6.2 The energy band diagram of the Metal-Oxide-Silicon (MOS) Capacitor


Table of Contents - Glossary - Study Aids -
In this Section

  1. Flat band conditions
  2. Surface depletion
  3. Inversion layer formation
  4. Accumulation
Reading: Neamen 10.1,10.1.2 pp 419-428

Required background: Energy bands of semiconductors

Next: 6.3 Flat band voltage


6.2 Energy band diagram of an MOS capacitor

The energy band diagram contains the electron energy levels in the MOS structure as deliniated with the fermi energy in the metal and semiconductor as well as the conduction and valence band edge in the oxide and the silicon. A typical diagram is shown under voltage bias in the following figure:


moseband.xls - mosinv.gif
The electron energy is assumed to be zero deep into the semiconductor. The oxide has a bandgap energy of 8 eV and the silicon has a bandgap energy of 1.12 eV. A positive voltage of 1 Volt is applied to the aluminum gate metal. This is an active figure. The reader is encouraged to open the corresponding spreadsheet and to vary the bias conditions as well as the MOS parameters to get a feel for the MOS capacitor.

We will distinguish between four modes of operation: Flat band, Depletion, Inversion and Accumulation. Flat band conditions exist when no charge is present in the semiconductor so that the silicon energy band is flat. Initially we will assume that this occurs at zero gate bias. Later we will consider the actual flat band voltage in more detail. Surface depletion occurs when the holes in the substrate are pushed away by a positive gate voltage. A more positive voltage also attracts electrons (the minority carriers) to the surface which form the so-called inversion layer. Under negative gate bias, one attracts holes from the p-type substrate to the surface, yielding accumulation.


6.2.1 Flat band conditions

The flat band diagram is by far the easiest energy band diagram. The term flat band referes to fact that the energy band diagram of the semiconductor is flat, which implies that no charge exists in the semiconductor. An example is shown in the figure below. This figure is obtained by applying a gate voltage of -1.09 Volt.


moseband.xls - modflat.gif
The flat band voltage is obtained when the applied gate voltage equals the workfunction difference between the gate metal and the semiconductor. However if there is also a fixed charge in the oxide and/or at the oxide-silicon interface, the expression for the flat band voltage must be modified accordingly.

6.2.2 Surface depletion

As a more positive voltage than the flatband voltage is applied, a negaitive charge buids-up in the semiconductor. Initially this charge is due to the depletion of the semiconductor starting from the oxide-semiconductor interface. The depletion layer width further increases with increasing gate voltage. An example is shown in the figure below.


moseband.xls - mosdep.gif

6.2.3 Inversion layer formation

As the potential across the semiconductor increases beyond twice the bulk potential, another type of positive charge emerges at the oxide-semiconductor interface: this charge is due to minority carriers which form a so-called inversion layer. As one further increases the gate voltage the depletion layer width barely increases further since the charge in the inversion layer increases exponentially with the surface potential. An energy band diagram of an MOS capacitor in inversion is shown in the figure below:


moseband.xls - mosdep.gif

6.2.4 Accumulation

Accumulation occurs when one applies a voltage which is less than the flatband voltage. The negative charge on the gate attracts holes from the substrate to the oxide-semiconductor interface. Only a small of band bending is needed to build up the accumulation charge so that almost all of the potential variation is within the oxide. A band diagram of an MOS capacitor in accumulation is shown in the figure below:


moseband.xls - mosacc.gif

6.1 6.3

Bart J. Van Zeghbroeck, 1996, 1997