Prospective and future work - 國立中山大學材料與光電科學學系博士論文

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Table 1 Fundamental properties of III-V group semiconductors [11].

GaN AlN InN

Structure Wurtzite Zinc blende Wurtzite Zinc blende Wurtzite Zinc blende Band gap energy

(eV)

3.4 3.3 6.2 5.1 1.9 2.2

Lattice constants a-axis (Å )

3.189 4.52 3.112 4.38 3.548 4.98

Lattice constants c-axis (Å )

5.185 - 4.982 - 5.76 -

c/a ratio 1.626 - 1.601 - 1.623 -

Thermal expansion Δa/a

(10^-6K)

5.59 - 4.2 - 4 -

Thermal expansion Δc/c

(10^-7K)

3.17 - 5.3 - 3 -

Thermal conductivity

(W/m-K) 130 - 200 - 80 -

Table 2 The mechanical properties of polycrystalline ZnO, single crystallize ZnO wafer, thin films, nanowires, nanobelts measured by different testing techniques [59, 94, 100].

Structure Method

E H

Slip system Ref.

(GPa) (GPa)

Poly crystal Bulk Calculation 120 - - [59]

Experiment 140 - - [59]

Single crystal

Bulk

Calculation 140 - - [59]

Nanoindentation

111 5 Pyramidal [57]

112 5.4 Pyramidal [99]

140 7.1 - [60]

Nanorod Nanoindentation 63 9.7 - [101]

Nanowire Tension

21 - - [102]

160 - - [103]

Nanobelt Bending

31.1 2.5 - [100]

51 - - [104]

Micropillar Microcompression 123 - Pyramidal [60]

Table 3 The plane abbreviation and polarity of two semiconductors which used in this thesis.

Material Polarity Plane

ZnO Polar c-plane (0001)

Non-polar m-plane (10 1 0)

Non-polar a-plane (2 1 1 0)

GaN Polar c-plane (0001)

Semi polar r-plane (11 02)

Table 4 Comparison of the relevant III-V nitride material properties with perspective substrate materials [11, 29, 30].

Substrate material

Lattice parameters (Å )

Thermal conductivity (W/m-K)

Coefficients of thermal expansion

(K^-1)

GaN a = 3.189 130 5.59x10^-6

c = 5.185 3.17x10^-6

AlN a = 3.112 200 4.2x10^-6

c = 4.982 5.3x10^-6

Sapphire a = 4.758 50 7.5x10^-6

c = 12.99 8.5x10^-6

ZnO a = 3.252 100 2.9x10^-6

c = 5.213 4.75x10^-6

MgO a = 4.216 30 10.5x10^-6

Si a = 5.430 150 3.59x10^-6

GaAs a = 5.653 50 6.00x10^-6

Table 5 Structure, lattice constant, space group and density of five different LAO phases [89, 105].

Table 6 Lattice mismatch and thermal expansion coefficient between (200) γ-LAO and GaN [90, 106].

Plane Direction Mismatch

Thermal expansion

(10 1 0)GaN

[0001]GaN∥[010]LAO [1 2 10]GaN∥[001]LAO

0.62%

-0.65%

-25%

[0001]GaN∥[010]LAO [1 2 10]GaN∥[001]LAO

0.3%

1.7%

-25%

[1 2 10]GaN∥[010]LAO [0001]GaN∥[001]LAO

9.08%

22.19%

-25%

(0001)GaN

[1 2 10]GaN∥[010]LAO [10 1 0]GaN∥[001]LAO

9.08%

14.72%

[10 1 0]GaN∥[010]LAO [1 2 10]GaN∥[001]LAO

-5.53%

-0.65%

Table 7 Lattice parameters of a number of the prospective substrate materials for ZnO [16].

Material Crystal structure

Lattice parameters

(Å )

Lattice Mismatch

(%)

Thermal-expansion (K^-1)

ZnO Hexagonal a = 3.252 - a = 2.9x10^-6

c = 5.213 c = 4.75x10^-6

GaN Hexagonal a = 3.189 1.8 a = 5.17x10^-6

c = 5.185 c = 4.55x10^-6

AlN Hexagonal a = 3.112 4.5 a = 5.3x10^-6

c = 4.980 c = 4.2x10^-6

-Al2O₃ Hexagonal a = 4.757 (18.4% after 30^o in-plane rotation)

a = 7.3x10^-6

c = 12.983 c = 8.1x10^-6

6H-SiC Hexagonal a = 3.080 3.5 _a= 4.2x10^-6

c = 15.117 c = 4.68x10^-6

Si Cubic a = 5.430 40.1 a = 3.59x10^-6

ScAlMgO₄ Hexagonal a = 3.246 0.09 -

c = 25.195

GaAs Cubic a = 5.652 42.4 a = 6.0x10^-6

Table 8 The ZnO elastic constants extracted from different methods: (a) ultrasonic measurement, (b) surface Brillouin scattering, (c) acoustic investigation technique, (d) polarized Brillouin scattering, (e) ultrasonic resonance method, (f) calculated using LDA, (g) calculated using GGA (h) atomistic calculations based on an inter-atomic pair potential within the shell-model approach and (i) calculated using ab initio periodic linear combination of the atomic orbital method [16].

Method (a) (b) (c) (d) (e) (f) (g) (h) (i)

C₁₁ (GPa) 209.7 206 157 190 207 209 230 231 246 C₁₂ (GPa) 121.1 117 89 110 117.7 85 82 111 127 C₁₃ (GPa) 105.1 118 83 90 106.1 95 64 104 105 C₃₃ (GPa) 210.9 211 208 196 209.5 270 247 183 246

C44 (GPa) 42.47 44.3 38 39 44.8 46 75 72 56

C₆₆ (GPa) 44.29 44.6 34 40 44.6 62 - 60 115

Table 9 Hardness and Young’s modulus of GaN from different kinds of indentation methods [20, 91].

GaN thin film H (GPa) E (GPa) Indentation tip

Drovy et al. As-grown 122 287 Vickers

Nowak et al. As-grown 20 295 Spherical

Kucheyev et al. As-grown 13.4 233 Spherical

Ion-damaged 15.1 164

Amorphized 2.4 65

Jain et al. As-grown 19.342.13 314.9340.58 Berkovich Si-doped 20.122.51 247.1614.89

Kavouras et al. As-grown 13.670.13 Knoop

O-doped 14.740.22 Mg-doped 16.870.13 Au-doped 12.160.09 Xe-doped 11.350.12 Ar-Doped 9.980.14

Chien et al. As-grown 19.311.05 286.1225.34 Berkovich

Table 10 List of main luminescence lines and bands in GaN [72].

Table 11 Valance and ionic radii of candidate dopant atoms [30].

Atom Valence Radius (Å )

Zn 2+ 0.6

Li 1+ 0.59

Ag 1+ 1.00

Ga 3+ 0.47

Al 3+ 0.39

In 3+ 0.62

O 2- 1.38

N 3- 1.46

P 3- 2.12

As 3- 2.22

F 1- 1.31

Table 12 Migration barriers for native defects in Wurtzite GaN [74].

Defect Charge state Barrier (eV)

Ga_f 3+ 0.9

2+ ≤ 0.9

1+ ≤ 0.9

N_f 3+ 1.4

2+ 2.5

1+ 2.1

0 2.4

1- 1.6

V_N 3+ 2.6

1+ 4.3

VGa 3- 1.9

Table 13 Comparison of the theoretical and experimental mechanical properties of ZnO.

ZnO

c-plane a-plane

Theoretical Experimental Theoretical Experimental

Poisson's ratio 0.33 0.33 0.25 -

Young's modulus (GPa) 144 140 148 150

Shear modulus (GPa) 40 - - -

Yield stress (GPa) 10 12 - 13

Shear stress (GPa) 4 3.6 - -

Table 14 The elastic constants and estimated mechanical properties of GaN by different group [108].

C11 (GPa) 296 315 353 390 370 373

C12 (GPa) 120 118 135 145 145 141

C₁₃ (GPa) 158 96 104 106 110 80.4

C33 (GPa) 267 324 367 398 390 387

Ec-plane (GPa) 147 281 323 123 343 362

E_a-plane (GPa) 242 341 381 105 395 422

V_c-plane 0.38 0.22 0.21 0.20 0.21 0.16

Va-plane 0.49 0.40 0.38 0.38 0.36 0.31

S (GPa) 2×10^-5 8×10^-6 6×10^-6 5×10^-6 6×10^-6 5×10^-6

G (GPa) 88 99 109 123 113 109

theo (GPa) 9 10 11 12 11 11

Ref.

Savastenko et al.

Davydov et al.

Ayer et al.

Polian et al.

Deger et al.

Deguchi et al.

Table 15 Comparison of the theoretical and experimental mechanical properties of GaN.

GaN

c-plane a-plane

Theoretical Experimental Theoretical

Poisson's ratio 0.22 0.35 0.4

Young's modulus (GPa) 281 272 341

Shear modulus (GPa) 99 - -

Yield stress (GPa) - 29.8 -

Shear stress (GPa) 10 12.2 -

Table 16 The Raman spectra peak position and FWHM of bulk ZnO.

Film Pillar Preset 40 nm Preset 300 nm

Lorentzian multipeak fitting (cm^-1)

A1(TO) 331.6 332.0 329.2 331.4

FWHM 13.9 19.8 17.1 12.5

E₂ 438.6 438.0 438.2 438.2

FWHM 4.9 6.0 6.0 6.4

A1(LO) 549.0 551.1 538.9

FWHM 77.3 70.5 88.9

E_1(LO) 576.8 578.9 576.7

FWHM 18.2 19.2 21.7

Table 17 The fundamental optical modes of the Wurtzite crystal (frequency expressed in cm^-1) [82].

Mode (cm^-1)

BeO ZnO CdS

(25 K)

ZnS (298 K)

ZnS (25 K)

E₂ 338 101 43 55 -

E2 684 444 256 724 280

A1(TO) 678 380 234 274 280

Quasi-A_1(TO) 700 395 240 274 280

Quasi-E1(TO) 702 398 239 274 280

E1(TO) 722 413 243 274 280

A_1(LO) 1081 579 205 352 356

Quasi-A1(LO) 1088 585 306 352 356

Quasi-E_1(LO) 1089 585 306 352 356

E1(LO) 1097 591 307 352 356

Table 18 The measurement of Raman E₂ peak position and FWHM of GaN films and micropillars [54].

E2 peak (cm^-1)

E2 FWHM (cm^-1)

Residual stress (MPa)

Free standing GaN 567.0 - 0

As-deposited film 570.6 2.1 -1508

As-FIB-milled pillar 567.7 2.6 -280

Pillar compressed to preset 100 nm 567.5 5.7 -198

Pillar compressed to preset 200 nm 567.0 6.2 24

Table 19 Young’s modulus measured from different kinds of indentation methods [56, 60, 70].

Sung et al.

[60]

Basu et al.

[56]

Coleman et al.

[70]

Coleman et al.

[70]

Specimen type Wafer Wafer Wafer Thin film

Indenter tip Berkovich Spherical Spherical Spherical

c-plane modulus (GPa) 140 135 ±3 163 ± 6 318 ± 50

a-plane modulus (GPa) 150 144 ± 4 143 ± 6 310 ± 40

Table 20 Comparison of the crystal structure, mechanical data, and dominant deformation modes in the four optoelectronic materials [54, 60, 110].

InP GaAs ZnO GaN

Crystal structure Cubic Cubic Hexagonal Hexagonal

Horizontal plane (100) (100) (0001) (0001)

E (GPa) 74 123 123 226

Hardness (GPa) 5 8 7 15

Yield stress (GPa) 2.5 1.8 3 10

microcompression (GPa) 1 0.7 1.2 4.1

nanoindentation(GPa) 2.8–3.5 4.1–5.2 3.2–4.4 7.6–9.4

Deformation mode Twinning Twinning Dislocation Dislocation

Shear plane (111) (111) (101 1) (101 1)

Figure 1 Three structure types of II-IV group binary compound (a) Rocksalt (b) Zincblende (c) Wurtzite [16].

Figure 2 The corresponding band gap range of luminescence semiconductors [13, 18].

Figure 3 Schematic diagrams showing the transitions across (a) a direct band gap and (b) an indirect band gap.

Conduction Band Conduction Band

Valence Band Valence Band

Figure 4 Direct band gap of GaN [11].

Figure 5 Direct band gap of ZnO [16].

Figure 6 The Wurtzite hexagonal structure.

Cation Anion

Figure 7 The Wurtzite structure along [0001] c-axis.

Cation Anion

- P +

Figure 8 A sketch of induce the intrinsic electric field [37, 51].

Cation Anion

Figure 9 Non-polarity directions of GaN.

Cation Anion

Figure 10 The figures show the reflectance spectra of unstrained A-plane GaN with the light polarized parallel (a) and perpendicular (b) to the c-axis. Clearly, the A exciton is visible only in (b), demonstrating a polarization anisotropy of 100% in this spectral range [22-25].

Figure 11 Growth of hetero-epilayer (a) pseudomorphic (b) strain free layer [92, 108].

Figure 12 Schematic diagram showing the epitaxial relationships of c-plane ZnO grown on sapphire (0001) [16].

Figure 13 Chemical vapor deposition (CVD) process [93, 109].

Figure 14 Low temperature, pressure and high gas velocity conditions of CVD [93, 109].

Figure 15 High temperature, pressure and low gas velocity conditions of CVD [93, 109].

Figure 16 Two-Flow MOCVD (TF-MOCVD) [48].

Figure 17 Projection of wurzite hexagonal structure [55].

h

_max

h

P

_max

Indenter Surface profile after

Load removal Initial Surface

Surface profile at Mazimum Load

Figure 18 The sketch of the nanoindentation testing [52].

Figure 19 The sketch of the nanoindentation load-displacement (p-h) curve [52].

Figure 20 Contour plot of the CRSS of Berkovich tip at (011 2) slip plane (a) and (2 1 1 3) slip plane (b), where distances r and z are normalized by the contact radius a [53].

Figure 21 The bright field cross section TEM image of spherical indent in ZnO at maximum load of 50 mN, the black arrow point out the basal plane (0001) and the white arrow point out the pyramidal plane {10 1} [57].

Pyramidal plane

Basal plane

Figure 22 The sketch of slip directions. Thin lines represent the first slip system.

Thick lines represent the secondary slip system [53].

Figure 23 Typical nanoindentation load–displacement data for annealed (100) Ni obtained using a 0.58 m radius spherical indenter. Elastic contact (Hertzian) solutions are shown for the data below the pop-in loads [69].

Figure 24 The sketch of resolve shear stress.

Figure 25 Annular milling patterns have been used to mill a roughly defined micropillar sample of Ni single crystal [48, 62].

Figure 26 The microcompression samples were fabricated into (A) a Ni3Al alloy and (B) Ni-based superalloy by using lathe milling program. The diameter of microcompression samples are 43 m and 2.3m, respectively [48, 62].

Figure 27 SEM micrographs of the flat-punch tip: (a) top view and (b) side view and (c) projected area of the punch tip.

(b)

10 m 20 m (a)

(c)

Figure 28 Schematic drawing of the microcompression test setup [64].

Figure 29 Schematic of a cylindrical pillar and its base [64].

Figure 30 Effect of fillet radius/pillar radius ratio on numerical simulation output. The inset shows an enlargement of the circled region to facilitate comparison [21].

Figure 31 (a) Deformed configuration of a circular cylindrical pillar with an aspect ratio = 5 at a strain of 0.1. (b) Deformed configuration of the pillar at the same strain of 0.1, but now considering friction. (c) Input and output stress-strain curves for a pillar

=2~5, both with friction and without friction (NF) [21].

Figure 32 Effect of taper on numerical simulation output [21].

Figure 33 Effect of misalignment of the system on the error in elastic modulus [21].

Figure 34 (a) The microcompressive engineering stress-strain curve of the Ni₇₆Al₂₄ alloy with 2m diameter. (b) SEM micrograph of a micropillar after microcompression test. Strain bursts are indicated by arrows in figure (a), and appearance of slip lines are also observed on the micropillar surface, as also indicated by arrows [67].

Figure 35 Typical load–penetration curve for a maximum load of 250 mN showing a pop-in event. Inset: Load–penetration curve for a maximum load of 50 mN showing multiple pop-in events at 28 and 34 mN [57].

Figure 36 Room-temperature monochromatic CL images of spherical indents in GaN.

The maximum loads and horizontal field widths are (a) 25 mN and 15 mm, (b) 50 mN and 15 mm, and (c) 200 mN and 30 mm. CL imaging conditions: electron beam energy 520 keV, CL wavelength =366 nm, and CL bandpass 52.5 nm [57].

Figure 37 The threading dislocation density decreases with increasing thickness for thin film GaN/sapphire [80, 96].

Figure 38 Formation energies as a function of Fermi level for native point defects in GaN [74]

Figure 39 Transition levels and formation energy of native defects in GaN [74].

Figure 40 Experimental set up of a micro-Raman spectrometer [82].

Figure 41 The diagram of anti-Stokes scattering [82].

Figure 42 The Raman spectra of back scattering, near forward scattering and right angle scattering modes [82].

Figure 43 The backscattering diagram of wurtzite micro-Raman spectrum: (a) input-output z axis [0001], (b, c and d) input-output a-axis [101 0] [82].

Figure 44 The right angle scattering diagram of wurtzite micro-Raman spectrum [82].

Figure 45 The E1 phonon propagation in the (0001) plane. The transverse phonon is illustrated by the solid-line polarization vector, and the dashed line corresponds to the (112 0) polarization component of Raman spectrum. The k2 and k3 lines represent the quasi QA peak between the E_1(TO) and A_1(TO) peaks [82].

Figure 46 Deconvolution of c-plane GaN XRD rocking curve (0002) Peaks [80, 96].

Figure 47 Schematic illustration of TEM sample procedure using FIB [97].

Figure 48 The XRD pattern shows GaN has a shark peak located at 2=34.62^o.

Figure 49 The XRD pattern of GaN estimate by CaRine software.

Intensity (%)



30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0 10 20 30 40 50 60 70 80 90 100 (32.39,100.0)

1,0,0

(34.57,20.3) 0,0,2

(36.84,76.5) 1,0,1

(48.10,44.0) 1,0,2

(52.93,6.4) 0,0,3

(57.77,15.1) 2,-1,0

(60.72,15.9) 2,-1,1

(63.44,20.0) 1,0,3

(67.81,8.3) 2,0,0

(69.10,12.3) 2,-1,2

(70.52,9.4) 2,0,1

(72.92,1.3) 0,0,4

(78.40,7.9) 2,0,2

Figure 50 The XRD Rocking curve pattern shows a broad peak ranging from 16.45^o to 17^o with full width of middle height (FWMH) = 0.341^o.

Figure 51 The EBSD patterns and SEM SEI image of c-plane ZnO.

Figure 52 The EBSD pattern and SEM SEI image of c-plane GaN.

Figure 53 Showing the load-displacement and modulus-depth curves of c-plane ZnO at CSM constant displacement rate mode.

Figure 54 Representative nanoindentation load-displacement curves of the as-grown, annealed wafer and the curve predicted by the Hertzain contact theory.

Hertzian contact theory

As-grown Annealed

Figure 55 Representative nanoindentation load-displacement curves of the c-plane, a-plane, m-plane ZnO wafer and the curve predicted by the Hertzain contact theory.

m-plan e

c-plane

Hertzian contact theory

a-plane

0 200 400 600 800 1000 0

20 40 60 80 100 120 140 160 180 200 220

Load on sample (mN)

Displacement into surface (nm)

Figure 56 Showing the data of c-plane GaN CSM mode depth 1000 nm nanoindentation testing.

Figure 57 Showing the first pop-in data of CSM mode depth 500 nm (~10% to total thickness) indentation testing.

Hertzian contact theory

c-plane

Figure 58 The representative as-grown preset 300 nm pillar and the annealed preset 300 nm pillar stress-strain curves of microcompression testing.

As-grown

Annealed

Figure 59 Representative load-displacement curves for microcompression of c-plane GaN micropillars.

Figure 60 Representative load-displacement curve for microcompression of a-plane ZnO micropillars.

Figure 61 Representative load-displacement curve for microcompression of m-plane ZnO micropillars.

300 400 500 600 0

200 400 600 800 1000 1200

A_1(TO)

E₂

In te n sit y

Film

Figure 62 The recorded data and Gaussian fitting Raman spectra of film ZnO.

200 300 400 500 600 0

200 400 600 800 1000

1200 E₂

A1(LO) E

1(LO)

A_1(TO)

In te n sit y

Wavenumber (cm

^-1

) Film

Ufine Mid Rough

Figure 63 The Raman spectra of ZnO after Ufine, middle and rough beam FIB Ga implanted conditions.

300 400 500 600 200

400 600 800 1000 1200 1400

A_1(LO) E_1(LO)

A_1(TO)

E₂

Wavenumber (cm

^-1

)

In te n sit y

As-grown ZnO pillar

Figure 65 The recorded data and Gaussian fitting Raman spectra of As-grown ZnO pillar.

300 400 500 600 200

400 600 800 1000

A_1(LO) E_1(LO) A_1(TO)

E₂

Wavenumber (cm^-1)

Intensity

Preset 40 nm pillar

Figure 66 The recorded data and Gaussian fitting Raman spectra of preset 40 nm ZnO pillar.

在文檔中國立中山大學材料與光電科學學系博士論文 (頁 106-200)