Log-normal Work Function Distribution Vs. Gaussian Work Function Distribution

The research considered the role of Log-normal distribution and Gaussian work function distribution.


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:::info Authors:

(1) Nandan Pakhira, Department of Physics, Kazi Nazrul University, Asansol, West Bengal 713340, India;

(2) Rajib Mahato, Department of Physics, Kazi Nazrul University, Asansol, West Bengal 713340, India and Central Electronics Engineering Research Institute, Pilani, Rajasthan 333031, India.

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Abstract and 1 Introduction

II. Mathematical Formalism

III. Work Function Distribution

IV. Results

A. Gaussian work function distribution

B. Log-normal work function distribution

V. Conclusion, Acknowledgements, and References

B. Log-normal work function distribution

Next we consider log-normal distribution for the work function. In Fig. 8 we show the histogram plot of the work function, sampled over log-normal distribution for four choice of median work function M ≡ e µ = 3.0, 3.5, 4.0 and 4.5 eV with σ = 0.05. From this plot we can see that our choice of random variables for Φ are well sampled over the log-normal distribution.

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\ FIG. 8: (Color online) Histogram plot of work function, Φ, sampled over log normal distribution for various µ (see text). We have chosen σ = 0.05 for all the figures.

\ 1. Case with Φ ≪ EF

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\ 2. Case with Φ ≫ EF

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V. CONCLUSIONS

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Acknowledgements

We would like to thank Nei Lopes, Arghya Taraphder for many valuable discussions. One of us (N. P) would like to thank IIT, Kharagpur for local hospitality where part of the work was done. One of us (R. M) would like to thank Cetral Electronics Engineering Research Institute, Pilani for providing local hospitality and research support where part of the work was done.


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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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