ImpedanceMismatchModeler

clear % Clears variables.
clc % Clears commands.

%% Models impedance mismatch effect of voltage dropping off rapidly as device forms.
% Useful in thinking about how the behaviour of measurements made using
% conductive atomic force microscopy might differ from those made using a
% semiconductor parameter analyser, as a result of impedance mismatch. I.e.
% the voltage drop across the CAFM probe/contact becomes significant for
% low sample resistances. This is a significant issue in studying
% resistance switching devices/memristors.

Vip = 10 ; % Input voltage across device and probe.
Vik = 3 ; % Input voltage across device and Keithley.
Rd = 10 : 10 : 1E8 ; % Device resistance.
%Rdp = Rd .* 1 ; % Device resistance when using probe.
%Rdk = Rd .* 1 ; % Device resistance when using Keithley.
Rp = 1E4 ; % Probe output impedance.
Rk = 50 ; % Keithley output impedance.

Vop = ( Vip ./ ( Rp + Rd ) ) .* Rd ; % Outut voltage across device when using probe from Luca's equation.
Vok = ( Vik ./ ( Rk + Rd ) ) .* Rd ; % Outut voltage across device when using Keithley from Luca's equation.
% Vd = Vok - Vop ; % Difference in voltage.

Ip = Vip ./ ( Rd + Rp ) .* 1000 ; % Current in device when using probe, scaled to mA.
Ik = Vik ./ ( Rd + Rk ) .* 1000 ; % Current in device when using Keithley, scaled to mA.
% Id = ( Ik - Ip ) ; % Difference in current.


%% Plot device voltage against device resistance.
figure ;
semilogx ( Rd , Vop , Rd , Vok , 'Linewidth' , 6 ) ;
legend ( 'CAFM probe' , 'Keithley' , 'Location' , 'West' ) ;
set ( gca , 'FontSize' , 38 , 'XDir' , 'Reverse' ) ;
xlabel ( 'Device resistance (Ohms) - effective time axis ' ) ;
ylabel ( 'Device voltage (V)' ) ;
xlim ( gca , [ 100 1E8 ] ) ;
% ylim ( gca , [ 6 7 ] ) ;

%% Plot device current against device resistance.
figure ;
loglog ( Rd , Ip , Rd , Ik , 'Linewidth' , 6 ) ;
legend ( 'CAFM probe' , 'Keithley' , 'Location' , 'NorthWest' ) ;
set ( gca , 'FontSize' , 38 , 'XDir' , 'Reverse' ) ;
xlabel ( 'Device resistance (Ohms) - effective time axis ' ) ;
ylabel ( 'Device current (mA)' ) ;
xlim ( gca , [ 100 1E8 ] ) ;
ylim ( gca , [ 0 10 ] ) ;