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) 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 ● 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
Set-up for D II measurement using thermal grating technique E.V. Ivakin, Quantum Electronics (Moscow), 32 (2002) 367. Period of thermal grating µm
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 K║K║ K┴K┴
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 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. In agreement with the correlation found by J. Graebner, DRM, 4 (1995) 1196 for white light absorption and k. Absorption spectra in the visible A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589
Thermal conductivity k II at elevated temperatures 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) ~ T 3. ● 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-phonon scattering 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. scattering on boundary defects
Temperature dependence of thermal conductivity for certain crystals R. Berman, Diamond. Res. (1976) Occurrence a maximum in k(T) at low temperatures ( 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 θ D =1860K for diamond (very high phonon frequencies are excited). k, W/mK
Thermal conductivity k II at elevated temperatures T = K Approximation k ~ 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 ( 12 C) 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 A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589
GB - grain boundaries T - twins SF - stacking faults D - 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 scale K.J. Gray, Diamond Relat. Mater. (1999) Typical dimensions of defects Point defects are atomic scale defects: - isolated foreign atoms; - different isotopes; - vacancies Nitrogen ~ 1 ppm or less Boron << 1ppm Hydrogen ppm (poly) Vacancies - few ppm (?) Isotope 13 C ~10,000 ppm (main impurity!) Scattering rate of phonons with frequency ω on isotopic atom with mass m +Δm: 1/τ iso = Ã iso ω 4 Ã iso = C iso (V 0 /4πv 3 )[Δm/m] 2 C iso is isotope concentration, V 0 is atomic volume, v is sound velocity. For diamond Δm=1 : A iso (nat) = × c -1 K -1.
Natural and synthetic diamonds (and any carbon material) contain 1.1% of isotope 13 C. The 13 C 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 13 C 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 ElementIsotopes content, % C 12 C C 1.07 Si 28 Si Si Si 3.09 Ge 70 Ge Ge Ge Ge Ge 7.83
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% 12 C and 1.07% 13 C. Phonon scattering on 13 C atoms results in thermal resistance. Isotopic effect on thermal conductivity of diamond 12 C-enriched polycrystalline CVD diamond films: k = 21,8 W/cmK; k = 26 W/cmK G.E. Graebner, Appl. Phys. Lett. 64 (1994) Isotopically modified 12 C (99.90%) single crystal HPHT diamond, General Electric ( ) k=33.2 W/cmK 50% increase vs “normal” diamond. L. Wei, PRL, 70 (1993) 3764 Highly enriched (99.98%) 28 Si. 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 12 C CVD diamond CO isotope separation by diffusion. “Colonna” system, Kourchatov Institute, Moscow. ● production of 12 CO with purity 12 C 99.96% ● conversion to 12 CH 4 ● diamond deposition by MPCVD (purity is preserved) ● cutting to 12x2x0.46 mm 3 bar ● TC measurements, steady state method k = 2510 W/mK at 298K for 12 C 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 12 C diamond is limited by defects, impurities, grain boundaries. ► single crystals
Diamond bar 14x2x0.5 mm 3 Heater (resistor) Resistor thermometer (Cernox, LakeShore Cryotronics) Copper block Measurement cell to determine thermal conductivity at T = K Steady state method of constant thermal gradient. Kourchatov Institute, Moscow Sample – polycrystalline CVD diamond. The cryostat in vacuum lower 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 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 13 C 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 = W/cmK at RT is 200 times lower than for single crystal diamond, but still higher than for amorphous sp 3 carbon ta-C k a-C = 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 conductivity of UNCD measured by a laser flash technique Thermal conductivity vs N 2 % V. Ralchenko, et al. DRM, 16 (2007) 2067
● k NCD 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= for UNCD, t=0.9 for polycrystalline film. Thermal conductivity of UNCD Temperature dependences measured by “3 Omega” method W.L. Liu et al. APL 89 (2006) a-C
C-H stretch absorption bands cm -1 Nitrogen and hydrogen impurities in CVD diamond N and H content evaluation from optical absorption spectra S. Nistor et al. J. Appl. Phys. 87 (2000) N-induced UV absorption 270 nm Diamond samples of different qualities A - E 2-phonon absorptio n
Correlation of (bonded) H and N impurities Hydrogen and nitrogen concentrations are determined from IR and UV absorption 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 NV 0. ● PL lines на 738 nm from SiV. ● All these centers are stable at room temperature. ● Doping during growth process
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 μm in depth. Si impurity in CVD diamond: depth mapping V. Ralchenko, in Nanostructured Thin Films and Nanodispersion Strengthened Coatings, 2004, p Si-diamond interface Mapping PL in cross section
Optical transmission ● Cut-off wavelength 225 nm. ● 2-phonon absorption band at µm ● Loss tangent at 170 GHz. Extremely broad transparency window: from UV to RF, including THz range
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 CO 2 laser windows Non-contact phase photothermal method to absolute measurements of optical absorption coefficient The absorption of heating CO 2 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 Simulation and experiment show that the level of low absorption achieved is enough for use of CVD diamond as window of multi-kilowatt cw CO 2 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 ~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 10 140 GHz for Element Six polydiamond. Dielectric losses in CVD diamond (170 GHz) B. Garin et al. Techn. Phys. Lett. 25 (1999) 288 Sample: GPI 0.74 mm thick diamond film tgδ ~10 5 stable up to 400ºC
MicroRaman mapping of stress in diamond films The 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 cm -1 position is the evidence of stress. ◄ no stress ◄ compressive stress ◄ tensile stress
I.I. Vlasov, Appl. Phys. Lett. 71 (1997) 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
MicroRaman Stress mapping around grain boundary laser 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
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, F с 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 unit bar thickness of 0.5 mm only L = 8 mm, loading rate 0.5 N/s V.G. Ralchenko et al. Diamond and Related Materials 23 (2012) 172.
Fracture strength vs film thickness white diamond ● Rapid increase in strength towards small thickness h: σ = 600 h ≈ 1000 µm ► 2.2 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. Grain size ranges with thickness from 10 µm to ~ 200 µm σ fr = MPa for 0.5 mm thick plate
Fracture strength vs grain size Growth side and substrate side are under tensile load. White diamond. Hall-Petch relation σ f = σ 0 +Kd -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 strength σ N = 550 MPa for growth side in tension σ N =1060 MPa for substrate side in tension Higher modulus m for growth side P(σ) = 1 – exp[– (σ)/σ N ) 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).
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 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