### Astronomy 512 -- Spring 2006 -- Assignment 5 -- Due Tuesday Apr 18

1. In the Infrared Laboratory you will find a single InSb photodiode packaged inside an LN2 cryostat. You need to do the following:

• As a group --

• Pump the vacuum jacket to a pressure less than 60 mT.

• Fill the dewar with liquid nitrogen (from the 10 liter storage dewar). Observing handling precautions for LN2.

• After the system has thermally stabilized. Estimate the dewar's hold time and devise a plan to keep the system cold for the duration of the experiment.

• Individually --

• Power up the system (when it is completely stable at LN2 temperature) and obtain a "load curve" for the photodiode by adjusting the bias and noting the DC output. Locate the optimal operating point for the diode.

• Estimate the frequency repsonse of the system by looking at a "chopped" source.

• Make an estimate of the noise and Noise Equivalent Power of the system.

• In small groups (2-3 people) --

• Using the lab's blackbody source

• Characterize the systems response vs. wavelength (i.e. in the various filters).

• Demonstrate that the Planck equation works.

• Highly recommended (in any configuration you want).

• Use the lab breadboard to lay out a simple op amp analog to the detector circuit in the dewar. Use a 1N4148 diode in place of the detector. Configure the amplifier for a transimpedance gain of 10V/milliamp. Construct a load curve for the 1N4148 and compare it with expected ideal diode performance.

Individual problems

2. Consider an 0.5mm diameter intrinsic semiconductor photoconductor made of Germanium. Assume the detector operates at a bias of 50mV (See (better yet read) Rieke Chapter 2).

• a) What is the bandgap in eV and the longest detectable wavelength?

• b) Suggest a thickness for this detector to provide for good quantum efficiency. Estimate the quantum efficiency and photoconductive gain for your choice of thickness.

• c) What will the responsivity be (in amps/watt) for this configuration?

• d) At an operating temperature of 200K, what is the estimated density of conduction band carriers in the material? Given this density of carriers and the detector's other material properties -- what is the resistance of the detector.

• e) How will the resistance change if the detector is cooled to 100K? By how much will the detector's Johnson noise contribution decrease?

• f) The detector (operating once again at 200K) is attached to a 1.5-meter telescope and pointed at a K=12.0 magnitude star. If the filter is the standard astronomical Ks band (2.00-2.32um). At what SNR will the star be detected in a 5-second integration assuming detector Johnson noise and photon statistics are the only considerations.

3. Suppose the germanium detector above is doped with Gallium with an acceptor concentration of 5.0x1014.

• a) What is the wavelength cutoff of this material.

• b) How thick would the detector have to be to achieve a resonable photoconductive gain.

• c) At what temperature would you recommend operating this detector?