Erik Bodegom

Temperature dependence of dark current in a CCD

We present data for dark current of a back-illuminated CCD over the temperature range of 222 to 291 K. Using an Arrhenius law, we found that the analysis of the data leads to the relation between the prefactor and the apparent activation energy as described by the Meyer-Neldel rule. However, a more detailed analysis shows that the activation energy for the dark current changes in the temperature range investigated. This transition can be explained by the larger relative importance at high temperatures of the diffusion dark current and at low temperatures by the depletion dark current. The diffusion dark current, characterized by the band gap of silicon, is uniform for all pixels. At low temperatures, the depletion dark current, characterized by half the band gap, prevails, but it varies for different pixels. Dark current spikes are pronounced at low temperatures and can be explained by large concentrations of deep level impurities in those particular pixels. We show that fitting the data with the impurity concentration as the only variable can explain the dark current characteristics of all the pixels on the chip.

The Meyer–Neldel rule for a property determined by two transport mechanisms

We propose that the Meyer‐Neldel rule ~MNR! arises naturally for a quantity where both an intrinsic process as well as a process involving impurities contribute. The strength of the latter depends solely on the density of the impurities. This leads to a spread in the apparent activation energy of the measured quantity and the observation of the MNR, even though the intrinsic processes have fixed activation energies. A consequence of the MNR is the occurrence of a temperature TMN where a measured parameter is independent of the activation energy. For the system studied, the MNR does not accurately predict the results at temperatures larger than TMN . Our model for the MNR is supported by experimental data and it also can explain the inverse MNR for low activation energies.

Meyer-Neldel rule for dark current in charge- coupled devices

We present the results of a systematic study of the dark current in each pixel of a charged-coupled device chip. It was found that the Arrhenius plot, at temperatures between 222 and 291 K, deviated from a linear behavior in the form of continuous bending. However, as a first approximation, the dark current, D, can be expressed as: D=D0 exp(−ΔE/kT), where ΔE is the activation energy, k is Boltzmann’s constant, and T the absolute temperature. It was found that ΔE and the exponential prefactor D0 follow the Meyer–Neldel rule (MNR) for all of the more than 222,000 investigated pixels. The isokinetic temperature, T0, for the process was found as 294 K. However, measurements at 313 K did not show the predicted inversion in the dark current. It was found that the dark current for different pixels merged at temperatures higher than T0. A model is presented which explains the nonlinearity and the merging of the dark current for different pixels with increasing temperature. Possible implications of this finding re...

A simple model for the dynamics towards metastable states

Circumstances under which a quenched system will “freeze” in a metastable state are studied in simple systems with long-range order. The model used is the time-dependent pair approximation, based on the most probable path (MPP) method. The time dependence of the solution is shown by means of flow diagrams. The fixed points and other features of the differential equations in time are independent of the choice of the rate constants. It is explained qualitatively how the system behaves under varying descending temperatures: the role of the initial conditions, the dependence on the quenching rate, and the response to precooling.

Exposure Time Dependence of Dark Current in CCD Imagers

In this paper, we present a systematic study on the rate of dark current generation of two scientific charge-coupled device imagers. The dark current in both imagers was measured for exposure times from 5 to 7200 s at a constant temperature. As one would expect, the majority of pixels show a linear increase in dark count with exposure time. However, we found distinct groups of pixels that show a nonlinear dark current dependence versus exposure time well below saturation. Since the dark count is often assumed to scale linearly with exposure time, these pixels can pose a problem during dark current correction. We also discuss what could cause some pixels to produce a dark count that is linear versus exposure time whereas others do not.

Dark current measurements in a CMOS imager

We present data for the dark current of a commercially available CMOS image sensor for different gain settings and bias offsets over the temperature range of 295 to 340 K and exposure times of 0 to 500 ms. The analysis of hot pixels shows two different sources of dark current. One source results in hot pixels with high but constant count for exposure times smaller than the frame time. Other hot pixels exhibit a linear increase with exposure time. We discuss how these hot pixels can be used to calculate the dark current for all pixels. Finally, we show that for low bias settings with universally zero counts for the dark frame one still needs to correct for dark current. The correction of thermal noise can therefore result in dark frames with negative pixel values. We show how one can calculate dark frames with negative pixel count.

Computation of dark frames in digital imagers

Dark current is caused by electrons that are thermally exited into the conduction band. These electrons are collected by the well of the CCD and add a false signal to the chip. We will present an algorithm that automatically corrects for dark current. It uses a calibration protocol to characterize the image sensor for different temperatures. For a given exposure time, the dark current of every pixel is characteristic of a specific temperature. The dark current of every pixel can therefore be used as an indicator of the temperature. Hot pixels have the highest signal-to-noise ratio and are the best temperature sensors. We use the dark current of a several hundred hot pixels to sense the chip temperature and predict the dark current of all pixels on the chip. Dark current computation is not a new concept, but our approach is unique. Some advantages of our method include applicability for poorly temperature-controlled camera systems and the possibility of ex post facto dark current correction.

Residual images in charged-coupled device detectors

We present results of a systematic study of persistent, or residual, images that occur in charged-coupled device (CCD) detectors. A phenomenological model for these residual images, also known as “ghosting,” is introduced. This model relates the excess dark current in a CCD after exposure to the number of filled impurity sites which is tested for various temperatures and exposure times. We experimentally derive values for the cross section, density, and characteristic energy of the impurity sites responsible for the residual images.We present results of a systematic study of persistent, or residual, images that occur in charged-coupled device (CCD) detectors. A phenomenological model for these residual images, also known as “ghosting,” is introduced. This model relates the excess dark current in a CCD after exposure to the number of filled impurity sites which is tested for various temperatures and exposure times. We experimentally derive values for the cross section, density, and characteristic energy of the impurity sites responsible for the residual images.

The Meyer-Neldel rule for diodes in forward bias

We analyzed the temperature dependence of the forward current of a silicon diode. Instead of representing the data in the ordinarily used current versus voltage graph, the currents are plotted for different voltages as a function of the inverse temperature. The constant voltage curves can be fitted linearly and the extrapolations of the fits seem to merge to one common focal point. Hence, we demonstrate that a real diode follows the Meyer-Neldel rule (MNR). It is shown that the MNR is due to a shift of the current from ideal-diode to high-injection-diode behavior. We will argue that the merging of the different Arrhenius plots toward one focal point, and hence a MNR, can be the result of various mechanisms. The general requirements to observe a MNR are not very restrictive. It is therefore not surprising that the MNR has been observed in a multitude of systems. The origin that gives rise to the MNR can be manifold and allows for different models to explain its occurrence.

Diffraction of light by a focused ultrasonic wave

The measurement of the acoustic pressure of a planar ultrasonic wave by light diffraction is well established. The ability to do similar measurements in the case of spherical waves has been doubted. However, we show that the range of validity can be extended to the focal region of a spherical concave piezoelectric transducer. Light is passed through the focal plane of a spherical concave transducer and is diffracted as a result of the variation in the index of refraction. The peak pressure can be calculated from the diffraction intensity by making the following simplification. We assume that in the focal plane the ultrasound can be approximated by a profiled planar wave, which in turn can be modeled by a wave of constant amplitude and effective width. The experimental results for moderate‐pressure amplitudes in water compare favorably with the calculations using the Khokhlov–Zabolotskaya–Kuznetsov equation, which incorporates both nonlinearity and diffraction effects of the acoustic field.