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Lecture 3. Properties of diamond films. ● Thermal conductivity ● Isotopic effect ● Impurities ● Optical properties ● Stress ● Fracture strength. Thermal conductivity of diamond and some optical and electronic materials at room temperature. bulk materials.

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Lecture 3

Properties of diamond films

● Thermal conductivity

● Isotopic effect

● Impurities

● Optical properties

● Stress

● Fracture strength


Thermal conductivity of diamond and some optical and electronic materials at room temperature

bulk materials

3 GHz, 50 W transistor on

CVD diamond heat spreader.

“Pulsar” company, Moscow

● thermal conductivity of diamond:

5 times higher than for copper, and 50 times higher than for sapphire.

● ultimate bulk material for thermal management and high power optics.


Anisotropy of thermal conductivity

in polycrystalline CVDdiamond

Phonon scattering on grain boundaries.

Columnar grain structure  TC anisotropy.

Depth inhomogeneity due to crystal size variation.

Perpendicular values k should higher than the in-plane values k.

J. Graebner, et al., J. Appl. Phys. 71 (1992) 5353.


IR detector

laser beam


metal film (absorber)

Measurements of thermal diffusivity by Laser Flash Technique (LFT)

●Delivery of laser pulse through an optical fiber to improve uniformity of irradiation on the sample.

● Software for automatic evaluation of thermal diffusivity and TC.

●Vacuum Cryostat. Measurements thermal diffusivity in the temperature range 180 – 430 К.

● LFT measures perpendicularthermal diffusivityD.

Method: heating of the front side by short laser pulse and tracing the T(t) on rear side.

Temperature evolution (T(t) on rear side of the film


He - Ne


Transient thermal grating technique

measures parallelthermaldiffusivityD

  • ●thermal grating formation due to
  • refraction coefficient modulation by
  • two interfering laser (Nd:YAG) beams.
  • ● diffraction of probe He-Ne laser beam
  • on the transient grating with period Λ.

Diffraction signal decay due to thermal dissipation


Set-up for DIImeasurement using thermal grating technique

Period of thermal grating 30-120 µm

E.V. Ivakin, QuantumElectronics(Moscow),32 (2002) 367.


Thermal conductivity at room temperature

sensitive to content of hydrogen impurity in diamond

● Bonded hydrogen (C-H) decorates defects and grain boundaries.

● Hydrogen concentration as an indicator the defect abundance in CVD diamond.



● Thermal conductivity as high as 2100 W/mK.

● anisotropy: k (perpendicular ) > k (in-plane); Δk/k=10-15%.

A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589


Thermal conductivity k┴ vs hydrogen impurity in diamond

Open squares – samples from Element Six [S.E. Coe, Diamond Relat. Mater. 9 (2000) 1726];

full squares – GPI samples.

V. Ralchenko, in Hydrogen Materials Science and Chemistry of Metal Hydrides, Kluwer, 2002, p. 203.


Thermal conductivity along diamond wafer

as measured by LFT at room temperature

disk diameter 63 mm, thickness 1.28 mm

k, W/cmK

Distance along disk diameter, mm


Correlation of optical absorption and

parallel thermal conductivity

Absorption spectra in the visible

In agreement with the correlation found by

J. Graebner, DRM,4 (1995) 1196 for white light absorption and k.

At least a part of defects contribute both in enhanced absorption and in thermal resistance.

A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589


Thermal conductivity kII at elevated temperatures

The decrease of thermal conductivity with T is mostly due to phonon-phonon scattering mechanism (phonon population increases with T).

Well fitted with the relationship k ~ T –n (solid lines).

  • Samples compared:
  • - undoped diamond film (poly),
  • B-doped film poly);
  • type IIa single crystal diamond
  • [T.D. Ositinskaya, Superhard Materials (Kiev), No. 4 (1980) 13].

k(T) : general form for an insulator

Heat is transferred by phonons

k = ⅓ C(T)· v· λ(T)

C is the heat capacity per unit volume, v is the average phonon velocity,

λ is the mean free path of phonons between collisions.

Any phonon scattering mechanism reducing λ decreases the thermal conductivity.


on boundary



● The peak in k occurs at a temperature about 10% of Debye temperature, D.

● At low T: λ is constant, and k ~C(T) ~ T3.

● Phonon-phonon scattering dominates at high T (k~ T-1).

● Scattering on defects is essential at intermediate temperatures.


Temperature dependence of thermal conductivity

for certain crystals

k, W/mK

Occurrence a maximum in k(T) at low temperatures (80-100 K).

Diamond – not the champion in the value of maximum TC,

but its k is uniquely high at high temperatures (T>70K), particularly at room temperature.

This is the consequence of record high Debye temperature θD =1860K for diamond (very high phonon frequencies are excited).

R. Berman, Diamond. Res. (1976)


Thermal conductivity kII at elevated temperatures

T = 293-460 K

Exponent n = 0.17 – 1.02 increases with diamond quality

Approximationk ~ T –n

  • ● Comparison with data for single crystal natural diamonds [ Burgemeister, Physica,  1978].
  • ● Weak temperature dependence for highly defective CVD diamond.

● Concentration of H impurity (in ppm) is indicated for each sample.

● The data for isotopically pure (12C) synthetic HPHT single crystal diamond [Olson PB’1993] give n=1.36, the highest slope for any diamond.

A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589


Defects in transparent CVD diamond (poly)

GB - grain boundaries

T - twins

SF - stacking faults

D - dislocations

L. Nistor et al, Phys. Stat. Sol.(a), 174 (1999) 5.


Typical dimensions of defects

Point defects are atomic scale defects:

- isolated foreign atoms;

- different isotopes;

- vacancies

Nitrogen ~ 1 ppm or less

Boron << 1ppm

Hydrogen 20 -1000 ppm (poly)

Vacancies - few ppm (?)

Isotope 13C ~10,000 ppm (main impurity!)

Scattering rate of phonons with frequency ωon isotopic atom with mass m +Δm:

1/τiso = Ãisoω4

Ãiso = Ciso(V0/4πv3)[Δm/m]2

Ciso is isotope concentration, V0 is atomic volume, v is sound velocity.

For diamond Δm=1 :

Aiso(nat) = 4.045 × 10-3 c-1K-1.

Defects present in polycrystalline CVD diamond and their scale

K.J. Gray, Diamond Relat. Mater. (1999)


Thermal conductivity of isotopically “pure” diamond

Is it possible to increase K for diamond above 2400 W/mK at room temperature?

Natural and synthetic diamonds (and any carbon material) contain 1.1% of isotope 13C.The 13C atoms are scattering centers for phonons – carriers of heat, thus restricting the thermal conductivity of diamond.

Concentration of 13C isotope is much higher than other impurities–point defects.

Solution – eliminate 13C isotope from CVD diamond.


Isotopic effect on thermal conductivity of diamond

The ultimate opportunity to achieve TC values > 2400 W/mK relays on purification of isotopic composition of diamond.

The natural isotope content in diamond is 98.93% 12C and 1.07% 13C.

Phonon scattering on 13C atoms results in thermal resistance.

Previous works



Isotopically modified 12C (99.90%) single crystalHPHT diamond, General Electric (1990-1993)

k=33.2 W/cmK

50% increase vs “normal” diamond.

L. Wei, PRL, 70 (1993) 3764

12C-enriched polycrystallineCVD diamond films:

k = 21,8 W/cmK; k = 26 W/cmK

G.E. Graebner, Appl. Phys. Lett. 64 (1994)2549.

Highly enriched (99.98%) 28Si.

At room temperature:

thermal conductivity enhancement of 10%

compared to k = 140 W/mK for natural Si.

In the maximum at 26K the TC gain is 8 times.

R.K. Kremer et al. Sol. State Comm. 131 (2004) 499.


Growth of isotopically enriched poly12C CVD diamond

● production of 12CO with purity 12C 99.96%

● conversion to 12CH4

● diamond deposition by MPCVD (purity is preserved)

● cutting to 12x2x0.46 mm3 bar

● TC measurements, steady state method

CO isotope separation by diffusion. “Colonna” system,

Kourchatov Institute, Moscow.

k = 2510W/mK at 298K for 12C diamond (higher than for type IIa single crystals) - isotopic effect of 32%.

k = 1900W/mKfor 0.5 mm thick film with natural isotope abundance.

k=2600W/mK- perpendicularly to the film plane.

The isotopic effect increases with temperature decrease - the maximum TC of 4700 W/mK at T=160K.

A. Inyushkin et al. Bull. Lebedev Phys. Inst. 34 (2007) 329

The further increase in TC for 12C diamond is limited by defects, impurities, grain boundaries.

► single crystals


Measurement cell to determine thermal conductivity at T = 4 - 450K

Steady state method of constant thermal gradient.

Sample – polycrystalline CVD diamond.

The cryostat in vacuum lower 10-5 Torr.

Multilayer thermal radiation shield (at T>200K).

Measurement accuracy of k is better 3% (primarily due to an error in distance between thermometers).

Copper block

Diamond bar 14x2x0.5 mm3

Resistor thermometer

(Cernox, LakeShore Cryotronics)



Kourchatov Institute, Moscow


Applications of isotopically modified diamonds

with extraordinary thermal conductivity

● Heat spreaders for high power electronic devices

● Single crystals and nanocrystals with nitrogen-vacancy (NV)

fluorescent color centers for quantum computing and cryptography -

isotope 13C with nuclear spin should be eliminated to increase spin

relaxation (coherence) time of NV centers to µs level.

● Reflecting and transmission X-ray optics for high intensitybeams

(synchrotron sources)

a combination of high TC, low atomic number Z and structure

perfection is required.

● Laser optics (including diamond Raman lasers) with increased damage



Thermalconductivity of UNCD

measured by a laser flash technique

● k = 0.06-0.10 W/cmK at RT is 200 times lower than for single crystal diamond, but still higher than for amorphous sp3 carbon ta-C ka-C= 0.035 W/cmK.

● Thermal conductivity decreases with nitrogen “doping”.

● k = 1/3 C*V*L, where C – heat capacity, V – sound velocity, L – phonon free path. For single crystal L=240 nm; for NCD L2 nm (of the order of grain size).

Thermal conductivityvs N2%

V. Ralchenko, et al. DRM, 16 (2007) 2067


Thermalconductivity of UNCD

Temperature dependences measured by “3 Omega” method

W.L. Liu et al.APL 89 (2006) 171915


● kNCDis between polycrystalline diamond and amorphous carbon;

● slow and monotonic temperature dependence;

● in a phonon-hopping model (PHM) the reduction in thermal conductivity is

due to decrease in phonon transparency parameter (t) through grain boundaries:

t=0.2-0.32 for UNCD, t=0.9 for polycrystalline film.


Nitrogen and hydrogen impurities in CVD diamond

N and H content evaluation from optical absorption spectra

N-induced UV absorption

270 nm

C-H stretch absorption bands

2800-3100 cm-1

2-phonon absorption

Diamond samples of different qualities A - E

S. Nistor et al. J. Appl. Phys. 87 (2000) 8741.

Correlation of (bonded) H and N impuritiesHydrogen and nitrogen concentrations are determined from IR and UV absorption

V. Ralchenkoet al. in Hydrogen Materials Science and Chemistry of Metal Hydrides, Kluwer, 2002, p. 203;

A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589.


Luminescent nitrogen-vacancy (N-V) and nitrogen-vacancy (Si-V) color centers in diamond

PL spectrum on moderate quality of polycrystalline diamond film.

● Bright PL lines на 637 nm (1,945 эВ) from NV-and 575 nm from NV0.

● PL lines на 738nmfrom SiV.

● All these centers are stable at room temperature.

● Dopingduring growth process


Si impurity in CVD diamond: depth mapping

V. Ralchenko, inNanostructured Thin Films and NanodispersionStrengthened Coatings, 2004, p. 209.

Mapping PL in cross section

The diamond films were deposited on Si substrate at temperature 700ºC (squares) and 800ºC (triangles), and on Mo substrate at 700ºC (circles).

Si impurity extends to 20-60 μm in depth.

Si-diamond interface


Optical transmission

Extremely broad transparency window: from UV to RF, including THz range

● Cut-off wavelength 225 nm.

● 2-phonon absorption band at 2.5- 6.3 µm

● Loss tangent 10-5 at 170 GHz.


Optical transmission in UV and visible range for natural IIa type single crystal diamond and poly CVD film

absorption and scattering on

defects and grain boundaries


Polycrystalline CVD diamond as material for high power CO2laser windows

Non-contact phase photothermalmethod to absolute measurements of optical absorption coefficient

The absorption of heating CO2laser (λ=10.6 μm) leads to local variable (at the modulation frequency) heating and to changes in the refractive index, which, in turn, caused the change in the phase difference between two probe beams of He-Ne laser (633 nm) detected by the probe interferometer.

Simulation and experiment show that the level of low absorption achieved is enough for use of CVD diamond as window of multi-kilowatt cw CO2 lasers.

A.Yu. Luk’yanov, QuantumElectronics (Moscow) 38 (2008)1171


Dielectric losses in CVD diamond (170 GHz)

● Far infrared (Microwave) absorption of dielectrics is due to lattice absorption owing to unharmonism (two phonon absorption - TPA). Diamond has very low TPA, hence low loss tangent.

● Theory: tgδ ~109 for λ=2 mm (150 GHz) [B. Garin, JTP Lett. 1994, No. 21, p.56]– record low for any material. Compare with tgδ ~105 for Si.

● Experiment: best result tgδ ~ 3106@ 140 GHz for Element Six polydiamond.

Sample: GPI 0.74 mm thick diamond film

tgδ ~105 stable up to 400ºC

B. Garin et al. Techn. Phys. Lett. 25 (1999) 288


MicroRaman mapping of stress in diamond films

The confocal optical scheme – high spatial resolution

◄ no stress

◄ compressive stress

◄ tensile stress

Raman spectra taken at 5 different locations on the surface of diamond film within one grain (≈100x100 µm). The shift of the peak from 1332. 5 cm-1 position is the evidence of stress.


MicroRaman stress mapping on a surface over a selected 160x160 μm grain in the diamond film

local stress regions

 [cm-1] = -2.2 [GPa] stress along (111);

 [cm-1] = -0,7 [GPa] stress along (100).

max  ≈ 6 cm-1max  ≈ 3 GPa

I.I. Vlasov, Appl. Phys. Lett. 71 (1997) 1789.


MicroRaman Stress mapping around grain boundary

laser beam scanning in depth and along the surface

in-depth, grain B

in-depth, grain A

lateral, from A to B

I. Vlasov, Physica Status Solidi (a), 174 (1999) 11.


Fracture strength by 3-point measurement techniques

Advantage of 3 point method: ability to handle with small size samples

Observation: the fracture happens close to the central part of the bars (in locations of maximum stress)

Testing apparatus at Fraunhofer Institute IAF, Friburg


Fracture strength



b and h are the specimen width and thickness,

Fс is critical load value,

l= 7.8 mm is distance between supports,

Dis displacement of the bar under load

(measured by an inductive sensor with a resolution ~ 1µm).

Similar principle atUSTB (Beijing) DF-100 test unit

bar thickness of 0.5 mm only

L = 8 mm, loading rate 0.5 N/s

two supporting cylinders 3mm diameter.

V.G. Ralchenko et al.Diamond and Related Materials 23 (2012) 172.


Fracture strength vs film thickness

white diamond

Grain size ranges with thickness from 10 µm to ~ 200 µm

σfr = 400 - 1400 MPa

for 0.5 mm thick plate

● Rapid increase in strength towards small thickness h:

σ= 600 MPa @ h ≈ 1000 µm ► 2.2 GPa @ h = 60 µm (nucleation side in tension).

● Similar tendency for growth side.

● Compatible with Hall-Petch relation if the length of critical cracks is proportional to grain size.

● Results similar to Element Six data.

● The Young’ modulus of Е=1072 ± 153 GPameasured from the bending tests is only 10% lower compared to therotetical Young’ modulus of polycrystalline diamond.


Fracture strength vs grain size

Hall-Petch relationσf = σ0 +Kd-1/2

Growth side and substrate side are under tensile load.White diamond.


Fracture patterns close to growth and nucleation sides

white diamond

Growth side, top view –

evidence of transgrain fracture

Growth side

Cleavage steps

Nucleation side

●Transcrystallitefracture over entire film thickness

● Strong grain boundaries


Fractures statistics. Weibull analysis for white diamond

P(σ) = 1 – exp[– (σ)/σN)m]

m is Weibull modulus, can found from slope of eq. or ln[–ln(1 – P)] = – mln(σN) + mln(σ)

High m value means more narrow strength interval (more predictable behavior).

Nominal strength

σN = 550 MPa for growth side in tension

σN =1060 MPa for substrate side in tension

Higher modulus m for growth side


Comparison of fracture strength of white and black diamond

film thickness 0.5 mm

Independent on what side is under tension, a factor of 2 – 2.5 lower σ for opaque material in spite of the smaller grain size.


Black diamond. Fracture surface

Cleavage along GB ►smooth surface planes along boundaries of columnar grains

► reduced bending strength

intergranular fracture

transgranular fracture

Growth side

Nucleation side

Area in the middle of the cross- section

Columnar structure is seen even in a few microns thin layer adjacent to the substrate.