semiconductor & photoelectric effects ccds: definition...

Charged Coupled Devices

Semiconductor & Photoelectric EffectsCCDs: DefinitionCCDs: CharacterizationCCDs: Calibration

Semiconductors and Photoelectric Effect

What is ‘metal’?

What is ‘insulator’?

What is ‘semiconductor’?

What is ‘photoelectric effect’?

Why do we need to ‘cool down CCDs’?

Why ‘Silicon’?

Why do we need ‘Semiconductors’ for ‘astronomical observations’?

Semiconductors

Semiconductors in the periodic table: elemental and diatomic compound

Most commonly used (elemental) semiconductors:Si & Ge (in the future C too? “graphene”)

(Elementary) Semiconductors: Si, Ge

• Column IVa elements (e.g., Si, Ge), outermost shell contains 4 electrons, half needed to complete shell.

In crystal form, column IVa elements form covalent bonded, diamond-like structures. Electrons very strongly held in their bonds

Covalent bond: sharing one electron with each of four similar atoms in large matrices or lattices.

Silicon Crystal Structure

• Valence band = "ground states" that are normally completely filled

• Conduction band = "excited states" that are normally completely unfilled, electron in the conduction band can move if there is electric field

• no electrons between valence and conduction bands

• If somehow electrons can be moved from valence band to conduction band, then semiconductors act like metal.

• For insulator, the band gap energy is too large to move electrons.

Eg(Metal) « Eg(Semiconductor) « Eg(Insulator)

Eg: band gap energy (energy between valence

and conduction band)

Semiconductor: Valance & Conduction Bands

Semiconductor: Valance & Conduction BandsHow do we move electrons from valence band to conduction band in semiconductors?

Thermal Excitation of Electrons in Valence Band

Photo-electric Effect by Photons from Outside



• (Intrinsic) Thermal Excitation of Electrons in Valence Band:

If semiconductor absorbs outside photons of which energy is larger than the band gap energy, then photo-electrons can jump into conduction band.

Energy (valence electrons) exp(B/T), B:constant, T:temperature

• Photo-electric Effect by Photons from Outside

Therefore, some electrons in valence band with energy higher than the band gap energy can jump into conduction band if temperature is not absolute zero.

This is basically why semiconductors are used for astronomical observations.

Photon energy (h) band gap energy (Eg):

photo-electron can jump into conduction band

Electrons have energy distribution for a given temperature.

This is in fact the origin of the CCD dark noise, and why we need cooling.

Semiconductors for Astronomical Detectors

It is based on photo-electric effects.

The photons from a star (or other objects) can generate photo-electrons in conduction band of semiconductor.

The material of semiconductors determines band gap energy which determines the wavelength of photons (e.g., optical, infrared, UV, X-ray, ……) because photon energy is wavelength dependent.

The photo-electrons needed to be transferred, be amplified, and eventually be digitized.

Semiconductor-based detector for astronomical observations

CCD Components

Scientific CCD

CCDs are also used for commercial digital cameras.

Charge Coupled Devices (CCDs)

CCD is structurally a 2D (sometimes 1D) array of thousands to millions of “metal insulator semiconductor photosensitive capacitors” (= pixels).

Effectively CCD pixels are light-sensitive capacitors: Q = C V = N e-, where Q: total charge, C: capacitance, V: voltage, N: number of total electrons, e-: electron charge. Therefore, the total number of photo-electrons that can be stored in the pixel is dependent on C & V. If C & V are small, one cannot observe bright sources or cannot expose long.

“Q determines full well capacity which is the maximum number of electrons that can be stored in a pixel: e.g., N 100,000.”


CCD basically collects light, produce photo-electrons, and transfers the photo-electrons.

For the visible waveband (i.e., 3001,000 nm = 0.31.0 μm = 3,00010,000 Å), CCD is made of Silicon.

Silicon band gap energy: 1.12 eV (1 eV 1.6 10-12 ergs)

E = hc/ (h: Planck const., c: speed of light) 1.12 eV 1.1 μm

Photons of 1.1 μm can generate photo-electrons into the conduction band. This defines longer wavelength limit of Silicon CCDs, and this is why Silicon CCDs cannot be used for infrared (or longer wavelength) astronomy.


Photo-electrons are transferred along the column first by changing the gate voltage and then transferred horizontallyby serial shift register. Therefore, the pixels are read out successively, not independently. They are connected each other, and it is why the device is called CCD.

CCD: array of interconnected capacitors (= pixels)

Charge Coupled Devices (CCDs)How are electrons transferred in CCDs?

After transferred by the serial shift register, the charges are converted to voltages by amplifier by adding (small) bias voltage. The converted voltages are eventually converted digital number by analog-to-digital (A/D) converted and stored as image.

Charge Coupled Devices (CCDs)How are electrons transferred in CCDs?

CCD Operation

Exposure: collecting photo-electrons;

Photo-electrons moved to the electrode;

Electrons transferred along column and then horizontally;

Electrons transferred to the output amplifier;

Amplifier converts the charges to output voltages;

Output voltages converted to the digital number by A/D converts;

Converted number stored in the computer as image.

Quantum Efficiency (QE):

QE = (# photo electrons)/(# incoming photons)

80 % for most of modern CCDs

• Different CCDs have different QEs.

• QE is dependent on wavelength and temperature.

CCD Characterization:Quantum Efficiency, Charge Transfer Efficiency, Full Well Capacity, Gain and Digital Number, Digitization Error, etc

Charge Transfer Efficiency (CTE):

CTE = (electrons transferred) / (electrons produced)

~ 0.9999

Full Well Capacity:

= the amount of charge (= number of electrons)

that a CCD pixel can produce

: depends on CCD, but usually 100,000 electrons


Digital Number (DN): digitized data number in computer after A/D converter; it is proportional to the intensity of incoming light, in principle

(incoming photons)

→ (photo electrons: current)

→ (voltage after amplification)

→ (digital number after A/D converter)

A/D converter: 14-bit, 15-bit, 16-bit resolution

e.g., 16-bit: 0 – 65535, so CCD with 16-bit A/D

converter has DN between 0 and 65535


Gain: the number of electrons (or the amount of voltage) needed to produce 1 digital number (DN)

e.g., if the full well capacity is 150,000 electrons and A/D converter has 15-bit resolution, what’s the gain of this CCD ?

Gain = 150000/215 ≈ 4.6Low gain for fainter or brighter objects?


Gain: the number of electrons (or the amount of voltage) needed to produce 1 digital number (DN)

Exercise: When is a CCD image saturated? Describe this with the aforementioned CCD characterization parameters.

e.g., if the full well capacity is 150,000 electrons and A/D converter has 15-bit resolution, what’s the gain of this CCD ?

Gain = 150000/215 ≈ 4.6

Digitization Noise: the degeneracy in the number of electrons that produce the same digital number due to gain. If the gain is 1, there is no digitization noise.

“Low gain for fainter objects, high gain for bright ones”


Basic Processes of CCD Observations

Suppose that an observe took an image of a source in the sky with a CCD on computer.

What kind of signals are included in the image?

A. Source signals: e.g., stars, galaxies, ……

B. Sky background: radiation from the Earth’s atmosphere

C. Thermal Noise of the CCD: note that thermal distribution of valence electrons in semiconductor

D. Bias for the CCD readout: zero second dark noise

E. Also, we need to consider non-uniform sensitivities among pixels. This is known as flat-fielding.

A, B, C: proportional to the exposure timeD: independent of exposure time zero second dark noiseE: need to be determined by dome flat or sky flat (= e.g. twilight flat)

How do we separate A and B?

Bias: obtained with zero exposure time, CCD shutter closed (or overscan region)

Dark: CCD shutter closed, normalize to the exposure time (or overscan region)

CCD Sensitivity: Uniformly illumination of CCD with dome lamp or twilight sky, bias and dark subtracted “Flat fielding”

So the first order task is to obtain Source Signal and Sky Background, and then separate them..

We need to determine CCD Sensitivity, Dark, and Bias for this.

For Bias, Dark, and Flat, take several frames and obtain median value in order to reduce statistical noise and avoid cosmic rays.


Observed Image =

[(Source + Sky) (CCD Sensitivity) (Exposure Time)] (Dark for the same exposure time) (Bias)

Observed Image =


Example:

If an observe obtain data number 52 for a given pixel in the dark frame with 10-sec exposure, what’s the data number from (pure) dark noise that can be obtained with 1-sec exposure? The bias of the given pixel is known to be 2 in data number.

Answer: dark noise per second = (52 2) / 10 = 5/sec

Then, if the observe obtain data number 702 from the same pixel in a flat frame (which is obtained by uniformly illuminating a screen in the dome = dome flat), what’s the value used for flat fielding (= pixel sensitivity)? The exposure was 50 seconds.

Answer: flat value = [702 2 (5 50)] / 50 = 9


Continued ……

Now, if the observer has 2002 data number from the same pixel by observing a star with 100-sec exposure, what’s the number after the flat fielding?

Answer: [(2002 2 (5 100))] / 100 / 9 1.67

Note: The exposure is the same for all the pixels in a CCD, but pixel sensitivity (= values for flat fielding) is different from a pixel to a pixel. So in the above Answer, dividing by 100 is not important when you compare values obtained with different pixels. However, dividing by 9 is critical.


Observed Image =


CCD Observations: Signal and Noise

What kind of CCD noises do we expect?

CCD Observations: Signal and Noise

Noise from the object (e.g., stars, galaxies, …) brightness.

Noise from the sky background brightness.

Dark noise from the CCD.

Readout noise from the readout electronics.

How accurately can we measure the object brightness?

How do we quantify the relevant uncertainties?

[1] If we take several measurements, we can in principle calculate the uncertainty of each noise.

[2] Or sometimes we can use their statistical properties (e.g., Poisson statistics).

CCD Random Noise

There are basically two types of CCD random noise: Readout noise from “readout electronics:” Non-Poisson noise. Photon noise from the “object, sky background, and dark noise:” Poisson noise.

CCD Noise (per pixel): 2 = ph

2 + R2

(ph is photon noise; R is readout noise.

Note the unit of , ph, and R is number of photo-electrons.)

= G #(G is “Gain.” Number of electrons to increase data number by unity, e.g. 4. # is the noise in the data number)

ph2 = Nph,e = G Nph,# ( Poisson statistics!)

(Nph,e is the number of photo-electrons; Nph,# is the data number of the photo-electrons)

G2 #2 = G Nph,# + R

2

#2 = Nph,#/G + R

2/G2

CCD Noise (in data number) is #

2 = Nph,#/G + R2/G2

# , Nph,# estimated from the observed image G, R can be obtained by simple analysis which is known as variance plot (or photon-transfer curve);

Bright images: photon-noise dominates;

#2 ≈ Nph,#/G

Usually, readout noise (= R) is relatively small.

CCD Random Noise

[Data number] [Electron]

Variance Plot or Photon-transfer Curvelog # = ½ log (Nph,#/G + R

2/G2) ½ log (Nph,#/G) photon noise regime ½ log (R/G) read noise regime

G and R can be obtained using variance plot of # and Nph,#.

Slope = 1/2

CCD Random Noise


2/G2)

Systematic errors that can affect the estimation of G and R?

CCD Random Noise


2/G2)


• Non-uniform illumination

CCD Random Noise


2/G2)



• Scalenoise (= QE variations)

CCD Random Noise


2/G2)



• Scalenoise (= QE variations)

• Nonlinearity.

“Image differencing” is a useful tool for removing systematic errors.

CCD Random Noise

Let’s assume that you observe a star emitting Nnumber of photons per second.

What’s the S/N ratio when you observe the star with tint exposure time?

Neglect dark noise and sky background noise and consider only readout noise and photon noise from the star itself.

Also assume that the CCD gain is 1.

(Use R as a symbol representing the readout noise.)

CCD Signal-to-Noise Ration (S/N)

CCD Signal-to-Noise Ration (S/N)

First, the signal is (N tint).

Next, the noise is equal to sqrt[(N tint) + R2].

Now, the S/N ratio is

S/N = (N tint)/ sqrt[(N tint) + R2].

If the source is bright, photon noise dominates:

S/N tint1/2

CCD S/N: CCD Equation

Light from a star is spread over npix number of CCD pixels.

What will be the total noise?

Consider:Source noise (N*: total source light), Sky noise (NS: sky noise/pixel), Dark noise (ND: sky noise/pixel) and Readout noise (NR: sky noise/pixel).

All in the unit of the number of electrons.

CCD S/N: CCD Equation

Total Noise =

Consider:Source noise (N*: total source light), Sky noise (NS: sky noise/pixel), Dark noise (ND: sky noise/pixel) and Readout noise (NR: sky noise/pixel).

All in the unit of the number of electrons.

CCD Photometry: Aperture Photometry

Handbook of CCD Astronomy (Howell)

How do we calculate N* and NS in real data?

The background pixels around the star do not show a constant value. There is a significant pixel-to-pixel variation in the background pixels where there is no stellar emission.

Why?




The background pixels around the star do not show a constant value. There is a significant pixel-to-pixel variation in the background pixels where there is no stellar emission.

Why?

It’s because of the sky (background) noise, dark noise, and readout nose.




N* from a proper aperture around the star. The background emission needs to be subtracted out.

NS from a proper sky annulus around the star.



[1] From the sky background annulus, Nsky,med sky,med,

median (or mean) and standard deviation of the pixel values in the annulus. (What are the origins of sky,med?)

[2] From the star aperture, N* = Nsum – (Nsky,med npix)where Nsum is the total integrated value, npix is the number of pixels in the aperture. Then N* gives the net count of the star.

[3] * (source noise) = sqrt[N* + (npix sky,med2)]

If you increase the aperture of the source, your noise increases!

What’s the magnitude of the star and its error?

There are two ways: Differential Photometry and Absolute Photometry.

In Differential Photometry you know the magnitude of at least one star in your field (= same image). Then you compare the intensities of the source and star and calculate the magnitude of the source.

In Absolute Photometry you need to observe a standard star (or several standard stars) separately and then compare its intensity with your source. In this case, you need to compensate the atmospheric effect because the standard star suffers from different atmospheric condition, including transmission.


semiconductor & photoelectric effects ccds: definition...

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