Transcript High Electron Mobility Transistor (HEMT) Course code: EE4209 Md. Nur Kutubul Alam Department of EEE KUET.

High Electron Mobility Transistor
(HEMT)
Course code: EE4209
Md. Nur Kutubul Alam
Department of EEE
KUET
Types of HFET/HEMT
In terms of doping, HEMTs are of two types1. Modulation doped: Whole wide band gap
material is doped
2. Delta-doped: Only a portion of wide band
gap material is doped
Modulation doped FET
Spacer layer
Two dimensional electron Gas
(2DEG):
Here electrons are not allowed to move along ‘z’, but they obviously can move along
‘x’ or ‘y’ direction! The two dimensional movement on “x-y” plane, which is attached
at the interface of two materials is very much interesting. This type of electrons are
called “Two Dimensional Electron Gas” or “2DEG”.
Effect of Gate bias (MODFET)
Delta-doped FET
Difference between MODFET and
Delta-doped FET
How to obtain band diagram?
Band diagram means the potential energy of “electron” in conduction band.
Electrostatic potential at some position is defined as- “Energy required to bring +1C
charge at that position.”
That means, if electrostatic potential at some position is V volt,
energy required to bring +1C charge at that position will be V jule.
Or,
energy required to bring +Q charge at that position will be QV jule.
Or,
energy required to bring -q charge at that position will be -qV jule.
If, “-q” is the charge of an electron, then potential energy for an electron =“-qV”
Volt, or equivalently “-V” electron-volt.
So, conduction band = - electrostatic potential in “electron-volt” unit.
How to obtain band diagram?
Electrostatic potential is given by
Poisson’s equation. If “V” is the
electrostatic potential, then the Poisson’s
equation is-
And conduction band edge potential (By
not considering any band offset)-
Electric field “E” is given by negative of
the gradient of the electrostatic potential.
Or,
Or,
How to obtain band diagram?
Therefore, we need the following equations-
Steps:
1. Integrate the charge density to obtain the electric field.
2. Integrate the electric field to obtain the “Conduction band”.
Conduction band of HEMT:
(Calculation)
Conduction band of HEMT:
(Step 1)
Step 1: Integrate the charge
density to obtain the “Electric
field”
Conduction band of HEMT:
(Step 2)
Step 2: Integrate the
“Electric field”, to get the
conduction band. But, here
we need to add the band
offsets at every junctions.
At z= - d, we need to use the
boundary condition. At that
boundary,
band
edge
potential
Conduction band of HEMT:
(Step 2)
Step 2: Integrate the
“Electric field”, to get the
conduction band. But, here
we need to add the band
offsets at every junctions.
Integral of Negative field
leads to decrease in
Integral of Positive field
leads to Increase in
At the interface of two
material, we add the
band offset
Finally, Positive field increases the
Charge control model
Charge at the
Channel (2DEG),
ns = CVG
Calculation of ns
The band diagram at the interface of wide band gap and narrow band gap material
looks like a triangle. Therefore, 2DEG inside this triangular quantum well is
confined and can not move along the “z” direction.
Any confinement discretize the allowed
energy of electron. Therefore, z-confinement
allows enegy E0, E1 … Ei. Each discrete
energy can accommodate two electron with
opposite spin.
Calculation of ns
Along x, and y direction, there is no confinement. Therefore in (x,y) plane, energy
of electron possess an parabolic relation with the wave vector “k(x,y)”.
When energy is not discrete, we use “Density of states” or “DOS” to calculate the
carrier concentration.
Number of electron
Therefore, in case of 2DEG, for each eigen level
(produced by z confinement),
Calculation of ns
=
Here notice
the limit of
integral! I did
not calculate
the limit, just
let it to be *
Again limit
changes!
Calculation of ns
=
=
Thickness of 2DEG
Although E0 is not at the bottom of the
conduction band, we are assuming so for
the sake of simplicity. Then, we can say,
Whenever we need to relate energy with
number of particle/charge concentration,
we use statistical mechanics. In this case,
we need the relation derived from Fermi
Dirac statistics.
Thickness of 2DEG
From Fermi Dirac statistics, we got-
Thickness of 2DEG
Now, from Fermi Dirac statistics-
From
Electrostatistics,
Equation-
i,e.
Poisson’s
2DEG as a function of Gate bias
eV1
eV2
E
Ec
eV-di
2DEG as a function of Gate bias
eV1
eV2
E
Ec
eV-di
2DEG as a function of Gate bias
eV1
eV2
E
Ec
eV-di
2DEG as a function of Gate bias
eV1
eV2
E
Ec
eV-di
Charge control model (Again)
Finally
This is exactly the definition of
charge control model.
Pinch-off voltage
Definition:
The value of gate voltage at which charge in the channel is
“zero”.
Put nS(VG)=0 and find the VG
…………………………………………………
Modulation Efficiency:
From the definition of charge
control model:
But it happens only in ideal
case. At low temperature, it
might not be true.
Modulation Efficiency:
Polar material & polarization
Two types of polarization
 Spontaneous Polarization
 Piezoelectric Polarization
Spontaneous Polarization
Each unit cell of
GaN (or other
polar material)
can be thought
as a charged
capacitor.
Since, there is
always a voltage
between
two
plates
of
a
charged
capacitor, GaN
unit cell can also
be thought as a
voltage source.
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
Thicker the epilayer, greater the charge separation & higher
the internal/built-in voltage…..
One more unit
cell
Two unit cell
Only one unit cell
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
In respond to built in
electric field, or internal
voltage, both
conduction band and
valence band bends.
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
In respond to built in
electric field, or internal
voltage, both
conduction band and
valence band bends.
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
More voltage, more
bending in the bands.
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
But, hole actually
means an electron
liberated from that
position.
At some critical
thickness, valence
band will touch (or tend
to go above) Fermi
level. It creates a hole
Spontaneous Polarization
Now, what happens if we grow more and more atomic layer of GaN on a substrate
epitaxially?
This thickness of epilayer
is called critical thickness
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
But, hole actually
means an electron
liberated from that
position.
At some critical
thickness, valence
band will touch (or tend
to go above) Fermi
level. It creates a hole
Spontaneous Polarization
Above critical thickness, we get polarization charge at the substrate-epilayer
interface.
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
At some critical
thickness, valence
band will touch (or tend
to go above) Fermi
level. It creates a hole
Spontaneous Polarization
Now, lets calculate the value of critical thickness.
Total voltage across
epilayer,
Voltage at critical
thickness,
No current flows in the
growth process.
Therefore, Fermi level
must be flat.
In the figure, total band
bending is almost equal
to the band gap.
And, band bending =
e*applied voltage…..