junction formation the position of the junction for a limited source diffused impurity in a constant...

Junction FormationJunction Formation The position of the junction for a The position of the junction for a

limited source diffused impurity in a limited source diffused impurity in a constant background is given byconstant background is given by

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

x Dt NNjB

2 0ln

x Dt NNj

B 2 1

0erfc

Junction FormationJunction Formation

Junction Depth Lateral Diffusion

Design and EvaluationDesign and Evaluation

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

These parameters are not independentThese parameters are not independent

Irvin developed a relationship that Irvin developed a relationship that describes these parametersdescribes these parameters

jx

B

jS

dxxnNxnqx

0

)()(

11

Irvin’s CurvesIrvin’s Curves

In designing processes, we need to In designing processes, we need to use all available datause all available data– We need to determine if one of the We need to determine if one of the

analytic solutions appliesanalytic solutions applies For example, For example,

– If the surface concentration is near the solubility If the surface concentration is near the solubility limit, the continuous (erf) solution may be appliedlimit, the continuous (erf) solution may be applied

– If we have a low surface concentration, the If we have a low surface concentration, the limited source (Gaussian) solution may be appliedlimited source (Gaussian) solution may be applied

Irvin’s CurvesIrvin’s Curves If we describe the dopant profile by either the If we describe the dopant profile by either the

Gaussian or the erf modelGaussian or the erf model– The surface concentration becomes a parameter in The surface concentration becomes a parameter in

this integrationthis integration– By rearranging the variables, we find that the surface By rearranging the variables, we find that the surface

concentration and the product of sheet resistance and concentration and the product of sheet resistance and the junction depth are related by the definite integral the junction depth are related by the definite integral of the profileof the profile

There are four separate curves to be evaluatedThere are four separate curves to be evaluated– one pair using either the Gaussian or the erf function, one pair using either the Gaussian or the erf function,

and the other pair for n- or p-type materials because and the other pair for n- or p-type materials because the mobility is different for electrons and holesthe mobility is different for electrons and holes

Irvin’s CurvesIrvin’s Curves

Irvin’s CurvesIrvin’s Curves An alternative way of presenting the data may be An alternative way of presenting the data may be

found if we set found if we set effeff=1/=1/ssxxjj

ExampleExample Design a B diffusion for a CMOS tub such that Design a B diffusion for a CMOS tub such that

ss=900=900/sq, x/sq, xjj=3=3m, and CB=1m, and CB=110101515/cc/cc

– First, we calculate the average conductivityFirst, we calculate the average conductivity

– We cannot calculate n or We cannot calculate n or because both are functions of because both are functions of depthdepth

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

Therefore, we can use the P-type Gaussian Irvin Therefore, we can use the P-type Gaussian Irvin curvecurve

1

4cm7.3

cm103/sq900

11

jS x

ExampleExample Reading from the p-type Gaussian Irvin’s Reading from the p-type Gaussian Irvin’s

curve, curve, CCSS4x104x101717/cc/cc– This is well below the solid solubility limit for B This is well below the solid solubility limit for B

in Si so we may conclude that it will be driven in Si so we may conclude that it will be driven in from a fixed source provided either by ion in from a fixed source provided either by ion implantation or possibly by solid state implantation or possibly by solid state predeposition followed by an etchpredeposition followed by an etch

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

29

15

17

242

cm 107.3

10104

ln4

103

ln4

B

S

j

CC

xDt

ExampleExample

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

C where D for B in Si is 1.5 x 10C where D for B in Si is 1.5 x 10-13-13cmcm22/s, the /s, the drive-in time will bedrive-in time will be

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

hrs 8.6/scm105.1

cm107.3213

29

drive

t

213917 cm 103.4107.3104),0( -DttCQ

ExampleExample

Consider a predep process from the solid Consider a predep process from the solid state source (as is done in the VT lab course)state source (as is done in the VT lab course)– The text uses a predep temperature of 950 The text uses a predep temperature of 950 ooCC– In this case, we will make a glass-like oxide on In this case, we will make a glass-like oxide on

the surface that will introduce the B at the solid the surface that will introduce the B at the solid solubility limitsolubility limit

– At 950 At 950 ooC, the solubility limit is 2.5x10C, the solubility limit is 2.5x102020cmcm-3-3 and and D=4.2x10D=4.2x10-15-15 cm cm22/s/s

Solving for tSolving for t

DtC

Q S

2

s 5.5102.4

1

2105.2

103.415

22

20

13

predep

t

ExampleExample

This is a very short time and hard to This is a very short time and hard to control in a furnace; thus, we should do control in a furnace; thus, we should do the predep at a lower temperaturethe predep at a lower temperature– In the VT lab, we use 830 – 860 In the VT lab, we use 830 – 860 ooCC

Does the predep affect the drive in?Does the predep affect the drive in?

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

9indrive

14predep 107.3103.2

DtDt

DIFFUSION SYSTEMSDIFFUSION SYSTEMS Open tube furnaces of the 3-Zone Open tube furnaces of the 3-Zone

designdesign Wafers are loaded in quartz boat in Wafers are loaded in quartz boat in

center zonecenter zone Solid, liquid or gaseous impurities may Solid, liquid or gaseous impurities may

be usedbe used– Common gases are extremely toxic Common gases are extremely toxic

(AsH(AsH33 , PH , PH33))

– Use NUse N22 or O or O22 as carrier gas to move as carrier gas to move impurity downstream to crystalsimpurity downstream to crystals

SOLID-SOURCE DIFFUSION SOLID-SOURCE DIFFUSION SYSTEMS SYSTEMS

N2O2

Valves andflow meters

Platinumsource boat

Slices oncarrier

Quartzdiffusion

tube

Quartzdiffusion boat

burn boxand/or scrubber

Exhaust

LIQUID-SOURCE DIFFUSION LIQUID-SOURCE DIFFUSION SYSTEMSSYSTEMS

Burn boxand/or scrubber

ExhaustSlices on

carrier

Quartzdiffusion tube

Valves andflow meters

Liquid source

Temperature-controlled bath

N2O2

GAS-SOURCE DIFFUSION GAS-SOURCE DIFFUSION SYSTEMSSYSTEMS

Burn boxand/or scrubber

Exhaust

N2 Dopantgas

O2

Valves and flow meter

To scrubber system

Trap

Slices on carrier

Quartz diffusion tube

DIFFUSION SYSTEMSDIFFUSION SYSTEMS Typical reactions for solid impurities Typical reactions for solid impurities

are: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

Rapid Thermal AnnealingRapid Thermal Annealing

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

Rapid Thermal AnnelingRapid Thermal Anneling

Absorption of IR light will heat the wafer Absorption of IR light will heat the wafer quickly (but not so as to introduce quickly (but not so as to introduce fracture stresses)fracture stresses)– It is possible to ramp the wafer at 100 It is possible to ramp the wafer at 100 ooC/sC/s– Because of the thermal conductivity of Si, a Because of the thermal conductivity of Si, a

12 in wafer can be heated to a uniform 12 in wafer can be heated to a uniform temperature in millisecondstemperature in milliseconds 1 – 100 s drive or anneal times are possible1 – 100 s drive or anneal times are possible

RTAs are used to diffuse shallow RTAs are used to diffuse shallow junctions and to anneal radiation junctions and to anneal radiation damagedamage

Rapid Thermal AnnealingRapid Thermal Annealing

Concentration-Dependent Concentration-Dependent DiffusionDiffusion

When the concentration of the doping When the concentration of the doping exceeds the intrinsic carrier exceeds the intrinsic carrier concentration at the diffusion concentration at the diffusion temperaturetemperature– We have assumed that the diffusion We have assumed that the diffusion

coefficient, D, is dependent of concentrationcoefficient, D, is dependent of concentration In this case, we see that diffusion is In this case, we see that diffusion is

faster in the higher concentration faster in the higher concentration regions regions


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


We can still use Fick’s law to We can still use Fick’s law to describe the dopant diffusiondescribe the dopant diffusion– Cannot directly integrate/solve the Cannot directly integrate/solve the

differential equations when D is a differential equations when D is a function of Cfunction of C

– We thus must solve the equation We thus must solve the equation numericallynumerically

x

CD

xt

C effA


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

2)/(or )/( ii nnDnnD


B has two isotopes: BB has two isotopes: B1010 and B and B1111

Create a wafer with a high concentration Create a wafer with a high concentration of one isotope and then diffuse the of one isotope and then diffuse the second isotope into this materialsecond isotope into this material– SIMS is used to determine the concentration SIMS is used to determine the concentration

of the second isotope as a function of xof the second isotope as a function of x The experiment has been done using The experiment has been done using

many of the dopants in Si to determine many of the dopants in Si to determine the concentration dependence of Dthe concentration dependence of D


Diffusion constant can usually be Diffusion constant can usually be written in the formwritten in the form

for n-type dopants andfor n-type dopants and

for p-type dopantsfor p-type dopants

2

0effA

ii n

nD

n

nDDD

2

0effA

ii n

pD

n

pDDD


It is assumed that there is an It is assumed that there is an interaction between charged vacancies interaction between charged vacancies and the charged diffusing speciesand the charged diffusing species

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

– All of the various diffusivities are assumed All of the various diffusivities are assumed to follow the Arrhenius formto follow the Arrhenius form

DDDD 0effA

kT

EDDD

.exp0


The values for all the pre-exponential The values for all the pre-exponential factors and activation energies are factors and activation energies are knownknown– If we substitute into the expression for the If we substitute into the expression for the

effective diffusion coefficient, we findeffective diffusion coefficient, we find

here, here, =D=D--/D/D0 0 andand =D=D==/D/D00

1

12

*effA

iiA

nn

nn

DD


is the linear variation with is the linear variation with composition and composition and is the quadratic is the quadratic variationvariation– Simulators like SUPREM include these Simulators like SUPREM include these

effects and are capable of modeling effects and are capable of modeling very complex structuresvery complex structures

junction formation the position of the junction for a limited source diffused impurity in a constant...

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