A high-precision hexagonal spiral silicon drift detector
By using Taylor expansion to perform first- and second-order approximate calculations of the spiral ring of the silicon drift detector, the problem of inaccurate spiral ring radius calculation is solved, improving the detector's accuracy and electric field distribution uniformity, and enhancing its electrical characteristics and flexibility.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- LUDONG UNIVERSITY
- Filing Date
- 2022-08-15
- Publication Date
- 2026-06-23
AI Technical Summary
In existing silicon drift detectors, the radius of the spiral ring is usually calculated using a first-order approximation, which cannot obtain a more accurate value, thus affecting the detector's accuracy and electric field distribution.
Taylor expansion method is used to perform first-order and second-order approximation calculations on the radius of the spiral ring. Combined with relevant formulas, the distribution of the spiral ring is optimized to improve accuracy. The radius and number of turns are obtained through second-order approximation calculation.
This achieves a more precise spiral ring distribution, reduces detector capacitance, improves energy resolution and electric field uniformity, reduces noise, and enhances detector flexibility and electrical characteristics.
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Figure CN115548158B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor detection technology, specifically a high-precision hexagonal spiral silicon drift detector. Background Technology
[0002] Silicon drift detectors, based on planar fabrication techniques and using lightly doped N-type ultrapure high-resistivity silicon as the substrate, utilize the principle of lateral depletion. Compared to traditional silicon detectors and photodiode detectors, they offer numerous performance advantages, most notably low capacitance, low noise, fast response time, high sensitivity, high energy and position resolution, wide linear range, and ease of integration. They are primarily used in high-energy physics, aerospace, and pulsar navigation, and their applications are increasingly prevalent in nuclear medicine, including various medical imaging technologies such as computed tomography (CT), fluoroscopy, magnetic resonance imaging (MRI), ultrasound imaging, and computed radiography (CR). Compared to other types of detectors, the fabrication technology of silicon drift detectors has matured, and they maintain outstanding performance during operation, meeting the needs of a growing number of practical applications, leading to their widespread adoption.
[0003] Currently, silicon drift detectors are generally manufactured in three shapes: quadrilateral, hexagonal, and circular. Helical ring silicon drift detectors can be designed circularly, offering the best symmetry and electrical characteristics as individual detector units. However, when arranged in an array, there are large dead zones between detector units, resulting in significant material waste and increased costs. They can also be designed squarely; while not as good in terms of electrical characteristics and symmetry as circular, the resulting array has virtually no dead zones. Hexagonal designs are easier to install and offer better symmetry than quadrilateral designs, resulting in better electrical characteristics, and the unit electric field is closest to that of a circle. Compared to traditional pixel detectors, they have lower leakage current and capacitance, lower noise, and higher energy resolution. With current technology, pixels can be made at the micro-nano level, achieving very high positional resolution. The detector allows for flexible voltage settings and automatic voltage division, and the helical ring design provides sufficient space for the electrode to serve as a readout electrode or to apply a bias voltage.
[0004] However, one problem that has been waiting to be solved in existing silicon drift detectors is the greater accuracy of the number of helical loops, that is, the precise calculation of the radius of the helical loops. Summary of the Invention
[0005] The purpose of this invention is to provide a high-precision hexagonal spiral silicon drift detector to solve the problem mentioned in the background art that the radius of the traditional spiral ring is usually obtained by a first-order approximation, which cannot obtain a more accurate value.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a high-precision hexagonal spiral silicon drift detector, comprising a substrate with an outermost boundary ring at its edge, a P-type heavily doped cathode on the back surface of the substrate, an N-type heavily doped anode at the center of the front surface of the substrate, and a P-type heavily doped cathode ring surrounding the N-type heavily doped anode, wherein a hexagonal P-type heavily doped spiral ring is provided between the cathode ring and the outermost boundary ring, characterized in that the radius of the P-type heavily doped spiral ring is approximately calculated as follows:
[0007] Formula for radius Performing a Taylor expansion, we obtain the following expansion:
[0008]
[0009] The first-order approximation yields:
[0010]
[0011] In the formula, r is the radius, r1 is the initial radius of the spiral ring, and r (1) p1 is the radius obtained by first-order approximation; p1 is the initial interval. The angle is the angle between the line connecting the origin and the point in question and the positive direction of the coordinate axis.
[0012] Preferably, the radius of the heavily doped p-type spiral ring is obtained by combining the first-order approximation formula with a second-order approximation calculation:
[0013]
[0014] In the formula, r (2) The radius is obtained by the second-order approximation; β is a constant less than 1.
[0015] Preferably, the formula for calculating the coordinates of each point on the inner ring of the P-type heavily doped spiral ring is as follows:
[0016]
[0017] The formula for calculating the coordinates of each point on the outer ring of the P-type heavily doped spiral ring plus the ring width is as follows:
[0018]
[0019] Preferably, if the ratio of the difference between the number of revolutions calculated by the second order and the number of revolutions calculated by the first order to the number of revolutions calculated by the second order exceeds 5%, then a higher-order Taylor expansion calculation is performed until the difference is within 5%.
[0020] Preferably, the substrate is N-type lightly doped ultrapure high-resistivity silicon, and the N-type heavily doped anode is located at the axis of the substrate.
[0021] Preferably, a gap is left between the outer side of the P-type heavily doped cathode ring and the P-type heavily doped spiral ring.
[0022] Preferably, the innermost electrode contact point is provided at one end of the P-type heavily doped spiral ring, and the outermost electrode contact point is provided at one end of the P-type heavily doped spiral ring. The outer side of the P-type heavily doped spiral ring is connected to the outermost boundary ring.
[0023] Preferably, the upper surface of the N-type heavily doped anode of the substrate is covered with an anode aluminum electrode contact layer, the cathode ring is covered with an upper surface cathode aluminum electrode contact layer, the interring gap of the P-type heavily doped spiral ring is covered with a silicon dioxide layer, and the lower surface of the substrate is covered with a lower surface cathode aluminum electrode contact layer.
[0024] Preferably, the beginning and end of the P-type heavily doped spiral ring are covered with a cathode aluminum electrode contact layer.
[0025] Preferably, the back side of the substrate is also provided with a P-type heavily doped spiral ring, and the P-type heavily doped spiral rings on the front and back sides are symmetrical with respect to the substrate.
[0026] Compared with the prior art, the beneficial effects of the present invention are:
[0027] 1. The detector in this invention is hexagonal. Although it is not as good as a circle in terms of electrical characteristics and symmetry, the biggest advantage is that the array has no dead zones. The hexagonal design facilitates splicing and is closer to a circle than a quadrilateral design, resulting in better symmetry and therefore better electrical characteristics. Its unit electric field distribution is also the closest to a circular electric field distribution.
[0028] 2. In this invention, the radius and spiral ring distribution obtained by the second-order approximation based on relevant formulas are more accurate than those obtained by the first-order approximation. Therefore, the potential and electric field distribution are closer to the design requirements. The actual number of turns is calculated more accurately.
[0029] 3. In this invention, the anode electrode area of the spiral silicon drift detector is much smaller than the entire detector area, resulting in a very small capacitance, thus leading to low noise and high energy resolution. The pressure application method can be flexibly set; the spiral ring design allows the detector to achieve flexible bias settings with a minimal number of pressure electrodes. Attached Figure Description
[0030] Figure 1 This is an overall structural diagram of the hexagonal spiral silicon drift detector of the present invention;
[0031] Figure 2 This is a cross-sectional view along the X-axis of the hexagonal spiral silicon drift detector of the present invention;
[0032] Figure 3This is an enlarged view of the upper surface of the cross-sectional view along the X-axis of the hexagonal spiral silicon drift detector of the present invention;
[0033] Figure 4 This is an enlarged view of the lower surface of the cross-section along the X-axis of the hexagonal spiral silicon drift detector of the present invention;
[0034] Figure 5 This is a simulation diagram of the potential distribution of the hexagonal spiral silicon drift detector of the present invention under depletion voltage;
[0035] Figure 6 This is a simulation diagram of the electric field distribution of the hexagonal spiral silicon drift detector of the present invention under depletion voltage;
[0036] Figure 7 This is a simulation diagram of the electron concentration distribution of the hexagonal spiral silicon drift detector of the present invention under depletion voltage;
[0037] Figure 8 This is a diagram showing the structural parameters of the hexagonal spiral silicon drift detector of the present invention.
[0038] In the picture:
[0039] 1. N-type heavily doped anode; 2. P-type heavily doped cathode ring; 3. P-type heavily doped spiral ring; 4. Innermost electrode contact point; 5. Outermost electrode contact point; 6. Outermost boundary ring; 7. Lower surface P-type heavily doped cathode; 8. Substrate; 9. Anode aluminum electrode contact layer; 10. Silica layer; 11. Lower surface cathode aluminum electrode contact layer; 12. Upper surface cathode aluminum electrode contact layer. Detailed Implementation
[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0041] Silicon detectors operate under reverse bias. First, majority carrier diffusion occurs. Acceptor impurity ions provide holes, which diffuse towards donor impurity ions, forming negatively charged centers. Donor impurity ions provide electrons, which diffuse towards acceptor impurity ions, forming positively charged centers. This creates a space charge region, or depletion layer, forming an internal electric field. As diffusion continues, the space charge region widens, and the internal electric field strengthens, thus hindering further diffusion. Next, due to the internal electric field, minority carriers drift, narrowing the space charge region and weakening the internal electric field. Finally, in the absence of an external electric field or other excitation, the number of majority carriers participating in diffusion and the number of minority carriers participating in drift reach a dynamic equilibrium, forming a PN junction. When an external particle enters the sensitive region inside the detector, an electron-hole pair is generated under the applied voltage. The positive electrode collects electrons that drift to the positive electrode, while holes move towards the negative electrode and are collected there. The resulting electrical signal, reflecting the particle information, is then output to the external circuitry.
[0042] Compared to other types of detectors, silicon drift detectors have matured in manufacturing technology and maintain outstanding performance during operation, meeting the needs of an increasing number of practical applications. This has led to their widespread use. The spiral drift ring can generate a transverse drift electric field and replace an external voltage divider. It eliminates the need for voltage dividers between the drift rings; a voltage is applied to the beginning and end of the spiral ring, allowing it to autonomously divide the voltage, reducing manufacturing steps. By adjusting the applied voltage, the drift electric field distribution of the detector can be made uniform, shortening the drift time and ensuring that more charge carriers drift laterally to the anode under the influence of the drift electric field, thus improving the charge energy resolution.
[0043] Reference Figure 1-8 As shown in the example, this application proposes a high-precision hexagonal spiral silicon drift detector, using a hexagonal detector unit as an example. The approximate three-dimensional model of the detector is as follows. Figure 1 As shown.
[0044] The following description uses a detector with specific parameters as an example. It includes a substrate 8 with an outermost boundary ring 6 at its edge. The back of the substrate 8 has a P-type heavily doped cathode 7 on its lower surface. The front of the substrate 8 has an N-type heavily doped anode 1 at its center, and a P-type heavily doped cathode ring 2 surrounding the N-type heavily doped anode 1. A hexagonal P-type heavily doped spiral ring 3 is located between the cathode ring 2 and the outermost boundary ring 6. The substrate 8 is made of lightly doped N-type ultrapure high-resistivity silicon with a doping concentration of 4 × 10⁻⁶. 11 / cm 3 The central anode 1 is heavily N-type doped and located at the axis of the substrate 8, with a doping concentration of 1×10⁻⁶. 19 / cm 3 The doping depth is 1 μm, and the surface is covered with an anode aluminum electrode contact layer 9.
[0045] The entire silicon substrate 8 has a thickness of 300 μm and a radius of 2155.45 μm. The closest point to the N-type heavily doped anode 1, at a distance of 20 μm, is the P-type heavily doped cathode ring 2, with a ring width of 40 μm, an inner diameter of 140 μm, and an outer diameter of 180 μm. The P-type heavily doped cathode ring 2 is P-type heavily doped with a doping concentration of 1 × 10⁻⁶. 19 / cm 3 The doping depth is 1μm, and the surface is covered with an upper surface cathode aluminum electrode contact layer 12.
[0046] A p-type heavily doped spiral ring 3 surrounds the p-type heavily doped cathode ring 2. The p-type heavily doped spiral ring 3 and the p-type heavily doped cathode ring 2 are not in contact but are separated by a gap. The closest distance between the p-type heavily doped cathode ring 2 and the first spiral ring is 20 μm. Outside the p-type heavily doped spiral ring 3 is a closed regular hexagonal outermost boundary ring 6 that is in contact with the spiral ring. The inner diameter is 2095.4457 μm and the outer diameter is 2155.4457 μm. This is to ensure boundary conditions and reduce boundary effects. The gaps between the p-type heavily doped spiral ring 3 are covered with a silicon dioxide layer 10, that is, SiO2 is covered in the area on the top surface where there is no electrode contact layer to prevent the silicon substrate from oxidizing in the air.
[0047] The P-type heavily doped spiral ring 3 automatically divides the voltage, acting as a voltage divider to evenly distribute the voltage from the first ring to the last. Therefore, this invention applies voltage to a section at both the beginning and end of the spiral ring; that is, both the beginning and end of the P-type heavily doped spiral ring 3 are covered with a cathode aluminum electrode contact layer. The thickness of the aluminum electrode contact layer on both the upper and lower surfaces of the silicon detector is 1 μm, and the thickness of the SiO2 layer on the upper surface is 0.5 μm.
[0048] The entire hexagonal bottom cathode is heavily P-type doped with a doping concentration of 1×10⁻⁶. 19 / cm 3 The doping depth is 1 μm, and the surface is covered with a cathode aluminum electrode contact layer 11.
[0049] We use the radius formula Performing a Taylor expansion, we obtain the following expansion:
[0050]
[0051] The first-order approximation of the radius of the heavily doped p-type spiral ring 3 yields the following:
[0052]
[0053] In the formula, r is the radius, r1 is the initial radius of the spiral ring, and r (1) p1 is the radius obtained by first-order approximation; p1 is the initial interval. Let w(r) be the angle, which is the angle between the line connecting the origin and the point in question and the positive direction of the coordinate axis. The width w(r) of the spiral ring gradually increases as the ring spacing p(r) increases. As p(r) changes, w(r) also changes continuously.
[0054] Furthermore, this invention aims to draw the spiral loop more accurately, obtain more precise values, and further perform Taylor expansion. By combining the first-order approximation formula of the radius with the second-order approximation formula of the radius, the point coordinates can be calculated, thereby more accurately obtaining the final number of loops to obtain the structure.
[0055] The second-order approximation of the radius yields:
[0056]
[0057] In the formula, r (2) The radius is obtained by the second-order approximation; β is a constant less than 1, such as 0.8 or 0.5.
[0058] The coordinates of each point on the inner ring of the P-type heavily doped spiral ring (3) are further calculated using the following formulas:
[0059]
[0060] The formula for calculating the coordinates of each point on the outer ring of the P-type heavily doped spiral ring (3) with increased ring width is as follows:
[0061]
[0062] The structural diagram can be drawn based on the coordinates of each point in the spiral ring. Generally, after second-order calculation, the accuracy of the coordinates and number of turns of the spiral ring can basically meet the requirements, and the performance of the detector is basically no different from that obtained by further improving the accuracy through higher-order calculations. Through experimental testing, it can be concluded that if the difference between the number of turns obtained by the current-order calculation and the number of turns obtained by the previous-order calculation (the ratio of the difference between the number of turns obtained by the two-order calculations to the number of turns obtained by the current-order calculation) is within 5%, the calculation accuracy is considered to meet the requirements, and there is no need to continue with higher-order Taylor expansion calculations. If the difference exceeds 5%, then third-order, fourth-order, and so on calculations are performed until the difference is within 5%.
[0063] Based on the specific substrate dimensions mentioned above, the number of turns of the hexagonal spiral silicon drift detector is 16.31907668 according to first-order calculation, and 16.9184099 according to second-order calculation, with a difference of 3.5%, which is less than 5%. Simulation tests were then conducted on the detector with the obtained specific structure, and the test results were obtained. Figures 5-7 It can be seen that the electric potential and electric field distribution of the spiral ring calculated in the second order are uniform, and the electron channel is close to a plane, which is closer to the design requirements and can achieve the ideal design effect.
[0064] The back side of the substrate 8 can be entirely a cathode, or it can be provided with a P-type heavily doped spiral ring 3. The P-type heavily doped spiral ring 3 on the front and back sides are symmetrical with respect to the substrate 8 to achieve a better distribution of electric field and electron concentration.
[0065] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A high-precision hexagonal spiral silicon drift detector, comprising a substrate (8) with an outermost boundary ring (6) at its edge, a P-type heavily doped cathode (7) on the back side of the substrate (8), an N-type heavily doped anode (1) and a P-type heavily doped cathode ring (2) surrounding the N-type heavily doped anode (1) at the center of the front side of the substrate (8), and a hexagonal P-type heavily doped spiral ring (3) between the cathode ring (2) and the outermost boundary ring (6), characterized in that, The first-order approximation of the radius of the heavily doped P-type spiral ring (3) is as follows: Formula for radius Performing a Taylor expansion, we obtain the following expansion: The first-order approximation yields: In the formula, r is the radius, r1 is the initial radius of the spiral ring, and r (1) p1 is the radius obtained by first-order approximation; p1 is the initial interval. The angle is the angle between the line connecting the origin and the point in question and the positive direction of the coordinate axis.
2. The high-precision hexagonal spiral silicon drift detector according to claim 1, characterized in that: It also includes a second-order approximation calculation of the radius of the p-type heavily doped spiral ring (3) using a first-order approximation formula: In the formula, r (2) The radius is obtained by the second-order approximation; β is a constant less than 1.
3. The high-precision hexagonal spiral silicon drift detector according to claim 2, characterized in that: The formulas for calculating the coordinates of each point on the inner ring of the P-type heavily doped spiral ring (3) are as follows: The formula for calculating the coordinates of each point on the outer ring of the P-type heavily doped spiral ring (3) with increased ring width is as follows:
4. The high-precision hexagonal spiral silicon drift detector according to claim 3, characterized in that: If the difference between the number of revolutions calculated by the second order and the number of revolutions calculated by the first order exceeds 5% in ratio to the number of revolutions calculated by the second order, then a higher-order Taylor expansion is performed until the difference is within 5%.
5. The high-precision hexagonal spiral silicon drift detector according to claim 4, characterized in that: The substrate (8) is N-type lightly doped ultrapure high-resistivity silicon, and the N-type heavily doped anode (1) is located at the axis of the substrate (8).
6. The high-precision hexagonal spiral silicon drift detector according to claim 5, characterized in that: A gap is left between the outer side of the P-type heavily doped cathode ring (2) and the P-type heavily doped spiral ring (3).
7. The high-precision hexagonal spiral silicon drift detector according to claim 6, characterized in that: The innermost electrode contact point (4) is provided at one end of the P-type heavily doped spiral ring (3), and the outermost electrode contact point (5) is provided at one end of the outer side of the P-type heavily doped spiral ring (3). The outer side of the P-type heavily doped spiral ring (3) is connected to the outermost boundary ring (6).
8. The high-precision hexagonal spiral silicon drift detector according to claim 7, characterized in that: The upper surface of the N-type heavily doped anode (1) of the substrate (8) is covered with an anode aluminum electrode contact layer (9), the cathode ring (2) is covered with an upper surface cathode aluminum electrode contact layer (12), the interring gap of the P-type heavily doped spiral ring (3) is covered with a silicon dioxide layer (10), and the lower surface of the substrate (8) is covered with a lower surface cathode aluminum electrode contact layer (11).
9. The high-precision hexagonal spiral silicon drift detector according to claim 8, characterized in that: The beginning and end of the P-type heavily doped spiral ring (3) are covered with a cathode aluminum electrode contact layer.
10. The high-precision hexagonal spiral silicon drift detector according to any one of claims 1 to 7, characterized in that: The back side of the substrate (8) is also provided with a P-type heavily doped spiral ring (3), and the P-type heavily doped spiral ring (3) on the front and back sides is symmetrical with respect to the substrate (8).