314 Chapter 5. Solid State Detectors
Problems
1.Show that the probability for an electron to occupy the Fermi level in an
intrinsic semiconductor is independent of the material’s temperature.2.Assuming equal charge concentrations in conduction and valence bands, com-
pute the ratios of the intrinsic charge concentrations to the conduction band
charge concentrations in germanium and silicon at 300K.3.Calculate the intrinsic carrier concentration of silicon and germanium at room
temperature (23^0 C)andat− 100 C.4.Compare the statistical fluctuations and relative uncertainty in the number of
charge pairs produced in silicon and gallium arsenide whenγ-rays of 520keV
are completely absorbed in the material.5.Estimate the range of 6MeVprotons in silicon.6.Abeamof5MeV electrons passes through a 300μmthick silicon detector.
Using Bethe-Bloch formula (see chapter 2), estimate the energy lost by the
electrons when crossing 100μm, 200μm, and the full thickness of the detector.7.Compare the change in intrinsic charge concentration in silicon with that in
germanium if the temperature is increased from− 50 Cto the room temperature
of 23^0 C.8.An n-type germanium is doped with a donor concentration of 4. 5 × 1023 m^3.
Calculate the ratio of intrinsic to extrinsic conductivities at 300Kand at 263
K.9.Compute the energy resolution of a germanium detector for 680keVphotons.
What would be the resolution if the production of charge pairs were a perfectly
Poisson process?10.Repeat the previous exercise for silicon and compare the results for germanium.11.Estimate the fraction of holes remaining in an n-type gallium arsenide having
dopant level of 10^14 cm−^3. The lifetime of holes at this dopant level can be
taken to be 3μs.12.We learned that the band gap in a semiconductor has temperature depen-
dence. Plot the variation of band gap for silicon and germanium with respect
to absolute temperature.13.Calculate the capacitances per unit area of a germanium based pn diode having
acceptor and donor impurities of 2× 1018 cm−^3 and 5× 1016 cm−^3 respectively
when no bias is applied across its junction and when a potential of 200V is
established.
14.How many electron hole pairs you would expect to be produced in a silicon
detector when incidentγrays deposit 1MeVof energy.15.Compare the drift velocity of electrons in silicon to that in germanium in the
presence of an electric field intensity of 1.5kV cm−^1.