1 microelectronics processing course - j. salzman - 2006 microelectronics processing diffusion

1Microelectronics Processing Course - J. Salzman - 2006

Microelectronics Processing Diffusion


Doping

Doping is the process that puts specific amounts of dopants in the wafer surface through openings in the surface layers.

Thermal diffusion is a chemical process that takes place when the wafer is heated (~1000 C) and exposed to dopant vapor. In this process the dopants move to regions of lower concentration.

Doping Control is critical in MOS device scaling. (Scaling down the gate length requires equal scaling in doping profile)

Thermal diffusion

Ion source

Ion implantation


Comparison of thermal diffusion Comparison of thermal diffusion and ion implantationand ion implantation


Mathematics of diffusion:Mathematics of diffusion:Fick’s First diffusion lawFick’s First diffusion law

F

F

D is thermally activated


Mathematics of diffusion:Mathematics of diffusion:Fick’s Second diffusion lawFick’s Second diffusion law

What goes in and does not go out, stays there

C/t = (Fin-Fout)/ x


Fick’s diffusion lawFick’s diffusion law

F

F

Concentration independent diffusion equation.Often referred to as Fick’s second law.


Analytic solutions of the diffusion Analytic solutions of the diffusion equations:equations:

Case of a spike delta function in infinite Case of a spike delta function in infinite mediamedia

QtxC

and

xfortasC

xfortasC

conditionsBoundary

),(

00

000

:

Dt

xtC

Dt

x

Dt

QtxC

profileGaussianadescribes

lawdiffusionsFickofsolutionThe

4exp),0(

4exp

2),(

:

'

22

(x)


The evolution of a Gaussian The evolution of a Gaussian diffusion profilediffusion profile

•Peak concentration decreases as 1/√t and is given by C(0,t).•Approximate measure of how far the dopant has diffused (the diffusion length) is given by x=2√Dt which is the distance from origin where the concentration has fallen by 1/e


Carl Friedrich Gauss (1777-1855)



Case of a spike delta function near the Case of a spike delta function near the surfacesurface

Dt

QtCwith

Dt

xtC

Dt

x

Dt

QtxC

),0(

4exp),0(

4exp),(

22

The symmetry of the problem is similar to previous case, with an effective dose of 2Q introduced into a (virtual) infinite medium.The solution is thus:


Constant total dopant (number) Constant total dopant (number) diffusion:diffusion:

Impurity profileImpurity profile

Three impurity profiles carried out under constant total dopant diffusion conditions. Note the reduction in the surface concentration C(0,t) with

time, and the corresponding rise in the bulk density.

Log scale Linear scale



Case of an infinite source of dopantCase of an infinite source of dopant

00

000

:

xfortatCC

xfortatC

conditionsboundaryThe

n

i

ii Dt

xxx

Dt

CtxC

1

2

4exp

2),(

Dt

x

dC

dDt

x

Dt

CtxC

Dtx

2

)(

)(exp4

exp2

),( 22/

0

2


The error functionThe error function

A related function is tabulated:

The solution of the diffusion equation from an infinite source is finally:

z

dzerf0

2)exp(2

)(

)2

(2

)2

(12

),(Dt

xerfc

C

Dt

xerf

CtxC


Constant surface concentration: Constant surface concentration: diffusion depthdiffusion depth

Log scale Linear scale

Plots of C(x,t)/Cs vs diffusion depth x(µm) under constant surface concentration conditions for three different values of √Dt . This could mean either a change of temperature (i.e D(T)) or time, t.


Total number of impuritiesTotal number of impurities(predeposition dose)(predeposition dose)

As seen in the figure, the error function solution is approximately triangular. The total dose may be estimated by an area of triangular of height Cs and a base of 2√Dt, giving Q= Cs √Dt.More accurately:

= Characteristic distance for diffusion.CS = Surface concentration (solid solubility limit).

t


Two-step junction formation:Two-step junction formation:(a) Predeposition from a constant source (a) Predeposition from a constant source

(erfc)(erfc)(b) Limited source diffusion (Gaussian)(b) Limited source diffusion (Gaussian)


Shallow predep approximationShallow predep approximation

)()0,(;)(2

xQtxCDtC

Qpredeps

Solution of Drive-in profile:

indriveindrive Dt

x

Dt

QtxC

)(4exp

)(),(

2

In summary:

22

22/1

22

11

4exp

2)(

tD

x

tD

tDCxC s

D1= Diffusivity at Predep temperaturet1= Predep timeD2= Diffusivity at Drive-in temperaturet2= Drive-in time


Two-step junction formationTwo-step junction formation


Temperature dependence of DTemperature dependence of D


Diffusion coefficients (constants) for a Diffusion coefficients (constants) for a number of impurities in Siliconnumber of impurities in Silicon

Substitutional Interstitial


Typical diffusion coefficient values

Element D0 (cm2/sec) EA(eV)

B 10.5 3.69

P 10.5 3.69

As 0.32 3.56


The two principal diffusion The two principal diffusion mechanisms:mechanisms:

Schematic diagramsSchematic diagrams

Vacancy diffusionin a semiconductor.

Interstitial diffusion in a semiconductor.


Vacancy Intersticial


Thermal diffusion – general Thermal diffusion – general commentscomments

Schematic diagram of a furnace for diffusing impurities (e.g. phosphorus) into silicon.


Rapid thermal annealingRapid thermal annealing

a) Concept. b) Applied Materials 300 mm RTP system.


Dopant diffusion sourcesDopant diffusion sources

(a) Gas Source: AsH3, PH3, B2H6

(b) Solid Sources: BN, NH4H2PO4, AlAsO4

(c) Spin-on-glass: SiO2+dopant oxide

(d) Liquid source: A typical bubbler arrangement for doping a silicon wafer using a liquid source. The gas flow is set using mass flow controller (MFC).


Junction depthJunction depth


Sheet resistanceSheet resistance

The resistance of a rectangular block is:R = ρL/A = (ρ/t)(L/W) ≡ Rs(L/W)

Rs is called the sheet resistance. Its units are termed Ω/ .

L/W is the number of unit squares of material in the resistor.


Sheet resistanceSheet resistance


Irving’s curves: Motivation to Irving’s curves: Motivation to generate themgenerate them


Irving’s curvesIrving’s curves


Figure illustrating the Figure illustrating the relationship ofrelationship of

NNoo, N, NBB, x, xjj, and R, and Rss


Diffusion of Gaussian Diffusion of Gaussian implantation profileimplantation profile

Note: Q is the implantation dose.

Q

1 microelectronics processing course - j. salzman - 2006 microelectronics processing diffusion

Documents

diffusion equations

mathematics of diffusion

diffusion length

activated slide

diffusion law f f d

infinite media x slide

log scalelinear scale

tcs vs diffusion depth