# Dark CurrentImaging Topics

## Dark Current

### Dark Current Noise

Dark current arises from thermal energy within the silicon lattice comprising the CCD. Electrons are created over time that are independent of the light falling on the detector. These electrons are captured by the CCD’s potential wells and counted as signal. Additionally, this increase in signal also carries a statistical fluctuation known as dark current noise. CCDs can be cooled either with thermoelectric coolers (TECs) or liquid nitrogen to reduce this effect. Ideally, the dark current noise should be reduced to a point where its contribution is negligible over a typical exposure time.

### MPP Operation

Some CCDs operate in multi-pinned-phase (MPP) mode. MPP devices are fabricated and operated in such a way as to significantly reduce thermal charge generation (dark current). The largest contribution to dark current results from the interface between the silicon dioxide and epitaxial silicon layer within the CCD. Boron implantation into the epitaxial silicon layer and proper biasing of the various clock phases drive the dark current electrons away from the potential wells that comprise a pixel, thus reducing the number of electrons per pixel per second (e-/p/s) collected due to dark current.

### Dark Current vs. Dark Current Noise

Each high-performance CCD camera carries a dark current specification. Dark current noise is the statistical variation of this specification. For instance, a given camera might have a dark current specification of 1.0 e-/p/s. For a 4-second exposure, a total of 4 electrons/pixel are generated (1.0 e-/p/s x 4 sec). Since dark current noise follows Poisson statistics, the rms dark current noise is the square root of the dark current or, in this case, 2 e-/p.

### Dark Current Noise Contributions

Noise sources in CCD cameras add in quadrature (the square root of the sum of the squares). In the low-light regime, the significant noise sources are read noise and dark current noise. Again, using the previously mentioned camera as an example, we can easily compare the relative sizes of these noise sources. Using 13 electrons/pixel as the read noise and the dark current noise calculated above (2 e-/p) for a 4-second exposure, the total camera noise is calculated as follows:

\begin{align} \text {Total Noise} & = \sqrt{(\text {read noise}^2 + \text{dark noise}^2)} \\ & = \sqrt{(13^2 + 2^2)} \\ & = \text {13.15 electrons (for a 4 second exposure)} \\ \end{align}

Thus, the dark current noise generated in a 4-second exposure has virtually no effect on the total camera system noise. Similarly, for a 30-second exposure we find that the total system noise equals 14.1 electrons. Again, even at a 30-second exposure, dark current noise barely contributes to the total camera system noise.

### Hot Pixels

Occasionally, an individual pixel may have a different dark current generation rate than the rest of the CCD array. Remember, the dark current specification is an ensemble average of the entire array. Those pixels that have a higher-than-average dark current are known as hot pixels. These pixels will repeatedly have higher backgrounds than the vast majority of pixels. Since this is an effect that arises from the CCD manufacturing process, each hot-pixel location will remain fixed and can therefore be corrected.