Semiconductor doping
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Si solar Cell
• Two Levels of Masks - photoresist, alignment
• Etch and oxidation to isolate – thermal oxide, deposited oxide,
wet etching, dry etching, isolation schemes
• Doping - diffusion/ion implantation
• Metallization - Materials deposition, PVD, CVD
What’s a metal, a semiconductor?
PHGN/CHEN/MLGN 435/535: Interdisciplinary Silicon Processing Laboratory
IV
How do we “dope” a
semiconductor
Electrons and holes
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Conduction Band
Ec
ED
EA
Ev
Valence Band
Sheet Resistance, what is it?
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What is the Resistance of this bar of material with resistivity ρ?
t
W
L
R = ρ L/Wt
We can rearrange to get a film dependent quantity called the
Sheet Resistance
Rs = ρ/t =R / (L/W)
Notice L/W is unit less, but gives us the number of “squares” in
the length of the bar. The units of Rs are ohms, but they are
often given as Ω / .
Sheet Resistance - Four Point Probe
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If Probe spacing is:
• Larger than film thickness
• Smaller than distance to
edge of film
• Probe points are “small”
Using a four point approach is
a standard technique for
eliminating the effects of
contact resistance
Rs=4.53 V/I and
ρ=Rst where t is thickness
How do we get the doping?
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Rs and t give us ρ,
which gives us
doping (but we must
know t)
Another way to get doping - from C-V of a diode
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Formation of a p-n junction
Formation of a Schottky junction
1/C2 vs V
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C-2
Slope gives carrier
Concentration
x-intercept give Vbiv
Assumes an abrupt junction Schottky, p+n or n+p
What if the line isn’t straight?
How about the thickness of our Oxide?
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Again, C = εA/W, so we should have another way to
measure W. In practice, we must be careful about
what C we use.
Corresponds to
oxide thickness
What about trapped charge?
Inversion in an MOS structure
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accumulation
(negative bias)
no bias
inversion
(positive bias)
What about I-V Characteristics?
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Forward biased pn junction:
Probability that carriers are over the
barrier is like a Boltzmann factor
But, there is also an electric field pushing carriers back so at V = 0
there should be no current.
We can write this in a simpler form as:
What about when light is shining on the device?
Note, there is a
sign difference
with respect to
the capacitance
analysis
How can we tell the carrier type
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Thermovoltage
ee e
Hall Effect
•  carrier type
•  mobility
•  sheet concentration
Hot Probe
V
e
e
e
ee
Other methods of getting at the carriers
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•
•
•
•
•
SIMS
RBS – Rutherford Backscattering
Polaron profiler
Spreading Resistance
...
Doping - reminder
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Goal of Doping: Substitution of atoms with excess or deficiency
of valence electrons e.g. B or P substituting for Si
Diffusion doping (in fact most doping) is typically done in two
steps: (Almost all doping is now ion implantation)
Predeposition - Use a source to create the desired dose
Drive in - Source at surface removed, additional diffusion to get
desired distribution (in ion implantation the anneal also removes
damage and activates the dopant).
Generic Predeposition Process
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Deliver Dopants to Partially Masked Substrates
•  Diffusion (Hot)
•  Ion Implantation (Cold)
Structure:
Dopants
Mask: Oxide, Nitride,
Photoresist
Silicon
Dopant delivery Options for Diffusion
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CB
Gas Source:
•  Nasty Gases: AsH3, PH3, B2H6
•  Very similar to Deal –Grove Oxidation
Liquid Source:
δ
Cs
xj
Co
Ci
•  SOG: Spin-On Glass
•  Doped SiO2 dissolved in solvents
•  Apply exactly like Photoresist
Solid Source:
•  Glass Discs (B2O3, P2O5)
•  Close-space Sublimation
•  Vapors sublime/diffuse/react
Which is Best?
Drive-in - estimating the profile
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Fick’s law - You need the PDE, but you also need the boundary
conditions!
C(z,0) = 0, Z ≠ 0
dC(0,t)/dz = 0
C(∞,t) = 0
∞
∫ C(z,t)dz = Q
T
= constant
0
Solution:
€
QT
C(z, t) =
e
πDt
⎛ -z 2 ⎞
⎜
⎟
⎜ 4 Dt ⎟
⎝
⎠
We can model the drive in step
from our homework, here after a
P predep with p8545 we had a
sheet resistance of 12Ω/ and
depth of 1.1µm. This gave a
carrier concentration of 5x1019/
cm3 and a surface concentration
of 5.5x1015/cm2
Characteristic Length Scale Diffusion Length
What about the diffusion Coefficient?
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Use first three terms in Fair’s vacancy model.
2
n − ⎡ n ⎤ 2− I told you to assume n~ni ~1019/cm3
o
D = D + D + ⎢ ⎥ D
Is this reasonable?
ni
⎣ ni ⎦
From Campbell table 3.2 (1100C=1373K)
Do = 3.9cm2/s e-(3.66/k1373) = 1.43 x 10-13cm2/s
D- = 4.4cm2/s e-(4.0/k1373) = 9.13 x 10-15cm2/s
D2- = 44cm2/s e-(4.37/k1373) = 4.00 x 10-15cm2/s
D = 1.56 x 10-13cm2/s
Simulations
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Suprem-IV is a process simulation tool
developed at Stanford University
nanoHub TCAD tools
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https://nanohub.org/tools
Suprem simulation of boron predep and drive-in
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Boron Diffusion
Log10(Boron)
20
Boron Predep 1100C
30 min.
15
Boron drivein 1100C
30 min.
10
Boron predep in gas at
5 x 1020/cm3 concentration
followed by drive-ins.
Boron drivein 1100C
60 min.
5
0
0
2
4
Depth in microns
Boron drivein 1100C
60 min 200 angstrom
oxide cap
Effect of oxide cap on
profile near the surface
Boron Diffusion
21.0
20.5
Log10(Boron)
Why 5x1020/cm3?
1)  Damage threshold
2)  Solubility limit
3) B partial pressure
1)  Dimensional argument
20.0
19.5
19.0
18.5
18.0
0
0.5
1
1.5
Depth in microns
2
2.5
Solid Solubility, what is it?
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1100C
5x1020/cm3
Oxide is an effective anti-diffusion barrier for Si VLSI?
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1)
2)
3)
4)
For boron but not for phosphorus
For phosphorus but not for boron
It works well for both
It depends
Final Topic on Diffusion: Oxide
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How fast do dopants diffuse through oxide? Diffusivity important, Solubility
important
Consider Do of Boron
Si prefactor
0.37cm2/s
SiO2 prefactor 0.0003cm2/s
Activation Energy
Activation Energy
3.46eV
3.53eV
Now Do of Phosphorous
Si prefactor
3.9 cm2/s
SiO2 prefactor 0.19 cm2/s
Activation Energy
Activation Energy
3.66eV
4.03eV
• Oxide is often used as a diffusion mask- how thick does it need to be?
• Oxide is used for isolation - does it isolate? What is the thermal load?
• Oxide is also a gate dielectric with heavily B doped polysilicon gates diffusion through gate is an issue
M Metal Doped polysilicon
O
Oxide
S
Silicon
Suprem-IV Wet Oxide then Diffusion
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Oxide antidiffusion barrier
Log10(Boron)
20
15
60 min wet O2 at 1000C,
30 min boron predep at
1100C
30 minute boron predep at
1100C
10
5
0
0
Effect of oxide cap on
1
2
3
profile near the surface
4
Depth in microns
Substrate is P doped at 1 x 1014/cm3, Wet oxide growth at atmospheric
pressure for 60 minutes at 1000C, Boron predep from 30 minutes at
1100C in gas with a concentration of 5 x 1020/cc.
Simulation of predep and drive-in to find junction depth
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1000°C P predep in p-type wafer doped at 1x1017/cm3.
1100°C drive in. How long to get a 4.0µm deep junction?