MatteoOrlandini/Single-Electron-Transistor

Master Equation vs Montecarlo for simulating Single Electron Transistor behavior in MATLAB

Single Electron Transistor

Introduction

This repository shows the characteristics of a Single Electron Transistor (SET). In this device the electrons flow through a tunnel junction between source/drain to a quantum dot (conductive island). Moreover, the electrical potential of the island can be tuned by a third electrode, known as the gate, which is capacitively coupled to the island. The conductive island is sandwiched between two tunnel junctions, which are modeled by a capacitor C_d and C_s and a resistor R_d and R_s in parallel.

The code

• The functions f_tunnel.m and f_tunnel0.m compute the tunneling rate

• The functions master_equation.m and master_equation0.m compute the master equation

• The function monte_carlo.m calculates the Monte Carlo method

For more information type:

• help f_tunnel
• help f_tunnel0
• help master_equation
• help master_equation0
• help monte_carlo in Matlab.

How to run

Open Matlab and run SET_characteristics.m to see some characteristics of a single electron transitor or run montecarlo_masterequation_comparison.m to see the comparison between Monte Carlo and Master Equation method to calculate current in a SET.

There is also a GUI SET_characteristics_app.mlapp made up to easy understand the SET characteristics.

Application design

Results

SET characteristics

Drain current vs. drain voltage

Electrons in dot

dI/dV vs. drain voltage

Coulomb blockade

Comparison between Monte Carlo and master equation

Tunneling rate

Charge density for different drain voltages

Drain current vs. drain voltage at fixed gate voltage

Charge density for different gate voltages

Drain current vs. gate voltage at fixed drain voltage

Sum of the number of charges that arrived and left the drain

Number of charges arrived at the drain at fixed gate voltage

Number of charges that left at the drain at fixed gate voltage

Drain current vs. time at fixed drain voltage

Drain current vs. time at fixed gate voltage

Drain current vs. drain voltage at fixed gate voltage comparison between Monte Carlo and master equation

Drain current vs. gate voltage at fixed drain voltage comparison between Monte Carlo and master equation

Charges stored into the dot varying gate and drain voltage

Drain current varying gate and drain voltage comparison between Monte Carlo and master equation