2 pages. MASSACHUSETTS TECHNOLOGY Closed book 3.155J/6.152J Microelectronics Processing Technology Spring term, 2003 Quiz 90 min/90 points total March 19 2003 Note: Be brief and relevant in your answers, and use sketches. Show your work kB=1.3810JK=86210°eV/K 40 1. Film deposition, cvd a)Discuss briefly what factors affect the microstructure of a film grown on a substrate [15] b)A CVd process is used to deposit P-doped silica at 1200 K. The reactions are SiH4 -- Si(s)+ 2H2(g) k=0. 1 exp(-E/kBT)cm/s where E=1.0ev Silane=10- cm2/s Silane=102 cm-3 PH(g)-->P(s)+3/2H2(g) k=2 exp (-E/kBT)cm/ where e= 1.2ev =106cm2/s In the reactor, the average boundary layer thickness is 2 mm. N=5x10" for the film Calculate the films growth rate and composition. [15] c) Suppose the flow velocity of the gases is doubled What happens to the answer to part(b)? [5 d)Cvd processes such as the one in part b) are often run at fairly high pressures, e.g. several Torr. Speculate briefly on what might be different if the process is instead run at a very low pressure, e.g. in the mTorr range. [5] 25 2. Diffusion a) a thin layer of As is deposited onto the surface of a Si wafer containing a uniform concentration of 10cmof B The As layer is only 10 nm thick If the sample is annealed for I hour at 1000 k, calculate the profile of the As (Assume Si and As atoms are the same size. I cm' of si contains 5x10 cm)[15] b)Write down the assumptions you used in reaching this answer, and discuss how valid they are.[10] For as:D°=0066cm2s;E°=34eV D=12 cm/s: E=4.0eV ForB:D°。=0.037cm2sE°=34eV Dt。=04cm2/s,E+=34eV 25 3. Lithography and etch a) Define in one or two sentences the differences between the following: [10] i. Depth of focus, Resolution of imaging system and Resolution of resist ii. Positive and negative resist iii. Proximity and projection printing
2 pages. M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y Closed book 3.155J/6.152J Microelectronics Processing Technology Spring Term, 2003 Quiz 1 90 min/ 90 points total March 19 2003 Note: Be brief and relevant in your answers, and use sketches. Show your work. kB = 1.38 10-23 J/K = 8.62 10-5 eV/K 40 1. Film deposition, CVD a) Discuss briefly what factors affect the microstructure of a film grown on a substrate [15] b) A CVD process is used to deposit P-doped silica at 1200 K. The reactions are: SiH4 --> Si (s) + 2H2 (g) k = 0.1 exp (-E/ kBT) cm/s where E = 1.0eV -3 Dsilane = 10-5 cm2 /s csilane = 1021 cm PH3(g) ---> P (s) + 3/2 H2 (g) k = 2 exp (-E/ kBT) cm/s where E = 1.2eV -3 Dphosphine = 10-6 cm 2 /s cphosphine = 1020 cm In the reactor, the average boundary layer thickness is 2 mm. N = 5x1022 cm-3 for the film. Calculate the film’s growth rate and composition. [15] c) Suppose the flow velocity of the gases is doubled. What happens to the answer to part (b)? [5] d) CVD processes such as the one in part b) are often run at fairly high pressures, e.g. several Torr. Speculate briefly on what might be different if the process is instead run at a very low pressure, e.g. in the mTorr range. [5] 25 2. Diffusion a) A thin layer of As is deposited onto the surface of a Si wafer containing a uniform concentration of 1018 cm-3 of B. The As layer is only 10 nm thick. If the sample is annealed for 1 hour at 1000 K, calculate the profile of the As. (Assume Si and As atoms are the same size. 1 cm3 of Si contains 5x1022 cm-3) [15] b) Write down the assumptions you used in reaching this answer, and discuuss how valid they are. [10] For As: Do o = 0.066 cm2 /s; Eo = 3.4 eV Do = 12 cm2 /s; E- = 4.0 eV For B: Do o = 0.037 cm2 /s; Eo = 3.4 eV D+ o = 0.4 cm2 /s; E+ = 3.4 eV 25 3. Lithography and Etch a) Define in one or two sentences the differences between the following: [10] i. Depth of focus, Resolution of imaging system and Resolution of resist ii. Positive and negative resist iii. Proximity and projection printing
b) For plasma etching, explain concisely how selectivity and anisotropy can be controlled by choice of etching parameters. [ 7] c)If you are etching the following sample, sketch what profiles you Nitride mask might expect from these three etch processes, and explain why:&K i etching in Koh solution li etching in an hf and nitric acid mixture iiL Ion milli
b) For plasma etching, explain concisely how selectivity and anisotropy can be controlled by choice of etching parameters. [7] c) If you are etching the following sample, sketch what profiles you Si (100) f Nitride mask might expect from these three etch processes, and explain why: [8] i. etching in KOH solution ii. etching in an HF and nitric acid mixture iii. Ion milling
Useful equations kg=1.381023J/K=86210°eVK Gas kinetics: Pre Cave=(8kB T/ms I atm=760 torr: 10 Pa P=nbT an free path Arrival rate at a surface J=P/(2kBT m)0.=3.5 102P(torr)(MT(g/mol K). s m= mass of a molecule. M= molar mass Oxidation: thickness xo after time t 2+Axo=B(t+t) )+A(xo-Xi= Bt B/A=cok/N, B= 2DoxCo/N Co= conc. of oxidant at surface, ks= rate constant for oxidation, Dox= diffusivity of oxidant in oxide n= number of oxidant molecules needed to make unit volume of oxide. t= time offset X: initial oxide thickness Chemical vapor deposition v=(cg/NChg k/(hg+ k)) Reaction flux Transport flux Fd=hg(cg-Cs) Gas phase transport coefficient h2=3/2(D2/L)(puL/n)03=D26e Boundary layer thickness δ=(xn/pu Reaction coefficient k=kexp(-△G/kgT cg is concentration of reactant species in bulk of gas; cs is concentration on the surface, N is density of film(atoms/cm ), Dg is the diffusivity in the gas, L is a characteristic length, x is distance along wafer, p is gas density, n is viscosity, u is gas velocity. kB=1.38 10-J/K 86210eV/K Semiconductor conductivity G=( Hn=electron mobility, Hh=hole mobility, n=number of electrons, p=number of holes,e Diffusion Source with constant surface concentration: C(z, t)=Csurf erfc(-z/(2v(D) This introduces dose Q Q=2CsurfV(Dt)/ Fixed amount of dopant diffusing into wafer: C(z, t)=Q/(rDt)exp(-27/4Dt) z=distance, t=time, C= concentration(atoms/cm), Csurf=conc. at surface, Q=dose (atoms/cm) Effective Intrinsic Diffusivity Deff=D+D+D+D+ where D=D°exp(-E/kn,D=D。exp(-E/kT,etc Extrinsic Diffusivity DefT=D+(n/ni)D+(n/ni-D +(p/ni)D
Useful equations kB = 1.38 10-23 J/K = 8.62 10-5 eV/K Gas kinetics: Pressure P = nkBT 1 atm = 760 torr ≈ 105 Pa Average speed cave = (8kBT/πm) 0.5 Mean free path λ = 1/(πd2 n√2) Arrival rate at a surface J = P/(2πkBT m) 0.5 = 3.5 1022 P(torr)/(MT (g/mol.K))0.5 m = mass of a molecule, M = molar mass. Oxidation: thickness xo after time t xo 2 + A xo = B (t + τ) or (xo 2 – xi 2 ) + A(xo – xi) = Bt B/A = coks/N, B = 2Doxco/N co = conc. of oxidant at surface, ks = rate constant for oxidation, Dox = diffusivity of oxidant in oxide, N = number of oxidant molecules needed to make unit volume of oxide, τ = time offset, xi = initial oxide thickness. Chemical vapor deposition film growth rate v = (cg / N)(hg k/(hg + k)) Reaction flux Fr = k cs Transport flux Fd = hg (cg -cs) Gas phase transport coefficient hg = 3/2 (Dg /L) (ρ u L/η)0.5 = Dg /δave Boundary layer thickness δ = (x η/ρ u ) 0.5 Reaction coefficient k = ko exp (-∆G/kBT) cg is concentration of reactant species in bulk of gas; cs is concentration on the surface, N is density of film (atoms/cm3 ), Dg is the diffusivity in the gas, L is a characteristic length, x is distance along wafer, ρ is gas density, η is viscosity, u is gas velocity. kB = 1.38 10-23 J/K, = 8.62 10-5 eV/K Semiconductor conductivity σ = (µnn + µhp)e µn = electron mobility, µh = hole mobility, n = number of electrons, p = number of holes, e = electronic charge 1.6 10-19 C. Difffusion: Source with constant surface concentration: C(z,t) = Csurf erfc (-z/(2√(Dt))) This introduces dose Q Q = 2Csurf√(Dt)/√π Fixed amount of dopant diffusing into wafer: C(z,t) = Q/√(πDt) exp (-z2 /4Dt) z = distance, t = time, C = concentration(atoms/cm3 ), Csurf = conc. at surface, Q = dose (atoms/cm2 ) Effective Intrinsic Diffusivity Deff = Do + D- + D= + D+ … where Do = Do o exp (-Eo /kT), D+ = D+ o exp (-E+ /kT), etc 2 D= Extrinsic Diffusivity Deff = Do + (n/ni)D- + (n/ni) + (p/ni)D+ …
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Department of Materials Science and Engineering 6.152J3.155J IN-CLASS QUIZ 16 September 2002 (5 problems/9 pages total) 1)Defects(20 points) The equilibrium concentration of oxygen in Si is given by Cox=5x 10exp(-2.6eV/kBT)(cm")and that for vacancies is given by CVAC =2 x 10exp(-1.06 eV/kBT(cm). Recall kB=8.62 x 10eV/K a) At what temperature are Cvac and Cox equal? b) Which defect, oxygen impurities or vacancies, would have a greater equilibrium concentration at the melting temperature(1417C)of Si?
Name: ___________________________ MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Department of Materials Science and Engineering 6.152J/3.155J IN-CLASS QUIZ 16 September 2002 (5 problems/9 pages total) 1) Defects (20 points) The equilibrium concentration of oxygen in Si is given by COX = 5 × 1022 exp (-2.6 eV / kBT) (cm-3) and that for vacancies is given by CVAC = 2 × 1022 exp (-1.06 eV / kBT) (cm-3). Recall kB = 8.62 x 10-5 eV/K. a) At what temperature are CVAC and COX equal? b) Which defect, oxygen impurities or vacancies, would have a greater equilibrium concentration at the melting temperature (1417 °C) of Si? 1
c)Sketch In [C]vs 1000/T(i.e, an Arrhenius plot)identifying the slope and intercept for each plot In cl 1000/T 2
Name: ___________________________ c) Sketch ln [C] vs 1000 / T (i.e., an Arrhenius plot) identifying the slope and intercept for each plot. ln [C] 1000/T 2
2)Vacuum Systems(20 points) The Knudson number is defined as Nx=1/L, where n is the molecular mean free path and l is a characteristic dimension of the chamber(reaction vessel a) Write the numbers I to 7 corresponding to the terms below in the appropriate column, Nx>1, NK10mT 4)P<0.1mT 5)Atoms strike surface with a velocity that traces linearly back to the source 6) Gas diffusion regime 7) Atoms strike surface with a variety of angles of incidene NK<I
Name: ___________________________ 2) Vacuum Systems (20 points) The Knudson number is defined as NK = λ / L , where λ is the molecular mean free path and L is a characteristic dimension of the chamber (reaction vessel). a) Write the numbers 1 to 7 corresponding to the terms below in the appropriate column, NK > 1, NK 10 mT ~ 4) P 1 NK < 1 3
b)Select TWO steps that occur in film growth, as numbered below, and describe the physical process in one or two short, concise sentences 4)
Name: ___________________________ b) Select TWO steps that occur in film growth, as numbered below, and describe the physical process in one or two short, concise sentences. 1) 3) 5) 2) 4) 6) 4
3)Oxidation(20 points) a) Describe why Sio2 grows on Si at the Si/SiO2 interface, not at the SiO2/gas nterface b)(i Briefly describe the physical processes occurring at J1, J2 and J3 in the figure below Dead SiO C J1 J2 J
C Name: ___________________________ 3) Oxidation (20 points) a) Describe why SiO2 grows on Si at the Si / SiO2 interface, not at the SiO2 / gas interface. b) (i) Briefly describe the physical processes occurring at J1, J2 and J3 in the figure below. Dead J1 layer J3 gas SiO2 Si J2 C 5
c) Oxide growth on Si is described by the deal-Grove quadratic equation lox+ Atox=b(t+r with t=( t0 Ato)/B Write the expression for growth rate dtox/dt in one of the limits below I thin oxide fox > Atox d) Give a physical reason why oxide growth is generally faster on doped Si than on pure si 6
Name: ___________________________ c) Oxide growth on Si is described by the Deal-Grove quadratic equation t 2 + At = B(t + τ) with τ = ( t0 2 ox ox + At0 ) / B Write the expression for growth rate dtox / dt in ONE of the limits below: I) thin oxide tox2 > Atox d) Give a physical reason why oxide growth is generally faster on doped Si than on pure Si. 6
4)Chemical vapor deposition(CvD)20 points You want to deposit a p+ doped gate oxide for a MOSFET using CVD You chose for the sio reaction SiH4(g)+O22P(s)+3H2(g)or B2H6(g)4>2B(s)+3H2(g) b) Define the terms in the Cvd growth equation and give the dimensions, e.g. number/(sec-area), of each C/N h k c) Write the equation for the film growth rate in the regime where it is limited by reaction kinetics
Name: ___________________________ 4) Chemical vapor deposition (CVD) [20 points] You want to deposit a p+ doped gate oxide for a MOSFET using CVD. You chose for the SiO2 reaction: SiH4 (g) + O2 ↔ Si O2(s) + 2H2 (g). a) Circle one of the following reactions that will give you p+ doping of your gate oxide. i. 2PH3 (g) ↔ 2 P (s) + 3H2 (g) or ii. B2H6 (g) ↔ 2B (s) + 3H2 (g) b) Define the terms in the CVD growth equation and give the dimensions, e.g. number/(sec-area), of each: C /N v = g 1 1 + h k g s c) Write the equation for the film growth rate in the regime where it is limited by reaction kinetics. 7
