Figure 6.23: Charge collection efficiency as a function of the charge carriers transit time.
The effective deep trapping / recombination time for electrons (Left panel) and holes (Right panel) was estimated from Hecht (Equation 3.38), fit to data and indicated as plot param-eter on the graphs.
thermal velocity of carriers of υth ≈ 107 cm/s, and by taking into account measured lifetimes, the range of the defect density for the investigated scCVD material is determined to 1013<
ND < 1015 cm−3. This result is in good agreement with the values obtained from the material characterization presented in Chapter 4.
Average pair-production energy in diamond The average energy needed to produce an e-h pair is measured from the extrapolation of the collected charge at a charge carriers drift time approaching zero (no trapping). From Figure 6.23 at CCEttr=0=100% a Qgen = 68.3± 0.3 fC is obtained, which corresponds to an Diamavg = 12.86± 0.05 eV/e − h. A cross-check was performed, comparing α-spectra measured with a Si PIN diode using the identical electronics chain (Figure 6.24). The ratio of the amplitudes in both detectors amounts to 3.55± 0.01, that corresponds to Diamavg = 12.84±0.05 eV/e−h, if taking into account the e-h pair production energy in silicon Siavg = 3.62±0.03eV/e−h [Owe04a,ORT94]. The measured avg is slightly less than the value of 13.1 eV/e-h [Owe04a, Kan96] reported for IIa natural diamonds and HPHT IIa diamonds and is in contradiction to the recently published values of 17.6 ± 2.7 eV/e-h [Per05], 16.1 ± 0.5 eV/e-h [Kan03] measured for scCVD diamond.
However, theoretical calculations point out an even lower value of 11.6 eV/e-h [Ali80].
6.4 Detector Response to Minimum Ionizing Electrons
6.4.1 Set-up and Methodology
The geometrical arrangement for MIPs detection is shown in Figure 6.25 (Left panel). A
90Sr source emits electrons with a continuous β− energy spectrum. The decay scheme as well as the parameters of the energy are given in Figure 6.25 (Right panel). In order to form a parallel electron beam, the 90Sr source was enclosed in a collimator made out of plexiglas. The size of the collimator aperture was about 2 mm φ. A scintillator
Figure 6.24: Spectrum of a mixed nuclide (239Pu, 241Am, 244Cm) α-particle source, measured with a silicon PIN diode detector and a scCVD-DD. About 3.55 times more energy is needed to create an e-h pair in diamond.
counter was placed directly behind the diamond detector. Coincidence in both detectors guaranties geometrically, that signals in the diamond detector are generated from electrons that traverse the active volume of the diamond detector and have an energy beyond 1 MeV (MIP). The same kind of spectroscopy electronics as for the α-particles measurements was used (section 6.3).
Figure 6.25: (Left panel) Geometrical arrangement for CCE measurements with 90Sr elec-trons of an energy Eβ > 1 MeV, triggered by a plastic scintilator detector. (Right panel) The decay scheme of a90Sr β-source.
Figure 6.26 (Left panel) shows a Geant4 generated spectrum of electrons emitted from a
90Sr source and the energy distribution of the electrons which impinge the plastic scintillator after passing 300 µm thick diamond sample (Right panel). The majority of the low energetic electrons do not reach the active volume of the scintillator due to absorption and scattering in the diamond. The mean value of 1.2 MeV of coincident electrons reaching the diamond detector is close to the MIP energy (β ≥ 0.957). Additionally, an electronic threshold discriminates the plastic signals above ∼1.5 MeV, as indicated in Figure 6.27.
The measured energy distributions are fitted with a Moyal [Moy55] approximation of
6.4. Detector Response to Minimum Ionizing Electrons 79
Figure 6.26: (Left panel) Geant4-generated spectrum of electrons emitted from a 90Sr source. (Right panel) The energy distribution of the electrons, which produce a coincident signal in the plastic scintillator and in a 300 µm diamond [Kuz06].
the Landau distribution (in following called ’Landau’):
Ψ(λ) = exp[−(λ + eλ)/2]
√2π (6.17)
where λ = (E− Ep)/σ, with E the energy loss, Ep the most probable energy loss, called in following the most probable value (MPV), and σ the width of the distribution which depends on the type of material (F W HMlandau ≈ 3.98σ). The electronic noise (σ = 140 e) is included in the fitting procedure by convoluting the Landau distribution with a Gaussian [langaus].
The assumption of the minimum ionizing approximation of the90Sr electrons, triggered in the above setup has been confirmed with a 2.2 GeV proton beam. The measured energy loss distributions of90Sr electrons and of 2.2 GeV protons are shown in Figure 6.27 (Right panel). Both measurements were performed using the same electronics chain and the spectra were fitted with the Landau distribution. As can be seen, the shape of the proton spectrum is well reproduced by the fast electrons, showing a MPV differing only by 1.4 %, and a distribution width (σ) by 4 %, respectively. The low energy tail in the proton spectrum is caused by events localized at the electrode edges. The high energy tail of the proton spectrum can not be reproduced by 90Sr electrons due to the limited maximum energy transfer of ∼0.8 MeV, which is the energy difference between the maximum energy of electrons ∼2.3 MeV and energy needed to trigger the event ∼1.5 MeV.
6.4.2 Results and Discussion
Figure 6.28 (Left panel) shows the pulse height spectra of minimum ionizing electrons mea-sured with three scCVD-DDs. The diamonds are 114, 324 and 460 µm thick, respectively.
Assuming a production of 36.7 e-h/µm, the observed collection distances are consistent with almost complete charge collection in the sensors. The corresponding charge-collection parameters are: most probable collected charge: 4,050 e, 12,050 e and 17,300 e; FWHM:
1260 e, 3735 e, 5360 e; separation between the pedestal and the beginning of the charge distribution: 2,800 e, 9,270 e and 13,370 e . The cut-off on the low energetic side of the Landau distribution occurs at about 75 % of the charge at the MPV Landau peak,
0.0 0.2 0.4 0.6 0.8 1.0 1.2
2.2 GeV protons 2.2 GeV protons mpv=293253
Figure 6.27: (Left panel) The total pulse height distribution of90Sr electrons measured with a plastic scintillator detector: in black - without electronic threshold, in red - with electronic threshold of 400 mV. (Right panel) Comparison of the energy loss spectra obtained with
90Sr electrons (red curve) and with 2.2 GeV protons (black curve), respectively.
which is more favorable than in silicon - cut-off at about 50 %. The σ/MPV ratio for the scCVD-DDs is approximately 0.078 (Figure 6.28 (Right panel), that corresponds to a ratio of 0.31 for FWHM/MPV. This value is one third of that obtained from high quality pcCVD-DDs [Dir99], and about two thirds that of the width of silicon detector spectra, measured with a sensor of identical thickness [Ada07].
0 5000 10000 15000 20000
0
Figure 6.28: (Left panel) Spectra of minimum ionizing electrons measured with three scCVD-DDs of various thickness. (Right panel) Most probable values (MPV) as a function of the width σ of the Landau distributions scCVD-DDs. For comparison the same ratio is shown for measurements realized with a pcCVD-DD [Dir99].
Figure 6.29 shows the collected charge as a function of the applied electric field. For both bias polarities, the saturation of the collected charge starts at low fields (E < 0.1 V/µm) as indicated in the figure inset.