The CVD diamond booklet

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The CVD diamond booklet

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Content

1. General properties of diamond... 2

2. Optical Properties ... 4

Optical transparency...4

Absorption coefficient at 10.6 µm ...5

Refractive index: n vs. λ...6

Refractive index: nd vs. T...7

Refractive index: Thermal coefficient ...8

X-ray absorption ...9

THz dielectric properties... 10

Optical specifications of Diamond Materials... 11

Surface finish, optical coatings and mounting ...12

3. Thermal Properties ... 13

Thermal conductivity ... 13

Thermal conductivity vs. T ... 14

Specific heat vs. T ... 15

Thermal expansion... 16

Thermal specifications of Diamond Materials ... 17

4. Mechanical Properties ... 18

Vickers-Hardness ... 18

Mechanical specifications of Diamond Materials... 19

5. Examples of CVD diamond applications ... 20

6. Useful formula ... 23

Bowing of a circular disk under pressure... 23

Thickness requirements ... 23

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CVD Diamond wafers prepared by Microwave Plasma CVD: boron doped disk (blue), optical grade diamond, mechanical grade, unpolished disk

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1. General properties of diamond

The most important properties of CVD diamond are the • unsurpassed hardness

• extremely high thermal conductivity (>1800 W/mK, five times that of copper) • broad band optical transparency

• extremely chemically inert:

Not affected by any acid or other chemicals • Graphitization only at very high temperatures

(T > 700°C in an oxygen containing and 1500°C in an inert atmosphere)

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*highest value of all solid materials

Property Value

Vickers hardness* 10,000 kg/mm2

Young's modulus* 1050 GPa

Poisson's ratio 0.1

Density 3.515 g/cm3

Atom density* 1.77×1023_1/cm3

Thermal expansion coefficient 1.0×10-6_{/K @300K}

Sound velocity* 17,500 m/s Friction coefficient 0.1 Specific heat @ 20°C 0.502 J/gK Debye temperature* 1860±10K Bandgap 5.45 eV Resistivity 1013_{- 10}16 _Ω_cm

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2. Optical Properties

Optical transparency

1 10 100 0 10 20 30 40 50 60 70 80 Tran smi ssio n (%) Wavelength (µm)

Optical transparency of CVD diamond In the UV, Visible, IR and far IR

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Absorption coefficient at 10.6 µm

9.0 9.5 10.0 10.5 11.0 0.08 0.09 0.10 0.11 0.12 0.13 0.14 Ab so rp ti o n co eff. ( cm -1 ) Wavelength (µm)

Absorption coefficient of CVD diamond as measured by laser calorimetry

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Refractive index: n vs.

λ

1 10 100 2.35 2.40 2.45 2.50 R efr active in dex Wavelength (µm)

The spectral variation of n is described by the Sellmeier equation:1

1 106 3356 . 4 175 3306 . 0 2 2 2 2 2 2 2 2 + − + − = nm x x nm x x n

where x is the wavelength in nm

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Refractive index: nd vs. T

0 200 400 600 800 1000 0 2 4 6 8 10 12 14 16 ∆ nd /n d (1 0 -3 ) Temperature (°C)

Variation of nd with temperature Patterson et al.2

our data

measured at 633 nm wavelength

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Refractive index: Thermal coefficient

-200 0 200 400 600 800 0.0 1.0 2.0 3.0 4.0 5.0 dn /d T (1 0 -5 /K) Temperature (°C)

Thermal coefficient of the refractive index Measured by laser refraction

of a diamond prism

Measured with laser interferometry Fontanella et al.3

3

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X-ray absorption

0 10 20 30 40 50 1E-5 1E-4 1E-3 0.01 0.1 1 Tin Lead Titanium Beryllium Diamond Ab so rpti o n C o efficie n t ( 1/ µ m) Energy (keV)

X-ray absorption coefficient of various materials. Data from http://www.photcoef.com

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THz dielectric properties

0.5 1.0 1.5 2.0 2.5 3.0 3.5 -20 -15 -10 -5 0 5 10 15 20 10 20 30 40 50 60 70 80 90 100 110 10 20 30 40 50 60 70 80 90 100 110 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 CVD Diamond Ab so rp ti on Co ef fi ci en t [ c m -1 ] Frequency [THz] Wavenumbers [cm-1] Re fr act iv e I n dex Wavenumbers [cm-1]

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Optical specifications of Diamond Materials

The core competences of Diamond Materials include the

manufacturing of high purity CVD diamond disks with properties approaching those of perfect natural diamond crystals.

Property Value

Transmission 225nm to far IR , > 70% @ 10µm Refractive index 2.38 @ 10µm, 2.41 @ 500nm Absorption coefficient ≤ 0.10 cm-1 _{@ 10µm}

Bandgap 5.45 eV

Tensile strength (0.5mm thick)

Nucleation surface in tension 600 MPa Growth surface in tension 400 MPa Loss tangent (tanδ @140 GHz) < 2.0×10-5

Dielectric constant 5.7

Properties of optical grade CVD-diamond by Diamond Materials

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Surface finish, optical coatings and mounting

Property Value

Dimensions

Thickness 10 - 2000 µm

Diameter up to 100 mm

Surface finish

Shape flat, spherical (convex & concave)

Roughness < 5 nm*

Flatness 1 fringe/cm*

Wedge 0 – 1°*

Antireflection Coatings (visible and infrared) Spec. Transmission at 10.6 µm >98.6 % Wavefront distortion

< 4 fringes at 633 nm over 30 mm* Mounting

Diamond windows mounted e.g. in UHV flanges (bakeable at 250°C, vacuum tight < 10-10_{mbar l/s)*}

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3. Thermal Properties

Thermal conductivity

0 500 1000 1500 2000 Sa pphi re Silic o n Al N Copper CV D Di amond Thermal Con ductiv ity (W/mK) Material

The thermal conductivity of diamond in comparison to other materials

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Thermal conductivity vs. T

-200 -100 0 100 200 300 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Th er m al Co nduc ti vi ty ( W /m K ) Temperature (°C)

Thermal conductivity of CVD diamond vs. temperature

CVD diamond Theory

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Specific heat vs. T

50 100 150 200 250 300 350 400 450 500 1E-5 1E-4 1E-3 0.01 0.1 1 Spec if ic he at (k J/ KgK ) Temperature (K)

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Thermal expansion

0 100 200 300 400 500 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Th er mal Expan si o n (1 0 -6 /K) Temperature (°C)

Thermal expansion vs. temperature High quality CVD diamond

Medium quality CVD diamond Values recommended by Slack4

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Thermal specifications of Diamond Materials

Optimized CVD-diamond as provided by Diamond Materials reaches a thermal conductivity of up to 2000 W/mK e.g. it exceeds that of copper by a factor of five. In contrast to metals, where heat is

conducted by electrons, lattice vibrations are responsible for the high thermal conductivity of diamond.

Property Value Thermal conductivity @300 K > 1200 W/mK* > 1500 W/mK* > 1800 W/mK* Thermal expansion coefficient

@300 K 1.0 +/- 0.1 × 10-6_/K

@700 K 4.4 +/- 0.1 × 10-6_/K

Specific heat @ 20°C 0.502 J/gK Debye temperature 1860±10K

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4. Mechanical Properties

Vickers-Hardness

0 2000 4000 6000 8000 10000 Talc Gyps um C alcite _Fluo ri te Aptite Corundum Topa z Qu ar tz Ort h oc al se _CVD Dia m ond Vi ck ers-Ha rd n ess ( kg /m m 2 ) Material

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Mechanical specifications of Diamond Materials

CVD diamond manufactured by Diamond Materials exhibits an exceptional wear resistance and a low coefficient of friction. Highly demanding applications such as cutting tools, surgical knives and wear resistant components have been demonstrated.

Property Value

Vickers hardness 10,000 kg/mm2

Young's modulus 1050 GPa

Poisson's ratio 0.1

Thermal expansion coefficient 1.0×10-6_{/K @300K}

Tensile strength (0.5mm thick)

Nucleation surface in tension 1100 MPa Growth surface in tension 500 MPa

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5. Examples of CVD diamond applications

CVD diamond window in UHV flange

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Flexible CVD diamond heatspreaders

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CVD diamond anchor wheel

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6. Useful formulae

Bowing of a circular disk under pressure

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(

ν+ν

)

+ = 1 64 5 Pr4 S wss S wcl 64 1 Pr4 = ) 1 ( 12 2 3 ν − = El S

where w = central deflection (ss = simply supported, cl = clamped), E = Young’s modulus, L = thickness, P = pressure, v = Poisson ratio, r = radius

Thickness requirements

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For flat windows, the minimum thickness as determined by pressure-induced fracture is given by

f /σ sf pS D L =0.554 ∆

where L = minimum thickness, σf = mechanical strength, ∆p = pressure

difference, D = diameter, Ssf = safety factor

Typically mechanical strength values are in the 2000-400 MPa range

depending on thickness. As a rule of thumb the minimum thickness is 1.7 % of the free diameter (one bar pressure difference, Ssf = 4).

5_{Warren C. Young, “Roark’s Formulas for Stress & Strain”, McGraw-Hill, New York (1989)}

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Contact Diamond Materials

Contact persons: Dr. Christoph Wild Dr. Eckhard Wörner

Internet: www.diamond-materials.com

E-mail: [email protected] Telefon: +49 (0)761 600 6554

Fax: +49 (0)761 600 6553 Address: Diamond Materials GmbH

Tullastr. 72

79108 Freiburg

Germany

This booklet may be freely distributed provided that it is unaltered and that no charge is made and this copyright notice is retained.