Two-dimensional electron gas in a Si MOSFET
Header
- Files for the tutorial located in nextnano++\examples
2DEG_Si_MOSFET_1D_nnp.in
- Main adjustable parameters in the input file:
parameter
$min_density_e
parameter
$max_density_e
parameter
$min_density_h
parameter
$max_density_h
- Relevant output files:
bias_*\bandedges.dat
bias_*\Quantum\probabilities_shift_Quantum_region_X1.dat
bias_*\Quantum\probabilities_shift_Quantum_region_X2.dat
bias_*\Quantum\density_electron.dat
integrated_density_electron.dat
Introduction
In this tutorial, you can learn how to obtain carrier sheet densities in the inversion layer of MOSFET.
Layer sequence
The table below shows the materials, their widths, and their dopant concentrations for this tutorial.
material |
width (nm) |
doping |
---|---|---|
contact |
||
p-Si |
||
SiO2 |
||
n-Si (poly-Si) |
||
Gate contact |
The applied gate voltage leads to confined electron states at the p-Si/SiO2 interface (n-type inversion layer) whereas the holes are repelled from the p-Si/SiO2 surface towards the interior of the device (i.e. to the left side).
An applied source-drain voltage in the plane of the inversion layer will lead to a flow of current which depends on the sheet density in the inversion layer. The magnitude of the current is governed by the applied gate voltage, i.e. the gate controls the sheet density and thus switches the current on or off (MOSFET, metal-oxide-semiconductor field effect transistor).
Calculations
The temperature was set to
We vary the gate voltage from
Results
The following two figures show the band profiles and the electron density for two different gate voltages:
Figure 2.4.498: 0.7 V (The electron ground state is above the electron Fermi level
Figure 2.4.499: 2.5 V (The electron ground state is below the electron Fermi level
Figure 2.4.498 The calculated band edges are shown in (a). The quasi Fermi level of electrons
The amplitude of the ground state
Figure 2.4.499 The calculated band edges are shown in (a). The quasi Fermi level of electrons
The amplitude of the ground state
In the figures above, cb and vb represent the conduction band and the valence band, respectively.
In the poly-silicon on the right side of the SiO2 barrier, the electrons get depleted from the oxide interface.
Due to the fact that the quasi Fermi level is nearly constant outside the SiO2 barrier, almost no current is flowing. Inside the SiO2 barrier, the quasi Fermi level has a step-like feature. However, as the electron density is close to zero inside the barrier, almost no current is eventually flowing.
The ground state electron level is associated with the longitudinal electron mass (
The eigenvalues for
At
(to be fixed)
Electron sheet density in the inversion channel as a function of applied gate voltage
The file bias_*\Quantum\density_electron.dat` contains the electron density across the MOSFET.
Since the p-Si region, where the inversion channel is located, extends from structure{ region { integrate } }
is used as following (structure{ region{ integrate{ } } }).
109region{
110 line{ x = [ $itf_start_contact, $itf_p_Si_SiO2 ] }
111 binary{ name = "Si" }
112 doping{
113 constant{
114 name = "B_acceptor"
115 conc = $acceptor_conc
116 }
117 }
118 integrate{ electron_density{} }
119}
The output is in the file integrated_density_electron.dat.
Figure 2.4.500 shows the electron sheet density of the p-Si inversion layer.
Figure 2.4.500 The electron sheet density of the p-Si inversion layer is shown.
To obtain the capacitance-voltage characteristics, you have to calculate the derivative of the sheet density.
Last update: 18/12/2024