The silicon substrate and
adding to it—Part 1
 Explain how single crystalline Si wafers are made
 Give a number of uses of p-n junctions
 Describe the crystalline structure of Si
 Calculate
 Find the Miller indices of a planes and directions in crystals
 Concentration distributions for thermal diffusion
and give the most important direction/planes in silicon
 Concentration distributions for ion implantation, and
 p-n junction depths
 Use wafer flats to identify types of Si wafers
 Define
 Semiconductor
 Doping/dopant
 Resistivity
 Implantation
 Diffusion
 p-n junction
Silicon—The big green Lego®
1
Three forms of material
Creating silicon wafers
•
•
•
The Czochralski method
•
2
Creating silicon wafers
Grains
Polycrystalline silicon
(American Ceramics Society)
Photo (foto) of a monocrystalline silicon ingot
It’s a crystal
a ‐
,
3
It’s a crystal
The diamond
(diamante) lattice
Miller indices
The Miller indices give us a way to identify different
directions and planes in a crystalline structure.
Indices: h, k and l
• [h k l ]  a specific direction in the crystal
• <h k l >  a family of equivalent directions
• (h k l )  a specific plane
• {h k l }  a family of equivalent planes
How to find Miller indices:
1. Identify where the plane of interest
intersects the three axes forming the unit
cell. Express this in terms of an integer
multiple of the lattice constant for the
appropriate axis.
2. Next, take the reciprocal of each quantity.
This eliminates infinities.
3. Finally, multiply the set by the least common
denominator. Enclose the set with the
appropriate brackets. Negative quantities are
usually indicated with an over-score above
the number.
4
Te toca a ti
Find the Miller indices of the plane
shown in the figure.
1. Identify where the plane of interest
intersects the three axes forming the unit
cell. Express this in terms of an integer
multiple of the lattice constant for the
appropriate axis.
4
3
2
2. Next, take the reciprocal of each quantity.
This eliminates infinities.
1
c
a
1
How to find Miller indices:
3. Finally, multiply the set by the least common
denominator. Enclose the set with the
appropriate brackets. Negative quantities are
usually indicated with an over-score above
the number.
b
1
2
2
For cubic crystals the Miller indices represent a direction vector perpendicular to a plane with integer
components. Es decir,
[h k l] ٣ (h k l)
¡Ojo!
Non-cubic material example
__________ is an
example of an
important material
with a non-cubic
crystalline structure.
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5
Miller indices
What are the Miller indices of the shaded planes in the figure below?
a. (
)
b. (
)
c. (
)
Te toca a ti:
Find the angles between
a. {1 0 0} and {1 1 1} planes, and
b. {1 1 0} and {1 1 1} planes.
Wafer types
Si wafers differ based on the orientation of their crystal
planes in relation to the surface plane of the wafer.
Wafers “________” are used to identify
•
• whether the wafer is _____ or _____.
<1 0 0> direction
(1 0 0) wafer
6
Relative position of crystalline planes in a (100) wafer
Orientations of various crystal directions and planes in a (100)
wafer (Adapted from Peeters, 1994)
It’s a semiconductor
(a) _________
(b) _________
(c) _________
The “jump” is affected by both _________ and _________ 
7
Conductivity, resistivity, and resistance
Electrical conductivity (σ) 
•
•
Electrical resistivity (ρ) 
•
•
By doping, the resistivity of silicon can be varied
over a range of about 1×10-4 to 1×108 Ω•m!
Conductivity, resistivity, and resistance
Te toca a ti
Find the total resistance (in Ω) for the MEMS snake
(serpiente) resistor shown in the figure if it is made of
• Aluminum (ρ = 2.52×10-8 Ω·m) and
• Silicon
1 μm
100 bends total
100 μm
1 μm
Entire resistor is 0.5 μm thick
8
Doping
(a) Phosphorus is a ________ – donates
electrons
(b) Boron is an ________ – accepts
electrons from Si
 Charge carriers are “_______”
Phosphorus and boron are both ________.
P creates
B creates
Doping
Two major methods
• Build into wafer itself during silicon growth
• Gives a uniform distribution of dopant
•  ________________________
• Introduce to existing wafer
• ___________ or ___________ (or both!)
• Non-uniform distribution of dopant
• Usually the opposite type of dopant (Es decir, si
wafer es p-type, el otro es n-type y vice versa)
• Location where dopant concentration matches
background concentration se llama ___________
Uses of doping and p-n junctions:
•
•
•
9
Doping
Often implantation and diffusion are done
through masks in the wafer surface in order
to create p-n junctions at specific locations.
How do we determine the distribution of
diffused and/or implanted dopant?
___________ :
Frequency factor and activation energy for diffusion of dopants in silicon
Doping by diffusion
C
x
Conservation of mass (applied to any point in the wafer)
Need
• ___ initial condition
• ___boundary condition
erfc( ) is the ____________________________________:
Solución 
Appendix C
10
Doping by diffusion
x
Diffusion of boron in silicon at 1050°C for various times
_____________ rough estimate of
how far dopant has penetrated wafer
Doping by diffusion
Total amount of dopant diffused into a surface per unit area is called the _____ _____.
C(x = 0, t > 0) = Cs
time
x
11
Doping by implantation
Distribution is also Gaussian, but it is more complicated.
• CP –
• RP – the _________ ______ (the depth of peak concentration of
dopant in wafer)
• ΔRP –
Doping by ion implantation
Range affected by the mass of the dopant, its acceleration energy,
and the stopping power of the substrate material.
Peak concentration 
Doping by implantation
Doping is often (de hecho, usually) a twostep process:
1st implantation – _______________
2nd thermal diffusion – ___________
If projected range of pre-deposition is
small, can approximate distribution with
Typical concentration profiles for ion implantation of
various dopant species
12
Junction depth
C
x
Te toca a ti
A n-type Si-wafer with background doping concentration of 2.00×1015 cm-3 is doped
by ion implantation with a dose of boron atoms of 1015 cm-2, located on the surface of
the wafer. Next thermal diffusion is used for the drive-in of boron atoms into the wafer
a 900°C for 4 hours.
a. What is the diffusion constant of boron in silicon at this temperature?
b. What is the junction depth after drive-in?
Hints:
• Assume that the distribution of ions due
to implantation is very close to the wafer
surface
• Useful information:
− kb = 1.381×10-23 J/K
− eV = 1.602×10-19 J
13
Te toca a ti
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