Microelectronics Technology

Dopant Diffusion

DOPANT DIFFUSION

1. To form source and drain regions in MOS devices and also to dope poly-Si gate material.

2. Used to form base regions, emitters, and resistors in bipolar devices.

Process by which controlled amount of chemical impurities are introduced into semiconductor lattice.

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani

Various ways of introducing dopants into silicon by diffusion have been studied with the goals:

• Controlling dopant concentration

• Total dopant concentration

• Uniformity of the dopant

• Reproducibility of the dopant profile

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani

Important Parameters of Diffusion

Basic Concepts

• Placement of doped regions (main source/drain, S/D extensions, threshold adjust) determine many short-channel characteristics of a MOS device.

• Resistance impacts drive current.

• As device shrinks by a factor K, junction depths should also scale by K to maintain same e –field patterns (assuming the voltage supply also scales down by the same factor).

• Gate doping affects poly-depletion and limits howthe gate voltage controls the channel potential.

Rcontact

RsourceRext Rchan

Rpoly

Silicide

VG

VS VD

Sidewall Spacers

xJ

xW

Channel Doping Requirement: Projections(NTRS RoadMap)

Year of 1st DRAM Shipment 1997 1999 2003 2006 2009 2012

Min Feature Size (nm) 250 180 130 100 70 50

DRAM Bits/Chip 256M 1G 4G 16G 64G 256G

Minimum Supply Voltage (volts)

1.8-2.5

1.5-1.8 1.2-1.5

0.9-1.2 0.6-0.9 0.5-0.6

Gate Oxide Tox Equivalent (nm) 4-5 3-4 2-3 1.5-2 <1.5 <1.0

Sidewall Spacer Thickness xW (nm)

100-200 72-144 52-104 20-40 7.5-15 5-10

Contact xj (nm) 100-200 70-140 50-100 40-80 15-30 10-20

xj at Channel (nm) 50-100 36-72 26-52 20-40 15-30 10-20

Drain Ext Conc (cm-3) 1x1018 1x1019 1x1019 1x1020 1x1020 1x1020

Introduction

R = ρ ρS = ρ/xj

xja) b)

• The resistivity of a cube is given by

€

J =nqv =nqµε=1ρε ∴ ρ=ε

J Ωcm (1)

• The sheet resistance of a shallow junction is

€

R =ρxj

Ω/ Square≡ρS (2)

Introduction

Depth

• For a non-uniformly doped layer,

€

ρs = ρ xj

= 1

q n x()−NB[ ]0

xj

∫ µn x()[ ]dx(3)

• Sheet resistance can be experimentally measured by a four point probe technique.

• Doping profiles can be measured by SIMS (chemical) or spreading R (electrical).

• Generally doping levels need to increase and xJ values need to decrease as the devices are scaled.

Two Step Diffusion• Diffusion is the redistribution of atoms from regions of high

concentration of mobile species to regions of low concentration. It occurs at all temperatures, but the diffusivity has an exponential dependence on T.

• Predeposition : doping often proceeds by an initial predep step to introduce the required dose of dopant into the substrate.

• Drive-In : a subsequent drive-in anneal then redistributes the dopant

giving the required junction depth

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani

Impurity Sources for Boron Diffusion

Impurity Source

State at Room Temp

Source Temp Range

Impurity Conc

RangeAdvantages

Boron Nitride

Solid Kept along with wafers

High and low

Very clean process. Requires activation

Boric Acid Solid 600-1200oC High and low

Readily available and proven source

Boron Tribromide

Liquid 10-30oC High and Low

Clean system. Good control over impurity

Methyl Borate

Liquid 10-30oC High Simple to prepare and operate

Boron Trichloride

Gas Room Temperature

High and Low

Accurate control of gas concentration

Diborane Gas Room Temperature

High and Low

Accurate control of gas concentration, but highly toxic

Impurity Sources for Phosphorus Diffusion

Impurity Source

State at Room Temp

Source Tem. Range

Concentra-tion Range Advantages

Red Phosphorus

Solid 200-300oC < 1020 cm-3 Low surface concentration

Phosphorus Pentoxide

Solid 200-300oC > 1020 cm-3 Proven source for high concentration

Phosphorus Oxychloride

Liquid 2-40oC High and low

Clean systemGood control over wide range conc.

Phosphorus Tribromide

Liquid 170oC High and low

Clean system

Phosphine Gas Room Temperature

High and low

Accurate control by gas monito-ring, highly toxic

Oxidation and Diffusion Furnace Stack, Wafer Loading

Boron Predeposition Boron Drive-inPhosphorus PredepositionPhosphorus Drive-in

SEPARATE FURNACES FOR EACH IMPURITY TYPE

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani

Diffusion vs Ion Implantation

Advantages

Problems

Ion Implantation and Annealing

Solid/Gas Phase Diffusion

Room temperature mask No damage created by doping

Precise dose control Batch fabrication

1011 - 1016 atoms cm-2 doses

Accurate depth control

Implant damage enhances diffusion

Usually limited to solid solubility

Dislocations caused by damage may cause junction leakage

Low surface concentration hard to achieve without a long drive-in

Implant channeling may affect profile

Low dose predeps very difficult

Dopant Solid Solubility

• Maximum conc.of a dopant that can be dissolved in Si under equilibrium conditions without forming a separate phase is termed as solid solubility.

.

AsP

Sb

Sn

Ga

Al

B

Solid

Sol

ubili

ty (at

oms cm

-3 )

1022

1020

1021

1019

Temperature (ÞC)800 900 1000 1100 1200 1300

• Dopants may have an “electrical” solubility that is different than the solid solubility defined in previous slide.

• One example - As4V – electrically inactive complex.

V

Si As

As+

Dopant Solid Solubility

Dopant Diffusion

.

t1 t2Con

centra

tion F = - D dC/dx

Distance

Conc

entr

atio

n

• Macroscopic dopant redistribution is described by Fick’s first law, which describes how the flux (or flow) of dopant depends on the concentration gradient.

€

F =−D∂C∂x (4)

Analytical Solution of Fick’s Law

( ) ( )

( ) ( ) constQdxtxctc

dxt0,dc 0, x xc

===∞

=≠=

∫∞

,,0,

,0/00,

The solution to Fick’s Second Law for these conditions is a Gaussian centered at x =0

Gaussian solution in infinite medium: Consider a fixed dose Q introduced as Delta function at the origin: Drive in

(7)

2. Gaussian Solution : Constant Source Near A Surface:

Analytic Solutions of Fick’s Laws

• This is similar to the previous case except the diffusion only goes in one direction.

• Dopant dose Q introduced at the surface.• Can be treated as an effective dose of 2Q being introduced in a

virtual infinite medium.

Delta FunctionDose Q

(Initial Profile)

ImaginaryDelta Function

Dose Q

DiffusedGaussian

VirtualDiffusion

x0

(8)

Analytic Solutions of Fick’s Laws3.Error Function Solution : Infinite Source:

• The infinite source is made up of small slices each diffusing as a Gaussian.

€

C x,t( )= C

2 πDt∆x i exp−

x−x i( )2

4Dti=1

n∑ (9)

• The solution which satisfies Fick’s second law is

€

C(x, t)=C2

1−erf x2 Dt

=CS erfc x

2 Dt

(10)

C

² x

Dose C² x

InitialProfile

DiffusedProfile

xix

0

Dose CΔx

Δx

Boundary conditions: C=0 at t=0 for x> 0 C=C at t=0 for x< 0

Analytic Solutions of Fick’s LawsImportant consequences of error function solution:

• Symmetry about mid-point allows solution for constant surface concentration to be derived.

• Error function solution is made up of a sum of Gaussian delta function solutions.

• Dose beyond x = 0 continues to increase with annealing time.

.

0

0.2

0.4

0.6

0.8

1

-5 -4 -3 -2 -1 0 1 2 3 4 5

t=9*t0

t=4*t0

Initialt=t

0

erf(x/

2¦D

t)

X (Units of 2¦Dt 0)

Analytic Solutions of Fick’s Laws

4. Error Function Solution: Constant Surface Concentration:

• Just the right hand side of the figure on previous slide

€

C x,t( )=CS erfcx

2 Dt

(11)

• Note that the dose is given by

€

Q= CS0

∞∫ 1−erf

x

2 Dt

=

2CS

πDt (12)

• Diffusion through Gas ambient

Intrinsic Dopant Diffusion Coefficients

• Intrinsic dopant diffusion coefficients are found to be of the form:

€

D=D0 exp−EA

kT

(13)

Si B In As Sb P UnitsD0 560 1.0 1.2 9.17 4.58 4.70 cm2 sec-1

EA 4.76 3.5 3.5 3.99 3.88 3.68 eV

• Note that ni is very large at process temperatures, so "intrinsic" actually applies under many conditions.

• Note the "slow" and "fast" diffusers. Solubility is also an issue in choosing a particular dopant.

Effect of Successive Diffusions

• If a dopant is diffused at temperature T1 for time t1 and then is diffused at temperature T2 for time t2, the total effective Dt is given by the sum of all the individual Dt products.

€

Dteff =Dt=D1∑ t1 +D2t2 +..... (14)

• The Gaussian solution only holds if the Dt used to introduce the dopant is small compared with the final Dt for the drive-in; i.e. if an initial delta function approximation is reasonable.

Design of Diffused Layers

• Eqn. (3) has been numerically integrated for specific cases (erfc and Gaussian).

• Example of Irvin’s curves, in this case for P type Gaussian profiles.

.

1 10 100Effective Conductivity (ohm-cm)-1

Surf

ace Con

cent

ration

(cm

-3 )

CB = 1015

CB = 1017CB = 1014

CB = 1016

CB = 1018

1020

1019

1018

1017

Design of Diffused Layers

• We can now consider how to design a boron diffusion process (say for the well or tub of a CMOS process), such that:

P

P WellN Well

€

ρS =900 Ω/ square

xj =3 µm

NBC =1x1015 cm-3 (substrate concentration)

Design of Diffused Layers

• The average conductivity of the layer is

€

σ_

= 1ρSxj

= 1

(900Ω/ sq)(3×10−4 cm)=3.7 Ω⋅cm( )−1

• From Irvin’s curve we obtain

€

CS ≈4×1017 / cm3

• We can surmise that the profile is Gaussian after drive-in.

€

∴CBC = Q

πDtexp −

xj2

4Dt

=CS exp −

xj2

4Dt

so that

€

Dt =Xj

2

4lnCs

C bc

=3x10−4( )2

4ln4x1017

1015

=3.7x10−9 cm2

Design of Diffused Layers

• If the drive-in is done at 1100 ˚C, then the boron diffusivity is

€

D=1.5×10−13 cm2 sec−1

• The drive-in time is therefore

€

tdrive−in = 3.7×10−9 cm2

1.5×10−13 cm2 / sec=6.8 hours

• Given both the surface concentration and Dt, the initial dose can be calculated for this Gaussian profile.

€

Q=CS πDt =4×1017( )π()3.7×10−9( )=4.3×1013 cm−2

• This dose could easily be implanted in a narrow layer close to the surface, justifying the implicit assumption in the Gaussian profile that the initial distribution approximates a delta function.

Design of Diffused Layers

• If a gas/solid phase predeposition step at 950˚C were used, then

B solid solubility at 950 ˚C is B diffusivity is

€

2.5×1020 cm−3

€

4.2×10−15 cm2 sec−1

• The dose for an erfc profile is

€

Q =2Cs

πDt

• So that the time required for the predeposition is

€

t pre−dep = 4.3×1013

2.5×1020

2π

2

21

4.2×10−15=5.5sec

Check: ( ) ( )914 107.3103.2 −−

− ×<<× indrivepredep DtDt

Four Point Probe:

Characterization

When t << s, as in the case of diffused or implanted layer,

Sheet Resistance

Resistivity=

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani

Junction Depth Measurements by Grooving and Staining

Spreading Resistance Technique to Get Impurity Profiles within Transistor Regions (Destructive Technique)

Dr. G. Eranna Integrated Circuit Fabrication Technology © CEERI Pilani