Energy Band Diagram of MOSFET
Energy band diagram:
Equilibrium :
In ideal conditions there is no external supply to the device so the energy gap between conduction and valence band is high.
The gap between Evac and Efm is called the work function qΦm is the energy required by an electron to move from Fermi energy to vacuum energy level.
Electron affinity (χ): It is the energy required to move an electron from the conduction band of a semiconductor to vacuum energy.
Ionization energy: The energy required to move an electron from the valence band of semiconductor to vacuum energy.
Fig: Equilibrium condition of MOSFET
Accumulation:
Accumulation of charges at the channel takes place when we apply VGS<0.
As we apply external supply VGS<0 the holes get accumulated at the surface this is called accumulation.
The electrons in metal increases so the EFM increases but it is known that the work function of a material doesn’t change so EVAC is increased with equal rise of EFM thus tilting the Evac of the oxide layer upwards.
Valence band of bends upwards indicating that the hole concentration towards oxide layer is increased and as the energy gap between conduction band and valence band has to be maintained the conduction band is also tilted upward.
The work function and energy gap has to be maintained with respect to the device property because once they are changed the overall behaviour of the device changes and it no longer behaves as expected.
Fig: Accumulation condition of MOSFET
Depletion:
The depletion occurs when VGS > VT and VDS > 0 as the electron concentration at channel increases thereby increasing the hole concentration at metal due to the presence of external supply. The conduction band of oxide layer near the semiconductor is tilted upwards indicating the increase of electrons at the semiconductor.
Thus maintaining the work function and energy gap equally the conduction band and valence band are tilted downwards.
Fig: Depletion condition of MOSFET
Inversion:
The inversion occurs when VGS >> VT and VDS >> 0.
The band bending of the valence band is so high because intrinsic energy crosses EF in N type EF is above EI and in P type Ei is below EF.
Since voltage applied is positive to the gate, electrons travel towards the gate and accumulate near the semiconductor-oxide junction resulting in the development of surface potential. Due to surface potential energy band bending takes place.
Fig: Inversion condition of MOSFET
VT equation:
VT = Vto + ϒ (2∅F+VSB- 2∅F )
At VSB = 0 vT = Vto
Body bias: VSB if there exists a potential difference between source and substrate it is known as body bias.
Check on VSB potential for NMOS for VB = -1v
VS connected to +1v
VSB = VS – VB
= 1-(-1)
= 2v
When VSB is connected with forward bias there are chances that the electrons flow might be distorted and current direction will change leading to improper function of the device.
VS connected to 0v
VSB = VS – VB
= 1-(0)
= 1v
When VSB is connected with forward bias there are chances that the electrons flow might be distorted and current direction will change leading to improper function of the device.
VS connected to 1v
VSB = VS – VB
= 1-(1)
= 0v
When VSB is connected with reverse bias then due to the space charge region there exists a leakage current and the electrons flow can be controlled thereby having a proper functioning device.
So it is recommended to connect source – substrate in reverse bias.
Ideal VTO components:
Voltage requirement for depletion charge:
The VT is affected by the depletion charge and can be computed by Qd/Ci
As the channel forms there exists a charge in the depletion region and due to parallel plate and dielectric medium the channel acts as a parallel plate capacitor, this charge has some voltage called depletion charge voltage.
Voltage requirement for inversion charge:
The inversion charge is denoted by 2∅F, it is the potential to form inversion at the channel of a MOSFET.
∴ Ideal Vto component = -Qd/Ci + 2∅F
Real VTO components:
Voltage requirement for depletion charge:
The VT is affected by the depletion charge and can be computed by Qd/Ci
As the channel forms there exists a charge in the depletion region and due to parallel plate and dielectric medium the channel acts as a parallel plate capacitor, this charge has some voltage called depletion charge voltage.
Voltage requirement for inversion charge:
The inversion charge is denoted by 2∅F, it is the potential to form inversion at the channel of a MOSFET.
∅ms : metal semiconductor work function difference
This occurs with the way fabrication chooses the materials for metal and semiconductor. In ideal we consider the same materials so EF to Evac it was equal for metal and semiconductor. But in reality there exists some difference between EF and Evac. The metal semiconductor work function difference acts in such a way that there exists a positive potential at the gate terminal due to this band bending down and depletion occurs.
Oxide charge: Qi/Ci:
The positive potential seen at the gate terminal needs to be nullified to bring the device back to ideal condition.
The positive potential is formed due to the process of forming an oxide layer.
∴ The amount of negative potential added to bring the bent bands to flat is called flat band potential = VFB = - Qi/Ci + ∅ms
∴ Real Vto component = -Qd/Ci + 2∅F –Qi/Ci + ∅ms
Formation of Oxide charge:
In the formation of an oxide layer there may be alkaline metal ions which are acted as they are active causing the positive charge to exist.
The Si atom of source and drain at the edge due to physical termination has an electron without bond called dangling bond leading to positive charge. (Dangling bond results in positive charge because O2 has less electrons with respect to Si so absence of electrons causes positive charge).
Due to insufficient oxygen at oxidation process i.e. SiO2 the Si may not have sufficient O2 this results in positive charge.
Due to defects in the crystalline structure of the oxide layer may cause positive charge.
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