lecture 3 properties of diamond films ● thermal conductivity ● isotopic effect ● impurities...
TRANSCRIPT
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