Two question about InAS p-i-n junction metal gate workfunction

[ocdor]

Hi ATK experts!
          In the picture which from ATK manual, we can see the metal gate workfunction is 5.7.When the bias=0.42V, the metal gate workfunction is shift down to 5.28. So i have two questions . First, in the manual , do not clearly declare the material of the metal gate , so why the workfunction is 5.7  ? and how to realise this goal in ATK ?  Second, in the p-i-n junction, we can know that workfunction of p doped is   5.98, Why no doped i workfunction is decide by metal gate? Thank you !

[Petr Khomyakov]

The definition and actual calculation of metal gate work function is discussed in this tutorial http://docs.quantumwise.com/tutorials/inas_p-i-n_junction/inas_p-i-n_junction.html.

A gate electrode is treated as a continuum (nonatomistic) material  having dielectric properties of metal, i.e., assuming that the dielectric constant is infinite for this continuum material, and the electrostatic potential is constant across the entire metal gate region.

In the ATK, the default value for the gate electrostatic potential defined with respect to the Fermi energy is set to zero, and in the tutorial, the Fermi energy is considered as a reference (zero) energy . However, the Fermi energy and gate potential value defined with respect to the vacuum level are not zero, and the Fermi energy defined with respect to the vacuum level (in the gate region) is called work function (of metal gate). The metal gate treated within the continuum approximation can, in principle, be related to a real atomisic metal with similar work function.

The work function of the metal gate electrode can be tuned by applying a gate voltage that means that we set the gate electrostatic potential (defined with respect to the Fermi level) of the metal gate to a non-zero value, changing the energy difference (=work function) between the vacuum level in the gate region and the Fermi level. This also gives rise to a shift of the semiconductor bands  in the semiconductor channel (under or above the top or bottom gate, respectively) with respect to the Fermi level. This can be seen as a local electrostatic doping of the channel material because either conduction or valence band of the channel semiconductor material gets closer to the Fermi level due to the band structure shift, becoming more occupied by electrons or holes, respectively. 

Note that the Fermi level is fixed by the electrodes and does not shift upon gating the channel region.

[Petr Khomyakov]

If the work function of metal changes by applying voltage, so we can conclude that in each voltage we have a new metal. It is hard for me to accept this conclusion. If I get a wrong impression, please help me how can I correct it?

It is a matter of interpretation. In the continuum approximation, metal gate electrodes are mathematical constructs that account for boundary conditions that are to be imposed on the electrostatic potential to solve the Poisson equation.  For any metal, the macroscopic electrostatic potential should be constant inside the metal gate and on the metal gate surfaces. 

Actually, work function of real metals can be tuned by applying an external electrical field. You may think of a planar capacitor system with a non-zero electrostatic potential difference between the two identical metal plates; removing an electron from one metal plate becomes easier than for the other one, even so they are made of the same metal.

I notice, however, that I made this relation between a virtual metal gate material and real metal for the case of no gating. The virtual metal models only general dielectric property of any real metal, i.e., its response to electric field.