CN111370527B - Equal-gap gradient increasing concentric circle type double-sided silicon drift detector and design method thereof - Google Patents
Equal-gap gradient increasing concentric circle type double-sided silicon drift detector and design method thereof Download PDFInfo
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Abstract
The invention discloses an equal-gap gradient increasing concentric circle type double-sided silicon drift detector and a design method thereof, wherein the equal-gap gradient increasing concentric circle type double-sided silicon drift detector comprises a silicon substrate, the upper surface of the silicon substrate is etched with a front concentric circle type circular cathode ring, the lower surface of the silicon substrate is etched with a back concentric circle type circular cathode ring, the front concentric circle type circular cathode ring and the back concentric circle type circular cathode ring are respectively composed of a plurality of circular cathode rings which are sleeved in sequence from inside to outside, the gaps of two adjacent circular cathode rings are equal, the intervals between the two adjacent circular cathode rings are sequentially increased in a gradient manner from inside to outside, and particularly the intervals between the two adjacent circular cathode rings are increased in a gradient manner of two thirds of the inner radius of the circular cathode ring positioned inside; and the structure and the size are the same, and a front anode electrode is etched in the first ring of the front concentric circular cathode ring. The problems of small area, large difficulty in splicing arrays and high cost of the conventional SDD unit are solved.
Description
Technical Field
The invention belongs to the technical field of pulsar X-ray detection, and relates to a design method of a concentric circle type cylindrical double-sided silicon drift detector with a large-area equal gap and a radius of which the gradient increases by two thirds.
Background
With the development of scientific technology, the development of semiconductor materials and process technology is rapid, the process of the traditional detector is more and more perfect, and new material semiconductor detectors are more and more brought into the field of vision of people. Among a large number of semiconductor detectors, silicon detectors are widely used in the fields of high-energy physics, nuclear physics, etc. because of their superior performance and sophisticated process technology. In the current research field of silicon detectors, the influence of parameters such as depletion voltage, capacitance, dark current, charge collection and the like on noise, energy consumption, energy resolution, collection efficiency and the like of the silicon detector is generally used as an index for evaluating whether the performance of the detector is superior. However, the existing SDD has different cathode spacing, so that the potential gradient is uneven, and electrons cannot smoothly drift to the cathode. And the large-area SDD array are required at present, the corresponding SDD unit area is increased, the difficulty of splicing the array can be reduced, and the splicing cost is reduced. However, the larger the area, the more difficult the design of the drift channel, and the more difficult it is to produce a large area SDD due to process limitations. Meanwhile, due to foreign technical blockade and the lack of domestic basic research, no research and development technology such as design and manufacture of large-area SDD (Silicon Drift Detector ) and arrays thereof exists in China at present.
Disclosure of Invention
The embodiment of the invention aims to provide an equal-gap gradient increasing concentric circle type double-sided silicon drift detector, which solves the problems that the prior SDD unit area is small, the difficulty in splicing the SDD unit into an SDD array is large and the cost is high, and the prior SDD electrons cannot smoothly drift to a cathode.
Another object of the embodiment of the invention is to provide a design method of an equal-gap gradient increasing concentric circle type double-sided silicon drift detector.
Aiming at the problems existing in the prior art, the technical scheme adopted by the embodiment of the invention is that the equal-gap gradient increasing concentric circle type double-sided silicon drift detector comprises a silicon substrate, wherein the upper surface of the silicon substrate is etched with a front concentric circle type circular cathode ring, the lower surface of the silicon substrate is etched with a back concentric circle type circular cathode ring, the front concentric circle type circular cathode ring and the back concentric circle type circular cathode ring are respectively composed of a plurality of circular cathode rings which are sleeved in sequence from inside to outside, and the gaps of two adjacent circular cathode rings in the front concentric circle type circular cathode ring and the back concentric circle type circular cathode ring are equal; the distance between two adjacent circular cathode rings in the front concentric circular cathode ring and the back concentric circular cathode ring is gradually increased from inside to outside in sequence; a front anode electrode is etched in the first ring of the front concentric circular cathode ring.
Further, the front concentric circular cathode ring and the back concentric circular cathode ring have the same structure and size.
Further, the inner radius of the first ring of the front concentric circular cathode ring and the inner radius of the first ring of the back concentric circular cathode ring are both r 1 The inner radius of the outermost ring of the front concentric circular cathode ring and the inner radius of the outermost ring of the back concentric circular cathode ring are both R;
the gaps between two adjacent rings in the front concentric circular cathode ring are equal to the gaps between two adjacent rings in the back concentric circular cathode ring.
Further, the distance between two adjacent circular cathode rings in the front concentric circular cathode ring and the back concentric circular cathode ring is gradually increased from inside to outside in a two-third square gradient of the inner radius of the circular cathode ring;
the front anode electrode is heavily doped N-type semiconductor silicon, the front concentric circular cathode ring and the back concentric circular cathode ring are heavily doped P-type semiconductor silicon, and the silicon substrate is lightly doped N-type semiconductor silicon;
the outermost ring of the front concentric circular cathode ring and the outermost ring of the back concentric circular cathode ring are provided with protection rings.
The other technical proposal adopted by the embodiment of the invention is that the design method of the equal-clearance gradient increasing concentric circle type double-sided silicon drift detector is that the radius r of the first ring of the positive concentric circle type circular cathode ring is according to the requirement 1 Voltage V E1 Radius R and voltage V of outermost ring of front concentric circular cathode ring out And the shape of the front concentric circular cathode ring, the current I and the sheet resistance ρ s And determining the width distribution, the surface electric field distribution and the drift electric field of the drift channels of the front concentric circular cathode ring and the back concentric circular cathode ring to obtain the equal-gap gradient increasing concentric circle type double-sided silicon drift detector meeting the design requirement.
Further, the specific steps are as follows:
step S1, according to the required shape, current I and square resistance rho of the positive concentric circular cathode ring s Determining the voltage distribution of a positive concentric circular cathode ring;
step S2, according to the required radius r of the first ring of the positive concentric circular cathode ring 1 Voltage V E1 Radius R and voltage V of outermost ring of positive concentric circular cathode ring out And determining a voltage distribution of the positive concentric circular cathode ring, determining a width of the positive concentric circular cathode ringDistribution and surface electric field distribution;
s3, determining the width distribution and the surface electric field distribution of the reverse concentric circular cathode ring according to the width distribution and the surface electric field distribution of the forward concentric circular cathode ring;
and S4, determining a drift electric field in the electron drift channel according to the determined width distribution and surface electric field distribution of the forward concentric circular cathode ring and the reverse concentric circular cathode ring.
Further, the specific implementation process of the step S1 is as follows:
the voltage difference DeltaV (r) between two adjacent concentric circular cathode rings at the radial r point is as follows, which is obtained by ohm's law and electric field integration:
ΔV(r)＝IR(r)＝E(r)P(r)； (1)
wherein E (R) is the surface electric field of the front concentric circular cathode ring at a radial R point, P (R) is the distance between two adjacent circular cathode rings of the concentric circular cathode ring at the radial R point, I is the current of the concentric circular cathode ring, and R (R) is the resistance of the concentric circular cathode ring at the radial R point;
p (r) is calculated from the following formula:
P(r)＝W(r)+G(r)； (2)
in the formula (2), W (r) is the width of the concentric circular cathode ring at a radial r point, and G (r) is the gap between two adjacent concentric circular cathode rings at the radial r point;
r (R) is calculated from the formula:
R(r)＝ρ s αr/W(r)； (3)
in the formula (3), α is determined by the geometry of the concentric circular cathode ring, and since the shape of the concentric circular cathode ring is circular, the circumference of the concentric circular cathode ring at the radial r point is αr, α=2pi.
Further, the specific implementation process of the step S2 is as follows:
step S21, keeping the gap between two adjacent concentric circular cathode rings constant G, and changing the formula (2):
P(r)＝W(r)+G； (4)
step S22, designing a distance P (r) between two adjacent circular cathode rings of the concentric circular cathode rings on the front surface at a radial r point as follows:
wherein eta is a real number, P 1 Is the distance between the first ring of the front concentric circular cathode ring and the adjacent ring;
step S23, according to formulas (4) and (5), the width distribution W (r) of the front concentric circular cathode ring is obtained as follows:
wherein g=kp 1 ，0＜K＜1；
Step S24, according to formulas (1) and (3), in combination with the geometry, current and surface electric field of the front concentric circular cathode ring, comprises:
ρ s αrI＝P(r)E(r)W(r)； (9)
and obtaining the corresponding surface electric field distribution of the front concentric circular cathode ring according to the formula (8) and the formula (9):
step S25, the surface potential distribution phi (r) of the front concentric circular cathode ring is as follows:
Φ(r)＝∫E(r)dr； (11)
substituting formula (10) into formula (11) has:
step S26, set up
Then P (r) =p 1 x，/>
Substituting it into formula (12) to obtain:
step S27, set up
m is an integer, and is obtained by substituting formula (13):
when r is taken to be r 1 When x=1, Φ (1) is the surface potential of the first ring of the front concentric circular cathode ring, Φ) 1 (=v E1 The method comprises the steps of carrying out a first treatment on the surface of the When R is taken as R, the R is taken as R,
is the surface potential of the outermost ring of the positive concentric circular cathode ring, namely
Step S28, setting m, simplifying (14), and then obtaining P under the current m by definite integration 1 And then G is obtained, the distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring at the radial r point is obtained through a formula (5), the width distribution W (r) of the front concentric circular cathode ring at the radial r point is obtained through a formula (8), and the surface electric field distribution E (r) of the front concentric circular cathode ring at the radial r point is obtained through a formula (10).
Further, in the step S28, m=3 is set, and the simplified formula (14) is obtained:
and then the fixed integral is obtained:
p when m=3 is calculated according to formula (17) 1 。
Further, the specific implementation process of the step S3 is as follows:
step S31, since the inner radius of the first ring of the back concentric circular cathode ring is the same as the inner radius of the first ring of the front concentric circular cathode ring, both are r 1 So that the distance P between two adjacent circular cathode rings at the radial r point B (r) is:
wherein P is 1 B Is the distance between the first ring of the reverse concentric circular cathode ring and the adjacent circular cathode ring;
step S32, because the gaps between two adjacent circular cathode rings in the back concentric circular cathode ring and the gaps between two adjacent circular cathode rings in the front concentric circular cathode ring are the same, and are constant G, the width W of the cathode rings in the radial direction r point B (r) is:
W B (r)＝P B (r)-G； (19)
in step S33, the voltage distribution of the back concentric circular cathode ring is determined by the voltage distribution of the front concentric circular cathode ring, so the potential ψ (r) of the back concentric circular cathode ring is set as:
Ψ(r)＝V B +γΦ(r)，0＜γ＜1； (20)
wherein V is B Is the voltage of the first ring of the reverse concentric circular cathode ring, namely V E1 Gamma is a proportional adjustment parameter, which is a constant;
step S34, obtaining the potential of the reverse concentric circular cathode ring according to the formula (12):
step S35, differentiating the obtained electric field distribution E of the reverse concentric circular cathode ring according to the formula (21) B (r) is:
step S36, setting P 1 B ＝P 1 Obtaining the distance P between two adjacent circular cathode rings of the concentric circular cathode rings on the reverse side at the radial r point through the method (18) B (r) deriving the width W of the reverse concentric circular cathode ring at the radial r point by equation (19) B (r) and obtaining the surface electric field distribution E of the reverse concentric circular cathode ring at the radial r point by the formula (22) B (r)；
In the step S4, a drift electric field E in the electron drift channel dr (r) is:
or alternatively
Wherein V is fd For the full depletion voltage, E (r) is determined by equation (10) and Φ (r) is determined by equation (12).
The embodiment of the invention has the beneficial effects that the large-area concentric cylindrical double-sided silicon drift detector and the design method thereof are provided, the cathode spacing of the SDD is increased gradually, so that the cell area of the SDD is increased, the splicing times are reduced under the condition of the same array area of the SDD, the splicing difficulty and the splicing cost are reduced, the cell area is increased, and the SDD performance is not affected. Solves the problems of small unit area, large array splicing difficulty and high cost of the international SDD. The cathode gaps are the same, so that the SDD potential is uniform, the electric field distribution is uniform, an optimal drift path can be obtained, an optimal drift channel is formed, and the problem that the existing SDD electrons cannot drift smoothly to the cathode is effectively solved. While achieving a soft X-ray high energy resolution of 2.0% @5.9keV override.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic structural diagram of an equal gap gradient increasing concentric circle type double-sided silicon drift detector according to an embodiment of the present invention.
FIG. 2 is a dimension definition diagram of a front concentric circular cathode ring of an equal gap gradient increasing concentric circle type double sided silicon drift detector according to an embodiment of the present invention.
Fig. 3 is a graph of possible and optimal path analysis for carrier drift in an SDD according to an embodiment of the invention.
In the figure, the anode electrode on the front surface, the circular cathode ring on the front surface, the first ring of the circular cathode ring on the front surface, the outermost ring of the circular cathode ring on the front surface, the silicon substrate, the circular cathode ring on the back surface, the circular cathode ring on the concentric circle on the back surface, the first ring of the circular cathode ring on the concentric circle on the back surface, the outermost ring of the circular cathode ring on the concentric circle on the back surface, and the outermost ring of the circular cathode ring on the circular circle on the back surface.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment provides a concentric circle type cylindrical double-sided silicon drift detector with large-area equal gap and increasing radius R in a two-thirds gradient manner, the structure is shown in figure 1, the detector comprises a silicon substrate 5, a front concentric circle type circular cathode ring 2 is etched on the upper surface of the silicon substrate 5, a back concentric circle type circular cathode ring 6 is etched on the lower surface of the silicon substrate 5, the front concentric circle type circular cathode ring 2 and the back concentric circle type circular cathode ring 6 are composed of a plurality of circular cathode rings which are sleeved in sequence from inside to outside, and the inner radius of the back concentric circle type circular cathode ring first ring 7 and the front concentric circle type circular cathode ring first ring 3 is R 1 The inner radius of the outermost ring 8 of the concentric circular cathode ring on the back and the outermost ring 4 of the concentric circular cathode ring on the front are both R, and in the concentric circular cathode ring 2 on the front and the concentric circular cathode ring 6 on the back, the gaps between the adjacent circular cathode rings are equal. The structure and the size of the front concentric circular cathode ring 2 and the back concentric circular cathode ring 6 are the same, the gap between two adjacent rings in the front concentric circular cathode ring 2 is equal to the gap between two adjacent rings in the back concentric circular cathode ring 6, the spacing between two adjacent rings in the front concentric circular cathode ring 2 and the back concentric circular cathode ring 6 gradually increases from inside to outside, and the front anode electrode 1 is etched in the first ring 3 of the front concentric circular cathode ring 2.
The front anode electrode 1 is heavily doped N-type semiconductor silicon, the front concentric circular cathode ring 2 and the back concentric circular cathode ring 6 are heavily doped P-type semiconductor silicon, and the silicon substrate 5 is lightly doped N-type semiconductor silicon, so that the PN junction is positioned at the cathode P-type semiconductor silicon, and the total depletion voltage is lower. The outermost ring 4 of the front concentric circular cathode ring and the outermost ring 8 of the back concentric circular cathode ring are provided with protection rings.
The design method of the concentric circle type cylindrical double-sided silicon drift detector with the equal gap gradient increasing comprises the following steps:
step S1, calculating the voltage distribution of the positive concentric circle type circular cathode ring 2:
the purpose of calculating the voltage distribution of the front concentric circular cathode ring 2 is to obtain its electric field distribution, which is determined by the front concentric circular cathode ring 2, which front concentric circular cathode ring 2 is formed by ion implantation.
The voltage difference DeltaV (r) between two adjacent concentric circular cathode rings at the radial r point is as follows, which is obtained by ohm's law and electric field integration:
ΔV(r)＝IR(r)＝E(r)P(r)； (1)
wherein E (R) is the surface electric field of the front concentric circular cathode ring 2 at a radial R point, P (R) is the distance between two adjacent circular cathode rings of the concentric circular cathode ring at the radial R point, I is the current of the concentric circular cathode ring, and R (R) is the resistance of the concentric circular cathode ring at the radial R point;
as shown in fig. 2, the width of the front concentric circular cathode ring 2 (ion implantation region) at the radial r point is W (r), i.e., W (r) defines the width of the front concentric circular cathode ring 2 at the radial r point. P (r) is the distance between two adjacent circular cathode rings of the front concentric circular cathode ring 2 at the radial r point, G (r) is the gap between two adjacent circular cathode rings of the front concentric circular cathode ring 2 at the radial r point, and then P (r) is calculated by the following formula:
P(r)＝W(r)+G(r)； (2)
in the formula (2), W (r) is the width of the concentric circular cathode ring at a radial r point, and G (r) is the gap between two adjacent concentric circular cathode rings at the radial r point;
the resistance R (R) of each ring of the front concentric circular cathode ring 2 varies with the variation of R, and R (R) is calculated from the following formula:
R(r)＝ρ s αr/W(r)； (3)
in the formula (3), α is determined by the geometry of the concentric circular cathode ring, and since the shape of the concentric circular cathode ring is circular, the circumference of the concentric circular cathode ring at the radial r point is αr, α=2pi.
Step S2, calculating the width distribution of the positive concentric circular cathode ring 2 to determine the cathode distribution of the SDD:
in step S21, for a special case of one front concentric circular cathode ring 2, that is, keeping the distance between two adjacent circular cathode rings constant G, equation (2) becomes:
P(r)＝W(r)+G； (4)
step S22, the present embodiment designs that the distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring 2 at the radial r point is:
wherein eta is a real number, P 1 Is the distance between the first ring 3 of the front concentric circular cathode ring and the adjacent ring;
step S23, according to formulas (4) and (5), the width distribution W (r) of the front concentric circular cathode ring 2 is obtained as follows:
wherein g=kp 1 K is more than 0 and less than 1, and in practical application, K can be more than 0.3 and less than 0.7.
Step S24, according to formulas (1) and (3), in combination with the geometry, current and surface electric field of the front concentric circular cathode ring 2, comprises:
ρ s αrI＝P(r)E(r)W(r)； (9)
and the corresponding surface electric field distribution of the front concentric circular cathode ring 2 is obtained according to the formula (8) and the formula (9):
step S25, a surface potential distribution Φ (r) of the front concentric circular cathode ring 2 is:
Φ(r)＝∫E(r)dr； (11)
substituting formula (10) into formula (11) has:
step S26, set up
Then P (r) =p 1 x，/>
Substituting it into formula (12) to obtain:
step S27, set up
m is an integer, and is obtained by substituting formula (13):
when r is taken to be r 1 When x=1, Φ (1) is the surface potential of the first ring 3 of the front concentric circular cathode ring, i.e., Φ (1) =v E1 The method comprises the steps of carrying out a first treatment on the surface of the When R is taken as R, the R is taken as R,
for the surface potential of the outermost ring 4 of the front concentric circular cathode ring, i.e
Step S28, setting a parameter m, simplifying (14), and then performing fixed integration to obtain P under the current m 1 。
In this embodiment, m=3 is set, that is, the distance between two adjacent circular cathode rings in the front concentric circular cathode ring 2 increases from inside to outside sequentially in a manner of two-thirds of the inner radius of the circular cathode ring located inside, and the formula (14) is simplified to obtain:
and then the fixed integral is obtained:
p when m=3 is calculated according to formula (17) 1 And then G is obtained, the distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring 2 at the radial r point is obtained through a formula (5), the width distribution W (r) of the front concentric circular cathode ring 2 at the radial r point is obtained through a formula (8), and the surface electric field distribution E (r) of the front concentric circular cathode ring 2 at the radial r point is obtained through a formula (10).
Step S3, determining the width distribution and the surface electric field distribution of the reverse concentric circular cathode ring 6 according to the width distribution and the surface electric field distribution of the forward concentric circular cathode ring 2;
step S31, since the inner radius of the first ring 7 of the back concentric circular cathode ring is the same as the inner radius of the first ring 3 of the front concentric circular cathode ring, both are r 1 So that the distance P between two adjacent circular cathode rings at the radial r point B (r) is:
wherein P is 1 B Is the distance between the first ring 7 of the reverse concentric circular cathode ring and the adjacent circular cathode ring;
step S32, since the gaps between two adjacent circular cathode rings in the back concentric circular cathode ring 6 and the gaps between two adjacent circular cathode rings in the front concentric circular cathode ring 2 are the same, and are constant G, the width W of the cathode rings at the radial r point is equal to the width W of the cathode rings at the front concentric circular cathode ring 2 B (r) is:
W B (r)＝P B (r)-G； (19)
in step S33, the voltage distribution of the back concentric circular cathode ring 6 is determined by the voltage distribution of the front concentric circular cathode ring 2, so the potential ψ (r) of the back concentric circular cathode ring 6 is set as:
Ψ(r)＝V B +γΦ(r)，0＜γ＜1； (20)
wherein V is B Is the voltage of the first ring 7 of the reverse concentric circular cathode ring, and gamma is a proportional adjustment parameter, which is a constant;
step S34, obtaining the potential of the back concentric circular cathode ring 6 according to formula (12) as follows:
step S35, since the radius of the first ring 3 of the back concentric circular cathode ring 6 is the same as the radius of the first ring 3 of the front concentric circular cathode ring 2, r is 1 Differentiating the formula (21) to obtain the electric field distribution E of the opposite concentric circular cathode ring 6 B (r) is:
Ψ(R)-Ψ(r 1 )＝γ(V out -V E1 )； (23)
wherein ψ (r) 1 ) Is the potential of the first ring 7 of the reverse concentric circular cathode ring, and ψ (R) is the potential of the outermost ring 8 of the reverse concentric circular cathode ring;
step S36, setting P 1 B ＝P 1 Obtaining the distance P between two adjacent circular cathode rings of the reverse concentric circular cathode ring 6 at the radial r point through the method (18) B (r) deriving the width W of the reverse concentric circular cathode ring 6 at the radial r point by equation (19) B (r) and obtaining the surface electric field distribution E of the reverse concentric circular cathode ring 6 at the radial r point by the formula (22) B (r)。
Step S4, determining a drift electric field in the electron drift channel according to the determined width distribution and surface electric field distribution of the positive concentric circular cathode ring 2 and the negative concentric circular cathode ring 6:
drift electric field E in electron drift channel dr (r) is:
or alternatively
Wherein V is fd The full depletion voltage can be obtained through calculation by simulation software; e (r) is determined by formula (10), and Φ (r) is determined by formula (12).
The parameters were calculated according to the above calculation methods (formulas (1) to (22)) and as follows: r=10000 μm, R 1 ＝200μm，K＝0.3，ρ s ＝2000Ω；I＝20×10 -6 A, radii R and R 1 K can be set arbitrarily in a selected range according to design requirements, ρ s And I is a fixed value; to form a more compact SDD array, α=2pi is set. Setting the voltage V of the first ring 3 of the positive concentric circular cathode ring 2 according to design requirements E1 Voltage V of outermost ring 4 of front concentric circular cathode ring 2 =10v out When=250v, Φ (1) =v E1 ＝10V，
Further, P when m=3 is obtained from equation (17) 1 26.48326 to obtain G, then obtaining the distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring 2 at the radial r point by the formula (5), obtaining the width distribution W (r) of the front concentric circular cathode ring 2 at the radial r point by the formula (8), obtaining the surface electric field distribution E (r) of the front concentric circular cathode ring 2 at the radial r point by the formula (10), and obtaining the surface electric field distribution E of the back concentric circular cathode ring 6 at the radial r point by the formula (22) B (r)。
To sum up, the SDD cell size and electric field distribution can be obtained, an equal gap with r spacing is obtained 2/3 Gradient increasing concentric circular double sided silicon drift detector. The design dimensional parameters of the detector and the drift electric field were derived, and the calculation of the drift electric field confirmed that the performance of the SDD unit area (circular shape with radius of 10000 μm) was not affected, as shown in Table 1.
Table 1 design dimensional parameters and drift electric field contrast data for detectors
| SDD index | SDD of the embodiment of the invention | German KETEK |
| Area of | >314mm 2 | Typical dimensions are 32-75mm 2 |
| Energy resolution | 2.0％@5.9keV | 2.5％@5.9keV |
| Price of | 0.29 ten thousand yuan/mm 2 | 0.44 ten thousand yuan/mm 2 |
| Array area | ≥0.36m 2 | --- |
The graph of possible and optimal path analysis for carrier drift in the SDD of an embodiment of the present invention is shown in FIG. 3, where S A Is the path with the shortest carrier drift time, namely the optimal path, S B Is a generalized optimum drift path (ideal path), S ⊥ Representing a vertical path S A ，S ∥ Representing parallel paths S A E represents an electric field, r θ The distance from the carrier to the center of the anode at a certain moment is shown, the ordinate x shows the thickness of the detector, S in the figure 1 、S 2 、r 1 、R、x 1 、x R 、x θ All are assumed values, and the purpose is to calculate the drift path by simulation software.
The foregoing description is only of the preferred embodiments of the present invention and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (10)
1. The equal-gap gradient increasing concentric circle type double-sided silicon drift detector is characterized by comprising a silicon substrate (5), wherein the upper surface of the silicon substrate (5) is etched with a front concentric circle type circular cathode ring (2), the lower surface of the silicon substrate (5) is etched with a back concentric circle type circular cathode ring (6), the front concentric circle type circular cathode ring (2) and the back concentric circle type circular cathode ring (6) are respectively composed of a plurality of circular cathode rings which are sequentially sleeved from inside to outside, and the gaps between two adjacent circular cathode rings in the front concentric circle type circular cathode ring (2) and the back concentric circle type circular cathode ring (6) are equal; the spacing between two adjacent circular cathode rings in the front concentric circular cathode ring (2) and the back concentric circular cathode ring (6) is gradually increased from inside to outside in sequence; a front anode electrode (1) is etched in the front concentric circular cathode ring first ring (3).
2. The equal gap gradient increasing concentric circle type double sided silicon drift detector as claimed in claim 1, characterized in that the front concentric circular cathode ring (2) and the back concentric circular cathode ring (6) are identical in structure and size.
3. The equal gap gradient increasing concentric circle type double sided silicon drift detector as claimed in claim 2, characterized in that the inner radius of the front concentric circle type circular cathode ring first ring (3) and the back concentric circle type circular cathode ring first ring (7) are both r 1 The inner radiuses of the outermost ring (4) of the front concentric circular cathode ring and the outermost ring (8) of the back concentric circular cathode ring are R;
the gaps between two adjacent rings in the front concentric circular cathode ring (2) are equal to the gaps between two adjacent rings in the back concentric circular cathode ring (6).
4. -an equi-gap gradient increasing concentric circle type double sided silicon drift detector according to any of claims 1-3, characterized in that the spacing between adjacent two circular cathode rings of the front concentric circular cathode ring (2) and the back concentric circular cathode ring (6) is sequentially increased from inside to outside with a two-third gradient of the inside circular cathode ring radius;
the front anode electrode (1) is heavily doped N-type semiconductor silicon, the front concentric circular cathode ring (2) and the back concentric circular cathode ring (6) are heavily doped P-type semiconductor silicon, and the silicon substrate (5) is lightly doped N-type semiconductor silicon;
the protection rings are arranged outside the outermost ring (4) of the front concentric circular cathode ring and the outermost ring (8) of the back concentric circular cathode ring.
5. The method for designing the equal-gap gradient increasing concentric circle type double-sided silicon drift detector as claimed in claim 3, characterized in that the radius r of the first ring (3) of the positive concentric circle type circular cathode ring is as required 1 Voltage V E1 Radius R and voltage V of the outermost ring (4) of the front concentric circular cathode ring out And the shape, current I and sheet resistance ρ of the front concentric circular cathode ring (2) s Determining a front concentric circle type circular cathode ring (2) and a back concentric circle type circularThe width distribution, the surface electric field distribution and the drift electric field of the drift channel of the cathode ring (6) are distributed to obtain the equal-gap gradient increasing concentric circle type double-sided silicon drift detector meeting the design requirement.
6. The method for designing an equal gap gradient increasing concentric circle type double-sided silicon drift detector according to claim 5, characterized by comprising the following specific steps:
step S1, according to the required shape, current I and square resistance rho of the positive concentric circular cathode ring (2) s Determining the voltage distribution of the positive concentric circular cathode ring (2);
step S2, according to the required radius r of the first ring (3) of the positive concentric circular cathode ring 1 Voltage V E1 Radius R and voltage V of the outermost ring (4) of the positive concentric circular cathode ring out The determined voltage distribution of the positive concentric circular cathode ring (2) is used for determining the width distribution and the surface electric field distribution of the positive concentric circular cathode ring (2);
s3, determining the width distribution and the surface electric field distribution of the reverse concentric circular cathode ring (6) according to the width distribution and the surface electric field distribution of the forward concentric circular cathode ring (2);
and S4, determining a drift electric field in the electron drift channel according to the determined width distribution and surface electric field distribution of the forward concentric circular cathode ring (2) and the reverse concentric circular cathode ring (6).
7. The method for designing an equal gap gradient increasing concentric circle type double-sided silicon drift detector according to claim 6, wherein the specific implementation process of the step S1 is as follows:
the voltage difference DeltaV (r) between two adjacent concentric circular cathode rings at the radial r point is as follows, which is obtained by ohm's law and electric field integration:
ΔV(r)＝IR(r)＝E(r)P(r)； (1)
wherein E (R) is the surface electric field of the front concentric circular cathode ring (2) at a radial R point, P (R) is the distance between two adjacent circular cathode rings of the concentric circular cathode ring at the radial R point, I is the current of the concentric circular cathode ring, and R (R) is the resistance of the concentric circular cathode ring at the radial R point;
p (r) is calculated from the following formula:
P(r)＝W(r)+G(r)； (2)
in the formula (2), W (r) is the width of the concentric circular cathode ring at a radial r point, and G (r) is the gap between two adjacent concentric circular cathode rings at the radial r point;
r (R) is calculated from the formula:
R(r)＝ρ s αr/W(r)； (3)
in the formula (3), α is determined by the geometry of the concentric circular cathode ring, and since the shape of the concentric circular cathode ring is circular, the circumference of the concentric circular cathode ring at the radial r point is αr, α=2pi.
8. The method for designing an equal gap gradient increasing concentric circle type double-sided silicon drift detector according to claim 7, wherein the specific implementation process of the step S2 is as follows:
step S21, keeping the gap between two adjacent concentric circular cathode rings constant G, and changing the formula (2):
P(r)＝W(r)+G； (4)
step S22, designing a distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring (2) at a radial r point as follows:
wherein eta is a real number, P 1 Is the distance between a first ring (3) of the front concentric circular cathode ring and a ring adjacent to the first ring;
step S23, according to formulas (4) and (5), the width distribution W (r) of the front concentric circular cathode ring (2) is obtained as follows:
wherein g=kp 1 ，0＜K＜1；
Step S24, according to formulae (1) and (3), in combination with the geometry, current and surface electric field of the front concentric circular cathode ring (2), has:
ρ s αrI＝P(r)E(r)W(r)； (9)
and the corresponding surface electric field distribution of the front concentric circular cathode ring (2) is obtained according to the formula (8) and the formula (9):
step S25, the surface potential distribution phi (r) of the front concentric circular cathode ring (2) is as follows:
Φ(r)＝∫E(r)dr； (11)
substituting formula (10) into formula (11) has:
step S26, set up
Then P (r) =p 1 x，/>
Substituting it into formula (12) to obtain:
step S27, set up
m is an integer, and is obtained by substituting formula (13):
when r is taken to be r 1 When x=1, Φ (1) is the surface potential of the first ring (3) of the front concentric circular cathode ring, i.e. Φ (1) =v E1 The method comprises the steps of carrying out a first treatment on the surface of the When R is taken as R, the R is taken as R,
is the surface potential of the outermost ring (4) of the positive concentric circular cathode ring, i.e
Step S28, setting m, simplifying (14), and then obtaining P under the current m by definite integration 1 And then G is obtained, the distance P (r) between two adjacent circular cathode rings of the front concentric circular cathode ring (2) at the radial r point is obtained through a formula (5), the width distribution W (r) of the front concentric circular cathode ring (2) at the radial r point is obtained through a formula (8), and the surface electric field distribution E (r) of the front concentric circular cathode ring (2) at the radial r point is obtained through a formula (10).
9. The method for designing an equal gap gradient increasing concentric circle type double sided silicon drift detector according to claim 8, wherein the step S28 sets m=3, and the simplified formula (14) is obtained by:
and then the fixed integral is obtained:
p when m=3 is calculated according to formula (17) 1 。
10. The method for designing an equal gap gradient increasing concentric circle type double-sided silicon drift detector according to claim 8 or 9, wherein the specific implementation process of the step S3 is as follows:
step S31, since the inner radius of the first ring (7) of the back concentric circular cathode ring is the same as the inner radius of the first ring (3) of the front concentric circular cathode ring, both are r 1 So that the distance P between two adjacent circular cathode rings at the radial r point B (r) is:
wherein P is 1 B Is the distance between the first ring (7) of the reverse concentric circular cathode ring and the circular cathode ring adjacent to the first ring;
step S32, because the gaps between two adjacent circular cathode rings in the back concentric circular cathode ring (6) and the gaps between two adjacent circular cathode rings in the front concentric circular cathode ring (2) are the same, and are constant G, the width W of the cathode rings at the radial r point is equal to the width W of the cathode rings at the front concentric circular cathode ring B (r) is:
W B (r)＝P B (r)-G； (19)
in step S33, the voltage distribution of the back concentric circular cathode ring (6) is determined by the voltage distribution of the front concentric circular cathode ring (2), so the potential ψ (r) of the back concentric circular cathode ring (6) is set as:
Ψ(r)＝V B +γΦ(r)，0＜γ＜1； (20)
wherein V is B Is the voltage V of the first ring (7) of the reverse concentric circular cathode ring E1 Gamma is a proportional adjustment parameter, which is a constant;
step S34, obtaining the potential of the reverse concentric circular cathode ring (6) according to the formula (12):
step S35, differentiating the obtained electric field distribution E of the reverse concentric circular cathode ring (6) by the formula (21) B (r) is:
step S36, setting P 1 B ＝P 1 Obtaining the distance P between two adjacent circular cathode rings of the reverse concentric circular cathode ring (6) at the radial r point by the formula (18) B (r) deriving the width W of the reverse concentric circular cathode ring (6) at the radial r point by the formula (19) B (r) and obtaining the surface electric field distribution E of the reverse concentric circular cathode ring (6) at the radial r point by the formula (22) B (r)；
In the step S4, a drift electric field E in the electron drift channel dr (r) is:
or alternatively
Wherein V is fd For the full depletion voltage, E (r) is determined by equation (10) and Φ (r) is determined by equation (12).
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| US3936687A (en) * | 1971-03-01 | 1976-02-03 | U.S. Philips Corporation | Photocathode with plurality of concentric conducting rings |
| CN108733953A (en) * | 2018-05-30 | 2018-11-02 | 湘潭大学 | The cylindrical two-sided silicon drifting detector (SDD) of large area helical form and its design method |
| CN108920758A (en) * | 2018-05-30 | 2018-11-30 | 李正 | The cylindrical two-sided silicon drifting detector (SDD) of large area concentric circles and its design method |
| CN110729382A (en) * | 2019-11-01 | 2020-01-24 | 湘潭大学 | Concentric ring type large-area silicon drift detector, design method and application |
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| US7968959B2 (en) * | 2008-10-17 | 2011-06-28 | The United States Of America As Represented By The Secretary Of The Navy | Methods and systems of thick semiconductor drift detector fabrication |
| US8421172B2 (en) * | 2009-07-16 | 2013-04-16 | Canberra Industries, Inc. | Simplified silicon drift detector and wraparound neutron detector |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US3936687A (en) * | 1971-03-01 | 1976-02-03 | U.S. Philips Corporation | Photocathode with plurality of concentric conducting rings |
| CN108733953A (en) * | 2018-05-30 | 2018-11-02 | 湘潭大学 | The cylindrical two-sided silicon drifting detector (SDD) of large area helical form and its design method |
| CN108920758A (en) * | 2018-05-30 | 2018-11-30 | 李正 | The cylindrical two-sided silicon drifting detector (SDD) of large area concentric circles and its design method |
| CN110729382A (en) * | 2019-11-01 | 2020-01-24 | 湘潭大学 | Concentric ring type large-area silicon drift detector, design method and application |
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