diffusion #2 ece/che 4752: microelectronics processing laboratory gary s. may february 5, 2004
TRANSCRIPT
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Diffusion #2
ECE/ChE 4752: Microelectronics ECE/ChE 4752: Microelectronics Processing LaboratoryProcessing Laboratory
Gary S. May
February 5, 2004
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Outline
ObjectivesObjectives Double DiffusionsDouble Diffusions Concentration-Dependent DiffusionConcentration-Dependent Diffusion Diffusion in SiliconDiffusion in Silicon Lateral DiffusionLateral Diffusion
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Objectives
Discuss the concept of double diffusions, an important part of how we fabricate our CMOS transistors in the lab.
Introduce some “second-order” diffusion effects.
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Outline
ObjectivesObjectives Double DiffusionsDouble Diffusions Concentration-Dependent DiffusionConcentration-Dependent Diffusion Diffusion in SiliconDiffusion in Silicon Lateral DiffusionLateral Diffusion
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After p-well Diffusion
C(x)
x
Csub
pn
xj0
NA(x)
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After NMOS Source/Drain n+ Diffusion
C(x)
Csub
n+
pn
ND(x)
NA(x)
xj1xj2
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Notation: p-well Pre-dep
Boron doping Pre-Dep: tpp @ Tpp => Dpp, Cspp
tpp = p-well pre-dep timeTpp = p-well pre-dep temperatureDpp = p-well diffusion constant at pre-dep
temperatureCspp = surface concentration for p-well pre-
dep
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Notation: p-well Drive-in
tpd @ Tpd => Dpd
tpd = p-well drive-in time
Tpd = p-well drive-in temperature
Dpd = p-well diffusion constant at drive-in temperature
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Notation: n+ Source/Drain Pre-dep
Phosphorus doping Pre-Dep: tnp @ Tnp => Dnp, Csnp; Dp1
tnp = n+ source/drain pre-dep time Tnp = n+ source/drain pre-dep temperature Dnp = n+ source/drain diffusion constant at pre-
dep temperature Csnp = surface concentration for n+ source/drain
pre-dep Dp1 = boron diffusion constant at source/drain
pre-dep temperature
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Notation: n+ Source/Drain Drive-in
tnd @ Tnd => Dnd; Dp2
tnd = n+ source/drain drive-in time
Tnd = n+ source/drain drive-in temperature
Dnd = n+ source/drain diffusion constant at drive-in temperature
Dp2 = boron diffusion constant at source/drain drive-in temperature
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Profile: After p-well Diffusion
NA x Sw
Dt w
----------------------x–
2
4 Dt w------------------exp=
Sw2Cspp
-------------- Dpptpp=where:
Dt w Dpptpp Dpd tpd+=
= well dose
= well “Dt”
There is a pn-junction xj0 where NA(x) = Csub
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Profile: After n+ Source/Drain Diffusion
ND x Ssd
Dt sd
-----------------------x–
2
4 Dt sd-------------------exp=
Ssd2Csnp
-------------- Dnp tnp=
Dt sd Dnptnp Dndtnd+=
where: = source/drain dose
= source/drain “Dt”
BUT: now the well profile has changed to…
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New Well Profile
There is a pn-junction xj1 where ND(x) = NA(x)
There is a new pn-junction xj2 where NA(x) = Csub (where xj2 > xj0)
NA x Sw
Dt eff
------------------------x–
2
4 Dt eff--------------------exp=
Dt eff Dpptpp D pdtpd Dp1tnp Dp2 tnd+ + +=where:
= overall effective “Dt”
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Example
Suppose we want to design a p-well CMOS diffusion process with a well depth of xj2 = 2.5 m. Assume the n-type substrate doping is 1015 cm-3.
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Example (cont.) If we start with a boron pre-dep with a dose of 5 × 1013 cm-2,
followed by a 1-hr drive-in at 1100 oC, what is the initial junction depth (xj0)? Neglect the depth of the pre-dep. The B diffusivity at this temperature is 1.5 × 10-13 cm2/s.
SOLUTION:
NA x Sw
Dt w
----------------------x–
2
4 Dt w------------------exp= where: Sw = 5 × 1013 cm-2
(Dt)w = (1.5 × 10-13 cm2/s)(3600s) = 5.4 × 10-10 cm2
NA(xj0) = 1015 cm-3 =>x j0 4– Dt w
Dt w 1015
51310
--------------------------------------ln
12---
= = 1.24m
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Example (cont.) Find the necessary (Dt)eff for the p-well to reach the desired
junction depth of xj2 = 2.5 m.
SOLUTIONSOLUTION (This must be solved by iteration!!!): (This must be solved by iteration!!!):
where: x = xj2 = 2.5 m NA(xj2) = 1015 cm-3
Sw = 5 × 1013 cm-2
NA x Sw
Dt eff
------------------------x–
2
4 Dt eff--------------------exp=
=> (Dt)eff = 2.46 × 10-9 cm-2
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Example (cont.)
What is the approximate p-well drive-in time needed if all steps are carried out at 1100 oC?
SOLUTION:
tpdDt
ef f
Dpd---------------- 2.46 9–10
1.513–10
------------------------=
= 1.64 × 104 s = 273.3 min
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Example (cont.)
If the n+ source/drain junction depth required is xj1 = 2.0 m, what is the p-well doping at the source/drain junction?
SOLUTION:NA x Sw
Dt eff
------------------------x–
2
4 Dt eff--------------------exp=
where: x = xj1 = 2.0 m(Dt)eff = 2.46 × 10-9 cm2
=> NA(xj1 = 2.0 m) = 9.76 × 1015 cm-3
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Example (cont.) Suppose the source/drain dose (Ssd) is 5 × 1014 cm-2. What
is the surface concentration in the source/drain regions and the source/drain diffusion (Dt)sd?
SOLUTION: ND x Ssd
Dt sd
-----------------------x–
2
4 Dt sd-------------------exp=
where: x = xj1 = 2.0 m ND(x = xj1) = 9.76 × 1015 cm-3
(i) (Solving by iteration): (Dt)sd = 1.52 × 10-9 cm2
(ii) Surface Concentration:ND x 0=
Ssd
Dt sd
-----------------------5 1410
1.52 9–10 -------------------------------------= = = 7.24 × 1018 cm-3
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Example (cont.) The phosphorus source/drain regions are deposited and driven in
at 1050 oC. At this temperature, the phosphorus diffusivity is 5.8 × 10-14 cm2/s. Ignoring the contributions of the pre-dep, what is the approximate source/drain diffusion time (tnd)?
SOLUTION:
tndDt
sd
Dnd--------------- 1.52 9–10
5.814–10
------------------------= = 2.62 × 104 s = 436.8 min
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Example (cont.) If the boron diffusivity is 6.4 × 10-14 cm2/s at 1050 oC,
correct for the p-well diffusion time to account for the extra diffusion during the source/drain drive-in. (Neglect the contributions of pre-dep steps).
SOLUTIONSOLUTION::
Dp2tnd = 1.68 × 10-9 cm2
( “Dt” accumulated by boron during source/drain diffusion).
=> Initial p-well drive-in may be reduced by this amount, or:
tpd
Dt eff Dp2tnd–
Dpd---------------------------------------
2.469–10 1.68
9–10 –
1.513–10
-----------------------------------------------------------------== 86.9 min
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Outline
ObjectivesObjectives Double DiffusionsDouble Diffusions Concentration-Dependent DiffusionConcentration-Dependent Diffusion Diffusion in SiliconDiffusion in Silicon Lateral DiffusionLateral Diffusion
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Vacancies When host atom acquires sufficient energy to leave its
lattice site, a vacancy is created. Vacancy density of a given charge state (#
vacancies/unit volume, CV) has temperature dependence similar to carrier density:
where Ci = intrinsic vacancy density, EF = Fermi level, and Ei = intrinsic Fermi level
kT
EECC iF
iV exp
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Vacancy-Dependent Diffusion
If diffusion is dominated by the vacancy mechanism, D is proportional to vacancy density.
At low doping concentrations (n < ni), EF = Ei, and CV = Ci (independent of doping), so
D (which is proportional to CV = Ci ), also independent of doping concentration.
At high concentrations (n > ni), [exp(EF – Ei)/kT] becomes large, which causes CV and D to increase.
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Intrinsic and Extrinsic Diffusion
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Effect on Diffusivity
Cs = surface concentration
Ds = diffusion coefficient at the surface
= parameter to describe concentration dependence
x
CDF
ss C
CDD
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Diffusion Profiles
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Junction Depth
For > 0, D decreases with concentration Increasingly steep box-like profiles result Therefore, highly abrupt junctions are formed Junction depth is virtually independent of background concentration
tDx sj 6.1
tDx sj 1.1
tDx sj 1.1
tDx sj 87.0
= 1
= 2
= 3
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Outline
ObjectivesObjectives Double DiffusionsDouble Diffusions Concentration-Dependent DiffusionConcentration-Dependent Diffusion Diffusion in SiliconDiffusion in Silicon Lateral DiffusionLateral Diffusion
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Concentration Dependence
Boron, arsenic: ≈ 1
Gold, platinum: ≈ -2
Phosphorus: ≈ 2 (sort of)
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PhosphorusDiffusion
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Phosphorus Diffusion (cont.) When surface concentration is low, diffusion
profile is an erfc (curve a).
As concentration increases, the profile begins to deviate (b and c).
At high concentration (d), profile near the surface is similar b, but at ne, kink occurs, followed by rapid diffusion in tail region.
Because of high diffusivity, phosphorus is used to form deep junctions, such as the n-tubs in CMOS.
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Outline
ObjectivesObjectives Double DiffusionsDouble Diffusions Concentration-Dependent DiffusionConcentration-Dependent Diffusion Diffusion in SiliconDiffusion in Silicon Lateral DiffusionLateral Diffusion
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The Problem 1-D diffusion equation is not adequate at
the edge of the mask window. There, impurities diffuse downward and
sideways (i.e., laterally). In this case, we must consider a 2-D
diffusion equation and use numerical techniques to get the diffusion profiles under different initial and boundary conditions.
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Diffusion Contours
Contours of constant doping concentration for a constant Cs, assuming D is independent of concentration.
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Interpretation
Variation at far right corresponds to erfc distribution.
Example: at C/Cs = 10–4, the vertical penetration is about 2.8 µm, whereas the lateral penetration is about 2.3 µm (i.e., the penetration along the diffusion mask-semiconductor interface).
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Implications Because of lateral diffusion, the junction consists
of a central plane (or flat) region with approximately cylindrical edges with a radius of curvature rj.
If the mask has sharp corners, the shape of the junction near the corner will be roughly spherical.
Since the electric-field intensities are higher for cylindrical and spherical junctions, the avalanche breakdown voltages of such regions can be substantially lower than that of a plane junction.