 
nextnano^{3}  Tutorial
next generation 3D nano device simulator
2D Tutorial
DGMOS Structure  Double Gate MOSFET (Metal Oxide Semiconductor Field Effect
Transistor)
Note: This tutorial's copyright is owned by Stefan Birner,
www.nextnano.com.
Author:
Stefan Birner
If you want to obtain the input files that are used within this tutorial, please contact stefan.birner@nextnano.de.
> 2DDoubleGateMOSFET_nn3_05grid.in / *nnp*.in  input file for the nextnano^{3} and nextnano++ software
(2D simulation)
> 3DDoubleGateMOSFET_nn3_05grid.in
 input file for the nextnano^{3} software
(3D simulation)
DGMOS Structure  2 nm Double Gate MOSFET (Metal Oxide Semiconductor Field Effect
Transistor)
The main idea of a Double Gate MOSFET is to control the Si channel very
efficiently by choosing the Si channel width to be very small and by
applying a gate contact to both sides of the channel. This concept helps to
suppress short channel effects and leads to higher currents as compared with
a MOSFET having only one gate.
 Double Gate MOSFET (Metal Oxide Semiconductor Field Effect
Transistor)
(grown
on Si substrate, i.e. unstrained)
The Double Gate MOSFET contains the following regions
cluster 
region 

color 

1 
1 
Source and drain
are connected with the Si channel 
blue 

2 
2 
Source (metal) 
left 

3 
3 
Drain (metal) 
right 

4 
4 5 
Gate / Backgate (metal) 
top/bottom 

5 
6 7 
Doped source and drain
region (Si) 
blue 

6 
8 
The insulating material is SiO_{2}. 
red 
(default
region) 
Both the regions 4 (gate) and 5 (backgate) form the cluster no. 4.
The width of the Si channel is 2 nm. The distance between the two gates is 6 nm, i.e. the isolating SiO_{2}
is 2 nm thick on each side. The width of the two gates is 20 nm.
The distance between source and drain is 60 nm. The widths and the lengths of
source, drain, left and right doped source regions are 10 nm x 10 nm each. The
length of the 2 nm Si channel (without the square doped source and drain regions) is 40
nm.

Top gate (Schottky barrier 3.445 V)
0 V ... 0.2 V 

Source (0.0 V) 

Drain (0.2 V) 

Bottom gate (Schottky barrier 3.445 V) 0 V ... 0.2 V
Schematic top view of the Double Gate
MOSFET 

The blue squares (Si) are ndoped with a a
concentration of 1x10^{20} cm^{3}.
The 2 nm channel
is ndoped with the same concentration from 20 to 30 and from 50 to 60 nm.
$dopingfunction
dopingfunctionnumber = 1
! Source
impuritynumber =
1
dopingconcentration = 1d2
! 1 x 10^{20} cm^{3}
onlyregion
= 0d0 20d0
6d0 16d0 !
xmin xmax ymin ymax
dopingfunctionnumber = 2
! Si channel (left)
impuritynumber =
1
dopingconcentration = 1d2
! 1 x 10^{20} cm^{3}
onlyregion
= 20d0 30d0
10d0 12d0 ! xmin
xmax ymin ymax
dopingfunctionnumber = 3
! Si channel (right)
impuritynumber =
1
dopingconcentration = 1d2
! 1 x 10^{20} cm^{3}
onlyregion
= 50d0 60d0
10d0 12d0 ! xmin
xmax ymin ymax
dopingfunctionnumber = 4
! Drain
impuritynumber =
1
dopingconcentration = 1d2
! 1 x 10^{20} cm^{3}
onlyregion
= 60d0 80d0
6d0 16d0 !
xmin xmax ymin ymax
$end_dopingfunction
$impurityparameters
impuritynumber
= 1
impuritytype
= ntype
numberofenergylevels = 1
energylevelsrelative =
0.044d0 ! energy relative to
'nearest' conduction band edge in units of [eV]
degeneracyofenergylevels = 2
! degeneracy of energy levels, 2 for ntype
$end_impurityparameters
 At the two gates we apply a Schottky barrier of 3.443 eV:
$poissonboundaryconditions ... poissonclusternumber =
3
! top and bottom gate regionclusternumber =
4 appliedvoltage =
0d0 boundaryconditiontype =
schottky schottkybarrier =
3.443d0 contactcontrol =
voltage ...
$end_poissonboundaryconditions
The source and drain contacts are ohmic.
 Source: 0.0 V
 Drain: 0.2 V
A voltage sweep varies the gate (top gate and bottom gate) voltage from 0 to
2.0 V in 10 steps.
$voltagesweep
sweepnumber
= 1
sweepactive
= yes
poissonclusternumber = 3
! Gate: poissonclusternumber = 3
stepsize
= 0.1d0
numberofsteps =
10
dataouteverynthstep = 1
$end_voltagesweep
 Gridding

Grid lines of the Double Gate
MOSFET
Note: The grid lines that are shown in the figure are the
material grid lines. The grid lines that one specifies in the input file
are the physical grid lines. The material grid lines are placed
halfway between the physical grid lines. For more information on the
definition of the grid confer this page:
Grids and Geometry 
How to run the input file...
 The lattice temperature is taken to be 300 Kelvin.
The
flow scheme is 4 for a
classical selfconsistent calculation:  calculate nonlinear Poisson classically  calculate current classically No strain will be considered here.
 This time we perform a twodimensional simulation. The overall
simulation domain, that is the real space region in which the device is
defined, is taken to be a rectangle having the size 22 nm x 80 nm.
 Just a reminder: If you need additional information about the keywords and
their specifiers, you can look them up
here.
 Output
 The band structure (conduction and valence bands) will be saved into the directory band_structure/ .
 The densities (electron densities) will be saved into densities/ .
 Current data (Fermi levels, current density and IV characteristics) will be saved into current/ .
 The raw data for the potentials and the Fermi levels (can be read in
later in subsequent runs) will be saved into raw_data/ .
Output files that will be produced are:
Results
 The currentvoltage (IV) characteristic can be found in the following
file:
current/IV_characteristics2D.dat
The drain voltage is kept constant at 0.2 V, the gate voltage varies from
0 to 2.0 V.
The figure shows the IV characteristics for three different mobility
models, compared with the results obtained with a commercial software
package. The units for the current in a 2D simulation are [A/m] (but can
be adjusted to [A/cm]).
 mobilitymodelsimba0
(no dependence on electric field)

mobilitymodelsimba2 (mobility depends on parallel electric field)
In this case the current is smaller because the mobility
decreases when the applied voltage increases.

mobilitymodellom (Lombardi mobility
model)
More information on the mobility models can be found here:
 $mobilitymodelsimba
(SIMBA mobility model)
 $mobilitymodellom
(Lombardi mobility model)
Note: This is a classical calculation. So no quantum
mechanical effects are included. If you are interested in a quantum
mechanical calculation please contact stefan.birner@nextnano.de.
For a quantum mechanical calculation, the current is smaller. This is
mainly due to the difference in the classical and quantum
mechanical electron density.

Classical and quantum mechanical electron density as
seen when cutting through the Si channel.
(Note: In this figure, the Si channel is larger than 2 nm.)
In the classical simulation, the electron density has its maximum at
the SiO_{2}Si interface.
In the quantum mechanical simulation, however, the electron density is
basically zero at the SiO_{2}Si interface. 
3D
> 3DDoubleGateMOSFET_nn3_05grid.in
In order to test the nextnano³
implementation of the threedimensional driftdiffusion current, we calculated
this Double Gate MOSFET in a threedimensional simulation. We assume that the
structure is homogeneous along the z direction and assume the z direction to be
10 nm long (grid spacing 2 nm). The units of the current are in [A] (current/IV_characteristics3D.dat ).
The current has to be divided by the length of the device along the z direction,
i.e. by 10 nm, in order to obtain it in units of [A/m]. The 3D results are in
agreement with the 2D results.

Comparison of the 2D and 3D nextnano³
results for mobilitymodelsimba0. 
 Please help us to improve our tutorial. Send comments to
support
[at] nextnano.com .
