Thermionic vs Tunneling Based on Spectral Current for P-Type Semiconductor/Metal

[apnichol]

Hello QuantumATK Representative,

I have a question that stems from the "Modeling metal–semiconductor contacts: The Ag–Si interface" tutorial as well as the paper from D. Stradi et al. (Phys. Rev. B, 93:155302, Apr 2016). I will keep the question as general as possible when referencing my current model so that it is applicable to other similar systems and QuantumATK users.

I am currently modeling a two-probe semiconductor-metal system with the semiconductor layer being classified as a p-type semiconductor material, not n-type as in the tutorial. After calculating the Transmission Spectra at different bias conditions, I obtain the spectral current and plot it along with the Schottky barrier height determined from the p-type semiconductor-metal PLDOS analysis. My question is if one is dealing with a Schottky barrier that is pointing downward (i.e. band bending downward to create a barrier for holes coming from the p-type semiconductor layer to the metal contact), is the thermionic and tunneling mechanism classification still the same as in the tutorial (where above the Schottky barrier value line is thermionic emission and below the line is tunneling)? I have attached an image in an effort to show how I am plotting the HDP with respect to the valence band of the semiconductor and the right chemical potential mu_R in the metal contact as well as the spectral current with respect to mu_R. I have used absolute values for the E - mu_R y-axis and phi^pot value since I was unsure if I should specify them as negative values when defining a spectral current for a p-type semiconductor-metal. Please let me know if any other additional details are needed and thank you in advance.

[Anders Blom]

Everything is upside down in hole-land compared to electrons, so the thermionic emission "above the barrier" is for lower energies for p-type. Thus opposite the labels you have.

[apnichol]

Thank you for the response. Given that the "lower energies" would indicate a more negative energy to overcome the downward (negative) Schottky barrier height in the case of thermionic emission, I think it would make more sense to plot the data without the absolute values as shown in the attached image (updated_spectral_current_plot.png). Please correct me if I am wrong in the newly plotted interpretation.

My question stemmed from seeing how the Spectral Current tab from the Transmission analyzer shows the spectral current above the Fermi level E_f at an energy of around +0.7 eV for the "positive" (left-to-right) current as shown in the next attached image (atk_spectral_current_-0p25_V.png). I would have expected the spectral current to appear below E_f at -0.7 eV, thinking that the "positive" current from the holes that are flowing would be from the valence band (which is below E_f). Would it not be correct to plot the spectral current below E_f as I am now doing, rather than how QuantumATK does it by default?

[Anders Blom]

We always plot things from the electron perspective, so yes if you view it from a hole perspective, you need to invert. Also the current direction changes for holes.

[apnichol]

Ok, thank you for the help!