課程名稱：微製造技術Micro fabrication Technology

授課教師：王東安Lecture 9

Lecture Outline•Reading Campbell: Chapter 3•Today’s lecture

–Prologue

–Differential equation that describe diffusion–Diffusion physics–SUPREM: a program that calculates diffusion

profiles

Prologue•Semiconductor devices rely on the ability to fabricate well

controlled, locally doped regions of the wafer.•Chemical impurities must fist be introduced into some sections

of the wafer, they must be active so that they contribute thedesired carrier, and they must be the concentration desired bythe device designer.

•Number density of Si is 5x1022 atoms/cm3, so that typicalimpurity concentrations (1017 atoms/cm3) for active deviceregions are doped as lightly as a few parts per million.

•Motion of impurity atoms in wafer occurs primarily bydiffusion the net movement of a material that occurs near aconcentration gradient as a result of random thermal motion.

Diffusion equation•Fick’s first law

xtxC

DJ

),(

C: atoms/cm3

D: coefficient of diffusionJ: atoms/cm2/sec

Fick’s second law

)()()( 2221 xC

Dx

AdxxJ

AdxJJAJJAtC

Adx

If D is independent of position

CDtC

xC

DtC 2

2

2

mediumisotropicanfor

Atomistic models of diffusion•Interstitial impurities

diffuse rapidly, buy they donot directly contribute tohoping.

•Substitutional impurities–Direct change: 6 bonds be

broken for host atom andimpurity to exchangepositions

–Vacancy exchange: 3 bondsbe broken. Dominantdiffusion mechanism forsubstitutional impurities.

Interstitialcy method•A second important mechanism for diffusion in Si

replies on presence of Si self-interstitials.

Analytic Solutions of Fick’s law•Assume coefficient of diffusion is constant, which is

questionable in practice.•Two types of exact solution to Fick’s law are developed.

–Predeposition diffusion: source is fixed at the surface for all timesgreater than zero.

–Drive in diffusion: an initial amount of impurity QT is introduced intothe wafer and diffused subject to the boundary condition

0),(),0(

0)0,(

tCCtC

zC

s

solution

Dtz

erfcCtzC s 2),(

constQdztzC

tCdz

tdCzzC

T

0),(

0),(

0),0(

0,0)0,(

solution DtzT eDt

QtzC 4/2

),(

Analytic Solutions of Fick’s law

Analytic Solutions of Fick’s law•Boron is diffusing in a Si wafer that has a uniform

concentration of phosphorus, CB. Also assume that Cs>> CB.• Junction depth of the p-n junction

– In case of drive in diffusion

– In case of predeposition diffusion

DtCQ

DtxB

Tj

4

s

Bj C

CDtx 1-erfc2

Diffusion systems•Most doping is now done by ion implantation rather

than predeposition diffusion.•When very heavily doped layers are required,

diffusion tubes are used to introduce the desireddopants.

•Two methods used to heavily dope layers in furnacetube–Liquid source doping–Solid source doping

Liquid source doping•Container of the liquid is immersed in a const temp bath to

produce a known vapor pressure of the dopant above the liquidsurface.

An inert gas is injectedinto the bubbler.Partial pressure of dopant infurnace in controlled by•bath temp•gas pressure above liquid•Ratio of flow through

bubbler to the sum of allother flows into furnace

Usually an O2 source issupplied to react with thedopant gas.

Liquid source•Most common boron source is BBr3. reactions occur in

furnace–Dissociation

–Oxidation

•Oxide is transported to wafer surface where it oxidizes thesurface to release free boron

•Liquid source phosphorus doping is done using a bubbler ofPOCl3, oxide that forms is P2O5. this oxide dissociates at thewafer surface releasing P and forming SiO2.

23 3BrB22BBr

232 3SiOB4Si3O2Br

322 OB33O4B

Disadvantage of liquid source•Source is corrosive•Bubblers must be pressurized and have been known

to explode•Sensitive to bubbler temp change•Danger of forming insoluble silicon compounds at

wafer surface that are invisible, but are extremelyundesirable.

Solid source•Source discs are about the same size as wafer and are

loaded in alternate slots in furnace boats.•For diffusing p-type layers in Si, boron nitride disc is

used. When oxidized at 750-1100℃, a thin film ofB2O3 forms at the surface. In presence of H2, thevolatile compound HBO2 forms and diffuses to wafersurface where a borosilicate glass in formed. Thisglass serves as the boron source for diffusion into thesubstrate.

SUPREM simulations of diffusion profiles•Numerical methods have been developed for the

prediction of defused profiles.•One of the most popular packages for calculating

impurity profiles is SUPREM.•SUPREM IV performs calculations in 2-D.•SUPREM-IV.GS, a version of the process simulator

SUPREM-IV extended to both GaAs and Siliconprocess simulation.

•Download the software and manual from

http://web.nchu.edu.tw/~daw/Teaching/Microfab/microfab.htm

SUPREM•To run SUPREM, an input deck must be provided.

This file contains–Initialize statement–Materials statements–Process statements–Output statements

Example Boron Anneal - 1D•a simple anneal of a boron implant. An input file for the

simulation borin.in#some set stuffset echo option quietmode one.dim#the vertical definitionline x loc = 0 spacing = 0.02 tag = topline x loc = 0.50 spacing = 0.02line x loc = 2.0 spacing = 0.25 tag=bottom#the silicon waferregion silicon xlo = top xhi = bottom#set up the exposed surfacesbound exposed xlo = top xhi = top#calculate the meshinit boron conc=1.0e14

Example Boron Anneal - 1D#the pad oxidedeposit oxide thick=0.075#the uniform boron implantimplant boron dose=3e14 energy=70 pearson#save the datastructure out=boron1.str#the diffusion carddiffuse time=30 temp=1100#save the datastructure out=boron2.str

Example Boron Anneal - 1D•procedure to run suprem

1. type sustart on the command line (optional)2. type suprem <boron.in> boron.out

•structure files will be generated•then use gawk to process structure files for matlab to

plot the results

Structure files and Gawkv SUPREM-IV A.9130D 1 2 2c 1 0 0c 2 0.02 0c 3 0.04 0………..c 4 0.06 0c 40 1.54002 0c 41 1.75069 0c 42 2 0c 43 -0.075 0r 1 3r 2 1………..

s 2 5 23n 0 1 1.092978e+18 1.000000e+14n 0 3 1.092978e+18 1.000000e+14n 1 3 1.739449e+18 1.000000e+14n 2 3 2.712546e+18 1.000000e+14n 3 3 4.130481e+18 1.000000e+14n 4 3 6.114785e+18 1.000000e+14……….n 41 3 1.000000e+14 1.000000e+14n 42 0 1.000000e+05 0.000000e+00n 42 1 1.664685e+17 0.000000e+00

Structure files and Gawk# gawk -f boron1.awk boron1.str# 04/07/09 D.-A. Wang startedBEGIN{}{

if($1~/c/ && $2~/43/){f1=$3print f1 > "a.dat"

}if($1~/c/ && $2!~/43/){

f1=$3print f1 > "a.dat"

}if($1~/n/ && $2~/42/ &&$3~/1/){

f2=$4print f2 > "b.dat"

}if($1~/n/ && $3~/3/){

f2=$4print f2 > "b.dat"

}}END{}

v SUPREM-IV A.9130D 1 2 2c 1 0 0c 2 0.02 0c 3 0.04 0………..c 4 0.06 0c 40 1.54002 0c 41 1.75069 0c 42 2 0c 43 -0.075 0r 1 3r 2 1………..

Structure files and Gawk# gawk -f boron1.awk boron1.str# 04/07/09 D.-A. Wang startedBEGIN{}{

if($1~/c/ && $2~/43/){f1=$3print f1 > "a.dat"

}if($1~/c/ && $2!~/43/){

f1=$3print f1 > "a.dat"

}if($1~/n/ && $2~/42/ &&$3~/1/){

f2=$4print f2 > "b.dat"

}if($1~/n/ && $3~/3/){

f2=$4print f2 > "b.dat"

}}END{}

s 2 5 23n 0 1 1.092978e+18 1.000000e+14n 0 3 1.092978e+18 1.000000e+14n 1 3 1.739449e+18 1.000000e+14n 2 3 2.712546e+18 1.000000e+14n 3 3 4.130481e+18 1.000000e+14n 4 3 6.114785e+18 1.000000e+14……….n 41 3 1.000000e+14 1.000000e+14n 42 0 1.000000e+05 0.000000e+00n 42 1 1.664685e+17 0.000000e+00

Matlabclear all;load -ascii a.datload -ascii b.datload -ascii c.datload -ascii d.datkk=length(a);cc=length(c);x(1)=a(kk);y(1)=log10(b(kk));x2(1)=c(cc);y2(1)=log10(d(1));for i=2:kk,

x(i)=a(i-1);y(i)=log10(b(i-1));

endfor i=2:cc,

x2(i)=c(i-1);y2(i)=log10(d(i));

end

LW=2; % plot line widthFSLABEL=16;FSTEXT=15;FSLEGEND=13;figure(2);hndl = plot(x,y,'r-

',x2,y2,'b--');set( hndl, 'LineWidth',

LW );AXIS([x(1) x(kk) min(y)

max(y)])xlabel('x \mum');ylabel('log10 (boron)');