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MOS Electrostatics under Applied Bias

A normally-off MOSFET has a fully depleted channel without applied bias.

• N-Channel

When a bias between the metal Gate and the bulk semiconductor, Vgb, is applied which is more positive than the Threshold voltage, V_TN, then an inversion layer is formed under the gate oxide. This is because the positive gate bias attracts enough electrons to the channel region where the electron concentration in the channel is greater than the hole concentration in the bulk (inversion). The inversion charge depends on the applied voltage. If the bias is less positive than V_TN, no inversion layer is formed and the device is still not conducting between S and D.

• Inversion (V_gb > V_TN)

The channel charge is given by Q_N = - C_ox (V_gb - V_TN).  Here C_ox is the oxide-layer capacitance,

• Depletion ( 0 < V_gb < V_TN)

The channel is depleted (of holes) and the depletion layer (the white region) thickness increases with increasing gate-bulk bias (this increasing depletion thickness is not shown in the applet).

• applet note:
  The depletion region (white region) in Si chages with Vgb.  This has been ignored in this applet in order to focus on the channel only. However, the dependence of the depletion region thickness on Vgb leads to an associated capacitance and thus is important for device.
  
  
  
• P-Channel

When a bias between the metal Gate and the bulk semiconductor, Vgb, is applied which is more negative than the Threshold voltage, V_TP, then an inversion layer is formed under the gate oxide. This is because the negative gate bias attracts enough holes to the channel region where the hole concentration in the channel is greater than the hole concentration in the bulk (inversion). The inversion charge depends on the applied voltage. If the bias is less negative than V_TP, then the hole uder the gate oxide is not enogh to form the inversion layer and the device is still not conducting between S and D.

• Inversion (V_gb < V_TP)

The channel charge is given by Q_P = C_ox (V_gb - V_TP).  Here V_gb is the gate-bulk bias, V_TP is the threshold voltage of the MOS structure, and C_ox is the oxide capacitance,

• Depletion ( 0 > V_gb > V_TP)

The channel is depleted (of charge carrier holes) and the depletion layer (the white region) thickness increases with increasing gate-bulk bias (this increasing depletion thickness is not shown in the applet).