New atomistic method provides realistic simulations of metal-semiconductor interfaces

Jun 20 2016

In the article "General atomistic approach for modeling metal-semiconductor interfaces using density functional theory and nonequilibrium Green's function" published in Physical Review B, researchers from QuantumWise A/S demonstrate a new method for modeling metal-semiconductor contacts, which includes all the relevant ingredients required to describe metal-semiconductor interfaces realistically. Moreover, it allows for a direct comparison between theory and experiments via I−Vbias curve simulations. An online case study with all scripts is now available for all ATK users, making the results of the article fully reproducible.

Highlights

We present

  • a new method for describing infinite interfaces correctly, that
  • allows you to simulate what is measured in experiments directly.

The method

  • gets the band gap of the semiconductor side right, from first principles,
  • properly screens the interface dipole, since the semiconductor side can be made long enough,
  • accounts for image force barrier lowering,
  • treats thermionic emission and tunneling on equal footing, without assumptions,
  • includes the effect of doping on the Schottky barrier height,
  • and can account for a finite bias and its influence on the effective barrier.

Based on the published article, the scientific support team at QuantumWise has now created a case study on metal/semiconductor interfaces, which basically reproduces the results of the article General atomistic approach for modeling metal-semiconductor interfaces using density functional theory and nonequilibrium Green's function [Physical Review B 93, 155302 (2016)], by Daniele Stradi et al. from QuantumWise and DTU.

The focus of this work is to study the properties of a silver/n-silicon interface, and the case study provides all necessary scripts that enable users to reproduce the results themselves.

ATK uses density functional theory together with the non-equilibium Green's function method to describe an interface as two joined semi-infinite bulk materials, instead of the conventional method of repeating the structure or creating a finite-size slab model.

device vs slab  

DFT+NEGF two-probe device model (top) versus the conventional slab approach (bottom).
Besides correctly describing the boundary conditions of infinite non-periodic interface correctly, the device method also allows for simulating the interface under an applied bias.

The first analysis described in the article shows a plot of the projected local density of states aligned with the Hartree potential. This can be used to estimate the Shottky barrier.

  AgSi plot

 A second script analyzes the I-V curve of the Ag/Si device to calculate the ideality factor, which appears in the expression for the current as predicted by thermionic emission theory:

Ideality factor 

IV

 
IV-n-log  

Next, the linear response transmission spectrum is computed at different temperatures, making it possible to extract an Arrhenius plot. This is a way of directly simulating the Schottky barrier that would be measured in experiments using the "activation energy" method, i.e. assuming that all current is due to thermionic emission. The case study demonstrates how this assumption fails, in particular at higher doping levels, since it neglects tunneling, which however is explicitly included in the ATK calculations.

Activation-energy arrhenius

The final analysis looks at the spectral current which compares the maximum of this with the barrier of the Hartree potential. This is a method for investigating whether tunneling of thermionic emision is the dominant transfer mechanism for the device. At higher doping, tunneling is definitely the dominant process. This also means that the Schottky barrier estimated by the experimental procedure, which neglects tunneling, is much lower than the barrier of the Hartree potential.

  spectral current Thermionic emission tunelling  

 

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More information

Phys. Rev. B 93, 155302 (2016)
Online case study @ docs.quantumwise.com 

 

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