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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