Gated Silicon Drift Detector Fabricated from a Low-Cost Silicon Wafer

Inexpensive high-resolution silicon (Si) X-ray detectors are required for on-site surveys of traces of hazardous elements in food and soil by measuring the energies and counts of X-ray fluorescence photons radially emitted from these elements. Gated silicon drift detectors (GSDDs) are much cheaper to fabricate than commercial silicon drift detectors (SDDs). However, previous GSDDs were fabricated from 10-kΩ·cm Si wafers, which are more expensive than 2-kΩ·cm Si wafers used in commercial SDDs. To fabricate cheaper portable X-ray fluorescence instruments, we investigate GSDDs formed from 2-kΩ·cm Si wafers. The thicknesses of commercial SDDs are up to 0.5 mm, which can detect photons with energies up to 27 keV, whereas we describe GSDDs that can detect photons with energies of up to 35 keV. We simulate the electric potential distributions in GSDDs with Si thicknesses of 0.5 and 1 mm at a single high reverse bias. GSDDs with one gate pattern using any resistivity Si wafer can work well for changing the reverse bias that is inversely proportional to the resistivity of the Si wafer.


Introduction
Various types of X-ray detectors, such as silicon (Si) pin detectors and silicon drift detectors (SDDs) , are used to measure the energy and photon count of X-ray fluorescence photons. Si X-ray detectors with a thick Si substrate, a large active area, and small capacitance are desirable [29][30][31][32].
A pin structure is used to collect charge carriers, the number of which are proportional to the energy of an X-ray photon. In X-ray fluorescence spectroscopy, the capacitance of a pin detector increases with the active area of the detector because the anode (n-type layer) and the cathode (p-type layer) have equal areas. The increase in the capacitance degrades its performance. However, SDDs have a much smaller capacitance than pin detectors [1]. This is because the anode, which is on one surface of the n − Si substrate (n − or i-layer), is much smaller than the pin detector, whereas the entrance window layer, which is the cathode on the opposite surface, is kept large [1]. The anode is surrounded by multiple p-type rings (p-rings), to which a different bias voltage is applied. The resulting electric field makes the electrons flow smoothly toward the anode. To form a sufficiently strong electric field toward the anode in the SDD, the p-rings are electrically coupled with expensive built-in metal-oxide-semiconductor field-effect transistors (MOSFETs) or implanted resistors.
The 10-kΩ·cm Si wafers are more expensive than the 2-kΩ·cm Si wafers used in commercial SDDs. In the present study, to fabricate much cheaper X-ray detectors, we used a device simulation to design adequate gate patterns for GSDDs formed from 2-kΩ·cm Si wafers.

Structure and Advantages of Gated Silicon Drift Detectors
GSDDs have a cathode and only one p-ring, and to which the same reverse bias can be applied. Figure 1 shows half of a schematic cross section of a cylindrical GSDD with seven ring-shaped gates and one p-ring that does not contain MOSFETs or implanted resistors [37,38,[40][41][42][43].
In SDDs and GSDDs, n-type layers (anode and ground rings) and p-type layers (cathode, p-ring, and floating rings) are fabricated by the same processes. In SDDs, multiple inner p-rings located between the anode and the p-ring are formed. Compared with GSDDs, the extra fabrication processes in SDDs are for creating the built-in MOSFETs or implanted resistors to couple the p-rings together electrically, which lowers the yield rate of detectors. The passivating oxide layers (SiO 2 ) are formed, and the anode, p-ring, ground rings, and cathode are metallized. During metallization, the innermost p-ring is also metallized in SDDs, whereas gates are formed in GSDDs.
In GSDDs, no extra fabrication processes are required to form the gates because the metal gates are formed on the SiO 2 during metallization of the anode and the p-ring. As a result, the fabrication of GSDDs is much simpler than that of commercial SDDs. Moreover, the same high reverse bias can be applied to the cathode, the p-ring, and all the gates, which means that GSDDs require only one high-voltage source. Therefore, GSDDs greatly reduce the cost of the X-ray detection system. Figure 1. Half of a schematic cross section of a cylindrical GSDD structure with one p-ring and seven gates. The same negative voltage was applied to the cathode, the p-ring, and all the gates.

Device Simulation Processes
The device simulations were carried out by using the ATLAS Device Simulator (Silvaco International). All the simulations were performed by solving Poisson's equation and the carrier continuity equations. This provides a complete description of the system in terms of electrical quantities, such as electric potential and electric field distributions, carrier densities, and current densities.
The thicknesses of the n − Si substrate (d Si ) were 0.5 and 1 mm, and the values of ρ Si were 2 and 10 kΩ·cm. The radius of the anode (R a ) at the center of the cylindrical GSDD was fixed as 0.055 mm, which kept the capacitance of all GSDDs small. The widths of the p-ring (W p ), p-type floating rings (W f ), and n-type ground rings (W g ) were 0.545, 0.03 and 0.39 mm, respectively. The gap between the p-ring and the floating ring (G pf ) and the gap between the floating and ground rings (G fg ) were all 0.04 mm. The thickness of SiO 2 on the cathode (d c ) was 0.75 µm. The thickness of SiO 2 on the other side (d g ) was changed to constrain the electric field in the SiO 2 between the gates and the Si substrate at ≤ 2.5 MV/cm, which is less than the SiO 2 breakdown electric field of 10 MV/cm [44]. The sheet density of positive fixed charges in SiO 2 near the SiO 2 /Si interface (Q F ) was fixed as 3 × 10 10 cm −2 , which has been reported for the present fabrication process [45]. The acceptor densities of the cathode, p-ring, and floating rings were 1 × 10 18 cm −3 , and the donor densities of the anode and ground rings were 1 × 10 19 cm −3 . The depths of the cathode, p-ring, anode, ground rings, and floating rings were all 1 µm.
Seven gates were considered in this study. Figure 1 shows that G a1 was the gap between the anode and the innermost gate, and G 12 , G 23 , G 34 , G 45 , G 56 and G 67 were the gaps between the gates, from the innermost to outermost. G 7p was the gap between the outermost gate and the p-ring. W 1 , W 2 , W 3 , W 4 , W 5 , W 6 and W 7 were the widths of the seven gates, from the innermost to outermost, respectively. The radii of the cathode (R c = 3 mm) and the GSDD chip (R chip = 3.5 mm) were fixed. As a result, the area inside the inner edge of the p-ring (S area ) was 18.9 mm 2 , which is nearly equal to that of commercial small-area SDDs. The same reverse bias voltage (V R ) was applied to the cathode, the p-ring, and all the gates.

0.5-mm-Thick GSDD Formed from a 10-kΩ·cm Si Wafer
The d Si and ρ Si of the n − Si substrate were 0.5 mm and 10 kΩ·cm, respectively, and d g was 0.75 µm. In Gate A, the values of W 1 , W 2 , W 3 , W 4 , W 5 , W 6 , and W 7 were 0.1, 0.1, 0.19, 0.29, 0.39, 0.47 and 0.51 mm, respectively. G a1 was 0.04 mm and G 12 and G 23 were both 0.03 mm. G 34 , G 45 , G 56 , G 67 and G 7p were all 0.05 mm. Figure 2 shows the simulated electric potential distribution in the Si substrate inside the p-ring of the GSDD at V R of −60 V for Gate A. The voltage midway between the p-ring and the cathode was −37 V, and the electric field along the electric potential valley was strong enough to make all the electrons produced by an X-ray photon flow smoothly to the anode. Therefore, the electrons produced within the radius of the inner edge of the p-ring can be directed to the anode, indicating that the effective active area is approximately 18 mm 2 . Figure 2. Simulated electric potential distribution in the Si substrate inside the p-ring of a 0.5-mm-thick GSDD with R chip of 3.5 mm and ρ Si of 10 kΩ·cm for Gate A. A reverse bias voltage of −60 V was applied to the cathode, p-ring, and seven gates. Q F was assumed to be 3 × 10 10 cm −2 . Equipotential lines are shown at 1 V intervals.
We fabricated GSDDs using the design of Gate A. In the GSDD, an energy resolution of 145 eV at 5.9 keV was obtained from a 55 Fe source at −38 o C [41]. The effective active area of the detector was found to be approximately 18 mm 2 by irradiating X-ray photons through a pinhole with diameter 0.1 mm [40], which is in good agreement with our simulation. These experimental results indicate that GSDDs with the design from which the simulated electric potential distribution similar to that in Figure 2 is obtained can work well.

0.5-mm-Thick GSDD Formed from a 2-kΩ·cm Si Wafer
The value of ρ Si was decreased from 10 kΩ·cm to 2 kΩ·cm. Figure 3 shows the simulated electric potential distribution in the Si substrate inside the p-ring of the GSDD with Gate A at V R of −60 V. Because the voltage drops at G 67 and G 7p were too large, the electric potential was almost zero between the anode and the outermost gate, and also over approximately 60% of the n − Si substrate, where the electrons produced by an X-ray photon are recombined with the holes produced by the X-ray photon. To deplete the whole n − Si substrate, V R was increased from −60 to −300 V, following the relation Figure 4 shows the simulated electric potential distribution in the Si substrate inside the p-ring of the GSDD with Gate A at V R of −300 V. It is clear from Figure 4 that the whole Si substrate was depleted, and all the electrons produced by an X-ray photon flowed smoothly to the anode. This finding indicates that GSDDs with Gate A can work well for any Si resistivity if V R follows Equation (1).
V R of −300 V was twice that of a commercial 0.5-mm-thick SDD using a 2-kΩ·cm Si wafer. Therefore, a gate pattern that can reduce V R was investigated. Because in Figure 3 the voltage decreases at G 67 and G 7p is too large, G 67 and G 7p in Gate B were decreased from 0.05 to 0.02 mm. The G 34 , G 45 and G 56 values were also decreased from 0.05 to 0.02 mm, and G 23 was decreased from 0.03 to 0.02 mm. The value of G a1 was increased from 0.04 to 0.07 mm, so that the potential at the innermost gate could be increased and the potential around the anode would not be zero. To keep R c in Gate B the same as R c in Gate A, the values of W 3 , W 4 , W 5 , W 6 and W 7 were changed to 0.21, 0.31, 0.41, 0.51 and 0.54 mm, respectively.   To reduce V R from 200 to 150 V, which is V R of commercial 0.5-mm-thick SDDs using 2-kΩ·cm Si wafers, in Gate C the values of G a1 , G 12 , G 23 , G 34 , G 45 , G 56 , G 67 and G 7p were changed to 0.11, 0.02, 0.01, 0.01, 0.01, 0.01, 0.005 and 0.005 mm, respectively. To keep R c in Gate C the same as R c in Gate A, the values of W 1 , W 2 , W 3 , W 4 , W 5 , W 6 and W 7 were 0.01, 0.05, 0.24, 0.34, 0.44, 0.54 and 0.60 mm, respectively. Figure 6 shows the simulated electric potential distribution in the Si substrate inside the p-ring of the GSDD for Gate C at V R of −150 V. In the electric potential distribution, the voltage midway between the p-ring and the cathode was approximately −78 V, and consequently the electric field along the electric potential valley strong enough to make all the electrons produced by the X-ray photons flow smoothly to the anode. Figure 6. Simulated electric potential distribution in the Si substrate inside the p-ring of a 0.5-mm-thick GSDD with R chip of 3.5 mm and ρ Si of 2 kΩ·cm for Gate C. A reverse bias voltage of −150 V was applied to the cathode, p-ring, and seven gates. Equipotential lines are shown at 2.5 V intervals.

1-mm-Thick GSDD Formed from a 2-kΩ·cm Si Wafer
To detect traces of hazardous or radioactive elements in food, soil, and the human body effectively, the absorption of X-ray fluorescence photons of these elements, such as Cd (23.1 keV) and Cs (30.8 keV), by GSDDs must be increased. However, the thickness of the Si substrates in commercial SDDs is approximately 0.5 mm; thus, the absorbed fractions of Cd and Cs X-ray fluorescence photons are 29.1% and 14.4%, respectively. In contrast, for a 1-mm-thick Si substrate, the absorbed fractions increase to 49.7% and 26.8%, respectively. In other words, the commercial SSDs up to 0.5 mm thick can detect photons with energies up to 27 keV for X-ray absorbance higher than 20%, whereas our gate pattern for the GSDD can detect photons with energies up to 35 keV. Here, we simulate the electric potential distribution in the GSDD with a Si thickness of 1 mm.
In the 1-mm-thick GSDDs, d g was changed from 0.75 to 3 µm to avoid SiO 2 breakdown caused by the high electric field. In Gate D, the values of G a1 , G 12 , G 23 , G 34 , G 45 , G 56 , G 67 and G 7p were changed to 0.33, 0.06, 0.02, 0.02, 0.02, 0.02, 0.01 and 0.01 mm, respectively. To keep R c in Gate D the same as R c in Gate A, the values of W 1 , W 2 , W 3 , W 4 , W 5 , W 6 and W 7 were changed to 0.02, 0.07, 0.18, 0.28, 0.38, 0.47 and 0.51 mm, respectively.
To deplete the whole n − Si substrate, the value of V R was increased from 150 to 600 V, following the relation V R ∝ d 2

Si
(2) Figure 7 shows the simulated electric potential distribution for Gate D in the Si substrate inside the p-ring of the GSDD at V R of −600 V. The voltage at the saddleback was approximately −175 V. Because the average electric field toward the anode along the electric potential valley was approximately 950 V/cm, the average electron drift velocity was higher than 1 × 10 6 cm/s at the operating temperature (≤0 • C). This was caused by the electron mobility of 1450 cm 2 · V −1 ·s −1 in the Si substrate at room temperature [44]. This indicates that the electric field along the electric potential valley was strong enough to make all the electrons produced by the X-ray photons flow smoothly to the anode.
For a Si pin diode with d Si of 1 mm and ρ Si of 2 kΩ·cm, a reverse bias of approximately −1500 V is required to deplete the whole Si layer. However, for the GSDD, a reverse bias of only −600 V was required, which is an advantage of GSDDs. Figure 7. Simulated electric potential distributions in the Si substrate inside the p-ring of a 1-mm-thick GSDD with R chip of 3.5 mm and ρ Si of 2 kΩ·cm for Gate D. A reverse bias voltage of −600 V was applied to the cathode, p-ring, and seven gates. Equipotential lines are shown at 10 V intervals.

Conclusions
GSDDs are inexpensive Si X-ray detectors because of their simple structure. Although we have investigated GSDDs with 10-kΩ·cm Si because we have designed thicker GSDDs to detect X-ray photons with high energies, 10-kΩ·cm Si wafers are much more expensive than 2-kΩ·cm Si wafers, from which commercial SDDs are fabricated. Therefore, GSDDs with 2-kΩ·cm Si were investigated to develop low-cost X-ray detectors that can accurately detect photon counts and energies of X-ray fluorescence photons with energies of up to 35 keV. Device simulations of GSDDs with 0.5and 1-mm-thick, 2-kΩ·cm Si substrates indicated that the X-ray detectors should work well when they are produced by using current fabrication processes. GSDDs with one gate pattern can work well for any resistivity Si substrate if the reverse bias is inversely proportional to the resistivity of the Si substrate. These findings indicate that the cost of portable X-ray fluorescence instruments can be reduced considerably.