MATLAB Function for Modeling Interface Semiconductor/Oxide

This document provides a MATLAB function to model the interface properties between a semiconductor and an oxide layer. The function calculates essential parameters such as charge density, potential profile, and capacitance.

Function Overview

Purpose

The purpose of this function is to model the electrical interface between a semiconductor and an oxide layer, which is crucial in designing semiconductor devices. The model considers the impact of various parameters like oxide thickness, doping concentration, and applied voltage.

Parameters

• oxideThickness: Thickness of the oxide layer (in nm)
• dopingConcentration: Doping concentration in the semiconductor (in cm^-3)
• appliedVoltage: Voltage applied across the oxide layer (in V)
• epsilonOxide: Permittivity of the oxide (in F/m)
• epsilonSemiconductor: Permittivity of the semiconductor (in F/m)

Returns

• chargeDensity: Charge density at the interface (C/m^2)
• potentialProfile: Potential distribution across the oxide layer (V)
• capacitance: Capacitance of the oxide layer (F)

Exceptions

• Raises an error if any input parameter is negative.

Code Implementation

function [chargeDensity, potentialProfile, capacitance] = modelInterfaceSemiconductorOxide(oxideThickness, dopingConcentration, appliedVoltage, epsilonOxide, epsilonSemiconductor)
    % modelInterfaceSemiconductorOxide models the semiconductor/oxide interface.
    %
    % Args:
    %    oxideThickness (double): Thickness of the oxide layer (in nm)
    %    dopingConcentration (double): Doping concentration in the semiconductor (in cm^-3)
    %    appliedVoltage (double): Voltage applied across the oxide layer (in V)
    %    epsilonOxide (double): Permittivity of the oxide (in F/m)
    %    epsilonSemiconductor (double): Permittivity of the semiconductor (in F/m)
    %
    % Returns:
    %    chargeDensity (double): Charge density at the interface (C/m^2)
    %    potentialProfile (vector): Potential distribution across the oxide layer (V)
    %    capacitance (double): Capacitance of the oxide layer (F)
    %
    % Raises:
    %    error: If any input parameter is negative.
    
    % Input validation
    if any([oxideThickness, dopingConcentration, appliedVoltage, epsilonOxide, epsilonSemiconductor] < 0)
        error('All input parameters must be non-negative');
    end

    % Constants
    epsilon0 = 8.854e-12;  % Vacuum permittivity (F/m)
    
    % Convert thickness from nm to m
    oxideThickness_m = oxideThickness * 1e-9; 
    
    % Calculate charge density in the semiconductor using doping concentration
    q = 1.6e-19;  % Charge of an electron (C)
    chargeDensity = q * dopingConcentration * 1e6; % Convert from cm^-3 to m^-3

    % Capacitance of the oxide layer (C = ε/ d)
    capacitance = epsilonOxide / oxideThickness_m;  % Capacitance (F/m^2)
    
    % Potential distribution across the oxide layer (assuming linear distribution)
    % Consider a simple case where potential decreases linearly with distance
    potentialProfile = linspace(appliedVoltage, 0, 100);  % 100 points from V to 0 V

    % Output results
    fprintf('Charge Density: %.4e C/m^2\n', chargeDensity);
    fprintf('Capacitance: %.4e F\n', capacitance);
end

Usage Example

To utilize the function, you can call it with specific parameters as follows:

% Define parameters
oxideThickness = 5; % in nm
dopingConcentration = 1e16; % in cm^-3
appliedVoltage = 2; % in V
epsilonOxide = 3.45e-11; % Permittivity for SiO2 (F/m)
epsilonSemiconductor = 1.04e-10; % Approx for Silicon (F/m)

% Call the function
[chargeDensity, potentialProfile, capacitance] = modelInterfaceSemiconductorOxide(oxideThickness, dopingConcentration, appliedVoltage, epsilonOxide, epsilonSemiconductor);

% Display potential profile
figure;
plot(potentialProfile);
title('Potential Distribution Across Oxide Layer');
xlabel('Position (normalized)');
ylabel('Potential (V)');
grid on;

Conclusion

This MATLAB function effectively models the semiconductor/oxide interface, providing vital insights into charge density, potential distribution, and capacitive behavior. For further learning, exploring courses on the Enterprise DNA Platform will enhance your understanding of semiconductor physics and MATLAB programming.