Lecture 2 Silicon Properties and Growth

Transcription

1 Lecture 2 Silicon Properties and Growth Chapters 1 & 2 Wolf and Tauber 1/63

2 Lecture 2 Why Silicon? Crystal Structure. Defects. Sand to Electronic Grade Polysilicon. Polycrystalline to Single Crystal Silicon. Single Crystal Ingot to Wafer. 2/63

3 Why Silicon? 3/63

4 Why Silicon? Luck mainly. Cheap and naturally abundant raw materials. 1.1 ev band gap ideal for room temperature. High electron and hole mobilities. Native SiO 2 Insulating layer. 4/63

5 Germanium vs Silicon Germanium was used in first transistor. Bardeen Brattain Shockley in [1] Mobilities higher. Ge has narrow gap (0.66 ev). Larger background concentration Difficult to form stable native oxide: GeO 2. μ electrons μ holes Si 1, Ge 3,900 1,900 [1]Shockley, Bell Labs Technical Journal, 28 (1949) 435 5/63

6 GaAs vs Silicon Much higher electron mobility. Hole mobility is much lower. Direct band gap: 1.39 ev No native oxide. Arsenic is toxic. 6/63

7 Target Properties of Silicon Wafers: Extremely pure feed: % (9 nines) oxygen and carbon are carefully controlled some oxygen is beneficial. Very flat: 775μm +/- 10μm over 300 mm Precise diameter: 300 mm +/- 0.2 mm Precise resistivity and doping Crystalline orientation <111> or <100> Important for doping and for die separation. Very low crystalline defects. Very low numbers of surface particles (ppm). 7/63

8 Crystal Structure 8/63

9 Crystal Structure Unit cell 9/63

10 Crystal Structure Lattice is defined by vectors: a, b, c. Any position in the lattice (r ) is equivalent when translated by r: r = r + r r = la + mb + nc When l, m, n z. c b a r defines a translation to an identical environment. 10/63

11 Lattices A range of lattices exist: Below are so called Brevais Lattices 11/63

12 Cubic Lattices If a = b = c the lattice is cubic. Simple Cubic Body-Centered Cubic (bcc) Face-Centered Cubic (fcc) Simple Body-Centered Face-centered Volume of cell a 3 a 3 a 3 Lattice points / cell Nearest neighbors Nearest neighbor distance a a 3/2 a/ 2 Second nearest neighbors Second neighbor distance a 2 a a 12/63

13 Diamond Cubic Two interpenetrating fcc lattices, offset by 1/4a in each direction. All atoms are Si (despite colors)! Top-down view 0 1/2 0 3/4 1/4 1/2 0 1/2 1/4 3/4 0 1/2 0 Number represents height in cell 13/63

14 Diamond Cubic Crystalline silicon adopts the diamond structure. Each atom has 4 nearest neighbors. Tetragonal bonding. 14/63

15 Diamond Cubic See also the below URL to visualize : From undergraduate General Chemistry course CH /63

16 Example 5.43 Å. Question: What is the density of c-si? Express in g / cm 3. Lattice spacing is a = a = 5.43 Å. We need to first determine how many atoms are in the cell. 16/63

17 Example 5.43 Å. Corner atoms contribute 1/8 per unit cell. 8 1/8 = 1 17/63

18 Example 5.43 Å. Corner atoms contribute 1/8 per unit cell. 8 1/8 = 1 Face atoms contribute ½ per unit cell. 6 1/2 = 3 18/63

19 Example 5.43 Å. Corner atoms contribute 1/8 per unit cell. 8 1/8 = 1 Face atoms contribute ½ per unit cell. 6 1/2 = 3 Internal atoms contribute 1 per cell. 4 1 = 4 19/63

20 Example 5.43 Å. Number of atoms per cell: = 8 Unit cell length is a = a = 5.43 Å. a = 5.43Å a = m a = cm Unit cell volume is therefore: a 3 = ( ) 3 cm 3 a 3 = cm 3 20/63

21 Example Number of atoms per cell: = 8 Unit cell volume is: a 3 = cm 3 Mass of silicon atom is: m = 28 amu m = kg m = g m = g 21/63

22 Example Density: ρ = m a 3 ρ = gcm ρ = 2.32 gcm -3 This is in agreement with experimental values. ρ exp = gcm -3 (at 300K) Number of atoms per cell: = 8 Unit cell volume is: a 3 = cm 3 Mass of silicon atom is: m = g Mass of unit cell is: m = g m = g 22/63

23 Crystal Planes Miller indices are used to define a plane in a crystal: h,k,l. Z Y c b X a 23/63

24 Crystal Planes These are integers! Miller indices are used to define a plane in a crystal: h,k,l. They are identified as follows: 1. The intercept with the crystal axis are found. In the example these intercepts are: x = 1, y =, z =. 2. Take reciprocal of intercepts. E.g. 1/x = 1, 1/y = 0, 1/z = Multiply all reciprocals by the smallest number that makes them integers. In our example this is 1: hkl = (100). X 1 Z If there is no intercept, it is at (100) Y 24/63

25 Example Let s try a different example: 1. The intercept with the crystal axis are found. Here: x = 4, y = 3, z = Take reciprocal of intercepts. So: 1/x = 1/4, 1/y = 1/3, 1/z = 1/2. 3. Multiply all reciprocals by the smallest number that makes them integers. 1 x = y = 1 3 Start with = z = 1 2 X 4 2 Z (346) 1 x = 24 4 = 6 1 y = 24 3 = 8 1 z = 24 2 = 12 (3,4,6) Divide by 2 3 Y 25/63

26 Crystal Planes in c-si (100) Miller indices are used to define a plane in a crystal: h,k,l. Top View Si Plane of unit cell 26/63

27 Crystal Planes in c-si (111) Miller indices are used to define a plane in a crystal: h,k,l. Plane of unit cell Top View Si 27/63

28 Further Reading on Cells Wolf and Tauber Chapter 1. Ashcroft and Mermin, Solid State Physics, Chapter 4. Kittel, Introduction to Solid State Physics, Chapter 1. 28/63

29 Defects 29/63

30 Point (0D) Defects Vacancy (V) Interstitial (I) Called self-interstitial if Si atom. Called interstitial impurity if anything else. 30/63

31 Point (0D) Defects Schottky Defect Frenkel Defect Atom that migrates to surface, leaving a vacancy. Atom that migrates to interstitial site, leaving a vacancy. 31/63

32 Point (0D) Defects Point defect concentration is defined by Arrhenius relationship: N V = N 0 e E A Τ k B T N V : Vacancy concentration at equilibrium. N 0 : Lattice site density. E A : Activation energy for defect formation. k B : Boltzmann Constant. T: Temperature. For Si self-interstitial: E A = -2.6eV For Schottky Defect: E A = -4.5eV 32/63

33 1D Defects - Dislocations Edge Dislocation Screw Dislocation 33/63

34 Sand to Electronic Grade Polysilicon (EGS) 34/63

35 Sand to EGS EGS = Electronic grade (polycrystalline) silicon. The Czochralski (CZ) Process (next step) adds impurities to EGS. Hence EGS must be incredibly pure to begin with. EGS should have impurity levels of parts per billion (ppb), or /cm 3. We start with quartzite, a relatively pure form of SiO 2. 35/63

36 Sand to EGS Process flow: Sand Carbon Arc Furnace (2000 C) (Metallurgical Grade Si) MGS HCl Fluidized Bed (300 C) SiHCl 3 Separator SiHCl 3 SiO 2 Si + O 2 h = 911 kj/mol EGS CVD (950 C) (Electronic Grade Si) 36/63

37 Sand to EGS Step 1: Sand Carbon Arc Furnace (2000 C) (Metallurgical Grade Si) MGS HCl Fluidized Bed (300 C) SiHCl 3 Separator SiHCl 3 (Electronic Grade Si) EGS CVD (950 C) Reduction of quartzite to metallurgical grade Si (MGS) at 2000 C in an arc furnace: SiO 2 S + 2C S Si L + 2CO(G) h = 750 kj/mol Sources of C include wood chips, coal and coke. MGS formed is about 98% pure (Fe 1%, Al 0.5%, Cr 0.05%, Mn 0.02%, V 0.02%, Mg 0.01%, Ni 0.01%, Ti 0.01%.) 37/63

38 Sand to EGS Step 1: SiO 2 S + 2C S Si L + 2CO(G) h = 750 kj/mol 38/63

39 Sand to EGS Step 2: Sand Carbon Arc Furnace (2000 C) (Metallurgical Grade Si) MGS HCl Fluidized Bed (300 C) SiHCl 3 Separator SiHCl 3 (Electronic Grade Si) EGS CVD (950 C) Powdered MGS is converted to trichlorosilane at 300 C in a fluidized bed reactor: Si S + 3HCl G SiHCl 3 G + H 2 (G) h = 250 kj/mol Must be kept below 325 C to avoid byproducts Boron (BCl 3 ) and phosphorous (PCl 3 ), are the major impurities 39/63

40 Sand to EGS Step 3: Sand Carbon Arc Furnace (2000 C) (Metallurgical Grade Si) MGS HCl Fluidized Bed (300 C) SiHCl 3 Separator SiHCl 3 (Electronic Grade Si) EGS CVD (950 C) Use Distillation to separate the product mixture. 6-8 trays are used. SiHCl 3 is liquid at room temperature (boils at 32 C). 40/63

41 Sand to EGS Step 4: Sand Carbon Arc Furnace (2000 C) (Metallurgical Grade Si) MGS HCl Fluidized Bed (300 C) SiHCl 3 Separator SiHCl 3 Polycrystalline silicon rod (Electronic Grade Si) EGS CVD (950 C) Chemical Vapor Deposition (CVD) of polycrystalline electronic grade Si (EGS) at 950 C 1100 C. Siemens Process. h = 250 kj/mol SiHCl 3 G + 2H 2 G 2Si S + 6HCl (G) 41/63

42 Different Process for Different Applications 5N = %. 9N = % 42/63

43 Polycrystalline to Single Crystal Silicon 43/63

44 Czochralski (CZ) Growth Named after Jan Czochralski. Developed in the 1950s, and is still the dominant method for crystal growth. 44/63

45 Czochralski (CZ) Growth Crucible loaded with EGS. Chamber pumped down, and filled with inert gas (e.g. Argon). Charge is melted (melting point of silicon is 1421C). A seed crystal (5mm diameter, mm long) is lowered into melt. Seed and crystal rotated, in opposite directions. It is withdrawn at a controlled rate to form crystal ingot. 45/63

46 Modeling of CZ Inputs Geometry Properties Initial Conditions Governing Equations: Mass Momentum Energy (Charge) Outputs Growth velocity Concentrations Diameter e.g. pull rate, rotation rate, melt temperature We will consider: 1. Maximum growth velocity of the Si Boule (Energy) 2. Impurity concentrations along the Boule (Mass) 46/63

47 ~220mm Modeling of Heat Transfer T m A. Voit et al., Proceedings of ALGORITMY 2002, Conference on Scientific Computing, pp /63

48 Si/Impurity Phase Diagram T Liquid Solid b Solid b and liquid Eutectic point Solid a and liquid Solid a Solid a and b Impurity concentration xi 48/63

49 Segregation Coefficient: k 0 T T m Liquidus T Solid b Liquid Solid b and liquid Eutectic point Solid a and b Solid a and liquid Solid a xi C i S C i l Solidus Impurity concentration k 0 = C i s C i l C i Concentration at solidus line Concentration at liquidus line 49/63

50 Values of k 0 Values for common dopants and impurities: Element k 0 B 0.8 P 0.35 Ga 8 x 10-3 As 0.3 Sb O 1.4 Al 2 x 10-3 C 0.06 k 0 = C i s C i l Elements tend to segregate to the liquid (except O) Pulled crystals contain dopants, ~10 18 cm -3 oxygen and ~10 16 cm -3 carbon 50/63

51 Normal freezing relation Assumptions: Impurity uniformly distributed in melt. Impurity does not diffuse in solid crystal. Impurity concentration at solid-liquid same as melt. C s = k 0 C 0 1 X k 0 1 X is the fraction of the melt solidified. C 0 is the initial melt impurity concentration. C s is the solid impurity concentration. k 0 is the segregation coefficient. This relates concentration in the melt to concentration in the solid. 51/63

52 Example We seek to grow an Si ingot using the CZ process, with a boron (B) impurity concentration of atoms / cm 3, halfway through the process. For 60kg of Si charge, how many grams of B are required? For boron k 0 = 0.8 Atomic weight = 10.8 g/mol Density of liquid Si = 2.53g / cm 3. C s = k 0 C 0 1 X k 0 1 We seek C 0 : C 0 = C S k 0 1 X k /63

53 Example cm -3 C 0 = C S k 0 1 X k 0 1 Halfway through the process X 0.5. Therefore: C 0 = cm -3. Next determine volume of molten silicon: kg 2.53g / cm 3 V = m ρ = g 2.53 g/cm 3 = cm 3 Number of B atoms in the melt: N B = VC 0 = cm cm 3 = /63

54 Example Number of B atoms in the melt: N B = Determine mass of boron atoms: Use Avagadro s number N A = atoms / mol: m = N Bu N A = = g 10.8 g/mol 54/63

55 Generalizations Modifications from ideality: Impurity not uniformly distributed in melt Boundary layer exists at interface Impurities rejected by solid increases concentration in boundary layer. Impurity Concentration vs Position: C i Liquid C i l 0 Solid C i l,bulk C i l z C i s 0 = k 0 C i l 0 = k e C i l,bulk Boundary Thickness δ 0 z 55/63

56 Effective Segregation Coefficient: k e Use a modified version of segregation coefficient: k e = C i s 0 C i l,bulk k e = k k 0 k 0 exp Vl δ D l V l : Growth (pulling) rate. δ: Boundary thickness. D l : Impurity Diffusion coefficient. 56/63

57 Float Zone: 57/63

58 CZ vs Float Zone CZ Growth: More prevalent. Cheaper. Larger wafer sizes (300 mm). Reusable materials. Can handle thermal stresses better. Float Zone: Higher purity. Specialized applications. 58/63

59 Single Crystal Ingot to Wafer 59/63

60 From Boule to wafer Crystal Growth Wafer Lapping and Edge Grind Cleaning Shaping Etching Inspection Wafer Slicing Polishing Packaging 60/63

61 From Boule to wafer 61/63

62 Wafer Dimensions Thickness ( m) Area (cm 2 ) Weight (grams) Weight/25 Wafers (lbs) Diameter (mm) 10mm Die/Wafer DPW d d 1 4S 2S Dies per wafer d = wafer diameter (mm) S = die size (mm 2 ) 62/63