ASTR 3130 (Majewski) Lecture Notes

DETECTORS: FUNDAMENTALS OF CCDs

• Imagine three sets of interspersed gates put in a repeating pattern as shown.
• A group of gates with a common electrical link is a called a phase.
• For each pixel we have one gate of each phase.
• Each phase alters its voltage with a distinct and repeating clock-like signal, alternating between "high" and "low" states.
• The clocks for each phase are timed to work together in a pattern called a timing sequence (like the timing sequence provided by a car's rotor, which transfers electrical charge via a network of wires to the spark plugs).
• A clever timing sequence, like that shown, can change phase states in such a way as to drive packets of stored electrons from left to right.
  3-Phase Charge Transfer
  

• Note that in the above timing sequence at least one "high" well state (under a negatively charged gate) separates two consecutive electron packets to prevent mixing of information.
• The above three-phase transfer system is typically used in research grade astronomical CCD cameras.

• An important aspect of the three-phase mechanism is that the clocks must be carefully adjusted in a well-timed order to optimize the electron transfer speed without having the wells get out of phase with one another. This requires carefully constructed timing circuitry.

• Many CCD cameras sold on the mass market -- e.g., the SBIG STX-16803 CCD on the RRRT 24-inch telescope -- use a simpler, two-phase transfer.
• Two clocks easier to keep in step -- simpler and less expensive timing circuitry.
• To accomplish two-phase transfer, introduce an "intermediate" voltage level next to every normal gate -- make by having electrodes spaced from the Si substrate by different thicknesses of insulator -- changing effective capacitance and creating a specially shaped depletion zone under each pixel.
• Alternating high, 0, and low states with the shaped wells keep the electrons always "pouring" in one direction (to the right in the picture).
  2-Phase Charge Transfer
  

• During transfer from one pixel to another, a certain number of charges are left behind.
• Poor charge transfer efficiency (CTE) results in a "blurring" of the signal due to charge trailing behind and getting mixed with later packets.
• Example of poor CTE:


• CTE is technically defined as the fraction of any particular charge packet that is passed from one depletion zone to the next.

• Only a slight transfer inefficiency is tolerable:
• Let: N_o = # charges originally under gate
  N_t = # charges transferred to next gate
  Then the CTE is defiined as N_t / N_o.

• Imagine a simple case of a 100 electron packet with 1 charge that does not get transferred and is left behind during a single transfer:
N_o = 100
N_t = 99
CTE = N_t / N_o == 99/100 = 0.99
.
• This 99% CTE doesn't seem so bad for one packet transfer, but the inefficiency accumulates and can lead to horrible consequences.
  For example start with the same 100 e^- charge packet, but now make 100 transfers. At the end of those 100 transfers we are left with:
  

• In today's CCDs, with array sizes as large as 8192 pixels on a side, and with three phases per pixel, an individual charge packet can face as many as ~50,000 separate transfers!
--> You can easily show, then, that we require CTE's of > 0.99999 to maintain the integrity of the charge packets.




• What's happening at the micro level to affect CTE?:
  Two mechanisms operate to make the electrons want to transfer from one well to the next, and each has an associated exponential time constant for the process to occur:
• Self-induced drift from electrostatic repulsion
  • The electrons in a charge packet naturally repel each other, and will, in the absence of an overpowering bias potential keeping them in a potential well.

  • When the bias voltage is set to 0, this mechanism dominates for wells that are rather full of electrons:

  • For a 15μ gate under which there are 300,000 e^- the (exponential) time constant (i.e., for a dependence that goes as e^-t/τ ) is of order = 0.002 μs (microseconds).
  • As the electrons drain off from one depletion zone to the next, the repulsion force diminishes and grows. A second process eventual takes over...

• Simple thermal diffusion
  • This mechanism dominates in the case of small amounts of charge (not many charges left to repel one another forcefully enough).

  • Thermal diffusion is clearly slower, but the speed of course depends on the temperature of the device:
    @ T = 300 K, ~ 0.026 μs
    @ T = 77 K, ~ 0.1 μs



• Why does it take so long to read out a CCD image? (You now know from experience that this is so...)
  Clearly the faster you cycle your clock phases, the less time there is for charges to travel from one depletion zone to the next in the "bucket brigade".
  • We clearly want to have good CTE, and this means we need to clock the gates at a speed that is much slower than the thermal diffusion time constant if we want to ensure enough time for nearly 100% transfer of charges.

  • But the speed of the clocking affects the readout time of a CCD. We don't want to wait too long to make each transfer or it will take an intolerable amount of time to read a huge array with millions of pixels and even many more individual charge packet transfers.

  • We can determine how the CTE relates to the clock speed by accounting for the transfer as characterized by the exponential, statistical mechanical processes of diffusion discussed above:
    
    CTE = (1 - e ^{- t / τ}) ^m
    m = # transfer phases
    τ = the slower of the two time constants given above
    t = duration that the gates are in each voltage phase state
    

  • Nevertheless, even given the need to clear most charge, the above time constants suggest we can operate CCD clocks/timing sequences at tens of thousands of cycles per second (i.e. tens of kHz) -- but this still means it may take minutes for a full chip readout.

  • QUESTION: Explain how I got tens of kHz in the above statement.

  • QUESTION: Television cameras use CCD detectors for live video. Clearly in this situation you can't take a minute to read the full image out! What is going on here??
    • Think about temperature effects.

    • Think about size effects.

    • Think about quality needs.

  
  
  
• A few other problems can affect the CTE of a CCD other than the normal statistical mechanical processed mentioned above. These processed interfere with the normal transfer process:
• Fringing fields - Depletion zones affected by neighboring gate fields - if the gate matrix is made with improper levels of shielding.
  • This is a design problem and affects all CCDs made the same way.

• Traps - Caused by poorly shaped electrodes, diffusion of implanted dopants, lattice defects in the silicon substrate (which can be caused by radiation -- as may be seen in interplanetary space contexts), or other impurities.
• In the cartoon representation below I show the well shape for two different phase states of the CCD. The defect can create a "mini-well" trap.
  

• This is a problem that is typically unique to each individual CCD. Traps often leave obvious defects in the images taken with CCDs.
• A trap in a pixel "traps" charge during the charge transfering, and this charge moves out of the trap at a slow rate compared to the normal charges in the well. So charge gets left behind.
  Once a trap is filled up the pixel reaches a steady state in that no more charges can get lost in the trap, as long as charges keep getting dumped into the well faster than charges leave the trap.
  But once low levels of charge are passing through the pixel, the charge can leak out and be an annoyance, until another large charge packet comes through and refills the trap.
  Traps can be "low level" (filled with a few hundred or thousand electrons) or "high level" (of order 10,000 electrons).
  Large traps can be partly dealt with through a "pre-flash" of the detector with a uniform source of light at just enough level to fill the trap with every charge packet on the array.
  Traps often only become obvious when they have sizes of several hundred electrons.

• CCDs are typically sold on a sliding price scale that relates to the number of known traps in the device. You get what you pay for!
  An example of a website showing how CCDs are "graded" for cosmetic quality based on the number of defects like traps is shown at the bottom of this web page. We'll talk about some of the other defects in a future lecture.