -A of the degree matrix ∆ (the diagonal matrix with D ii = δ i ) and the adjacency matrix. For a graph with non-negative edge weights w ij , the analogue of the adjacency matrix is the matrix of weights W = (w ij ), the weighted Laplacian is LW = S -W, where S is the diagonal matrix of strengths, with elements S ii = s i . Lw is an object of interest because it arises as the discrete analog of the Dirichlet space metric. Symmetric functions of eigenvalues of Lw (convex or concave) are well-known invariants in the study of graph spectra. Total effective resistance, utilizes the decreasing set of eigenvalues of the weighted (normalized) Laplacian to define one such invariant as follows:

(

In analogy to the Kirchhoff circuit laws, T provides a global measure for the total resistance in a network of series-parallel connected elements [START_REF] Camberos | Hybrid Symbolic-Numeric Methodology for Fluid Dynamics Simulations[END_REF]. Key properties of the total effective resistance T have been explored in detail [START_REF] Camberos | Hybrid Symbolic-Numeric Methodology for Fluid Dynamics Simulations[END_REF]. For example, T is a non-increasing function of the edge weights and acts as a metric on the space of weights on the graph G. Furthermore, because T is directly related to network criticality [START_REF] Klein | Resistance distance[END_REF], it provides a key measure of network robustness. More specifically, viewing the branching vascular system and their corresponding lengths and diameters as an analog to a resistive network, T provides a suitable global invariant for the vascular bed.

Discussion

We have outlined the blueprint for construction of a probabilistic framework to integrate various heterogeneous pieces of information using a logic network representation discussed. In this setting, descriptive data such as a health caretaker's observations, prognosis and prescriptions, are analyzed for information extraction via a representation as a set of first-order logic predicates (e.g. hasVeryLimitedEyesight(PatientX).)

Then, using a manually written or automatically extracted set of rules from various sources, a scalable MLN engine will find the most probable state upon which inference could be done. A broad variety of questions could be asked about relationships among such different pieces of information that we have acquired from various sources. Thus one acquires knowledge from information, which comes with a confidence degree that could be utilized to keep track of the environment uncertainty and changes in the complexity of the diagnostic procedure.

Conclusions

We have outlined a flexible framework for unification of various types of data which could be employed to track diseases of the retina, and lay out the basis for preventive medicine and the most effective treatments according to phenotypic traits and other characteristics in individuals within a population. Information extracted from patients medical records in the form of descriptive data, images captured over the treatment time span and different forms of numerical data could be processed in this framework using a variety of techniques which in turn could be used to track the health status of patients and study the epidemiologic traits in the population. This enables the public health systems to look for early alerts and to account for preventive measures.

Fig. 1 .

 1 Fig.1. Components of Natural Language Analysis.

Fig. 2 .

 2 Fig.2. Flow chart of the symbolic active contour method.

Fig. 3 .

 3 Fig.3. Construction of resistance network from a raw image of retina. (a) Raw image from retina, (b) Retina in black and white, (c) Detection of network node, radius of vessels and crossovers, (d) the resistance network.

Acknowledgments:

The authors acknowledge the AF support for the development of that work under Contract FA8650-06-C-3621.