EE CRYSTAL GROWTH, WAFER FABRICATION AND BASIC PROPERTIES OF Si WAFERS- Chapter 3. Crystal Structure z a

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1 1 EE 1 FALL CRYSTAL GROWTH, WAFER FABRICATION AND BASIC PROPERTIES OF Si WAFERS- Chapter 3 z a B Crystal Structure z a z a C y y y A x x Cubic BCC FCC x Crystals are characterized by a unit cell which repeats in the x, y, z directions. z a z (100) plane a (110) plane z a [111] y y y x [100] x [110] (111) plane x Planes and directions are defined using an x, y, z coordinate system. [111] direction is defined by a vector having components of 1 unit in x, y and z. Planes are defined by Miller indices - reciprocals of the intercepts of the plane with the x, y and z axes.

2 Silicon has the basic diamond crystal structure - two merged FCC cells offset by a/4 in x, y and z. V Stacking Fault I Dislocation Precipitate Various types of defects can exist in crystal (or can be created by processing steps. In general these are detrimental to device performance.

3 3 Crystal Growth The raw Si used for crystal growth is purified from SiO (sand) through refining, fractional distillation and CVD. The raw material contains < 1 ppb impurities except for O ( cm -3 ) and C ( cm -3 ) Seed Single Crystal Silicon Quartz Crucible Water Cooled Chamber Heat Shield Carbon Heater Graphite Crucible Crucible Support Spill Tray Electrode Essentially all Si wafers used for ICs today come from Czochralski grown crystals. Polysilicon material is melted, held at close to 1415 C, and a single crystal seed is used to start the crystal growth. Pull rate, melt temperature and rotation rate are all important control parameters.

4 4 Polysilicon Ingot RF Coil Single Crystal Si An alternative growth process is the float zone process which can be used for either refining or single crystal growth.

5 5 After crystal pulling, the boule is shaped and cut into wafers which are then polished on one side. The details of these processes are described in the text. Modeling Crystal Growth We wish to find a relationship between pull rate and crystal diameter. Seed C B A Solid Si Isotherm X Liquid Si Isotherm X 1

6 6 Freezing occurs between isotherms X 1 and X. Heat balance: latent heat of crystallization + heat conducted from melt to crystal = heat conducted away. where: L dm dt + k dt A k dt L 1 = S 1 A (1) L = latent heat of fusion dm = dt kl = dt = 1 amount of freezing per unit time thermal conductivity of liquid thermal gradient at isotherm x1 ks = thermal conductivity of solid dt = thermal gradient at x The rate of growth of the crystal is dm dt = vpan () where v P is the pull rate and N is the density. Neglecting the middle term in Eqn. (1) and substituting, v PMAX = ks dt LN (3)

7 7 In order to replace dt/, we need to consider the heat transfer processes. Seed C B A Solid Si Isotherm X Liquid Si Isotherm X 1 Heat radiation from the crystal (C) is given by the Stefan-Boltzmann law 4 = ( )( ) dq πr σε T (4) Heat conduction up the crystal is given by dt Q ks πr (5) = ( ) Differentiating (5), we have dq d T dt dks d T = ks( πr ) + ( πr ) ks( πr ) (6)

8 8 Substituting (6) into (4), we have d T σε k r T 4 =0 S (7) k S varies roughly as 1/T, so if k M is the thermal conductivity at the melting point, k k T S = M M (8) T d T σε = k rt T 5 M M 0 (9) Solving this differential equation, evaluating it at x = 0 and substituting the result into (3), we obtain: (see text) v PMAX 5 k T = 1 σε M LN 3M r (10) This gives a max pull rate of 35 cm hr -1 for a 6 crystal. Actual values are X less than this. Modeling Dopant Behavior During Crystal Growth Dopants are added to the melt to provide a controlled N or P doping level in the wafers. However, the dopant incorporation process is complicated by dopant segregation.

9 9 k O C = S (11) C L As 0.3 Bi 7 x 10-4 C 0.07 Li 10 - O 0.5 P 0.35 Sb 0.03 Al.8 x 10-3 Ga 8 x 10-3 B 0.8 Au.5 x 10-5 Most k 0 values are <1 which means the impurity prefers to stay in the liquid. Thus as the crystal is pulled, N S will increase. V S, C S VO, I O, C O I L, C L If during growth, an additional volume dv freezes, the impurities incorporated into dv are given by I di = kocldv = k L O dv V V O S (1)

10 10 I L di = k I IO L O VS 0 V O dv V S (13) VS IL = IO 1 (14) V We are really interested in the impurity level in the crystal (C S ), so that O k O C S di = L (15) dv S ( ) C = C k 1 f S O O k O 1 (16) where f is the fraction of the melt frozen. 10 C S /CO 1 Boron Phosphorus, Arsenic 0.1 Antimony Fraction of Melt Solidified

11 11 L Zone C S (x) C O In the float zone process, dopants and other impurities tend to stay in the liquid and therefore refining can be accomplished, especially with multiple passes. See the text for models of this process. Modeling Point Defects in Silicon Point defects (V and I) will turn out to play fundamental roles in many process technologies. The total free energy of the crystal is minimized when finite concentrations of these defects exist. * * 0 0 = I V C, C N S f S H exp exp (17) k kt f * * In general C 0 C 0 and both are strong functions of I V temperature. Kinetics may determine the concentration in a wafer rather than thermodynamics. In equilibrium, values for these concentrations are given by:

12 1 * C x I eV exp. kt (18) * C x V eV exp. kt (19) * * These equations give C 0 & C 0 0 at room T and I V cm -3 at 1000 C - too small to measure. E F E C V = V - E i V + V ++ V and I also exist in charged states with discrete energies in the Si bandgap. In N type Si, V = and V - will dominate; in P type, V + and V ++ will dominate. Shockley and Last (1957) first described these charged defect concentrations (see text): E + E * * V F C + = C V 0 exp V kt (0) C * * = C V V E V EF E V 0 exp kt (1)

13 13 Note that: The defect concentrations are always << n i. ( doping E F point defect concentrations) As doping changes, the neutral point defect concentrations are constant. However, the charged defect concentrations change with doping. the total point defect concentrations change with doping. Example: (See text for details) N 5 x 1019 cm-3 P 1015 cm-3 At 1000 C, the P region will be intrinsic, the N region is extrinsic. P Region N Region Doping 1 x cm -3 5 x cm -3 n i 7.14 x cm x cm -3 V x cm x cm -3 V -.37 x cm x cm -3 V = 1.85 x cm x cm -3 V +.08 x 10 1 cm x cm -3 V x cm x 10 9 cm -3 I x cm x cm -3 I x cm x 10 1 cm -3 I x cm x cm -3

14 14 Note: ni relative to doping in the two regions. V 0 is the same in the two regions. Different charge states dominate in the different regions. The concentrations of these point defects will be important later in the quarter (diffusion, ion implantation, oxidation models). Oxygen and Carbon in CZ Silicon The CZ growth process inherently introduces O and C. Typically, C O cm -3 and C C cm -3. The O in CZ silicon often forms small SiO precipitates in the Si crystal under normal processing conditions. Stacking Fault V I O I O I SiO O I O I O I [O I ] SiO O I Diffusion O and these precipitates can actually be very useful. Provide mechanical strength. Internal gettering (Chapter 4 - later). See the text (Chapter 3) for more detailed information.