ECE 875: Electronic Devices

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ECE 875Electronic Devices

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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Lecture 20, 24 Feb 14
Chp. 02 pn junction Info Linearly graded
junction Multiple charge layers Example
Chp. 03 metal-semiconductor junction Schottky
barrier Review Examples New
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Linearly graded junction Why
Why get a more uniform E (x) over a bigger x
region
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Linearly graded junction How
Q and r
E (x)
yi(x)
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Linearly graded junction How
Q and r a x
E (x) ax2 B
yi(x) ax2 Bx C
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Linearly graded junction How
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Practical
The curvature of the initial C-V curve is
different from that for an abrupt junction The
slope gives the grading constant a The intercept
gives the equilibrium built in potential ybi
1/
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Lecture 20, 24 Feb 14
Chp. 02 pn junction Info Linearly graded
junction Multiple charge layers Example
Chp. 03 metal-semiconductor junction Schottky
barrier Review Examples New
VM Ayres, ECE875, S14
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Example Set up the answer
(a) Find ybi at equilibrium fro the following
doping profile in si at 300 K (b) Draw the
energy band-bending diagram
p 1017 cm-3
n 1016 cm-3
p 1015 cm-3
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1st
2nd
3rd
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q
q
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Lecture 20, 24 Feb 14
Chp. 02 pn junction Info Linearly graded
junction Multiple charge layers Example
Chp. 03 metal-semiconductor junction Schottky
barrier Review Examples New
VM Ayres, ECE875, S14
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_at_ Interconnects

• Use energy band diagrams to describe what is
  happening
• One question to answer is it an Ohmic contact or
  a Schottky barrier contact?
• Interconnect contacts are key for nanotechnology
• MOSFET Ohmic contact good
• NanoFET SB contact good

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Individual energy band diagrams
Different nature of a metal Lots of e- and NO
Egap EC at EF
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Need 2 descriptions Electron affinity qcs
where is EC relative to Evac Work Function qFs
where is EF relative to Evac
Need 1 description Work Function of the metal
qFm where is EF EC relative to Evac
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When in physical contact EFm and EFs align
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Four cases the same approach
1. metal with small work function/n-type
semiconductor Ohmic (barrier)2. metal with big
work function/n-type semiconductor Schottky
barrier3. metal with small work function/p-type
semiconductor Schottky barrier4. metal with big
work function/p-type semiconductor Ohmic
(barrier)In every case, use logic do I need to
make the metal more n-type (add e- from
semiconductor) or less n-type (e- move into
semiconductor)
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Four cases the same approach
1. metal with small work function/n-type
semiconductor Ohmic (barrier)2. metal with big
work function/n-type semiconductor Schottky
barrier3. metal with small work function/p-type
semiconductor Schottky barrier4. metal with big
work function/p-type semiconductor Ohmic
(barrier)In every case, use logic do I need to
make the metal more n-type (add e- from
semiconductor) or less n-type (e- move into
semiconductor)
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2. metal with big work function/n-type
semiconductor
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• electrons move to metal side leaving Nd behind
• Size of n-side strip is set by doping
  concentration and can be large

--Nd Nd n --Nd Nd
To bring the Fermi energy level of the metal up
make the metal more n-type
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Schottky Barrier
ND on n-side
--Nd Nd n --Nd Nd
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Schottky Barrier
Very narrow region with high concentration of e-
similar to ionized NA large
--Nd Nd n --Nd Nd
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3. metal with small work function/p-type
semiconductor
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• electrons move to p-side and recombine with its
  large hole population. This leaves Na- strip
• Size of p-side strip is set by doping
  concentration and can be large

Na- Na- p Na- Na-
To bring the Fermi energy level of the metal
down make the metal less n-type
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Schottky Barrier
NA- on p-side
Na- Na- p Na- Na-
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Schottky Barrier
Very narrow region high concentration exposed
nuclei similar to ionized ND large
NA- on p-side
Na- Na- p Na- Na-
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Lecture 20, 24 Feb 14
Chp. 02 pn junction Info Linearly graded
junction Multiple charge layers Example
Chp. 03 metal-semiconductor junction Schottky
barrier Review Examples New
VM Ayres, ECE875, S14
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Example from Exam
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Answer
Ei
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EC EF Egap/2 (EF Ei)

EF Ei kT ln(ND/ni)
Streetman ni
EC EF
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--Nd Nd n --Nd Nd
Made the metal more n-type to bring EFm up to
EFs Electrons left the semiconductor and went
into the metal. The semiconductor is n-type Nd
left behind.

• Size WD of n-side depletion region is set by
  doping concentration and can be large

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Example(a) Evaluate the energy barrier qV0 q
ybi for previous problem(b) Draw the
band-bending diagram
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Answer
(a) qV0
--Nd Nd n --Nd Nd
q ybi qV0 0.057 eV
(a) Band-bending diagram
Find W
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Equilibrium metal contact to n-type Si when work
functions qFm gt qFs
Junction
metal
n0 1017 cm-3
Although the charges are balanced, the layer on
the metal side is very thin, similar to ionized
NA large
qV0
EF
EF
- -
P P P P P P P P P
Ei
Neutral region n-side
E (x)
Depletion region W
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1.14 x 10-5 cm 0.14 mm
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Answer
(a) qV0
--Nd Nd n --Nd Nd
q ybi qV0 0.057 eV
Also qFB 4.0 -3.8 eV 0.2 eV
(a) Band-bending diagram
W 0.14 mm