Eugene A. Trabka

Steady-state photocarrier collection in silicon imaging devices

Solid-state imagers lose resolution when photocarriers generated in one imaging site diffuse to a nearby site where they are collected. These processes are modeled by solving the steady-state diffusion equation for minority carriers. A source term represents the absorption of photons and the generation of photocarriers, and a linear term represents the loss of photocarriers by recombination. This is equivalent to studying the Helmholtz equation with an inhomogeneous term. The problem is simplified when the light source has symmetry. A line source or a cylindrically symmetric source leads to a two-dimensional problem. The approach of Seib, Crowell, and Labuda allows a solution by quadrature if the further assumption of a smooth top boundary is made. We calculate the integrated normal flux over each imaging site to see how many carriers diffuse from under the illuminated site to another site. We compare our predicted line- and point-spread functions to those measured on imagers and find reasonable agreement. This allows us to extract minority-carrier diffusion lengths. Further calculations show how the diffusion of carriers depends on the photon wavelength and the pixel size. We generalize Seibs approach and apply it to a solid-state imager covered with color filters. This allows us to see the extent of color mixing due to carrier diffusion. We also discuss a finite-difference solution of the diffusion equation that employs the method of conjugate gradients. This approach is useful for problems where the top boundary is not smooth.

A model for charge transfer in buried-channel charge-coupled devices at low temperature

Charge transfer in buried-channel charge-coupled devices (CCDs) is explored with a one-dimensional numerical model which describes the capture and emission of electrons from a shallow donor level in silicon through the use of the Shockley-Read-Hall generation-recombination theory. Incorporated in the model are the three-dimensional Poole-Frenkel barrier lowering theory of A. K. Jonscher (1967) and J. L. Hartke (1968) and the low-temperature form of Poissons equation. Reasonable agreement of the model with experimental data taken from the buried-channel CCDs of a PtSi Schottky barrier infrared image sensor is found. Moreover, the value for the capture cross section of electrons to the shallow phosphorus level in silicon inferred from the model follows the cascade theory for capture by M. Lax (1959) and agrees roughly with determinations made by other experimenters. >

Crowded Emulsions: Granularity Theory for Multilayers*

A crowded photographic emulsion is viewed as a sandwich of stacked, crowded monolayers. An earlier renewal model of granularity in a crowded monolayer, combined with a new analysis of the general way in which granularity propagates through layers, leads to predictions of the granularity of the multilayer sandwich as a function of the number of layers. For a fixed concentration of grains per unit projected area in the sandwich, rms density fluctuations increase as the number of layers decreases because rms transmittance fluctuations decrease at a slower rate than mean transmittance. These changes are similar to the entropy decrease of grain configurations in the emulsion. For sandwiches consisting of at least 15 layers having a maximum density not greater than 2, the change of rms density fluctuations vs mean density for an exposure series is accurately predicted by the honest random-dot model. Any discrepancy between the theoretical predictions of the honest random-dot model and experimental data for normal emulsions cannot be attributed solely to the neglect of crowding constraints by that model.

Channel potential and channel width in narrow buried-channel MOSFET's

A new method is described for determining the effective width over which incremental charge spreads in a narrow buried-channel transistor. The method is based on the transconductance in the buried-channel mode. Experimental results for effective widths and channel potential shifts are presented for MOSFETs with effective channel widths from 2 to 10 µm. Two-dimensional numerical calculations verify the experimental results.

Alternating renewal model of photographic granularity

A crowded-monolayer emulsion is viewed in one dimension as an alternating renewal process. The model presented is sufficiently general to include the effects of arbitrary distributions of halide grain sizes and gap sizes and further arbitrary dependence of developability of the grains on grain size and exposure. In an example, we calculate the increase of granularity that accompanies the increased exposure latitude obtained by broadening the size distribution of maximally sensitized grains.

Characterization of generation currents in solid-state imagers

The study of dark current in CCDs is difficult because of the complexity of the process and because generation can come from a variety of sources. For scaled devices, generation from channel-stop sidewalls is particularly important, since the sidewall scales as a perimeter. Relatively little attention has been paid in the past to this source of generation. In this paper, analytical techniques are described for profiling interface states along channel-stop sidewalls. These techniques rely on changes in generation current caused by expansion of the surface depletion region. Two methods of determining the extent of surface depletion are discussed. The first relies heavily on two-dimensional modeling, while the second uses experimental measurements of interelectrode capacitance to avoid certain limitations associated with model parameters. These techniques are used to show that the generation-current density peaks strongly in the birdsbeak region of LOCOS isolation, resulting in a significant contribution to dark current during CCD operation, even for channel-stop spacings as far apart as 12 µm. These techniques are also used to compare the behavior of different regions of the oxide interface of CCD imagers as a function of post-oxidation annealing, including rapid thermal annealing.

Application Of Maximum-Entropy Spectrum Analysis To The Measurement Of Low-Frequency Radiographic Noise Spectra

The maximum-entropy method (MEM) for computing noise spectra has been extended to accommodate two-dimensional microdensitometric scans of uniformly exposed radiographs. Based on computer-simulated short scans, the MEM requires one-tenth the data of the conventional FFT method, for the same statistical stability. In particular, MEM estimates of very low-frequency noise power have proved to be substantially more stable than FFT estimates. MEM spectra also have the advantage of being smoother than the FFT method. For measured data, we found the results to be quite sensitive to the nature of the detrending algorithm which was applied to the raw data.

Colour Granularity: A Layered Model

AbstractWe show how the classical random-dot model of photographic granularity may be modified to yield quantitative predictions of the phenomenon reported by Zwick that it is possible “to attain an image of finite density that is essentially grainless” with dye systems. Our analysis also shows that substantial errors can arise in assuming that the variance of density fluctuations of sublayers is additive for layers that do not scatter light.

Lateral motion of the inversion layer of MOS structures in regions of variable doping density and oxide thickness

Abstract We describe computational methods and a new experimental technique for directly measuring the lateral spread of gate-induced surface inversion into the birdsbeak region of LOCOS (local oxidation of silicon) isolation. This method is of general use for characterizing all MOS structures with lateral variations in substrate doping, fixed charge, and/or oxide thickness. The procedure is applied to buried-channel CCDs to determine the location of generation sites along the channel-stop sidewalls.