microstructured semiconductor neutron...

Microstructured Semiconductor Neutron Detectors (MSNDs)

Douglas S. McGregor, Steven L. Bellinger, Ryan G. Fronk, Luke Henson, Taylor Ochs, J. Kenneth Shultis

Semiconductor Materials and Radiological Technologies Laboratory (SMART) Laboratory Department of Mechanical and Nuclear Engineering

Kansas State University Manhattan, KS 66506

Tim Sobering, Russell Taylor, David Huddleston

Electronics Design Laboratory

Outline

• Coated Semiconductor Neutron Detectors • Principles of Microstructured Semiconductor

Detectors (MSND) • MSND Results • Next Generation Detectors

Two alternative neutron reactions popular for thermal neutron detection are the 10B(n,α)7Li reaction and the 6Li(n,t)4He reaction.

Thin-Film Detectors

σth = 3840 barns

σth = 940 barns

There is presently a need for neutron detectors dependent upon reactions other than 3He(n,p)3H

Neutron Absorption Cross Sections - 1/v

( )( ) cc

EgE ≅Γ+−

γγ πλσ

YbaXvKEH

bba ),(reactionfor;)(

Radiative capture (Breit-Wigner)

Charged particle capture

Thin-Film-Coated Device Concept

D.S. McGregor, M.D. Hammig, H.K. Gersch, Y-H. Yang, and R.T. Klann, Nuclear Instrum. and Meth., A500 (2003) p. 272.

( ) 2 14

10.5 1 1 ;

Fp F Fp F F

FF Fp F

F xS D I e dxI L

DF e D LL L

−Σ −

= Σ −

= + − − ≤ Σ

∫( )

( ) ( )

( ) 2 14

10.5 1 1 1 ;

F Fp F F

F F Fp F

D L L D x

F e xS D I e dxI L

F e e D LL

−Σ −−Σ −

−Σ − −Σ

= Σ −

= + − − ≥ Σ

Bragg Ionization Distributionsin Boron-10

Ion Penetration Distance (in microns)0 1 2 3 4 5

840 keV 7Li Ion

1.777 MeV α - Particle

1.015 MeV 7Li Ion

Ion Penetration Distance (in microns)0 4 8 12 16 20 24 28 32

2.730 MeV 3H Ion

Thin-Film-Coated Device Concept: Ranges and Energy Deposition

Ion Penetration Distance, 6LiF Film(in microns)

0 4 8 12 16 20 24 28 32

2.050 MeVα - Particle

2.730 MeV 3H Ion

Bragg Ionization Curves in Boron Bragg Ionization Curves in LiF

Residual Energy in Boron

Ion Penetration Distance, 10B Film(in microns)

0 1 2 3 4

20001.470 MeVα− Particle

1.777 MeV α− Particle

840 keV7Li Ion

1.015 MeV 7Li Ion

Residual Energy in LiF

Channel Number0 100 200 300 400 500 600 700 800

20001.1 µm 10B35 µm 6LiF3.0%

efficiency4.6%

efficiency

10B-coated devices require less material for optimum performance. 6LiF-coated devices have improved gamma ray discrimination.

10B or 6LiF Film Thickness (microns)

0 5 10 15 20 25 30 35 40

Orthogonal FrontIrradiation

Orthogonal BackIrradiation

(LLD = 300 keV)

With the LLD set at 300 keV equivalent, maximum efficiencies range from 4% to 4.6% depending on the film and the irradiation direction. Hence, both 10B and 6LiF thin film devices have similar performance.

Thin-Film-Coated Device Concept

Main Design Considerations: 1. Neutron reactive backfill materials 2. Geometric pattern design 3. Substrate material

Basic Microstructure Detector Design

Improvement: Microstructures Semiconductor Neutron Detectors

D.S. McGregor, R.T. Klann, H.K. Gersch, E. Ariesanti, J.D. Sanders, and B. VanDerElzen, Conf. Rec. of the IEEE Nucl. Sci. Symp., San Diego, California, Nov. 4-9, 2001.

3% eff → 3.3% eff

Boron-10

Micro-Structured Semiconductor Neutron Detector

Trench Hole Pillar

We calculate intrinsic efficiency for a normally incident beam of thermal (2200 m-s-1) neutrons.

J.K. Shultis, D.S. McGregor, Nucl. Instrum. and Meth. A 606(2009) pp. 608-636.

Energy (MeV)0.001 0.01 0.1 1

PhotoelectricCompton ScatteringPair ProductionTotal

CS = PE at 58 keV

Silicon Photon Cross Sections

at 465 keV, CEmax = 300 keV

at 686 keV, CEmax = 500 keV

For Si, the cross over for Compton scattering to dominate interactions above photoelectric is at approximately 60 keV. We usually set the lower level discriminator at or above 5 times this value (> 300 keV) to reduce gamma ray background.

Photoelectrons or Compton electrons with energies above 65 keV have transit lengths in Si >40 microns, a dimension larger than the lateral dimensions of the 6LiF filled trench devices!

Gamma-Ray Background

Micro-Structured Devices (Boron-Filled, Cell Dimension = 4 Microns)

LLD Setting (MeV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

B RodsSi PillarsB Trenches

Cell Dimension = 4 micronsFeature Ratio = 50%Feature Depth = 10 microns

LLD Setting (MeV)0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

B RodsSi PillarsB Trenches

Energy (MeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

r of C

10B RodsSi Pillars10B Trenches

Energy (MeV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

r of C

10B RodsSi Pillars10B Trenches

10 micron deep features 40 micron deep features

pillar

trench

pillar

trench

LLD Setting (MeV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

LiF RodsSi PillarsLiF Trenches

LLD Setting (MeV)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

LiF RodsSi PillarsLiF Trenches

Energy (MeV)

0 1 2 3 4 5

r of C

6LiF RodsSi Pillars6LiF Trenches

Energy (MeV)

0 1 2 3 4 5

r of C

6LiF RodsSi Pillars6LiF Trenches

90 micron deep features 175 micron deep features

pillar

trench

pillar

trench

Micro-Structured Devices (LiF-Filled, Cell Dimension = 40 Microns)

6LiF-Filled Trench Design

The design can yield thermal neutron intrinsic detection efficiencies exceeding 30%.

6LiF Trench Device Obverse Irradiation(300 micron deep trench)

Cell Dimension (microns)20 30 40 50 60 70 80 90 100 110

No cap10 microns20 microns30 microns40 microns50 microns

Trench Width is50% of Cell Dimension

6LiF Trench Device Reverse Irradiation(300 micron deep trench)

40No cap10 microns20 microns30microns40 microns50 microns

Trench Width is50% of Cell Dimension

J.K. Shultis and D.S. McGregor, IEEE Trans. Nucl.Sci., NS-53 (2006) pp. 1659-1665.

Sidewall Width 10 um 12 um 14 um 16 um 18 um 20 umTrench Width 30 um 28 um 26 um 24 um 22 um 20 um

Total Eff. 36.33% 35.29% 34.05% 32.61% 30.98% 29.19%0.3 MeV LLD 34.04% 33.27% 32.27% 31.09% 29.66% 28.07%0.5 MeV LLD 32.29% 31.94% 31.13% 30.12% 28.82% 27.36%

Microstructured Semiconductor Neutron Detectors 6LiF backfilled

Efficiency Calculations

Calculated efficiencies for 6LiF-filled trench detectors as a function of cell fraction and perforation depth. For common etched features with a 40 micron cell width, over 30% efficiency can be reached with devices >350 microns deep. Unequal T/W ratios of 0.7 allows for over 35% efficiency.

LLD = 300 keV

Efficiency Calculations

Calculated efficiencies for 6LiF-filled trench detectors as a function of cell fraction and perforation depth. For common etched features with a 40 micron cell width, over 30% efficiency can be reached with devices >350 microns deep. Unequal T/W ratios of 0.7 allows for over 35% efficiency. For aggressive features (14 micron trenches, 6 micron semiconductor fins) – > 35% efficiency is reached for 350 micron deep features and 47% efficiency is reached for 350 micron deep features. Sandwiched detectors with 10 micron fins and trenches can exceed 70% efficiency!

LLD = 300 keV

Fabrication is performed with common VLSI processing methods and equipment.

MSND Fabrication

• Benefits – Better Uniformity Across Large Wafers

– This Leads to Uniform Responses From Each Device in an Array!

– Batch Wafer Processing (No Limit!) – Less Mechanical Damage than ICP RIE

• 3 Different perforation designs

– Straight Trench – Chevron Trench – Rhombus Hole/Pillar

Anisotropic Chemical (KOH) Wet Etching of (110) Si

Wet Etching of (110) Si

• 3 Different perforation designs – Straight Trench – Chevron Trench – Rhombus Hole/Pillar

• Benefits – Batch Wafer Processing – Less Mechanical Damage than ICP RIE – Easier Fabrication of Advanced

Designs

KOH Etched

Conformal Diode Fabrication Process

• Diffusion In Holes – Covers sensitive surfaces

• Consumes Damage and Contamination – Easier to fabricate

100 μm Conformal Diode Leakage Current Density: 0.1μA / cm2

Dopant Introduction

• PIN Diodes are fabrication by the controlled introduction of n-type and p-type dopants

• Isolation is achieved by the growth of thick field oxides

KOH Etched

Cavity Backfilling of Microstructured Devices

LiF nano-powder Production and Backfilling The LiF granules form to nano-sided tiny cubic crystals through a heat treatment process, and can pack firmly into the microstructured cavities.

6LiF nanomaterial

The LiF nanopowder is suspended in an solvent with an ultrasonic vibrator.

The LiF nanopowder is compacted into the microstructures with a centrifuge.

43.4 µm

492 µm deep

34.5 µm trench

25.7 µm fin

Diode Characterization •Diodes are tested for leakage current and capacitance prior to mounting.

– < 10 nA cm-2 at an operational bias of 0 to -3V. – < 150 pF at an operational bias of 0 to -3V.

MSND Characterization

Detector

Neutron Testing •Diffracted thermal neutron beam at KSU TRIGA Mark II Nuclear Reactor

• Reactor Power – 0 to 500 kW • Thermal (0.0253eV) Neutron Flux: 1.72 x 102 {n cm-2 s-1 kW-1} • Calibrated against 3He-Gas Detector

Gamma-ray Sensitivity •137Cs source

• γ-ray Energy: 662 keV • 1 meter from DSMSND • Assay: 68.27 mCi • Exposure: 21.8 mR hr

• 0.08 γ-ray µs-1 (per 4-cm2 area)

Kansas State University Efficiency Measurement Standard Method

Neutron Efficiency of 4-cm2 MSND Detector • 4 cm2 MSND, 440-µm deep trenches, 10-µs charge integration time.

• 30.1 ± 0.5% at a 650 keV LLD with normal beam incidence.

• 37.6 ± 0.7% at a 650 keV LLD with 45 deg. beam incidence.

neutron converter material

semiconductorvolume

uniform parallel neutron beam

MSND Incident Angle

neutron converter material

semiconductorvolume

uniform parallel neutron beam

MSND Angular Efficiency Comparisons

Stacked Perforation Designs

Pulse height spectrum taken with a 6LiF-filled microstructured semiconductor neutron detector formed from two devices. The microstructures were 250 microns deep. Intrinsic thermal neutron detection efficiency was measured to be >42%.

Channel Number0 20 40 60 80 100 120 140

Cd Shutter OpenCd Shutter Closed

4 cm2 Stacked Straight Trench Microstructure Design (200 micron deep Trenches)

200 um Deep Microstructure Stacked 4 cm2 Dual MSND Device

100000

0 25 50 75 100 125 150 175 200

Channel

New Design : 10 µs

New Design Background

Cs Response137

Stacked Perforation Design: 10 µs preAmp integration time

Pulse height spectrum taken with a 6LiF-filled microstructured semiconductor neutron detector formed from stacked 1cm2 devices. The microstructures were 250 microns deep. Intrinsic thermal neutron detection efficiency was measured for the new longer integration time and found to be 42.0 ± 0.25% at a 300 keV LLD.

DSMSND Future Work

Opposing PIN Design - Higher efficiency - Reduced neutron streaming

Adjacent PIN Design - Faster response

Opposing/Adjacent PIN Design - Higher efficiency - Reduced neutron streaming - Faster response

Dual-Sided Etched MSND Devices

• Diode fabrication – Devices are fabricated exactly as single-sided

devices. – Capable of batch processing. – Devices of similar dimensions have similar

theoretical maximum detection efficiencies – IHD Design is capable of +72% intrinsic

detection efficiency.

Opposing DSMSND Design

Interdigitated DSMSND Design

D.S. McGregor and R.T. Klann, patent US-6545281; allowed April 8, 2003. D.S. McGregor, R.T. Klann, patent US-7164138; allowed January 16, 2007.

DSMSNDs

• Ultra-high efficiency applications.

• Similar to Dual-Stacked MSND devices.

• Ultra-fast response applications.

• High charge-collection efficiency

LLD = 300 keVTr./Unit Cell 20 um 40 60 80 100

0.9 36.59% 35.54% 32.60% 26.54% 22.60%0.8 64.82% 52.28% 39.33% 32.23% 27.65%0.7 70.54% 57.05% 44.36% 36.20% 30.52%0.6 72.14% 60.03% 48.16% 38.37% 31.23%0.5 72.81% 61.25% 49.90% 38.96% 31.58%0.4 72.61% 60.65% 48.89% 39.13% 31.92%0.3 71.48% 58.29% 45.83% 37.66% 31.92%0.2 66.39% 54.09% 41.42% 34.36% 29.80%0.1 39.17% 38.08% 35.22% 29.25% 25.38%

Unit-Cell Width500-um-deep trenches, backfilled with LiF

DSMSND vs. MSND

DSMSND Efficiency Comparisons •Optimization of theoretical efficiencies occurs at 475-µm deep, 13/7-µm wide trenches with 20-µm pitch.

DSMSND Angular Efficiency Comparisons

DSMSND vs. MSND

MSNDs are now commercially available through Radiation Detection Technologies, Inc. (RDT)

Standard 2 cm x 2 cm 30% efficient devices and High-density arrayed devices are available, as well as custom detector configurations.

137F Ward Hall Mechanical and Nuclear Engineering Department

mcgregor@ksu.edu

http://www.mne.ksu.edu/research/centers/SMARTlab

Kansas State University SMART Laboratory

The presented research was funded in part by DTRA contract HDTRA1-12-C-0004

Additional Slides for Discussions

Reaction product ranges and residual energy in pure boron and LiF

Ion Penetration Distance, 10B Film(in microns)

0 1 2 3 4

20001.470 MeVα− Particle

1.777 MeV α− Particle

840 keV7Li Ion

1.015 MeV 7Li Ion

Ion Penetration Distance, 6LiF Film(in microns)

0 4 8 12 16 20 24 28 32

2.050 MeVα - Particle

2.730 MeV 3H Ion

1. 10B has higher macroscopic cross section, hence features need only be 60 microns deep to achieve 3 mean free path lengths.

2. Etch features must be on the order of 2-3 microns or less to reduce energy self absorption.

3. Energies are lower; LLD can not be set very high without losing significant counts.

4. Both alpha and Li ion contribute to electrical signal (3:1 ratio), causing more “wall effect” problems.

1. 6LiF has lower macroscopic cross section, hence features must be >350 microns deep to achieve 2 mean free path lengths.

2. Etch features can be larger, on the order of must be on the order of 28 – 32 microns or less without energy self absorption problems.

3. Energies are higher; LLD can be set high without losing significant counts.

4. Triton contributes much more to signal than alpha particle (7:1) – less wall effect issues.

“Sandwich” Designs

Double Outward Design

Requires that the applied voltage extend the depletion region entirely across the detector!

Double Inward Design

Difficult to manufacture!

“Sandwich” Designs

10B FilmThickness DF for Each Device (microns)

0 1 2 3 4 5 6

Double Inward DevicesDouble Outward Devices

(LLD = 300 keV)

6LiF Film Thickness DFfor Each Device (microns)

0 5 10 15 20 25 30 35 40

0123456789

(LLD = 300 keV)

6Li Film Thickness DFfor Each Device (microns)

0 20 40 60 80 100 120 140 160

(LLD = 300 keV)

Double-inward design has highest efficiency.

Channel Number0 100 200 300 400 500 600 700 800

5000 1.1 µm 10B/ 60 µm 6Li1.1 µm 10B/ 30 µm 6LiF1.1 µm 10B35 µm 6LiF

6.3% efficiency

11.6% efficiency

3.0% efficiency

4.6% efficiency

Channel Number0 100 200 300 400 500 600 700 800 900 1000

4000 4 µm 10B with via holesSandwich - 4 µm 10B with via holes 30 µm 6LiF

3.9% efficiency

13.0% efficiency

Layered and Stacked Detectors

Au contact

Encapsulate

10B coating

6LiF Film Thickness (microns)

0 5 10 15 20 25 30 35

3515 detectors

10 detectors

5 detectors

2 detectors

1 detector

Front Irradiation300 keV LLD

10B-coated and stacked devices.

10B Film Thickness (microns)

0 1 2 3 4 5

3515 detectors

10 detectors

5 detectors

2 detectors

1 detector

Front Irradiation300 keV LLD

6LiF-coated and stacked devices.

Why not just stack a bunch of detectors together? -“Stacked” Designs -

Micro-Structured Devices

Cell Length and Width

Cavity Diameter

Cap Depth

Semiconductor

Neutron Reactive Material

1. Ion ranges and energy deposition determined by TRIM (from SRIM 2003). 2. Empirical curve fitting performed by TableCurve (Jandel 1998). 3. Thermal neutron beam is perpendicular to device surface 4. Monte Carlo approach used to simulate randomized neutron absorption

and reaction ion trajectories. 5. We assume 70% packing of material in the structures. 6. After millions of histories, efficiency is determined

by the number of events depositing energy above the lower level discriminator setting.

6LiF Rod Device Reverse Irradiation(300 micron deep holes)

26No Cap10 microns20 microns30 microns40 microns

Hole Diameter is60% of Cell Dimension

6LiF Rod Device Obverse Irradiation(300 micron deep holes)

26No Cap10 microns20 microns30 microns40 microns

Hole Diameter is60% of Cell Dimension

J.K. Shultis and D.S. McGregor, IEEE Trans. Nucl.Sci., NS-53 (2006) pp. 1659-1665.

Effective intrinsic efficiency: the intrinsic efficiency at various irradiation angles normalized to the common irradiation direction and detector cross sectional area – or normalized to the highest interaction rate.

( )coscos

( ) 0.5 1 1 expc s ;oF F

Fp F p F

D DS D F D LL Lθ

− Σ ≈ + − − ≤ Σ

( ) cosco

( ) 0.5 exp 1 1 exp 1 ;s cos

cos F F Fp F p F

D L LS D F D LLθ

θ θθ

−Σ − −Σ ≈ + − − ≥ Σ

cosY θY

Y W>>Typically

Class 100 Cleanroom

Thin-Film Detectors

What are the choices? 1. The 10B(n,α)7Li reaction – inexpensive, good s, short ranges Q = 2.34 MeV (94%) – 1.47 MeV a, 840 MeV Li ion Q = 2.78 MeV (6%) – 1.78 MeV a, 1.02 MeV Li ion sth = 3840 barns 2. The 6Li(n,t)4He reaction – inexpensive, lower s, longer ranges Q = 4.78 MeV (100%) – 2.05 MeV α, 2.7 MeV 3H ion sth = 940 barns 3. The 157Gd(n,γ)158Gd reaction – expensive, high s, short ranges Energetic conversion electrons, emits only low energies between 70 keV- 220 keV (low particle yield) sth = 250,000 barns

Summary

1. Models should take into account accepted and realistic neutron detector calibration methods. - A model’s usefulness is diminished if the results can not be tested! 2. Efficiency tests should be performed with accepted characterization procedures – best performed following the original definition of cross section when possible. 3. A calibrated standard neutron detector should be used as a witness detector for efficiency calibrations. 4. Detectors with 1/v cross sections can be easily calibrated if the neutron intensity is constrained within the 1/v energy region. 5. Detectors using non-1/v reactions must be corrected for neutron energy. It is best to use a monoenergetic beam to reduce uncertainty.

Boron Filled Micro-Structured Devices

2 microns

Native oxide 50 nm

Thin pn contact diffusion > 150 nm

Dead region is 200 nm thick and consumes 36% of the volume. Probability of absorbing reaction products severely decreased.

“pillar”

“fin” Dead region is 200 nm thick and consumes 20% of the volume. Probability of absorbing reaction products decreased.

2 microns

“hole”

Dead region is 200 nm thick and consumes 10.75% of the volume. Minimal decrease in probability of absorbing reaction products.

6LiF Filled Micro-Structured Devices

Native oxide 50 nm

Thin pn contact diffusion > 150 nm

Dead region is 200 nm thick and consumes 4% of the volume. Very little decrease in volume.

“fin”

10 microns

“hole”

Dead region is 200 nm thick and consumes 2% of the volume. Very little decrease in volume.

10 microns

( ) ( ) ( )r rdF n N v v d dσ= v V v V

Why does this work?

Consider the laboratory system, where neutrons approach the nuclei with velocity

( ) rdI n v d= v v r rv = v

r = −v v V

To the capture nuclei, the neutrons compose a differential beam of intensity

which is equal to the relative velocity between the neutrons and nuclei.

and interact with the nuclei at a rate of

in interactions per cm3 s-1. The total interaction rate is

( ) ( ) ( )r rF n N v v d dσ= ∫∫ v V v V

Kansas State University Standard Method Calibration

McGregor et al., Nucl. Instrum. Meth., A608 (2009) 125.

Lamarsh, Nuclear Reactor Theory (Addison-Wesley, Reading, 1966)

Why does this work?

For materials with a 1/v cross section, such as 10B, 6Li, and 3He,

00( ) ( ) r

a r a rr

σ σ=

0 0( )a aF E nv= ∑

Where is an arbitrary relative speed and is the corresponding cross section. Therefore,

0rv 0( )a rvσ

( ) ( ) ( )

ra r r

F n N v v d d

vn N v v d dv

N v nv

∫∫∫∫

v V v V

where v0 is an arbitrary lab speed and E0 is the corresponding energy.

Why does this work?

0 0( )a aF E nv= ∑

What this means is that the interaction rate for 1/v materials is independent of neutron energy, provided that the neutrons are in the 1/v range. If the neutrons are not exactly 2200 m s-1 neutrons, the detector interaction rate, and measured efficiency, are the same as if they were!

What are the weaknesses?

1. If non- 1/v materials are also attenuating the beam, the measurement may have error.

Using detector containers with low neutron absorption reduces the effect of non-1/v

absorbers (the steel 3He tube has thin walls).

2. If there is neutron contamination from epithermal or fast neutrons, the measurement may have error.

The diffracted beam significantly reduces neutrons in the non-1/v region.

Large MSND Detectors

Am-241 100 sec, Probe at Corner, Source at Opposite Corner

0 20 40 60 80 100 120 140 160 180 200

Channel

0 Volts2 Volts4 Volts6 Volts8 Volts10 Volts12 Volts

Pulse tests from an 241Am alpha particle source.

Microstructured Semiconductor Neutron Detectors (MSNDs) •Mass-producible

– Dozen per 4” wafer, dozens of wafers per batch. •Same Adaptability

– Compact, rugged low-voltage operation, inexpensive. •Greater Neutron Absorption

– A single 500μm MSND absorbs >52% of incident flux. •Greater Neutron Efficiency (>45%)

Microstructured Semiconductor Neutron Detectors

Increased energy deposition from reaction products. Increased neutron absorption.

• Stacked 250 micron deep trench MSND devices • Straight Trench IHD Conformal Detector

• Neutron Detection Eff. = 36% • γ-Rejection Ratio > 3.0 x 106 {n/γ}; LLD = 22 ≈ 450 keV

Neutron/Gamma-Ray Rejection

Intrinsic efficiency: for a parallel beam, the intrinsic efficiency is the ratio of counts registered to radiation quanta passing through the detector.

( )( ) IAC

AreaDetectorCurrentNeutronRateCount

i ==ε

Effective intrinsic efficiency: the intrinsic efficiency at various irradiation angles normalized to the common irradiation direction and detector cross sectional area.

Typical dimensions (face perpendicular to neutrons): 10B films: 0.5 – 2.5 microns thick 6LiF films: 2 – 20 microns thick Substrate: 300 – 350 microns thick Area: 0.25 – 4 cm2

2exp exps s He Het toutd

− Σ −Σ= =

22 exp s sts

− Σ= =

exp He Hetoutg

−Σ= =

1 exp s st ss

−Σ = =

( )1/2

exp 1 exp 1s s He Het t s outHe

I II I

ε −Σ −Σ = − = −

HeHe cts

ctsdetdet εε

microstructured semiconductor neutron...

Documents

microstructured hydroxyapatite membranes for ion … ·...

microstructured and thermally integrated catalytic …

waves in microstructured solids: a unified viewpoint of

dispersion-engineered and highly-nonlinear microstructured...

fabrication of microstructured surface topologies for the

evolutionary design of single-mode microstructured...

modular microstructured reactors based on new manufacturing...

microstructured semiconductor neutron detectors (msnd...

elastic wave dispersion in microstructured...

microstructured optical waveguide-based endoscopic probe...

microstructured extracellular matrices in tissue ... ›...

superhydrophobic surfaces from nano- and microstructured...

development of rare-earth doped microstructured optical...

fouling in microstructured devices: a review

the design and modeling of microstructured optical fiber

microstructured shape memory polymer surfaces with...

microstructured products

microstructured vertically aligned carbon nanotube...

bioinspired microstructured polymer surfaces with

microstructured electrodes and diffusion layers for enhanced...