A. Simulation process

In this study, software including MAXWELL, GEANT4, ROOT, and Induced Current Calculation (ICC, which was developed by our group used to calculate the induced current on the electrode of semiconductor detector based on Shockly-Ramo theorem.) were used. Fig. 2 shows the global simulation process. Here, MAXWELL simulates the electrostatic field and weighting potential within the detector volume. GEANT4 are used to the initial interaction and the subsequent sub-interactions in the detector, and the initial γ-ray and the secondary particles created in the detector are tracked. The physics process taken into account includes photoelectric effect for γ-rays and multiple scattering and ionization for electrons, pair production, and Compton scattering. An energy threshold is usually set so that particles with a kinetic energy lower than this limit will be considered to have deposited their energy locally. In our simulation, thresholds of 20 keV for gamma-ray and 5 keV for electrons were used. Once an interaction ended, the list of energy deposition points is transferred as a parameter to our charge transport code. Then, ICC used to calculate the carriers drift trace in the detector volume caused by the electrostatic and the induced current on the electrode which depend on the weighting potential. The final calculated induced charges on anode are accumulated to get the energy spectrum.

Fig. 2.Full-screen View

Global simulation process.

B. Electrostatic & weighting fields

Both the electrostatic and weighting fields within the detector volume affect the charge collection performance critically. Based on Shockly-Ramo theorem [10], the induced charge Q_ind is given by the weighting potential. The change in the induced charge, ΔQ_ind and the current i at an electrode caused by a charge q moving from xi to xj are given by

where V(x) and E(x) are the weighting potential and the field at position x. The total induced charge is actually the sum of the charges induced by the drift of electrons and holes. The drift velocities μ_e and μ_h of free carriers through the detector volume depend on the electrostatic field, and the induced charge on the electrode is determined by the change of the weighting potentials. For CdZnTe, the drift velocities of μ_e and μ_h always selected around 1400 cm²/ (s⋅V) and 120 cm²/ (s⋅V).

Appling a positive bias voltage to the anode and 0 V to the side cathode, the electrostatic fields and the weighting potentials were given by MAXWELL. Fig. 3(b) shows the mesh plot of a 2D slice (through the center of the anodes, shown in the left panel) of the electric potential when an 800 volt bias is applied. It is immediately clear from Fig. 3 that due to the fact that the four sides of the cathode are at the same potential, the binode electrode geometry reduced the electric potential throughout the detector volume compared to a plannar detector. Fig. 4(a) shows a mesh plot of a 2D slice of the weighting potential of anode I, and Fig. 4(b) shows the weighting potential of anode II. The slice being shown is also indicated in Fig. 3(a). Though the reduced electric field strength will locally slow free carriers down and increase trapping probabilities, the benefit of the binode design is greatly improved charge collection, which due to a suppression of the weighting potential as seen in Fig. 4. In order to get a significant improvement in charge collection one has to pay for the reducing electric field strength in the Binode design.

Fig. 3.Full-screen View

(Color online) (a) Binode CdZnTe detector with 2D plane cut through the center of the pixel, (b) the electric potential (V) within the 2D plane is shown as a mesh plot.

Fig. 4.Full-screen View

(Color online) (a) Mesh plot of the weighting potential of anode I and (b) anode II within the 2D slice through the detector volume.

In order to understand the free carriers’ drift more closely, some positions in the detector volume have been selected to follow the track of electrons. Fig. 5 gives the calculation results (the detector volume is 10 mm×10 mm×5 mm), where the x-coordinate of the selected points are 0 mm, y-coordinate are between -5 mm and 5 mm (the interval is 1 mm), and z-coordinate are 2.4 mm and 2.6 mm. For the trace of the holes in the detector volume, one can simply exchange the start point and end point of electrons, because the holes drift just along the opposite direction of electrons.

Fig. 5.Full-screen View

(Color online) Electron drifts trace at some selected positions in the detector volume of Binode CdZnTe detector.

C. Correction of the Compton scattering effect (CCSE)

Obviously, when the carriers drift in the detector volume, both of the anodes will get signals. For a photoelectric effect event, the free carriers will induce positive signal on the anode where electrons are collected finally, while a negative signal will be induced on the other one. The positive signal will be bigger than the negative one because of the weighting potential of the collected anode getting a bigger charge than that of the other anode along the carrier motion trail. We add the absolute values of both the anodes’signal together as the final charge induced in this case. However, for an event of Compton scattering or pair production and the carriers created separated both in the upper detector volume and lower volume, the created carriers will be collected by both of the anodes, then two positive signals will be observed both on the anodes. In this case, we add both the positive signal together to get a final induced charge.

Figure 6 is the scatter diagram of the induced charge on the two separated anodes, where the positive charge induced means electron collected, while without electron collection there will be negative charge induced on the anode electrode. However, for those Compton scattering effect events and pairing effect mentioned above and the created electrons were collected by different anodes, both of the anodes will be induced positive charge, as shown in area (a). Area (b) shows the twice Compton scattering effect but without whole energy deposited, and area (c) shows the photoelectric effect events and single Compton scattering effect events.

Fig. 6.Full-screen View

(Color online) Scatter diagram of the induced charge on two separated anodes.

It shows that after CCSE, the performance of the Binode CdZnTe detector improved obviously. Fig. 7 shows the simulated energy spectrum before and after CCSE; Because of the CCSE, FWHM of ¹³⁷Cs 662 keV gamma-ray spectrum improved from 3.31% to 1.27% and the peak-Compton ratio increased from 2.4 to 7.4. Fig. 8 shows the simulation results of ¹³⁷Cs 662 keV and ⁵⁷Co 122 keV gamma-ray spectrum with a CCSE, where the detector dimensions X=Y=Z= 10 mm, bias voltage is 3000 V and the pixel anode diameter D=3 mm. 3.92% FWHM at 122 keV and 1.27% FWHM at 662 keV without electronic noise have been achieved by this CdZnTe detector with a CCSE.

Fig. 7.Full-screen View

(Color online) Binode CdZnTe detector spectrum before and after CCSE.

Fig. 8.Full-screen View

Simulation results of Cs-137 662 keV and ⁵⁷Co 122 keV gamma-ray spectrum.

A. Length-to-thickness ratios (X/Z)

Two kinds of length-to-thickness ratios (X/Z = 1 or 2) detector structures have been simulated, the results were shown as Fig. 9, both of them have been made CCSE. The simulation results demonstrate that when X/Z = 1 the detector has a better performance, which means the detector has the same dimensions (X=Y=Z).

Fig. 9.Full-screen View

(Color online) ¹³⁷Cs spectral performance for 10 mm×10 mm×10 mm (left) and 10 mm×10 mm×5 mm (right) Binode CdZnTe detector after CCSE.

B. Anode size and bias voltage

The left panel of Fig. 10(a) shows the spectral performance for 10 mm×10 mm×10 mm Binode CdZnTe detector with anode diameter between 1 mm and 4 mm. The results show that when D= 3 mm, the detector has an excellent performance that the energy resolution about 1.28% FWHM at 662 keV when 3000 V applied on both of the anode. The right panel of Fig. 10(a) shows the simulated ¹³⁷Cs spectral response of a 10 mm×10 mm×10 mm Binode CdZnTe detector with a D=3 mm pixel anodes at bias voltage between 2800 V and 3200 V. The CdZnTe crystal was chosen to have low electron transport with μ_eτ_e = 7×10^-3 cm²/V, and hole transport with μ_hτ_h = 3×10^-5 cm²/V.

Fig. 10.Full-screen View

(Color online) ¹³⁷Cs spectral performance for (a) 10 mm×10 mm×10 mm, (b) 5 mm×5 mm×5 mm and (c) 15 mm×15 mm×15 mm Binode CdZnTe designs with varying pixel size (left) and with varying anode voltage (right).

The simulation results demonstrate that the anode diameter D should not be too small, such as shown in Fig. 10(a) (left) with D= 1 mm. The bad spectrum performance is mainly due to the weak statistic field caused by the short anode diameter. However, with D=4 mm the spectrum also becomes worse, mainly because of the pixelated effect is not obviously caused by the longer anode diameter. The left panel of Fig. 10(b) and Fig. 10(c) shows the simulation results of spectrum performance of 5 mm×5 mm×5 mm and 15 mm×15 mm×15 mm Binode CdZnTe with varying anode sizes. The results show that the best ratio of anode size to detector thickness is about 0.2∼0.3, i.e. D/Z=0.2–0.3. The simulation results of Binode CdZnTe detector with varying anode voltages were also shown in Fig. 10 (right), and the results demonstrate that the anode voltage related to the detector thickness and the rationally design is about V/Z = 250∼300 V/mm.

From the results got above, for 5 mm×5 mm×5 mm Binode CdZnTe detector, the best energy resolution was about 1.24% with the anode of 1.5 mm diameter and 1400 V voltage. The best energy resolution for 10 mm×10 mm×10 mm and 15 mm×15 mm×15 mm Binode CdZnTe detector are 1.27% and 1.78%, at D= 1.5 mm, V= 2800 V and D= 2.25 mm, V= 3500 V, respectively.