CN116741845A - Equal-clearance spiral ring large-area silicon drift detector with controllable clearance gap - Google Patents
Equal-clearance spiral ring large-area silicon drift detector with controllable clearance gap Download PDFInfo
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Abstract
The invention discloses an equal-gap spiral ring large-area silicon drift detector with controllable gap, which comprises a front anode (1), a front spiral ring electrode (2), a back spiral ring electrode (3) and a silicon substrate (4). In the design of the invention, the pitch (5) of the spiral rings is P (r), the width (6) of the spiral rings is W (r), and the gap (7) of the spiral rings is G (r), wherein P (r) =W (r) +G (r). In the present design, the first ring pitch (8) of the spiral ring is P 1 Controlled by parameters m and k, the pitch P (r) and the gap G (r) both pass through the first ring pitch P 1 Calculated, the spiral gaps G (r) and P 1 The relation of (2) is: g (r) =kp 1 (0 < k < 1), the relationship between the pitch P (r) and r is:(m is a real number), and the gap G (r) is a fixed value. The invention relates to an equal-clearance spiral ring with controllable clearanceThe area silicon drift detector can control the gap width of the detector to reduce the surface leakage current, improve the resolution of the detector, and in addition, the design of the gap with controllable spacing also solves the problems that the size of the detector is increased, the spacing and the gap are widened in the past cathode ring design, and a larger ineffective area is formed.
Description
Technical Field
The invention relates to the technical field of detectors, in particular to an equal-clearance spiral ring large-area silicon drift detector with a controllable clearance.
Background
The silicon drift detector (Silicon Drift Detector, SDD for short) is one of semiconductor detectors, is used for detecting X-rays, has the outstanding advantages of high counting rate, high energy resolution, capability of working at normal temperature and the like compared with other detectors, and is widely applied to the fields of aerospace, civilian use, medical treatment and the like. International research on SDD is proceeding toward low noise, low power consumption, high energy resolution, and large area. The large area SDD has a higher count rate and can detect data more accurately at a shorter acquisition time. In particular to the aerospace field, the large-area SDD is taken as a core component of the pulsar navigator, is a subversion concept and is a great strategic requirement of the country. The X-ray detector is the 'eye' of the pulsar navigation system and is responsible for collecting X-ray photons emitted by the pulsar, recording the arrival time of the photons and restoring the pulse profile. Because the radiation flux of pulsar X-ray is very low, the energy is concentrated in 1-10 keV, and the intensity is rapidly attenuated along with the increase of the energy, so that the detection difficulty is high.
However, in order to realize autonomous navigation of a spacecraft by detecting pulsar X-ray particles in deep space, a large-area and high-energy-resolution X-ray detector needs to be developed so as to meet the important technical requirements of high performance, large-area coverage and high availability of an X-ray pulsar autonomous navigation time service system.
Disclosure of Invention
1. Technical problem to be solved
The invention aims to solve the problems that the gap is wider and wider due to the fact that the size of the area of a detector is larger, a larger invalid area of the detector is formed, fixed charges exist in the gap, leakage current of the detector is increased due to the increase of the gap, and resolution of the detector is reduced in the prior art, and provides an equal-gap spiral ring large-area silicon drift detector with controllable gap.
2. Technical proposal
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the utility model provides a controllable interval clearance's equidistant spiral ring large tracts of land silicon drift detector, includes positive electrode, positive spiral ring electrode, back spiral ring electrode and silicon substrate, positive spiral ring electrode encircles the outside that sets up in positive electrode, back spiral ring electrode sets up in the back of positive spiral ring electrode, silicon substrate encircles the outside that sets up in positive spiral ring electrode.
Preferably, the front anode electrode has a doping concentration of 1×10 19 /cm 3 Is heavily doped with N-type.
Preferably, the doping concentration of the front spiral ring electrode is 1×10 19 /cm 3 The shape of the P-type heavy doping is a regular hexagonal spiral ring.
Preferably, the back spiral ring electrode has a doping concentration of 1×10 19 /cm 3 The shape of the P-type heavy doping is a regular hexagonal spiral ring.
Preferably, the silicon substrate has a doping concentration of 4×10 11 /cm 3 The shape of the N-type light doping is regular hexagon.
The invention also provides a design method of the equal-clearance spiral ring large-area silicon drift detector with controllable clearance, which is characterized by comprising the following steps:
step 1: calculating the surface electric field distribution of the silicon drift detector;
step 2: calculating the width distribution of the spiral cathode of the silicon drift detector;
step 3: calculating the relation between the rotation angle and the radius of the spiral ring;
step 4: determining the potential distribution of the front and back of the silicon drift detector;
step 5: the spiral ring design of the rear surface of the silicon drift detector is determined.
Preferably, the voltage distribution in step 1 is provided by a heavily doped P-type cathode having a spiral shape, the P-type heavily doped cathode is formed by ion implantation, at a radial r point, 1 is a pitch P (r) of adjacent cathode spiral rings, 2 is a width W (r) of an ion implantation region at the radial r point, which defines a width of the spiral cathode in the radial r, and 3 is a pitch G (r) of adjacent implantation regions, and the pitch of the spiral rings is:
P(r)＝W(r)+G(r) (1)
ρ S the square resistance of the spiral ring cathode ion implantation area is that the ion implantation depth is t, t is a constant and does not change along with the change of r, and ρ is the resistivity of the P-type heavily doped cathode;
ρ/t＝ρ S (2)
the resistance (R)) of each turn of the spiral cathode also varies with R:
R(r)＝ρ S αr/W(r) (3)
ρ S is the sheet resistance of the spiral ring cathode ion implantation layer, alpha is determined by the geometry of the cylindrical spiral cathode, and the circumference of one circle is equal toIf the spiral shape is truly circular, α=2pi; to form a more compact SDD array, the spiral shape may be chosen to be nearly circular, such as regular hexagonal (α=6), or square +.>
The voltage difference Δv (r) between adjacent spiral cathode rings at the radial r point is:
ΔV(r)＝IR(r)＝E(r)P(r) (4)
IR (r) is derived from ohm's law and E (r) P (r) is derived from electric field integration; where I is the current of the spiral ring cathode and E (r) is the surface electric field at the radius r point.
Equation (3) and equation (4) relate the geometry of the cathode ring and the current to the SDD surface electric field:
preferably, in the specific case of one cathode ring in the step 2, that is, the cathode gap per ring is kept unchanged, G is a constant, and equation (1) becomes:
P(r)＝W(r)+G (6)
the relationship between the pitch P (r) and r in the design is:
wherein P is 1 Is the first helical pitch, r 1 Is the radius of the first turn thereof;
in design, pitch of the spirals G and P 1 The relation of (2) is:
G＝kP 1 (0＜k＜1) (8)
in practical applications, k may be selected to be 0.3< k <0.7;
width distribution of spiral-shaped cathodes for silicon drift detectors
W(r)＝P(r)-G (9)
Preferably, the radius of each revolution of the spiral ring in the step 3 is from r n-1 Increased to r n And (3) obtaining theta as a formula of a rotation angle of the spiral ring:
θ is the angle of each rotation, e.g. increase for each point of rotation when squareIncrease +/for every point of rotation of θ for hexagonal shape>
Substituting equation (7) into equation (10) can calculate the relationship between the rotation angle θ (r) of the spiral ring and the radius, and the corresponding rotation angle of the spiral ring is
Simplifying to obtain the relationship between the rotation angle of the spiral ring and the adjacent point of the spiral ring
Preferably, in the step 4, the corresponding surface electric field distribution is obtained according to equation (5):
the surface potential profile is determined by the following equation:
substituting the formula (13) into the formula (14) to obtain:
substituting equation (7) into equation (15), letObtain P (r) =P 1 x，dr＝mr 1 x m-1 dx, substituting equation (15) to obtain
The distribution of the back voltage corresponding to the detector is determined by the distribution of the front voltage, and the back potential distribution is set as follows:
Ψ(r)＝V B +γΦ(r)(0＜γ＜1) (17)
wherein V is B First turn voltage V of back spiral ring B ＝V fd +V E1 Gamma is a constant;
V B ＝V fd +V E1 (18)
V E1 is a positive spiralFirst turn voltage of ring, V fd For full depletion voltage, V fd ＝qN D d 2 /2ε 0 ε，N D For doping concentration of silicon substrate epsilon si Is silicon dielectric constant epsilon 0 D is the thickness of the detector matrix;
back surface potential distribution according to equation (17):
the radius of the first circle of the rear surface is selected to be the same as that of the front surface, and r is the same as that of the front surface 1 ，
Back spiral pitch P 1 B And P 1 The relation of (2) is:
the back spiral ring spacing is:
the back surface spiral gap is selected to be the same as the front surface, and is G;
the spiral ring width of the rear surface is:
W B (r)＝P B (r)-G (22)
the corresponding back surface spiral ring has a rotation angle of
From equation (23), the relationship between radius and angle can be found as:
obtaining the regular hexagon spiral according to the spiral ring rotation angle formula (12) by the formula (7)Anterior point r of ring n-1 And the latter point r n The relation is:
obtaining the front ring of the regular hexagonal spiral ring according to the formula (21) and the corresponding back spiral ring rotation angle formula (24)And the latter ring->The relation is:
and (3) obtaining the regular hexagon data of the front spiral ring according to the formula (25), and obtaining the regular hexagon data of the back spiral ring according to the formula (26).
3. Advantageous effects
Compared with the prior art, the invention has the advantages that:
(1) In the invention, the first ring spacing P of the spiral ring in design 1 Controlled by design formula parameters m and k, the pitch P (r) and the gap G (r) are both defined by the first ring pitch P 1 Calculated, the helical pitches G (r) and P 1 The relation of (2) is: g (r) =kp 1 (0 < k < 1), the relationship between the pitch P (r) of the spiral ring and r is:and (m is a real number), and the gap G (r) is a fixed value, so that the front and back spiral ring design of the equal-gap spiral ring large-area silicon drift detector with the controllable gap is obtained.
(2) In the invention, the gap width of the detector can be controlled to reduce the surface leakage current, the resolution of the detector is improved, and in addition, the design of the gap with controllable spacing also solves the problem that the size of the detector in the past cathode ring design is increased, the spacing and the gap distance are wider and wider, and a larger invalid area is formed.
Drawings
FIG. 1 is a schematic diagram illustrating a structure of an equal-gap spiral ring large-area silicon drift detector with controllable gap spacing according to the present invention;
FIG. 2 is a top view of a spiral ring structure of an equal-gap spiral ring large-area silicon drift detector with controllable gap spacing according to the present invention;
FIG. 3 is a front view of a spiral ring structure of an equal-gap spiral ring large-area silicon drift detector with controllable gap spacing according to the present invention;
FIG. 4 is a schematic diagram of the back surface of a spiral ring structure of a large-area silicon drift detector with an equal-gap spiral ring with controllable gap provided by the invention;
FIG. 5 is a three-dimensional simulation block diagram of a detector;
FIG. 6 is a cross-sectional potential distribution of the detector in the X-direction;
FIG. 7 is a Y-direction cross-sectional potential distribution of the detector;
FIG. 8 shows the electric field distribution of the detector in the X-direction cross section;
FIG. 9 shows the Y-direction cross-sectional electric field distribution of the detector;
FIG. 10 shows electron concentration distribution in the X-direction cross section of the detector;
FIG. 11 shows electron concentration distribution in a Y-direction cross section of the detector.
In the figure: the positive electrode comprises a positive anode electrode 1, a positive spiral ring electrode 2, a back spiral ring electrode 3, a silicon substrate 4, a spiral ring spacing 5, a spiral ring width 6, a spiral ring gap 7 and a spiral ring first ring spacing 8.
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.
Example 1:
referring to fig. 1, an equal-gap spiral ring large-area silicon drift detector with controllable gap comprises a front anode electrode 1, a front spiral ring electrode 2, a back spiral ring electrode 3 and a silicon substrate 4, wherein the front spiral ring electrode 2 is arranged outside the front anode electrode 1 in a surrounding manner, the back spiral ring electrode 3 is arranged on the back surface of the front spiral ring electrode 2, and the silicon substrate 4 is arranged outside the front spiral ring electrode 2 in a surrounding manner.
In this embodiment, the front anode electrode 1 is heavily doped N-type semiconductor silicon, the front spiral ring electrode 2 is heavily doped P-type semiconductor silicon, the shape thereof is a regular hexagonal spiral ring, the back spiral ring electrode 3 is heavily doped P-type semiconductor silicon, the shape thereof is a regular hexagonal spiral ring, and the silicon substrate 4 is lightly doped N-type semiconductor silicon.
In this embodiment, the first pitch P of the spiral ring 1 Controlled by design formula parameters m and k, the pitch P (r) and the gap G (r) are both defined by the first ring pitch P 1 Calculated, the helical pitches G (r) and P 1 The relation of (2) is: g (r) =kp 1 (0 < k < 1), the relationship between the pitch P (r) and r is:and (m is a real number), and the gap G (r) is a fixed value, so that the front and back spiral ring design of the equal-gap spiral ring large-area silicon drift detector with the controllable gap is obtained. The gap G (r) is the leakage current of the detector due to the fact that fixed charges exist at the interface between the silicon oxide and the silicon surface, so that the surface current can be reduced by controlling the gap size of the surface of the detector, the purpose of reducing the leakage current of the detector is achieved, and in addition, the problem that in the past spiral ring design, a larger invalid area is formed due to the fact that the gap distance is wider and wider when the size of the detector is larger is solved by the design of the gap with controllable spacing.
Example 2:
in this embodiment, referring to fig. 2, a design method of an equal-gap spiral ring large-area silicon drift detector with controllable gap is characterized by comprising the following steps:
step 1: calculating the surface electric field distribution of the silicon drift detector: the voltage profile is provided by a spiral-shaped heavily doped P-type cathode formed by ion implantation. As shown in fig. 2, at a radial r point, 5 is a pitch P (r) of adjacent cathode spiral rings, 2 is a width W (r) of the ion implantation region at the radial r point, which defines a width of the spiral cathode in the radial r. And 3 is the gap G (r) between adjacent implanted regions. The pitch of the spiral rings is as follows:
P(r)＝W(r)+G(r) (1)
ρ S the square resistance of the spiral ring cathode ion implantation area is that the ion implantation depth is t, t is a constant and does not change along with the change of r, and ρ is the resistivity of the P-type heavily doped cathode;
ρ/t＝ρ S (2)
the resistance R (R) of each turn of the spiral cathode also varies with R:
R(r)＝ρ S αr/W(r) (3)
ρ S is the square resistance of the spiral ring cathode ion implantation layer, alpha is determined by the geometry of the cylindrical spiral cathode, the circumference of one circle is equal to alpha r, and if the spiral shape is truly circular, alpha=2pi; to form a more compact SDD array, the spiral shape may be chosen to be nearly circular, such as regular hexagonal (α=6), or square
The voltage difference Δv (r) between adjacent spiral cathode rings at the radial r point is:
ΔV(r)＝IR(r)＝E(r)P(r) (4)
IR (r) is derived from ohm's law and E (r) P (r) is derived from electric field integration; wherein I is the current of the spiral ring cathode, E (r) is the surface electric field at the point of radius r;
equation (3) and equation (4) relate the geometry of the cathode ring and the current to the SDD surface electric field:
step 2: calculating the width distribution of a spiral-shaped cathode of a silicon drift detector
For the special case of one cathode ring, i.e. keeping the cathode gap per ring constant, G is a constant. Thus equation (1) becomes:
P(r)＝W(r)+G (6)
the relationship between the pitch P (r) and r in the design is:
wherein P is 1 Is the first helical pitch, r 1 Is the radius of the first turn thereof;
in design, pitch of the spirals G and P 1 The relation of (2) is:
G＝kP 1 (0＜k＜1) (8)
in practical applications, k may be selected to be 0.3< k <0.7;
width distribution of spiral-shaped cathodes for silicon drift detectors
W(r)＝P(r)-G (9)
Step 3: calculating the relation between the rotation angle of the spiral ring and the radius, wherein the radius is r from each rotation of the spiral ring n-1 Increased to r n Obtaining a formula of the rotation angle theta of the spiral ring:
θ is the angle of each rotation, e.g. increase for each point of rotation when squareIncrease +/for every point of rotation of θ for hexagonal shape>
Substituting equation (7) into equation (10) can calculate the relationship between the rotation angle θ of the spiral ring and the radius as
Simplifying to obtain the relationship between the rotation angle of the spiral ring and the adjacent point of the spiral ring
Step 4: determining the potential distribution of the front and back of a silicon drift detector
The corresponding surface electric field distribution is obtained according to equation (5) and equation (6):
the surface potential profile is determined by the following equation:
substituting the formula (13) into the formula (14) to obtain:
substituting equation (7) into equation (15), letObtain P (r) =P 1 x，dr＝mr 1 x m-1 dx, substituting equation (15) to obtain
The distribution of the back voltage corresponding to the detector is determined by the distribution of the front voltage, and the back potential distribution is set as follows:
Ψ(r)＝V B +γΦ(r)(0＜γ＜1) (17)
wherein V is B Is the first turn voltage of the back spiral ring, γ is a constant;
V B ＝V fd +V E1 (18)
V E1 the first turn voltage of the positive spiral ring, V fd For full depletion voltage, V fd ＝qN D d 2 /2ε 0 ε，N D For doping concentration of silicon substrate epsilon si Is silicon dielectric constant epsilon 0 D is the thickness of the detector matrix;
back surface potential distribution according to equation (17):
the radius of the first circle of the rear surface is selected to be the same as that of the front surface, and r is the same as that of the front surface 1 ，
Step 5: spiral ring design for determining silicon drift detector back surface
Back spiral pitch P 1 B And P 1 The relation of (2) is:
the back spiral ring spacing is:
the back surface spiral gap is selected to be the same as the front surface, and is G;
the spiral ring width of the rear surface is:
W B (r)＝P B (r)-G (22)
the corresponding back surface spiral ring has a rotation angle of
From equation (22), the radius versus angle can be found as:
parameters were calculated according to the above calculation methods (equation (1) to equation (24)) and as follows
The substrate thickness d=500 μm of the SDD, the anode radius 180 μm, the detector radius r=10000 μm, the first radius R 1 Gamma is 0.7676, g=kp, =200 μm 1 (0 < K < 1) K is 0.7, ρ S The square resistance of the ion implantation layer of the spiral ring cathode is 2000 omega, and I is the total current of the spiral ring cathode is 20.10 -6 A, the first circle voltage V of the front spiral ring E1 5V, the last circle of voltage V of the front spiral ring out 300V, the first turn voltage V of the back spiral ring B 81V, the last turn of voltage V of the back spiral ring Bout 311V.
Taking when m=1.5, to form a more compact SDD array, the regular hexagonal spiral shape α=6 is designed, and equation (16) is solved to obtain
In the first turn, i.e. when r=r 1 In the time-course of which the first and second contact surfaces,first turn voltage V E1 =5v, i.e. Φ (1) =v E1 =5v, when in the outermost circle, both r=r =j->Outermost ring voltage V out When =300V, i.e.)>
Solving the formula (25) to obtain:
P 1 ＝28.23437974，G＝19.76406582；
obtaining
Obtaining a front point r of the regular hexagonal spiral ring according to the spiral ring rotation angle formula (12) by the formula (26) n-1 And the latter point r n The relation is:
obtaining the front ring of the regular hexagonal spiral ring according to the formula (21) and the corresponding back spiral ring rotation angle formula (24)And the latter ring->The relation is:
as in the case of the front first ring, r 1 Starting from =200, P 1 = 28.23437974, the data of the regular hexagon of the front spiral ring is obtained according to formula (28), and the data of the regular hexagon of the back spiral ring is obtained according to formula (29).
Dot data for positive spiral ring hexagons:
dot data for back side spiral ring hexagons:
the radius of the silicon substrate is 10000 mu m, and the radius r of the spiral ring is n The design method of the equal-gap spiral ring large-area silicon drift detector with the controllable spacing gap alpha=6 when m=1.5 is obtained until the position near the radius 10000 μm set by us.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (10)
1. The equal-gap spiral ring large-area silicon drift detector with controllable gap comprises a front anode electrode (1), a front spiral ring electrode (2), a back spiral ring electrode (3) and a silicon substrate (4), and is characterized in that the front spiral ring electrode (2) is arranged outside the front anode electrode (1) in a surrounding way, the back spiral ring electrode (3) is arranged on the back of the front spiral ring electrode (2), and the front anode electrode (1), the front spiral ring electrode (2) and the back spiral ring electrode (3) are all arranged on the surface of the silicon substrate (4).
2. The equal-gap spiral ring large-area silicon drift detector with controllable gap according to claim 1, characterized in that the front-side anode electrode (1) is heavily doped N-type semiconductor silicon, circular in shape and 50-200 μm in size.
3. The equal-gap spiral ring large-area silicon drift detector with controllable gap according to claim 1, characterized in that the front spiral ring electrode (2) is heavily doped P-type semiconductor silicon, which is shaped as a regular hexagonal spiral ring.
4. The equal-gap spiral ring large-area silicon drift detector with controllable gap according to claim 1, wherein the back spiral ring electrode (3) is heavily doped P-type semiconductor silicon, the shape of the back spiral ring electrode is regular hexagonal spiral ring, and the silicon substrate (4) is lightly doped N-type semiconductor silicon.
5. A method of designing a pitch gap controllable equal gap spiral ring large area silicon drift detector according to any of claims 1-4, comprising the steps of:
step 1: calculating the surface electric field distribution of the silicon drift detector;
step 2: calculating the width distribution of the cathode in the spiral shape on the front surface of the silicon drift detector;
step 3: calculating the relation between the rotation angle and the radius of the spiral ring;
step 4: determining the potential distribution of the front and back of the silicon drift detector;
step 5: the spiral ring design of the rear surface of the silicon drift detector is determined.
6. The method of claim 5, wherein the voltage distribution in step 1 is provided by a heavily doped P-type cathode having a spiral shape, the P-type heavily doped cathode being formed by ion implantation, wherein at a radial point r, 1 is a distance P (r) between adjacent cathode spiral rings, 2 is a width W (r) of an ion implantation region at a radial point r, which defines a width of the spiral cathode in the radial direction r, 3 is a gap G (r) between adjacent implantation regions, and the pitch of the spiral rings is:
P(r)＝W(r)+G(r) (1)
ρ S the square resistance of the spiral ring cathode ion implantation area is that the ion implantation depth is t, t is a constant and does not change along with the change of r, and ρ is the resistivity of the P-type heavily doped cathode;
ρ/t＝ρ S (2)
the resistance R (R) of each turn of the spiral cathode also varies with R:
R(r)＝ρ S αr/W(r) (3)
ρ S is the square resistance of the spiral ring cathode ion implantation layer, alpha is determined by the geometry of the cylindrical spiral cathode, the circumference of one circle is equal to alpha r, and if the spiral shape is truly circular, alpha=2pi; to form a more compact SDD array, the spiral shape may be chosen to be nearly circular, such as regular hexagonal (α=6), or square
The voltage difference Δv (r) between adjacent spiral cathode rings at the radial r point is:
ΔV(r)＝IR(r)＝E(r)P(r) (4)
IR (r) is derived from ohm's law and E (r) P (r) is derived from electric field integration; where I is the current of the spiral ring cathode and E (r) is the surface electric field at the radius r point.
Equation (3) and equation (4) relate the geometry of the cathode ring and the current to the SDD surface electric field:
7. the method for designing a large area silicon drift detector with controllable pitch gap and spiral ring according to claim 5, wherein in step 2, for a specific case of one cathode ring, i.e. keeping the cathode gap of each ring unchanged, G is a constant, and equation (1) becomes:
P(r)＝W(r)+G (6)
the relationship between the pitch P (r) and r in the design is:
wherein P is 1 Is the first helical pitch, r 1 Is the radius of the first turn thereof;
in design, pitch of the spirals G (r) and P 1 The relation of (2) is:
G＝kP 1 (0＜k＜1) (8)
in practical applications, k may be selected to be 0.3< k <0.7;
width distribution of spiral-shaped cathodes for silicon drift detectors
W(r)＝P(r)-G (9)
8. The method for designing a pitch-gap-controllable isopass spiral ring large area silicon drift detector as defined in claim 5, which is characterized in thatCharacterized in that the radius of each revolution of the spiral ring in the step 3 is from r n-1 Increased to r n Obtaining a formula of the rotation angle theta of the spiral ring:
θ is the angle of each rotation, e.g. increase for each point of rotation when squareIncrease +/for every point of rotation of θ for hexagonal shape>
Substituting equation (11) into equation (12) can calculate the relationship between the rotation angle of the spiral ring and the radius, and the rotation angle of the spiral ring corresponding to θ is
Simplifying to obtain the relationship between the rotation angle of the spiral ring and the adjacent point of the spiral ring
9. The method for designing a large-area silicon drift detector with an equal-gap spiral ring with controllable gap according to claim 5, wherein the corresponding surface electric field distribution obtained according to equation (5) and equation (6) in step 4 is:
the surface potential profile is determined by the following equation:
substituting the formula (13) into the formula (14) to obtain:
substituting equation (7) into equation (15), letObtain P (r) =P 1 x，dr＝mr 1 x m-1 dx, substituting equation (15) to obtain
The distribution of the back voltage corresponding to the detector is determined by the distribution of the front voltage, and the back potential ψ (r) distribution is set as:
Ψ(r)＝V B +γΦ(r)(0＜γ＜1) (17)
wherein V is B First turn voltage V of back spiral ring B ＝V fd +V E1 Gamma is a constant;
V B ＝V fd +V E1 (18)
V E1 the first turn voltage of the positive spiral ring, V fd For full depletion voltage, V fd ＝qN D d 2 /2ε 0 ε si ，N D For doping concentration of silicon substrate epsilon si Is silicon dielectric constant epsilon 0 D is the thickness of the silicon substrate of the detector;
back surface potential distribution according to equation (17):
the radius of the first circle on the back is selected to be the same as that on the front, and r is the same as that on the front 1 。
10. The method for designing a gap-controllable equal-gap spiral ring large-area silicon drift detector according to claim 5, wherein said step 5 comprises a back-side spiral pitch P 1 B And P 1 The relation of (2) is:
the back spiral ring spacing is:
the back surface spiral gap is selected to be the same as the front surface, and is G;
the spiral ring width of the rear surface is:
W B (r)＝P B (r)-G (22)
the corresponding back surface spiral ring has a rotation angle of
From equation (23), the relationship between radius and angle can be found as:
obtaining a front point r of the regular hexagonal spiral ring according to a spiral ring rotation angle formula (12) by a formula (7) n-1 And the latter point r n The relation is:
according to the formula (21) and the corresponding back spiral ring rotation angle formula (24)Front ring of regular hexagon spiral ringAnd the latter ring->The relation is:
and (3) obtaining the regular hexagon data of the front spiral ring according to the formula (25), and obtaining the regular hexagon data of the back spiral ring according to the formula (26).
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| US20110012216A1 (en) * | 2009-07-16 | 2011-01-20 | Massimo Morichi | Simplified Silicon Drift Detector and Wraparound Neutron Detector |
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| WO2020075051A1 (en) * | 2018-10-09 | 2020-04-16 | Istituto Nazionale Di Fisica Nucleare | Semiconductor drift detector with an optimized effective area |
| CN210805786U (en) * | 2019-11-01 | 2020-06-19 | 湘潭大学 | Concentric ring type large-area silicon drift detector |
| CN115732578A (en) * | 2022-11-22 | 2023-03-03 | 鲁东大学 | Double-sided equal-cathode annular gap spiral silicon drift detector and design method thereof |
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| US20110012216A1 (en) * | 2009-07-16 | 2011-01-20 | Massimo Morichi | Simplified Silicon Drift Detector and Wraparound Neutron Detector |
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| 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 |
| CN108920809A (en) * | 2018-06-28 | 2018-11-30 | 李正 | The two-sided silicon drifting detector (SDD) of large area helical form hexagon and its design method |
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