Lecture 3

Properties of diamond films

● Thermal conductivity● Isotopic effect● Impurities● Optical properties● Stress● Fracture strength

0

500

1000

1500

2000

Al2O

3GaAs

GaNSiAlNBeO

Cu4H-SiC

CVD Diamond

Therm

al c

onduct

ivity

(W

/m*K

)

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

● 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.

bulk materials

3 GHz, 50 W transistor on CVD diamond heat spreader.“Pulsar” company, Moscow

Anisotropy of thermal conductivity in polycrystalline CVD diamond

Perpendicular values k should higher than the in-plane values k.J. Graebner, et al., J. Appl. Phys. 71 (1992) 5353.

Phonon scattering on grain boundaries.Columnar grain structure TC anisotropy.Depth inhomogeneity due to crystal size variation.

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

● 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 perpendicular thermal diffusivity D.

Measurements of thermal diffusivity by Laser Flash Technique (LFT)

laser beam

IR detector

metal film (absorber)

sample

Transient thermal grating technique

measures parallel thermal diffusivity D

-2 -1 0 1 2 3 4 5

0,00

0,02

0,04

0,06

0,08

0,10

1064 nm

Diff

ract

ion

inte

nsity

, a.u

.

Time, microseconds

II2

2

4 D

● 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

Nd:YAG

He - Ne

A custo -op tic g ate

H arm on ic s g en era to r

D iffractio na lbeam sp litter

S am ple

O ptica l fibe r

D ig ita l o sc ilo scopeand P C

S pa tia l filter

S pa tia l filter

Tri

gger

ring

1 0 64 , 532 , 35 5 , 26 6 , 2 13 nm

63 3 nm

P M T

H e-N e la se r

YA G :N d la ser 1

Set-up for DII measurement using thermal grating technique

E.V. Ivakin, Quantum Electronics (Moscow), 32 (2002) 367.

Period of thermal grating 30-120 µm

Thermal conductivity at room temperaturesensitive 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%.

0 200 400 600 800 1000

8

10

12

14

16

18

20

22

KII

K

k, W

/cm

К

Hydrogen concentration in diamond, ppm

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

K║

K┴

10 100 1000

5

10

15

20

25

The

rmal

con

duct

ivity

, W

/cm

K

Hydrogen concentration, ppm

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 k┴ vs hydrogen impurity in diamond

Thermal conductivity along diamond wafer as measured by LFT at room temperature

disk diameter 63 mm, thickness 1.28 mm

Distance along disk diameter, mm

k, W/cmK

Correlation of optical absorption and parallel thermal conductivity

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

0 5 10 15 20 25 30 35

8

10

12

14

16

18 = 500 nm

Th

erm

al c

on

du

ctiv

ity W

cm-1

K-1

Absorption, cm-1

In agreement with the correlation found by J. Graebner, DRM, 4 (1995) 1196 for white light absorption and k. 200 300 400 500 600 700

25

50

75

100

17.4

15.3

11.3

12.5

12.4

7 .9 W cm -1 K -1

, c

m-1

Wavelength, nm

Absorption spectra in the visible

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

Thermal conductivity kII at elevated temperatures

250 300 35 0 40 0 45 0 50 0 55 0 60 0 65 0

6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

type IIa B-dope CVDundoped CVD

Tem perature, K

Th

erm

al c

on

du

ctiv

ity,

W/c

mK

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].

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).

● 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.

k(T) : general form for an insulator

phonon-phononscattering

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.

scatteringon boundary

defects

Temperature dependence of thermal conductivityfor certain crystals

R. Berman, Diamond. Res. (1976)

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).

k, W/mK

Thermal conductivity kII at elevated temperaturesT = 293-460 K

Approximation k ~ T –n

● Comparison with data for single crystal natural diamonds [ Burgemeister, Physica,  1978].

● Weak temperature dependence for highly defective CVD diamond.

300300300 360 420 480

1010

8

12

16

20

24

28

32

36isotopically pure [Olson, 1993]

690

620

250

50

[H] = 150 ppm

K

II (W

cm/K

)

Temperature (K)

● 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.

Exponent n = 0.17 – 1.02 increases with diamond quality

0.2 0.4 0.6 0.8 1.0 1.2 1.4

4

6

8

10

12

14

16

18

20

22

CVD

Type Ia [5]

KII

(Wcm

/K)

n

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

GB - grain boundariesT - twinsSF - stacking faultsD - dislocations

Defects in transparent CVD diamond (poly)

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

Defects present in polycrystalline CVD diamond and their scaleK.J. Gray, Diamond Relat. Mater. (1999)

Typical dimensions of defects

Point defects are atomic scale defects: - isolated foreign atoms; - different isotopes; - vacanciesNitrogen ~ 1 ppm or lessBoron << 1ppmHydrogen 20 -1000 ppm (poly)Vacancies - few ppm (?) Isotope 13C ~10,000 ppm (main impurity!)

Scattering rate of phonons with

frequency ω on 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.

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.

Thermal conductivity of isotopically “pure” diamond

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

Isotopic composition of C, Si and Ge

Element Isotopes content, %

C 12C98.93

13C1.07

Si 28Si92.23

29Si4.68

30Si3.09

Ge 70Ge20.38

72Ge27.31

73Ge7.76

74Ge36.72

76Ge7.83

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.

Isotopic effect on thermal conductivity of diamond

12C-enriched polycrystalline CVD diamond films: k = 21,8 W/cmK; k = 26 W/cmK

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

Isotopically modified 12C (99.90%) single crystal HPHT diamond, General Electric (1990-1993) k=33.2 W/cmK50% increase vs “normal” diamond.

L. Wei, PRL, 70 (1993) 3764

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.

Previous works Si diamond

Growth of isotopically enriched poly 12C CVD diamond

CO isotope separation by diffusion. “Colonna” system, Kourchatov Institute, Moscow.

● 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

100 200 300 40010

15

20

25

30

35

40

45

25.1 W/cm K

19.0 W/cm K

12C

naturC (poly)

Th

erm

al

co

nd

ucti

vit

y

(W c

m1K1)

Temperature (K)

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

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

k=2600 W/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

Diamond bar 14x2x0.5 mm3

Heater(resistor)

Resistor thermometer(Cernox, LakeShore Cryotronics)

Copper block

Measurement cell to determine thermal conductivity at T = 4 - 450KSteady state method of constant thermal gradient.

Kourchatov Institute, Moscow

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).

Applications of isotopically modified diamondswith 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 intensity beams (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 threshold.

● 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 L2 nm (of the order of grain size).

0 5 10 15 20 25

0,030

0,035

0,040

0,045

0,050

0,055

0,060

0,065

0,070

0.12

0.11

0.1

0.09

0.08

0.07

0.06

0.05

Th

erm

al c

on

du

ctiv

ity,

W/c

m*К

Th

erm

al d

iffu

sivi

ty,

cm2 /s

N2, %

Thermal conductivity of UNCDmeasured by a laser flash technique

Thermal conductivity vs N2%

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

● kNCD is 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.

Thermal conductivity of UNCDTemperature dependences measured by “3 Omega” method

200 40010-3

10-2

10-1

100

101

102

Hopping Model (22nm, t=0.32)

Hopping Model (26nm, t=0.2)

Minimum K for Carbon

Hopping Model (2m, t=0.9)

Bulk Diamond: Callaway Model

Th

erm

al

Co

nd

uc

tiv

ity

(W

/cm

K)

Temperature (K)

Poly NCD_25 NCD_0

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

a-C

C-H stretch absorption bands2800-3100 cm-1

Nitrogen and hydrogen impurities in CVD diamondN and H content evaluation from optical absorption spectra

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

N-induced UV absorption270 nm

Diamond samples of different qualities A - E

2800 2900 3000 3100

5

10

15

20

25

EC

B

D

A

Abs

orba

nce,

cm

-1

Wavenumber, cm-1200 300 400 500 600 700

100

200

300

400

500

600

250 300 350 4000

50

100

150

, c

m-1

Wavelength, nm

EDC

B

A

Abs

orba

nce,

cm

-1

Wavelength, nm

4000 3500 3000 2500 2000 1500 1000 500

10

20

30

40

50

60

70

T,

%

Wavenumber, cm-1

2-phonon absorption

Correlation of (bonded) H and N impurities Hydrogen and nitrogen concentrations are determined from IR and UV

absorption

0 2 4 6 8 10 12 14 16 18

100

200

300

400

500

600

Substitutional nitrogen concentration, ppm

Bon

ded

hydr

ogen

con

cent

ratio

n, p

pm

V. Ralchenko et 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 738 nm from SiV.

● All these centers are stable at room temperature.

● Doping during growth process

500 600 700 8000

50

100

150

200

250

300

350

(N-V)-

575 nm (N-V)0

2-nd

ord

er

daim

ond

In

tens

ity, a

rb. u

nits

Wavelenght, nm

637 nm

Si-V 738 nm

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 impurity in CVD diamond: depth mappingV. Ralchenko, in Nanostructured Thin Films and Nanodispersion Strengthened Coatings, 2004, p. 209.

0 10 20 30 40 50 60

0

10

20

30

40

50

Mo, 700oC

Si, 700oC

Si, 800oC

Inte

nsity

, a.u

.

distance from substrate surface, m

Si-diamond interface

Mapping PL in cross section

Optical transmission

● Cut-off wavelength 225 nm.● 2-phonon absorption band at 2.5- 6.3 µm● Loss tangent 10-5 at 170 GHz.

1 10

20

40

60

80

# 109150 m thick

Tra

nsm

ittan

ce, %

Wavelength, m10 100 1000

0

1

Tra

nsm

itta

nce

Wavenumber, cm-1

Window 27_02_2009

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

200 300 400 500 600 700 8000

10

20

30

40

50

60

70

80

Single crystal

CVD diamond

Tra

nsm

issi

on,

%

Wavelength, nm

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 CO2 laser windows

Non-contact phase photothermal method to absolute measurements of optical absorption coefficient The absorption of heating CO2 laser (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.

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

Diamond type α, cm-1 (10.6 μm) HPHT single crystal (yellow) 0.09 – 0.50 Natural single crystal (white) 0.086 CVD polydiamond (GPI) 0.057 CVD polydiamond (Element Six) 0.03 Theoretical limit (due to two phonon absorption tail)

0.03

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.

● 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 ~109 for λ=2 mm (150 GHz) [B. Garin, JTP Lett. 1994, No. 21, p.56] – record low for any material. Compare with tgδ ~105 for Si.● Experiment: best result tgδ ~ 3106 @ 140 GHz for Element Six polydiamond.

Dielectric losses in CVD diamond (170 GHz)

0 100 200 300 400 500 600 Temperature, oC

5

10

15

20

25

30

35

tan [10 6

]

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

Sample: GPI 0.74 mm thick diamond filmtgδ ~105 stable up to 400ºC

50 100 150 2001

2

3

4

5

tan [10 5

]

f [GHz]

1

2

1320 1330 1340

e

d

c

b

a

1332.5 cm-1

Inte

nsit

y, a

.u.

Raman shift, cm-1

MicroRaman mapping of stress in diamond filmsThe confocal optical scheme – high spatial resolution

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.

◄ no stress

◄ compressive stress

◄ tensile stress

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

Ei

KsKi

{110} [110]

[1

10]

[001]

0

2

4

6

Spl

ittin

g

, c

m-1

E

D

C

B

A

{110} _

[110]

[001]

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-1 max ≈ 3 GPa

1320 1330 1340

tension (-) compression (+)

40 m

20 m

-20 m

-40 m

0 m

1332.5 cm-1

-60 m

Inte

nsi

ty, a

.u.

Raman shift, cm-1 1320 1330 1340

tension (-) compression (+)

40 m

20 m

0 m

1332.5 cm-1

Inte

nsi

ty, a

.u.

Raman shift, cm-1 1320 1330 1340

tension (-) compression (+)

40 m

20 m

0 m

1332.5 cm-1

60 m

Inte

nsi

ty, a

.u.

Raman shift, cm-1

MicroRaman Stress mapping around grain boundarylaser beam scanning in depth and along the surface

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

lateral, from A to B in-depth, grain A in-depth, grain B

fracFbh

l

22

3

DF

hb

lE

3

3

4

Fracture strength

Young’s modulus

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)

(1)

(2)

Testing apparatus at Fraunhofer Institute IAF, Friburg

two supporting cylinders 3mm diameter.

b and h are the specimen width and thickness, Fс is critical load value, l = 7.8 mm is distance between supports,D is displacement of the bar under load (measured by an inductive sensor with a resolution ~ 1µm).

Similar principle at USTB (Beijing) DF-100 test unitbar thickness of 0.5 mm onlyL = 8 mm, loading rate 0.5 N/s

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

Fracture strength vs film thicknesswhite diamond

● 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 GPa measured from the bending tests is only 10% lower compared to therotetical Young’ modulus of polycrystalline diamond.

0 300 600 900 12000

500

1000

1500

2000

2500

0 500 1000 1500 20000

50

100

150

200

250

300

Film Thickness, m

Gra

in S

ize,

m

Fr

actu

re s

treng

th

f, M

Pa

Film thickness, m

growth side

substrate side

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

σfr = 400 - 1400 MPafor 0.5 mm thick plate

Fracture strength vs grain size

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

Hall-Petch relation σf = σ0 +Kd-1/2

The plate side under

tension

0, MPa K, MPa·cm1/2

growth side (21 samples) 41±36 3900±270

substrate side (21 samples) 197±105 6910±780

0

400

800

1200

1600

2000

2400

0 0.05 0.10 0.15 0.20 0.25 0.30

growth side

substrate side

Frac

ture

stre

ngth

f ,

MP

a

Grain size d, m400 100 44 25 16 11

(Grain size d)- 1/2, m- 1/2

Fracture patterns close to growth and nucleation sides

white diamond

Growth side, top view – evidence of transgrain fracture

●Transcrystallite fracture over entire film thickness● Strong grain boundaries

Nucleation side

Growth side

Cleavage steps

Fractures statistics. Weibull analysis for white diamond

Nominal strengthσN = 550 MPa for growth side in tensionσN =1060 MPa for substrate side in tension

Higher modulus m for growth side

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).

-4

-3

-2

-1

0

1

2

7.26.96.66.36.05.7

(a)

growth side

m = 4.5

ln , MPa

ln (-

ln(1

-P))

substrate side

m = 6.4

0 300 600 900 1200 15000

0.2

0.4

0.6

0.8

1.0

(b)

Failu

re P

roba

bilit

y

, MPa

growth side

substrate side

Comparison of fracture strength of white and black diamondfilm thickness 0.5 mm

diamond grade

thickness t, μm

grain size, μm

σfg, MPa

σfn, MPa

black 538±39 10 141±10 316±109 white 490±10 60 312±33 812±86

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

transgranular fracture

intergranular fracture

Cleavage along GB ►smooth surface planes along boundaries of columnar grains ► reduced bending strength

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

Area in the middle of the cross- section

Growth side

Nucleation side