C06 - 1 Virginia Tech Chapter 7: DOPANT DIFFUSION.

C06- 1Virginia Tech

Chapter 7:DOPANT DIFFUSION

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DOPANT DIFFUSION

Introduction Basic Concepts

– Dopant solid solubility– Macroscopic view– Analytic solutions– Successive diffusions– Design of diffused layers

Manufacturing Methods

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Introduction

Main challenge of front-end processing is the accurate control of the placement of active doping regions

Understanding and control of diffusion and annealing is essential to obtaining the desired electrical performance

If the gate length is scaled down by 1/K (K>1) ideally the dimensions of all doped regions should also scale by 1/K to maintain the same electric field patterns

With the same field patterns, the device works the same as before, except that it is faster because of the shorter channel

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Introduction

Thus, there is a continuous drive to reduce the junction depth with each new technology generation

However, the diffusion cycles often become the limiting factor in junction depth

We need high activation levels to reduce parasitic resistances of the source, drain and extensions (see Figure 1)

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Introduction

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Introduction

The sheet resistance is given by

This is valid if the doping is uniform throughout the junction

If it is not, the expression becomes

/square j

S x

jx

B

jS

dxxnNxnqx

0

)()(

11

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Introduction

The challenge is to keep the junctions shallow and yet keep the resistance of the source and drain small to maximize drive current

These are conflicting requirements The NTRS has set goals for shallow junctions

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NTRS Projections

Note particularly the projected junction depth

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Basic Concepts

Since 1960, the planar process has dominated all methods for creating junctions

The fundamental change in the past 40 years has been how the “predep” has been done.

Predep (predeposition) controls how much impurity is introduced into the wafer

In the 1960s, this was done by solid state diffusion from glass layers or by gas phase diffusion

By the mid-1970s, ion implantation became (and remains) the method of choice

Its only drawback is radiation damage


Basic Concepts

In ion implantation, damaged-enhanced diffusion allows for significant diffusion of dopants

This is a major problem in very shallow junctions


Basic Concepts


Basic Concepts

The desired dopants (P, As, B) have only limited solid solubility in Si

The solubility increases with temperature Except, some dopants exhibit retrograde solubility

(where the solubility decreases at elevated temperatures)

If we dope above the solubility limit, precipitates form. When combined in precipitates (or clusters) the dopants do not contribute donors or acceptors (electrons or holes)

The dopant is not electrically active We therefore need to know the maximum amount of

dopant that we can put in Si and maintain electrically active donors and acceptors


Dopant Solubility in Si


Solubility Limit

Solubility and electrical activity of impurities in Si

1021

1020

1019

900 1000 1100 1200Temperature ( o C )

Sb

B

P

As

P

As

Solubility limitElectrical active

Impu

rity

con

cent

ratio

n, N

(at

oms/

cm3 )


Solubility Limit

III-V dopants have limited solubility in Si Surface concentrations can be high. At

1100oC:– B: 3.3 x 1020 cm-3

– P: 1.2 x 1021 cm-3

At high temperatures, impurities cluster without precipitating and have limited electrical activity

3 3As As n


Diffusion Models

We can discuss diffusion from a macroscopic or a microscopic point of view

The macroscopic view describes the overall motion of the dopant profiles

It predicts the motion of the profile by solving a differential equation subject to certain boundary conditions

The atomistic approach is used to understand some of the very complex mechanisms by which dopants move in Si

We will solve the macroscopic part first


Fick’s Laws

Diffusion is described by Fick’s Laws.Fick’s first law is:

D = diffusion coefficient

Conservation of mass requires

(This is the continuity equation)

J Dc

x

c

t

J

x


Fick’s Laws

Combining the continuity equation with the first law, we obtain Fick’s second law:

Solutions depend on the boundary conditions. We have assumed D is independent of concentration

Assume a semi-infinite slab with– Continuous supply (Models diffusion of impurities in

wafer)– Fixed supply (Models ion implantation of impurities in

wafer)

c

tD

c

x

2

2


Solutions To Fick’s Second Law

The simplest solution is when there is a steady state and there is no variation of the concentration with time

In this case

This steady-state solution shows that the concentration is linear over distance

This was the solution for the flow of oxygen from the surface to the Si/SiO2 interface in the last chapter

bxaxc

x

cD

)(

02

2



There are two other solutions of interest The text breaks these into two sub-solutions

each; one for an infinite slab and one for a semi-infinite slab

We will examine only the latter as they approach real conditions



For a semi-infinite slab with a constant (infinite) supply of atoms at the surface

The dose is

0 02, DtcdxtxcQ

c(x t) cx

Dto, erfc

2



In this solution, the complimentary error function (erfc) is defined as erfc(x)=1-erf(x)

The error function is defined as

This is a tabulated function. It also has several decent approximations, and is usually found as a built-in function in MatLab, MathCad, and Mathematica

z

dzerf0

2exp2

)(



This solution models diffusion from a gas-phase or liquid phase source

Typical solutions look like

c0

cB

Distance from surface, x

1 2 3

D3t3 > D2t2 > D1t1

Impu

rity

con

cent

rati

on, c

(x)

c ( x, t )



Constant source diffusion, as is performed for example with ion implantation, has a solution of the form

Here, Q is the does or the total number of dopant atoms diffused into the Si

The surface concentration is

dxtxcQ

0

),(

Dt

Qtc

),0(

c(x t)Q

Dte

x

Dt ,

2

4



Limited (fixed) source diffusion looks like

c ( x, t )c01

c02

c03

cB

1 2 3


D3t3 > D2t2 > D1t1

Impu

rity

con

cent

rati

on, c

(x)


Comparison Of Models

Comparison of constant source and continuous source models

1

10-1

10-2

10-3

10-4

10-5

10-6

0 0.5 1 1.5 2 2.5 3 3.5

Val

ue o

f fu

ncti

ons

Normalized distance from surface, x_

xx

Dt

_

2

exp(- )x_

2

erfc( )x_


Diffusion Coefficient

Probability of a jump is

Diffusion coefficient is proportional to jump probability

P P Pj v m

e eE kT E kTf m

D D e E kTD 0


Diffusion Coefficient

Typical diffusion coefficients in silicon

Element D0 (cm2/sec) ED (eV)

B 10.5 3.69Al 8.00 3.47Ga 3.60 3.51In 16.5 3.90P 10.5 3.69

As 0.32 3.56Sb 5.60 3.95


Diffusion Of Impurities In Silicon

Arrhenius plots of diffusion in silicon

1400 1300 1200 1100 1000Temperature (o C)

10-9

10-10

10-11

10-12

10-13

10-14

0.6 0.65 0.7 0.75 0.8 0.85Temperature, 1000/T (K-1)

Al

Ga

B,P

In

AsSb

Dif

fusi

on c

oeff

icie

nt, D

(cm

2 /se

c)

10-4

10-5

10-6

10-7

10-8

0.6 0.7 0.8 0.9 1.0 1.1

Temperature, 1000/T (K-1)

1200 1100 1000 900 800 700

Temperature (o C)

Dif

fusi

on c

oeff

icie

nt, D

(cm

2 /se

c)

Li

CuFe

Au



We recall that the intrinsic carrier concentration in Si is about 7 x 1018/cc at 1000 C

Thus, if NA and ND are <ni, the material will behave as if it were intrinsic; there are many practical situations where this is a good assumption

The solutions we have given will be valid so long as the concentrations are low enough so that the material is intrinsic at the diffusion temperature



Note that the dopants cluster into “fast” diffusers (P, B, In) and “slow” diffusers (As, Sb)

As we develop shallow devices, slow diffusers are becoming very important

Note that B is the only p-type dopant that has a high solubility; therefore, it is very hard to make shallow p-type junctions with this fast diffuser

We will also find that the theories given here break down as we go to higher concentrations of dopants


Successive Diffusions

To create devices, we must successively diffuse n- and p-type dopants

There are many high temperature steps and all preceding impurities can move as succeeding dopant or oxidation steps are performed

The effective Dt product is

There is no difference between doing diffusion in one step or in several steps at the same temperature

If we now increase the time of step 2 by the ratio D2/D1

2111211 )()( tDtDttDDt eff

2211

1

22111)( tDtDD

DtDtDDt eff


Successive Diffusions

The actual distribution is given by

Di , ti = diffusion coefficient and time for ith step

We need to bear in mind that, as will be seen later, D may be a function of more than T; thus these results will not hold

Dt D ttot i i

i


Junction Formation

When diffuse n- and p-type materials, we create a pn junction

When [donor]=[acceptor], the semiconductor material is compensated and we create a metallurgical junction

At metallurgical junction the material behaves intrinsic

We can calculate the position of the metallurgical junction for those systems for which our analytical model is a good fit


Junction Formation

Formation of a pn junction by diffusion

Impurity

concentrationN(x)

N0

NB

(log

sca

le)

xj

p-type Gaussian diffusion(boron)

n-type silicon

background


Net impurityconcentration

|N(x) - NB |

N0 - NB

p-type

region

n-type region

xj


(log

sca

le)


Junction Formation

The position of the junction for a fixed source diffused impurity in a constant background is given by

The position of the junction for a continuous source diffused impurity is given by

x Dt NNjB

2 0ln

x Dt NNj

B 2 1

0erfc


Junction Formation

Junction Depth Lateral Diffusion


Design and Evaluation

There are three parameters that define a diffused region– The surface concentration– The junction depth– The sheet resistance

These parameters are not independent Irvin developed a relationship that describes

these parameters very well Consider the equation for sheet resistance

jx

B

jS

dxxnNxnqx

0

)()(

11


Irvin’s Curves

In designing processes, we need to use all available data

We need to determine if one of the analytic solutions applies

For example, – if the surface concentration is near the

solubility limit, perhaps the continuous (erf) solution applies

– If we have a low surface concentration, perhaps the fixed (Gaussian) solution applies


Irvin’s Curves

If we describe the dopant profile by either the Gaussian or the erf model, we can evaluate the integral

The surface concentration becomes a parameter in this integration

By rearranging the variables, we find that the surface concentration and the product of sheet resistance and the junction depth are related by the definite integral of the profile

There are four separate curves to be evaluated; one pair using either the Gaussian or the erf function, and the other pair for n- or p-type materials (because the mobility is different for electrons and holes)

Typical examples are shown on the following slide


Irvin’s Curves


Irvin’s Curves

An alternative way of presenting the data may be found if we set eff=1/sxj


Example

Design a B diffusion for a CMOS tub such that s=900/sq, xj=3m, and CB=11015/cc

First, we calculate the average conductivity

We cannot calculate n or because both are functions of depth

We assume that because the tubs are of moderate concentration and thus assume (for now) that the distribution will be Gaussian

Therefore, we can use the P-type Gaussian Irvin curve to deduce that

1

4cm7.3

cm103/sq900

11

jS x


Example

Reading from the p-type Gaussian Irvin’s curve, CS4x1017/cc

This is well below the solid solubility limit for B in Si so we may conclude that it will be driven in from a fixed source provided either by ion implantation or possibly by solid state predeposition followed by an etch

In order for the junction to be at the required depth, we can compute the Dt value from the Gaussian junction equation

29

15

17

242

cm 107.3

10104

ln4

103

ln4

B

S

j

CC

xDt


Example

This value of Dt is the thermal budget for the process If this is done in one step at (for example) 1100 C

where D for B in Si is 1.5 x 10-13cm2/s, the drive-in time will be

Given Dt and the final surface concentration, we can estimate the dose

This is easy to deposit by ion implantation

hrs 8.6/scm105.1

cm107.3213

29

indrive

t

213917 cm 103.4107.3104),0( -DttCQ


Example

Let us also look at doing it by predep from the solid state (as is done in the VT lab course)

The text uses a predep temperature of 950 C In this case, we will make a glass-like oxide on the

surface that will introduce the B at the solid solubility limit

At 950 C, the solubility limit is 2.5x1020cm-3 and D=4.2x10-15 cm2/s

Solving for t

DtC

Q S

2

s 5.5102.4

1

2105.2

103.415

22

20

13

deppre

t


Example

This is a very short time and hard to control in a furnace; thus, we should do the pre-dep at lower temperatures

In the VT lab, we use 830 – 860 C Does the predep affect the drive in?

There is no affect on the thermal budget because it is done at such a “low” temperature

9indrive

14predep 107.3103.2

DtDt


DIFFUSION SYSTEMS

Use open tube furnaces of the 3-Zone design Wafers are mounted in quartz boat in center

zone Use solid, liquid or gaseous impurities for good

reproducibility Use N2 or O2 as carrier gas to move impurity

downstream to crystals Common gases are extremely toxic (AsH3 ,

PH3)


SOLID-SOURCE DIFFUSION SYSTEMS

N2O2

Valves andflow meters

Platinumsource boat

Slices oncarrier

Quartzdiffusion

tube

Quartzdiffusion boat

burn boxand/or scrubber

Exhaust


LIQUID-SOURCE DIFFUSION SYSTEMS

Burn boxand/or scrubber

ExhaustSlices on

carrier

Quartzdiffusion tube

Valves andflow meters

Liquid source

Temperature-controlled bath

N2O2


GAS-SOURCE DIFFUSION SYSTEMS

Burn boxand/or scrubber

Exhaust

N2 Dopantgas

O2

Valves and flow meter

To scrubber system

Trap

Slices on carrier

Quartz diffusion tube


DIFFUSION SYSTEMS

Al and Ga diffuse very rapidly in Si; B is the only p-dopant routinely used

Sb, P, As are all used as n-dopants


DIFFUSION SYSTEMS

Typical reactions for solid impurities are:

2 9 6 9

2 4

4 30 2 6

2 5 4

2 3 3 4

2 3 3 4

3 3 2900

2 3 2 2

2 3 2

3 2 2 5 2

2 5 2

2 3 2

2 3 2

CHO B O BO CO HO

BO Si SiO B

POCl PO Cl

PO Si SiO P

AsO Si SiO As

SbO Si SiO Sb

oC


PRODUCTION DIFFUSION FURNACES

Commercial diffusion furnace showing the furnace with wafers (left) and gas control system (right). (Photo courtesy of Tystar Corp.)


PRODUCTION DIFFUSION FURNACES

Close-up of diffusion furnace with wafers.


Rapid Thermal Annealing

An alternative to the diffusion furnaces is the RTA or RTP furnace


Rapid Thermal Anneling

In this system, we try to heat the wafer quickly (but not so as to introduce fracture stresses)

RTAs usually use infrared lamps and heat by radiation

It is possible to ramp the wafer at 100 C /sec Such devices are used to diffuse shallow

junctions and to anneal radiation damage In such a system, for the thermal conductivity

of Si, a 12 in wafer can be heated to a uniform temperature in milliseconds

Therefore, 1 – 100 s annealing times are very reasonable


Rapid Thermal Annealing


Concentration-Dependent Diffusion

If the concentration of the doping exceeds the intrinsic carrier concentration at the diffusion temperature, another effect occurs

We have assumed that the diffusion coefficient, D, is independent of concentration

This is not valid if the concentration of the diffusing species is greater than the intrinsic carrier concentration

In this case, we see that diffusion is faster in the higher concentration regions



The concentration profiles for P in Si look more like the solid lines than the dashed line for high concentrations (see French et al)



If we define the diffusivity to be a function of composition, then we can still use Fick’s law to describe the dopant diffusion

Usually, we cannot directly integrate/solve the differential equations when D is a function of C

We thus must solve the equation

numerically

x

CD

xt

C effA



It has been observed that the diffusion coefficient usually depends on concentration by either of the following relations

Look, for example, at the diffusion of P in Si observed by French et al

How do we obtain information about the concentration dependence of diffusivity?

There is a lovely experiment done with B

2)/(or )/( ii nnDnnD



B has two isotopes: B10 and B11

We create a wafer with a high concentration of one isotope (say B10) and then we diffuse the second isotope into this material

We use SIMS to determine the concentration of B11 as a function of distance

This gives us the diffusion of B as a function of the concentration of B

These experiments have been done for a great many of the dopants in Si



We find that the diffusivity can usually be written in the form

for n-type dopants and

for p-type dopants

2

0effA

ii n

nD

n

nDDD

2

0effA

ii n

pD

n

pDDD



The superscripts are chosen because we believe the interaction is between charged vacancies and the charged diffusing species

For an n-type dopant in an intrinsic material, the diffusivity is

All of the various diffusivities are of the Arrhenius form

DDDD 0effA

kT

EDDD

.exp0



The values for all the pre-exponential factors and activation energies are known (see next Table)

If we substitute into the expression for the effective diffusion coefficient, we find

here, =D-/D0 and =D=/D0

1

12

*effA

iiA

nn

nn

DD



Expressed this way, is the linear variation with composition and is the quadratic variation

Simulators like SUPREM include these effects and are capable of modeling very complex structures

C06 - 1 Virginia Tech Chapter 7: DOPANT DIFFUSION.

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