Optimization of Photodetector Thickness in Vertically-Integrated Image Sensors

Orit Skorka, Dan Sirbu, and Dileepan JosephUniversity of Alberta, CanadaOptimization of Photodetector Thickness in Vertically-Integrated Image Sensors1Outline2MotivationProblem statementPhotodetector modelMathematical methodOptimization of thicknessConclusions2Motivation3Image sensors are required to have high SNR, high dynamic range, high resolution, and high frame rateAll these features may not be achievable with current planar technologies (CCD and CMOS) There has been an increased interest in fabricating image sensors in which the photodetectors are vertically integrated with the CMOS circuitry3Motivation4

Example Vertically-integrated CMOS image sensor fabricated using flip-chip assembly

4Motivation5The photodetectors and the electronics can be optimized independently of each other in VI-CMOS image sensors.There are more degrees of freedom in the photodetector design. Material no longer restricted to c-Si.Photodetector thickness the vertical dimension can now be controlled.Advantages of Vertical-Integration5Problem Statement6Simplified 1D photodetector structure

Semiconductor layer thickness l 6Problem Statement7What is the optimal semiconductor thickness, lopt, for the photodetector to have a maximum contrast?Contrast

Initial HypothesisIf the semiconductor is made too thin then very little light is absorbed, which implies low photocurrentIf the semiconductor is made too thick then most photo-generated charge carriers recombine on their way to the contact, which also implies low photocurrent7Photodetector Model8Three-resistor systemThe illumination decays exponentially in the semiconductorThe absorbed photons generate extra electron-hole pairs (EHPs), or excess carriers, that improve conductivity

8Photodetector Model9Charge carrier equationsPoissons equation relates electric potential or electric field to concentration of charge carriersContinuity equations ensures charge carriers are neither created nor destroyed at any pointDrift-diffusion equations describe the current density as a sum of a drift current, which arises from existance of electric field, and diffusion current, which arises from concentration gradients 9Photodetector Model10Charge carrier equationsPoissons equation:

Continuity equations:

Drift-diffusion equations:

10Photodetector Model11Boundary conditionsKirchoffs voltage law forces the sum of the voltage drops over the three resistors to equal the applied potential, Vab.Kirchoffs current law forces the sum of the hole current and the electron current in the semiconductor to equal the current drawn from the power supply.Charge neutrality as electrons and holes are generated and recombined in pairs, the semiconductor must remain neutral, assuming initial charge neutrality.Generation-recombination balance in the steady state, every EHP generation must be offset by an EHP recombination (perhaps elsewhere) in the semiconductor.11Photodetector Model12Boundary conditionsKirchoffs voltage law:Kirchoffs current law:Charge neutrality:Generation-recombination balance:

12Photodetector Model13EHP boundary conditions are often defined through the recombination velocity of charge carriers at the boundaries. It relates the concentration of charge carriers and current density on the boundaries.We have defined EHP boundary conditions by charge neutrality and generation-recombination balance, which are easier to interpret. These conditions, fewer than those used in the literature, prove sufficient to solve the problem without inconsistency.13Mathematical Method14The solution process is based on the mean value of the different variables in the semiconductor, and on the deviation of the local quantity from its mean value. The mean is computed over the length l.Example Hole (p) and electron (n) concentration

local concentrationmean valuelocal perturbation14Mathematical Method15Analytical solutionIs derived by assuming gp(z) = 0 and gn(z) = 0 only.A systematic way was derived to solve all the remaining variables and, thereby, to find J = f (F0) for any F0.However, the solution does not satisfy all equations.Numerical solutionIs based on an iterative finite-differences method.It shows the equations are consistent and complete.15Mathematical Method16AnalyticalNumericalPoissons equationContinuity equationsDrift-diff. equationsK.s voltage law (KVL)K.s current law (KCL)Charge neutralityGen.-rec. balance

16Optimization of Thickness17Our initial hypothesis proved wrongIf the semiconductor is too thin, very little light is absorbed. However, the electric field becomes very strong for a constant applied voltage.According to the model, the contrast is low at this end because the resistance of the semiconductor is low in comparison to the contact resistances. The device is dominated by the contacts.17Optimization of Thickness18In the absence of contact resistances, the contrast is maximal at l equals zero, which is nonsensical.

18Optimization of Thickness19Our initial hypothesis proved wrongIf the semiconductor is too thick, there is more EHP recombination in the device, as predicted. However, the total generation rate of EHPs also increases with semiconductor thickness.According to the model, the contrast is low here because the mean value of excess charge carriers per unit volume decreases with device length and, thus, the mean photoconductivity also decreases.19Optimization of Thickness20Total EHP generation rate increases with semiconductor thickness. However, mean excess carriers, and hence conductivity and contrast decrease as l grows large.

20Optimization of Thickness21Optimal thickness was found analytically and numericallySee the paper for material (a-Si:H) and other parameters

Simulation results: lopt = 400 nm for maximum contrast21Conclusions22We presented a new approach to solve semiconductor charge carrier equations in 1D photodetectors.Our boundary conditions used Kirchoffs laws, charge neutrality, and generation-recombination balance.Our approach was based on mean values of variables and on deviations of local values from the mean values.The method was used for optimization of photodetector thickness in a vertically-integrated image sensor.

22Acknowledgments23The authors gratefully acknowledge the support of Alberta IngenuityThe Natural Sciences and Engineering Research Council (NSERC) of CanadaThe Mary Louise Imrie Graduate Student Award, University of Alberta23