Lecture 7 Oxidation Chapter 7 Wolf and Tauber 1/82
Announcements Homework: Homework will be returned to you today (please collect from me at front of class). Solutions will be also posted online on today at ~noon. Homework number 2 will be also be online this afternoon Thursday (12 th October). 2/82
Announcements Term Paper: You are expected to produce a 4-5 page term paper on a selected topic (from a list). Term paper contributes 25% of course grade. Details are on the course website now. Topics will be listed on Tuesday 17 th October. You need to list your favorite topics by Monday 23 rd October. You will be assigned a topic on Friday 27 th October. The term paper should be handed in at the start of class on Tuesday 21 st November. The term paper will be returned to you in class on Thursday 30 th November. 3/82
Announcements Mid-Term Exam: The exam will take place on Thursday (26 th October) at 10:00 am in Gleeson 100. You will have 90 minutes. Closed book and no notes. Will cover material covered in lectures 2-9. There will be a review lecture one week before (Thursday 19 th October). There will be no lecture on Tuesday 24 th October (exam preparation). 4/82
Useful Links UC Berkeley Notes: http://wwwinst.eecs.berkeley.edu/~ee143/fa10/lectures/lec_06.pdf UC Santa Barbara Notes: https://engineering.ucsb.edu/~sumita/courses/courses/me14 1B/ME141B_lecture_4_F10.pdf 5/82
Lecture 7 Oxidation in CMOS. Oxide Properties. Oxidation Process. Oxide Growth Model. Growth Rate. Oxide Growth in Practice. 6/82
Oxidation in CMOS 7/82
Dry Etching Processes Start with your (doped) semiconductor wafer. n + p + p + n + n + p + substrate 8/82
Dry Etching Processes Oxide is grown over entire substrate (this lecture). oxide n + p + p + n + n + p + substrate 9/82
Dry Etching Processes Oxide is etched in certain regions to allow contact with doped regions (Lecture 16). oxide n + p + p + n + n + p + substrate 10/82
Dry Etching Processes Metal is deposited everywhere on wafer (Lecture 5). oxide n + p + p + n + n + p + substrate 11/82
Dry Etching Processes Metal is selectively etched (Lecture 14-16). oxide n + p + p + n + n + p + substrate 12/82
Dry Etching Processes Wafer is covered everywhere with SiN 3 (Lecture 14-15). SiN 3 oxide n + p + p + n + n + p + substrate 13/82
Dry Etching Processes Wafer is covered everywhere with SiN 3 (Lecture 14-15). SiN 3 oxide n + p + p + n + n + p + substrate 14/82
Dry Etching Processes Photoresist is applied (Lecture 14-15). Photoresist SiN 3 oxide n + p + p + n + n + p + substrate 15/82
Dry Etching Processes Photoresist is treated (Lecture 14-15). Photoresist SiN 3 oxide n + p + p + n + n + p + substrate 16/82
Dry Etching Processes SiN 3 and photoresist is selectively etched (Lecture 6). Photoresist SiN 3 oxide n + p + p + n + n + p + substrate 17/82
Dry Etching Processes Photoresist is removed etched (Lecture 14-15). SiN 3 oxide n + p + p + n + n + p + substrate 18/82
Dry Etching Processes Metal is deposited everywhere on wafer (Lecture 5). SiN 3 oxide n + p + p + n + n + p + substrate 19/82
Dry Etching Processes Metal is selectively etched. SiN 3 oxide n + p + p + n + n + p + substrate 20/82
Oxide Properties 21/82
Oxidation Reasons that SiO 2 so widespread in VLSI: Forms directly from the Si substrate upon exposure to oxygen containing species (O 2 or H 2 O): Si S + O 2 (G) SiO 2 (S) Si S + 2H 2 O L SiO 2 S + 2H 2 (G) Dry Wet High quality electrical insulator (low interface trap density) Thin (10-50 Å) gate oxide for MOS gate. Thick (1000-2000 Å) field oxide for transistor isolation and barrier to dopant diffusion. 22/82
Other Compounds This is one of the main advantages of Si, and why it won. Germanium GaAs Hu et. al. Native Oxidation Growth on Ge(111) and (100) Surfaces Small 1(4) (2005) 429. Thomas et. al. High electron mobility thin-film transistors based on Ga2O3 grown by atmospheric ultrasonic spray pyrolysis at low temperatures APL 105 (2014) 092105. 23/82
Structure of SiO 2 Each Si surrounded tetrahedrally by 4 O atoms Open, amorphous structure. 1.6 A Si O Si O Si O Si O O O O O Si O Si O Si O Si O O O O O Si O Si O Si O Si O O O O O Si O Si O Si O Si O jcrystal.com/ 2.27 A Density of SiO 2 < crystalline SiO 2. Quartz = 2.65 gm/cm 3. Thermally grown oxide = 2.20 gm/cm 3. Silicon = 2.33 gm/cm 3. 24/82
Properties of SiO 2 Excellent electrical insulator. Resistivity > 10 15 Ωcm. Band gap ~ 8 ev. Crucial in devices. Al S Al D e - e - e - e - e - e - e - e - e - e - e - e - Dielectric SiO 2 Gate Si ++ +V D +V G 25/82
Properties of SiO 2 High breakdown electric field strength. >10 MV/cm. Al S Al D e - e - e - e - e - e - e - e - e - e - e - e - Dielectric SiO 2 Gate Si ++ +V D +V G 26/82
Properties of SiO 2 Stable: Down to 10-9 Torr, T > 900 C. Conformal oxide growth on exposed Si surface. SiO 2 Si Si Good diffusion mask for common dopants: D SiO2 D Si SiO 2 Si SiO 2 27/82
Properties of SiO 2 Excellent etch selectivity between Si and SiO 2. HF Dip SiO 2 Si Si 28/82
Oxidation: Applications Oxide grown by oxidation is used at two important steps in chip manufacture. Field oxide. Gate oxide. Field oxide: Field oxide isolates different transistors on a chip. Field oxide Gate Gate Source N-Well Drain Source P-Well Drain Transistor 1 Transistor 2 29/82
Oxidation: Applications Gate oxide Recall that the gate on a transistor works because the charge effects the holes and electrons across the oxide Source N-Si Gate P-Si Drain N-Si Gate Insulator oxide Currently the gate oxide is only 10-50 Å thick. (A sheet of paper is 1,000,000 Å thick!) 30/82
1995 1999 2003 Oxidation: Applications From Intel 31/82
Oxidation Process 32/82
Oxidation Techniques Thermal oxidation (heated in oxygen-rich environment). Chemical vapor deposition (CVD). Plasma anodization. Physical vapor deposition (PVD). Thermal oxidation is by far the prevalent in industry. Best quality oxide. Typically used for insulation. Unfortunately requires high temperature. We will focus on this technique. 33/82
Thermal Oxidation Two approaches: Dry Oxidation (O 2 ): Uses oxygen gas: Si S + O 2 (G) SiO 2 (S) High quality. Slow oxidation rate. Small maximum thickness (i.e. gate oxide). Wet Oxidation (H 2 O): Uses water vapor: Diffusion speed is higher. Lower quality. Faster oxidation rate. Si S + 2H 2 O Vapor SiO 2 S + 2H 2 (G) 34/82
Oxidation: Mechanism The oxygen containing species must diffuse through the oxide layer to the unreacted silicon. This makes for a cleaner process. Water vapor Oxygen species diffuses through oxide Water vapor OXIDE Silicon substrate Surface hydroxyl Silicon dioxide Silicon 35/82
Oxidation: Mechanism Oxygen reacts with silicon to form silicon dioxide: Si S + O 2 (G) SiO 2 (S) Si S + 2H 2 O Vapor SiO 2 S + 2H 2 (G) Time x Si Si Original Thickness SiO 2 Si x ox We can work out the thickness of Si consumed from the number density. x Si = x ox n ox n Si # density of SiO 2 # density of Si x Si = x ox 2.3 10 22 5 10 22 = 0.46x ox 36/82
Oxide Growth Model 37/82
Deal & Grove Model Without easy growth of SiO 2 on Si, there would be no semiconductor industry. It s no accident that the world leader in Si chip technology, Intel, has been led by Andy Grove. As a young researcher at Fairchild Semiconductor, he wrote the book on SiO 2 growth: the Deal-Grove model. 1997 38/82
Deal & Grove Model Mathematically describes the growth of an oxide layer on the surface of a material. Used to analyze thermal oxidation of silicon. Physical assumptions: Oxygen diffuses from the bulk to the ambient gas to the surface. It diffuses through the existing oxide layer to the oxide-substrate interface. It then reacts with the substrate. Also assume steady state conditions. 39/82
Deal & Grove Model We will talk about dry growth (O 2 ), but principles are the same for H 2 O. SiO 2 growth occurs at the Si/SiO 2 interface because: D O 2 SiO 2 D Si SiO 2 O 2 I.e. diffusion coefficient of O 2 in SiO 2 is much higher than the diffusion coefficient of Si in SiO 2. SiO 2 Si Si 40/82
Steps in the Growth Process 1) C g P O 2. O 2 concentration in gas 2) Transport occurs across boundary layer with flux J 1. 3) O 2 adsorption at SiO 2 ; O 2 concentration in oxide is C 0. 4) Diffusion of O 2 through SiO 2, with flux J 2. 5) Chemical reaction of O 2 with Si at flux J 3. [6) Escape of hydrogen.] O 2 pressure O 2 Conc. C g O 2 SiO 2 Si C 0 J 1 1 2 3 Boundary Layer C s C i J 2 J 3 x 41/82
Step 1 The O 2 concentration in the bulk of our reactor chamber (far from the substrate) is constant. Describe with Ideal Gas Law: O 2 pressure (Pa) N V = C g = P g k B T O 2 Conc. C g O 2 SiO 2 Si Gas concentration in bulk (m -3 ) 1 2 3 Boundary Layer x 42/82
Step 2 Transport occurs across boundary layer with flux J 1. We can quantify the flux in terms of the mass transfer coefficient: O 2 Conc. C g O 2 SiO 2 Si C s J 1 = h g C g C s Flux through boundary layer (m -2 s -1 ) Mass transfer coefficient (m/s) Difference in concentration across boundary layer (m -3 ) J 1 1 2 3 Boundary Layer x 43/82
Step 3 O 2 is adsorbed at SiO 2 interface. The concentration adsorbed, C 0, is related to the gas pressure at the surface, P s, by Henry s Law: C o = HP s O 2 pressure at surface (Pa) O 2 Conc. C g O 2 SiO 2 Si C 0 C s Concentration in SiO 2 at surface (m -3 ) Henry s solubility constant (mol m -3 Pa -1 ) Use Ideal Gas Law at surface: J 1 1 2 3 x C s = P s k B T C o = Hk B TC s Boundary Layer 44/82
Step 4 O 2 diffuses through SiO 2 to reach the Si/SiO 2 interface. Quantify flux using Fick s Law (Diffusion Equation): O 2 Conc. O 2 SiO 2 Si C g J 2 = D O 2(SiO 2 ) C 0 C i x ox Concentration difference across SiO 2 (m -3 ) C 0 C s C i Flux through SiO 2 (m -2 s -1 ) Diffusion coefficient of O 2 in SiO 2 (m 2 s -1 ) Oxide thickness (m) J 1 J 2 x ox 1 2 3 x Boundary Layer 45/82
Step 5 O 2 reacts with Si to form SiO 2 at Si/SiO 2 interface. We quantify this process using rate constant: O 2 Conc. C g O 2 SiO 2 Si J 3 = k i C i C s Flux into Si (m -2 s -1 ) Concentration at Si/SiO 2 interface (m -3 ) Reaction rate constant (ms -1 ) C 0 J 1 J 2 C i J 3 1 2 3 Boundary Layer x 46/82
Derivation of C i O2 SiO2 Si J 1 = h g C g C s O 2 Conc. J 2 = D O 2(SiO 2 ) C 0 C i x ox J 3 = k i C i C g C 0 C s C i In steady state, fluxes must be equal: h g C g C s J 1 = J 2 = J 3 = D C 0 C i x ox D = D O 2 SiO 2 = k i C i J 1 1 2 3 Boundary Layer We want an expression describing the concentration at the Si/SiO 2 interface, C i, in terms of the other parameters. J 2 J 3 x 47/82
Derivation of C i We need to remove all concentrations besides C i : h g C g C s = D C 0 C i x ox = k i C i Recall from Henry s Law and the Ideal Gas Law that: C g = P g k B T Therefore: C o = Hk B TC s h g P g k B T C s = D Hk BTC s C i x ox = k i C i We still have a C s term. 48/82
Derivation of C i Look at first equality: h g P g k B T C s = D Hk BTC s C i x ox = k i C i h g : Re-arrange: h gx ox D : h g P g k B T C s = D Hk BTC s C i x ox P g k B T C s = D h g Hk B TC s C i x ox C s = P g k B T D h g Hk B TC s C i x ox C s h g x ox D = P gh g x ox k B TD Hk BTC s + C i 49/82
Derivation of C i Re-arrange: C s h g x ox D C s h g x ox D = P gh g x ox k B TD Hk BTC s + C i + Hk BTC s = P gh g x ox k B TD + C i C s h g x ox D + Hk BT = P gh g x ox k B TD + C i Write in terms of C s : C s = top & bottom of RHS by D: P g h g x ox k B TD + C i h g x ox D + Hk BT P g h g x ox k C s = B T + C id h g x ox + DHk B T 50/82
Derivation of C i C s = Return to main expression: P g h g x ox k B T + C id h g x ox + DHk B T h g P g k B T C s = D Hk BTC s C i x ox = k i C i h g P g k B T C s = k i C i Substitute C s : h g P g k B T P g h g x ox k B T + C id h g x ox + DHk B T = k ic i Only concentration left is C i (progress ) 51/82
Derivation of C i Define: h g P g k B T Henry s solubility constant (mol m -3 Pa -1 ) Substitute for h g : hhk B T P g k B T P g h g x ox k B T + C id h g x ox + DHk B T h h g Hk B T P g hhk B Tx ox + C k B T i D hhk B Tx ox + DHk B T = k ic i Mass transfer coefficient (m/s) = k ic i Thermal Energy term Cancel energy terms: hhk B T P g k B T P ghhx ox + C i D hhk B Tx ox + DHk B T = k ic i 52/82
Derivation of C i hhk B T P g k B T Cancel energy terms again: Multiply out: Cancel H s: hh P ghhx ox + C i D hhk B Tx ox + DHk B T P g P ghhx ox + C i D hhx ox + DH hhp g P gh 2 H 2 x ox + C i DhH hhx ox + DH hhp g P gh 2 Hx ox + C i Dh hx ox + D = k ic i = k i C i = k i C i = k ic i 53/82
Derivation of C i Multiply by hx ox + D : hhp g P gh 2 Hx ox + C i Dh hx ox + D = k i C i Multiply out: hhp g hx ox + D P g h 2 Hx ox C i Dh = k i C i hx ox + D h 2 HP g x ox + hhp g D P g h 2 Hx ox C i Dh = k i C i hx ox + k i C i D Re-arrange to get C i s on one side: k i C i hx ox + k i C i D + C i Dh = h 2 HP g x ox + hhp g D P g h 2 Hx ox Bracket-up left hand terms: C i k i hx ox + k i D + Dh = h 2 HP g x ox + hhp g D P g h 2 Hx ox 54/82
Derivation of C i C i k i hx ox + k i D + Dh = h 2 HP g x ox + hhp g D P g h 2 Hx ox Pull HP g out of RHS: C i k i hx ox + k i D + Dh = HP g h 2 x ox + hd h 2 x ox h 2 x ox on RHS cancel: k i hd: C i k i hx ox + k i D + Dh = hdhp g C i x ox D + 1 h + 1 k i = HP g k i Finally we get: C i = HP g /k i 1 h + x ox D + 1 k i 55/82
Limits Slower process controls concentration of oxygen at interface, which in turn controls growth rate. C i = HP g /k i 1 h + x ox D + 1 k i Growth limited by: Recall: mass transport diffusion reaction at SiO 2 /Si Henry s solubility constant (mol m -3 Pa -1 ) for O 2 in SiO 2 h h g Hk B T Mass transfer coefficient (m/s) for O 2 across boundary layer Thermal Energy term 56/82
Limits mass transport Diffusion limited: D x < k i, h C i = HP g /k i 1 h + x ox D + 1 k i O 2 Conc. diffusion C g reaction at SiO 2 /Si O 2 SiO 2 Si C 0 C s Recall: C i HP gd x ox k i D D O 2(SiO 2 ) Diffusion coefficient of O 2 in SiO 2 (m 2 s -1 ) J 2 C i x 57/82
Limits mass transport Reaction-rate limited: k i < D x, h C i = HP g /k i 1 h + x ox D + 1 k i O 2 Conc. diffusion C g reaction at SiO 2 /Si O 2 SiO 2 Si C 0 C s C i HP g C i J 3 x 58/82
Growth Rate 59/82
Growth rate We have evaluated the oxygen concentration at Si/SiO 2 interface: C i = HP g /k i 1 h + x ox D + 1 k i We are really interested in the growth rate: dx ox dt Recall what flux is: material flowing per unit area, per unit time. We can therefore say: (ms -1 ) dx ox dt = J 3 n SiO2 (m -2 s -1 ) (m -3 ) Density of O 2 molecules in oxide 60/82
Growth rate We know from earlier: dx ox dt = J 3 n SiO2 Reaction rate constant (ms -1 ) Flux into Si (m -2 s -1 ) J 3 = k i C i Concentration at Si/SiO 2 interface (m -3 ) So: dx ox dt = C ik i n SiO2 Use C i we just derived: C i = HP g /k i 1 h + x ox D + 1 k i So: dx ox dt = HP g/n SiO2 1 h + x ox D + 1 k i 61/82
Growth rate Separate variables: dx ox dt = HP g/n SiO2 1 h + x ox D + 1 k i Tilde used for dummy integration variable x ox 1 න x 0 h + x D + 1 k i t HP g d x = න dtǁ 0 n SiO2 Where: x o is oxide thickness at t =0. (x 0 can be zero). x ox is final oxide thickness at t. t is growth time. 62/82
Growth rate Start with spatial integral: x ox 1 න x 0 h + x D + 1 k i d x = x h + x2 2D + x x ox k i x0 = x 1 h + 1 + x2 x ox k i 2D x0 = x ox 1 h + 1 k i + x 2 ox 2D x 0 2 1 h + 1 x 0 k i 2D 63/82
Growth rate Now integrate over time: Equate with spatial integral t HP g න dtǁ 0 n SiO2 = HP gt ǁ t n SiO2 0 = HP gt n SiO2 x ox 1 h + 1 k i + x 2 ox 2D x 0 1 h + 1 x 0 k i 2D = HP gt 2 n SiO2 64/82
Growth rate 2D: x ox 1 h + 1 k i + x 2 ox 2D x 0 1 h + 1 x 0 k i 2D = HP gt 2 n SiO2 x ox 2D 1 h + 1 + x 2 k ox x 0 2D 1 i h + 1 x 2 k 0 = 2DHP gt i n SiO2 Define: A A B A = 2D 1 h + 1 k i B = 2DHP gt n SiO2 65/82
Growth rate Define: Therefore: x ox A + x 2 ox x 0 A x 2 0 = Bt τ = x 0 2 + Ax 0 B Growth time corresponding to thickness of x 0 of preexisting oxide (has units of time) Where: x 2 ox + x ox A = B t + τ x ox = A + A2 + 4B t + τ 2 A = 2D 1 h + 1 k i B = 2DHP gt n SiO2 τ = x 0 2 + Ax 0 B 66/82
Growth rate Short time and thin-oxides: x 2 ox Ax ox x 2 ox + x ox A = B t + τ x ox B A t + τ Early in the oxidation process the growth rate is constant in time and is independent of the amount of gas and substrate that are consumed. x ox Linear x ox t t 67/82
Growth rate Long time and thick-oxides: x 2 ox Ax ox x 2 ox + x ox A = B t + τ x ox B t + τ Later in the oxidation process a thermallyactivated diffusion process is controlling the growth rate. x ox Linear x ox t Parabolic x ox t x 2 ox = Ax ox t 68/82
Oxidation Coefficients The parameters A, B, τ are routinely quoted in the literature: Parabolic regime: x 2 ox Ax ox or: x ox A At 1000 C: Parabolic regime: x ox > 165nm (dry) x ox > 226nm (wet) 69/82
Wet vs Dry Growth Recall: B = 2DHP gt n SiO2 H 2 O is much more soluble in SiO 2 than O 2 is, and: Wet oxidation is faster. D O 2 SiO 2 < D H 2O (SiO 2 ) Henry s solubility constant (mol m -3 Pa -1 ) for species in SiO 2 70/82
Dry vs Wet Growth Dry oxide: 700-1,200 C. 1 atm (101325 Pa). Typical = 100nm/hr. SiO 2 Density is higher. Used for gate oxide. Wet oxide: 750-1,100 C. 25 atm (2.5 10 6 Pa). Typical = 1μm/hr. SiO 2 Density is lower, more porus. Used for field oxide and etch oxide. 71/82
Oxide Growth in Practise 72/82
First Substrates are Cleaned RCA Clean (Lecture 4) Organic strip. Piranha Solution. Native oxide removal. HF. Heavy metal removal. HCl:H 2 O 2 :H 2 O. Dump rinse. 18 MΩcm DI H 2 O. Spin Dry. 73/82
Initial Oxidation Regime Experimentally, this is observed: How do we explain this? 74/82
Initial Oxidation Regime Many models have been proposed. It is likely the O 2 :SiO 2 interface is not abrupt: O 2 Conc. O 2 SiO 2 Si x 75/82
Dopants Common dopants in Si enhance oxidation at higher concentration Boron Phosphorus Oxide thickness vs. wet oxidation time at 640 mtorr for three different boron concentrations (Sze) Data for dry oxidation at 1 atm and 900 C Linear, B/A, and parabolic, B, rate constants vs. phosphorus concentration. 76/82
Oxidation Reactor Oxidation is carried out in a horizontal or vertical reactor. Many wafers are held in a vertical holder and pure water is pumped through. Water vapor Wafers Hydrogen Oxygen Pressure = 760 Torr (typical) High concentration to help diffusion. Temperature = 900 ± 1 o C (typical) High temperature to help diffusion. Exhaus t 77/82
Equipment 78/82
Dry Oxidation Growth Chart 1 atm, 100-Si. 79/82
Wet Oxidation Growth Chart 1 atm, 100-Si. 80/82
Optical Properties By measuring the intensity of reflected light as a function of wavelength, the oxide thickness can be determined from: x ox = λ 2n ox Change in wavelength wrt no oxide Refractive index of SiO 2 81/82
Optical Properties 82/82