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3D simulations of device performance for 3D-Trench electrode detector Jianwei Chen a,b, Hao Ding a,b, Zheng Li a,b,c, *, Shaoan Yan a,b a Xiangtan University, China b Center for Semiconductor Particle and photon Imaging Detector Development and Fabrication, Xiangtan, China c Brookhaven National Laboratory, Upton, NY, USA (before 2/7/2014) 2014.10

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Outline Structure and simulation of the square 3D-Trench electrode detector Leakage current at different radiation fluences Geometry capacitance Full depletion voltage Summary

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Structure and simulation of the square 3D-Trench electrode detector Zheng Li, Nucl. Instr. and Meth A658(2011) 90-97.

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Leakage current at different radiation fluences The effective doping concentration N eff caused by high energy protons irradiations in Si bulk can be approximated by (for Φ n >1x10 14 n eq /cm 2 ) β=0.01 Φ n is the 1-MeV neutron-equivalent fluence The leakage current is originated from the generation current of the depletion region if ignore the surface effects. When the recombination centers are assumed to be in the middle of the bandgap, the leakage current created in the depletion region can be calculated theoretically as [1]B. Dezillie, Z. Li, V. Eremin, W. Chen, L.J. Zhao, IEEE Trans. Nucl. Sci. NS47(6) (2000) 1892. [2] D.K. Schroder, Semiconductor Material and Device Characterization, second ed, Wiley, New Yord, 1998, pp. 420-429.

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（ Generation current ） （ Empirical equation ） （ Electron lifetime ） V dep Volume of the depletion region τ Electron lifetime α Damage constant (4x10 -17 A/cm) Φ n 1 MeV equivalent neutron fluence (It’s the foundation of the leakage current simulation.) Leakage current at different radiation fluences For fluence of 1x10 14, 1x10 15 and 1x10 16 n eq /cm 2, the theoretical calculation leakage current are 8x10 -9, 8x10 -8 and 8x10 -7 A (volume is 2x10 6 μm 3 ), respectively. H. W. Kraner et al., Nucl. Instr. and Meth A279 (1989) 266-271.

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Leakage current at different radiation fluences Saturation voltage

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Leakage current at different radiation fluences For fluence of 1x10 14, 1x10 15 and 1x10 16 n eq /cm 2, the saturation leakage current are 6.37x10 -9, 2.33x10 -8 and 3.13x10 -7 A (volume is 2x10 6 μm 3 ), respectively.

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Leakage current increase linearly with radiation fluence Leakage current at different radiation fluences

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Geometry capacitance The geometry capacitance of our structure can be calculated by : l=270 μm R/r=10 Theoretical capacitance of our structure is 97.8 fF

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Geometry capacitance The vertical lines denote the depletion voltage and the horizontal line is the geometry capacitance, which is 99 fF in our simulations. Theoretical calculation capacitance is 97.8 fF. Small capacitance can ensure small noise, which contribute to good device performance.

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Geometry capacitance Change the length (l) of the centre column Geometry capacitance is proportional to the length of centre column. When the length of the centre reduced to zero, capacitance can achieve the theoretical minimum value, 3 Ff. L

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Geometry capacitance Change the edge length (s) of the centre column Geometry capacitance increase with the edge length of centre column, but not increase linearly.

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Full depletion voltage The full depletion voltage was extracted from the two straight-line fits to the data in the log(C)-log(V) plot. As shown in this figure, the line with arrow is drawn through the intersection of two tangent lines. The x- coordinate of the crossing point gives the depletion voltage value V fd.

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Radiation fluence (n eq /cm 2 ) Full depletion voltage (V) 1x10 14 1 3x10 14 3 5x10 14 5 8x10 14 7 1x10 15 9 3x10 15 34 5x10 15 50 8x10 15 72 1x10 16 90 The full depletion voltage is only 90 V at 1x10 16 n eq /cm 2. In this optimal configuration the full depletion voltage can be up to 7 times less than that of a conventional 3D detector with all column electrodes. Full depletion voltage

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As bias voltage increases, the depletion region extends from trench electrode (region 3) into the bulk (region 3);. When the detector is depleted (see curves of 90 and 100V), the potential will increase immediately at 7.07μm, but this situation will not happen for the undepleted ones (see curves of 60 and 80 V). Region 1 is p + column, region 2 is p-bulk, and region 3 is n + trench. 1 2 3

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Full depletion voltage The holes concentration will decline at 7.07 μm for the fully depleted ones. From the potential and the holes concentration figures, we can confirm that the full depletion voltage of the detector is about 90 V, which give same results to those calculated by CV characteristics. 1 23

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Summary Both the leakage current and the voltage to reach the geometry capacitance (full depletion voltage, V fd ) increase with radiation fluence. The geometry capacitance is 99 fF for the structure in our study. The leakage current and full depletion voltage at 1x10 16 n eq /cm 2 are 41.3μA (volume is 2x10 6 μm 3 ) and 90 V, respectively. The full depletion voltage calculated by CV characteristics give similar results to those analyzed by the potential and hole concentration profile simulations.

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