Transcript Graphene FET - Web.UVic.ca

Fatemeh (Samira) Soltani
University of Victoria
June 11th 2010
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Semiconductor Devices
n-type semiconductor
(Electrons like to fall downhill)
Depletion Layer : Potential Barrier,
p-type semiconductor
(Holes want to drift upward)
X : Distance from surface
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Rectifying Contacts
n-type :
 M : Work function needed to transport an electrons from E to infinity
F
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p-type :
 M   S : Contact Potential
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Biasing
It is the estimation of the net current that flows across the potential barrier when a
metal and an n-type semiconductor are connected to a D.C. source.
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Current flows from metal into semiconductor :
 
( A : area of contact ,
I MS  ACT 2 exp[ ( M
)]
k BT
C : constant )
Current flows from semiconductor to metal :
   S  eV
( V : bias voltage )
I SM  ACT 2 exp[ ( M
)]
k BT
I net  I SM  I MS
Saturation current :
I S  ACT 2 exp[ (
I net  I S [exp(
M  S
)]
k BT
eV
)  1]
k BT
For forward bias (+V) the net current increases exponentially with voltage. For
reverse bias (-V) the current is essentially constant and equal to  I S .
The saturation current is about three orders of magnitude smaller than the forward
current.
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p-n Rectifier (Diode)
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Diode modes
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Bipolar Junction Transistor
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Amplifying transistor
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Metal-Oxide-Semiconductor Field-Effect Transistor
(MOSFET)
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MOSFET is a device used for amplifying or switching electronic signals.
VGS  VTH
VGS  VTH
•
•
No conduction between source and
drain
Switch is off
• Gate attracts electrons, including an n-type
conductive channel in the substrate below the
oxide
•
Electrons flow between n-doped terminals
•
The switch is on
The threshold voltage of a MOSFET is usually defined as the gate voltage where an
inversion layer forms at the interface between the insulating layer (oxide) and the
substrate (body) of the transistor.
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Graphene
Graphene is a one-atom-thick planar sheet of
carbon atoms that are densely packed in a
honeycomb crystal lattice. The name comes
from graphite + -ene; graphite itself consists of many
Graphene sheets stacked together.
In Graphene electrons / holes are confined to a plane
of atomic thickness. This makes Graphene devices
sensitive to the surrounding environment such as
substrate and the dielectric media in contact with
Graphene.
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Graphene-FET
Metal electrodes : Ti
Distance between source
and drain : 5 um
The center of the device
was exposed to each
solvent. After
measurement, the solvent
was removed and dried
with Nitrogen gas.
The source – drain bias
was kept constant at 10
mV.
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Related works
Authors
Method
Impurity
Mobility
(cm^(-2))
(cm^2/v.s)
Temperature
(k)
2-15 x
10^(11)
1-20 x 10^3
1.6
Tan et. al
(2007)
Charged
Impurity on
SiO2 substrate
Chen et. al
(2008)
Doping
Graphene with
potassium
atoms
40 x 10^3
room
Bolotin et. al
(2008)
Suspended
Graphene etched SiO2
substrate
1-20 x 10^4
5
Chen et. al
(2009)
Organic solvent
with dielectric
constant 1-200
7 x 10^4
room
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Dielectric Screening Effect
Minimum position : Dirac point
On both sides of Dirac point,
the conductivity increases
linearly with the carrier density
and then slows down.
Eventually, it approaches a
constant conductivity.
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The role of charged impurities
• The scattering by charged impurities leads to a linear dependence of conductivity on carrier
density. In addition charged impurities are believed to generate potential fluctuations that
create electron and hole puddles in Graphene.
n* : residual density – determines the conductivity of Graphene and also responsible for
observed finite conductivity at Dirac point.
n*
 2.rs2 .C0RPA n
( imp : impurity concentration , rs : coupling strength of dielectric ,
nimp
C 0RPA : normalized voltage fluctuation correlation )
• calculations predict that the density of effective charged impurities reduces as  2 increases
and the induced scattering in Graphene decreases accordingly.
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Mobility
  (1 / C g ).( / Vg )
Slopes of linear regions on both sides of the
conductivity minimum : electron / hole mobility
in each dielectric medium
C g : back gate capacitance
a) Both hole mobility (filled circles) and
electron mobility (empty circles) increase with  2
(decreasing with rs ) before reaching a plateau
value. (phonon scattering)
b) Asymmetry factor is the ratio of electron to
hole mobilities and at high 2 asymmetry in the
electron and hole mobilities diminishes. This
explains screening effect of charged impurities
for scattering.
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Dirac point changes
Vg . min : position of minimum conductivity and it
is a function of n*, which reduces as  2
increases.
Vg ,min
: width of minimum conductivity plateau
decreases with  2 .
 min : magnitude of minimum conductivity
decreases from 18 to 3.5 e 2 / h .
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Summery
Transport properties of Graphene FET in different dielectric solvents have
been studied.
Screening effect of charged impurities (esp. at high κ) improves device
performance.
Upon increasing the dielectric constant :
• Both electron and hole mobilities increase a few orders of magnitude
• The width of the conductivity minimum decreases sharply and approaches
zero in high κ solvents.
• The position of minimum conductivity tend to shifts positively
2
• The minimum conductivity value decreases from 18 to 3.5 e / h
• The conductivity saturation occurs at lower carrier densities , and the short
range conductivity changes little
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References :
• Fang Chen, Jilin Xia; Nano Lett. Vol. 9 , No. 7 , 2571 – 2574 (2009)
• Rolf E. Hummel; Electronic Properties of Materials; Springer; New
York; Third Edition; 2000
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