1

課程名稱：微製造技術Micro fabrication Technology

授課教師：王東安Lecture 10

2

Lecture Outline•Reading Campbell: Chapter 4•Today’s lecture

–Deal-Grove model of oxidation–Structure of SiO2–Effects of dopants during oxidation–SUPREM

3

Prologue•One of the major reasons fro the popularity of Si ICs

is the ease with which Si forms an excellent oxide,SiO2.

•Thermal oxidation produces oxides with the fewestdefects both in the bulk and at the interface with theunderlying Si.

4

Deal-Grove model of oxidation•Dry oxidation. Since it uses molecular oxygen rather than

water vapor as an oxidant.•The model works well for predicting oxide thicknesses for

thermal oxides larger than about 300 Å

22 SiO(gas)OSi(Solid)

Diffusivity of Si in SiO2 isseveral orders of magnitudesmaller than that of O2. as aresult chemical reaction occurs atSi-SiO2 interface.The interface has not seen theatmosphere. As a result, it is freeof impurities.

5

Deal-Grove model of oxidation•At room temp, neither Si nor O2 molecules are sufficiently

mobile to diffuse through the native oxide. After a while,reaction stops and oxide will not get thicker than 25 Å.

•For a sustained reaction to occur, Si wafer must be heated in thepresence of an oxidizing ambient.

J: oxygen flux, # of oxygenmolecules that crosses a plane of acertain area in a certain time.Flow through stagnant layer

Ideal gas lawhg: mass transport coefficient. k:Boltzmann’s const, Pg: partialpressure of oxygen

sgggas CChJJ 1

kTP

Vn

C gg

6

Deal-Grove model of oxidation

ox

iO t

CCDJ

0

2 2

isCkJ 3

Fick’s first law

Since an abundant supply of Si at the reacting surface, the reactionrate and the flux are proportional to the O2 concentration

In equilibriumHenry’s law: concentration of anadsorbed species at the surface of asolid is proportional to the partialpressure of that species in the gas justabove the solid

H: Henry’s gas const.

321 JJJ

ss HkTCHPC 0

7

Deal-Grove model of oxidation•One can derive that , where

•To obtain the growth rate, divide flux at the interface by # ofmolecules of O2 per unit volume of SiO2, which is labeled N1.For oxidation by molecular oxygen, N1 is half number densityof oxygen atoms in SiO2, 2.2x1022 cm-3.

•Assume•Sol of the differential eq.•A, B are know for a variety

of process conditions.

Dtk

hkHP

Coxss

gi

1HkThh g /

Dtk

hk

N

PHkdt

dtNJ

Roxss

gsox

111

0)0( ttox

BAtt

NDHP

B

hkDA

tBAtt

g

s

oxox

020

1

2

2

112

8

Deal-Grove model of oxidation•Most Si oxidation is done in atmosphere pressure. As a result,

and the growth rate is nearly independent of thegas phase mass transport and , therefore, of the reactorgeometry.

•When oxidizing species is H2O rather than O2, the sameequations apply.

hks

9

Thermal oxidation•Wet oxidation: a mixture of O2 and H2O used as

oxidant.•Advantage: higher growth rate than dry oxidation.•Reason for higher rate is higher diffusivity of H2O

compared with O2 and the much larger solubility(Henry’s const) for H2O compared with O2.

•Disadvantage is that oxides grown wet are less dense.Thus wet oxidation is typically used when a thickoxide is required that will not be subjected to anysignificant electrical stress.

•Under sufficient electrical stress, electricalbreakdown can occur within SiO2.

10

11

12

Thermal oxidation•Another gas ambient: dry molecular oxygen with a

small halogen concentration. The most commonlyused halogen is chlorine.

•Halogen elements are a series of nonmetal elementsfrom Group 17 (formerly: VII, VIIA) of the periodictable.

•Reason for using O2/Cl–Most heavy metal atoms react with Cl to form volatile

metal chloride. Metallic contaminants originate fromheating elements and insulation around the fused silicaflow tube in which the oxidation is done.

•Heavy metals are metallic elements which have ahigh atomic weight and a density much greater (atleast 5 times) than water.

13

Ex 4.1•Calculate thickness of oxide grown during a 120-min

920℃ steam oxidation. Wafer initially had 1000 Åof oxide.

14

15

16

Initial oxidation regime•Deal-Grove model severely understimates thickness

of thin oxides.•Values of given in Table 4.1 can be used to correct

the Deal-Grove model for dry oxidation done on bareSi to compensate for the excess growth that occurs inthe initial growth regime.

•Models to explain the excess growth of thin oxidation–An electric field exists across oxide that enhances diffusion

during early states of oxidation.–Thin microchannels in oxide aid in the movement of O2 to

the Si surface.–mismatch in thermal expansion coefficients of oxide and

Si causes stress in oxide and this stress may enhance thediffusivity of the oxidizing species.

17

Initial oxidation regime

18

Structure of SiO2•Fused Silica: one form of SiO2 that is important for

microelectronic fabrication.•Silica is manufactured in several forms including

glass, crystal, gel, aerogel, fumed silica (or pyrogenicsilica), and colloidal silica.

19

Structure of SiO2•Fused silica: amorphous, does not have long range

order, exhibit short range structure.•Some oxygen atoms, called

bridging oxygen sties, arebonded to two Si atoms.

•Some oxygen atoms arenonbridging, bonded to only oneSi.

•Larger the fraction of bridging tononbridging sites, the mostcohesive and less prone todamage the oxide is.

•Dry oxides have a much largerratio of bridging to nonbridgingsites compared to wet oxides.

20

21

Oxide characterization•Methods for estimating oxide thickness

–Physical: production of a step in oxide by apply mask, etch, removemask, a step nearly equal to oxide thickness is produced. Step can bemeasured using•SEM: if larger than 1000 Å.•TEM: if < 1000 Å.•Mechanical scanning: surface profilometer.

–Optical•Ellipsometry: a polarized coherent beam of light is reflected off

oxide surface at some angle. Reflected light intensity is measuredas a function of polarization angle. Compare incident and reflectedintensity and change in polarization angle, film thickness can befound.

•Interference: measure difference in wavelength between maxima orminima of the interference spectrum /2/(real part of index ofrefraction of oxide) = oxide thickness

22

Oxide characterization•Methods for estimating oxide thickness

–Electrical:•measurement of the breakdown voltage. Dielectric field strength of

thermal oxide is about 12 MV/cm.•Charge to breakdown test: oxide is stressed electrically to a point just

below the breakdown field.

Current through the oxidedecreases due to trapping ofelectrons in the bulk of oxide.Breakdown results fromaccumulation of trappedpositive charge near theinterface.

23

24

25

26

27

28

29

30

31

32

Effects of dopants during oxidation•Common Si

dopants all tend toenhance oxidationrate of Si whenpresent in thesubstrate in highconcentrations.

•Boron, whichsegregates intooxide, enters andweakens the glassystructure, reducingits viscosity.

33

Effects of dopants during oxidation•With heavy phosphorus

doping, parabolic ratecoefficient shows onlymodest increases, butlinear rate coefficientincreases rapidly forsurface doping levelsgreater than 1020 cm-3.

34

35

36

37

38

SUPREM Oxidations•SUPREM performs oxidations based on the Deal-

Grove model.•Oxidation processes are accessed by the same

command as diffusion processes: DIFFUSION.

39

SUPREM example•This example compares the oxide thickness grown for

different orientations. The input file for thesimulation is in the "examples/exam6" directory, inthe file "oxcalib.s4".

40

#---some set stuffoption quietunset echoforeach O (100 110 111)echo "---------- Orientation < O > --------------------"#---the minimal meshline x loc = 0.0 tag = leftline x loc = 1.0 tag = rightline y loc = 0.0 tag = topline y loc = 1.0 tag=bottomregion silicon xlo = left xhi = right ylo = top yhi = bottombound exposed xlo = left xhi = right ylo = top yhi = topinit ori=O

41

#---the oxidation stepmeth grid.ox=0.03diffuse time=30 temp=900 wetselect z=y*1e8 label="Depth(A)"; print.1d x.v=0

form=8.0fend

42

SUPREM•The first two lines keep the program as quiet as

possible. The minimum output is printed, and theinput is not echoed at all.

•The loop foreach O (100 110 111) end runs its bodythree times for three different orientations.

•The first seven lines of the loop body define thesimplest mesh possible. It has exactly four lines (onerectangle), and a front side.

43

SUPREM•The method command chooses the oxide grid spacing

to be 0.03 microns, knowing that 30 minutes at 900Cwill grow about 0.1 microns of oxide.

•The oxidation step chooses the vertical model bydefault. The vertical model solves the Deal-Grovediffusion equation for oxidant, and uses the calculatedvelocities to move the oxide vertically everywhere.

•Grid is added automatically to the oxide as it grows,by default at increments of 0.1 microns.

•The time step is initially 0.1 second; subsequently itis automatically chosen to add no more than 14 of thegrid increment per time step.

44

SUPREM•When the diffusion is done, the select statement fills

the "z vector" with the y (vertical) locations of thepoints, scaled to angstroms.

•The print statement then prints the y displacementsalong the left side of the mesh. The form parameterrounds off the thickness to the nearest angstrom.

•The output is:

45

SUPREM"---------- Orientation < 100 > --------------------"estimated first time step 1.286963e-16Solving 0 + 0.1 = 0.1, 100%, np 6Solving 0.1 + 302.52 = 302.62, 3025.20%, np 6Solving 302.62 + 302.522 = 605.142, 100.001%, np 6Solving 605.142 + 311.041 = 916.183, 102.816%, np 6Solving 916.183 + 319.326 = 1235.51, 102.664%, np 6Solving 1235.51 + 327.623 = 1563.13, 102.598%, np 8Solving 1563.13 + 236.869 = 1800, 72.2992%, np 8Layer material thickness IntegratedNum type microns Depth(A)0 oxide -0.043 0.000000e+001 oxide 0.000 -3.104514e-042 oxide 0.035 0.000000e+003 silicon 1.000 4.993907e-01

46

SUPREM"---------- Orientation < 110 > --------------------"estimated first time step 4.402759e-16Solving 0 + 0.1 = 0.1, 100%, np 6Solving 0.1 + 216.262 = 216.362, 2162.62%, np 6Solving 216.362 + 216.266 = 432.629, 100.002%, np 6Solving 432.629 + 224.785 = 657.413, 103.939%, np 6Solving 657.413 + 232.98 = 890.393, 103.646%, np 6Solving 890.393 + 241.199 = 1131.59, 103.528%, np 8Solving 1131.59 + 249.427 = 1381.02, 103.411%, np 8Solving 1381.02 + 257.664 = 1638.68, 103.302%, np 8Solving 1638.68 + 161.318 = 1800, 62.6078%, np 10layer material thickness Integratednum type microns Depth(A)0 oxide -0.056 0.000000e+001 oxide -0.000 -1.296132e-032 oxide 0.046 7.714586e-043 silicon 1.000 4.989346e-01