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Assignment Description
University Of Windsor Electrical and Computer Engineering W2019
ELEC2250: Physical Electronics
Lab Assignment 5
Resistivity and Mobility
Objective:
The objectives of this assignment are to compare the relative accuracies of the analytical and empirical equations to determine the resistivity of a semiconductor and the mobility of carriers. Review the slides on the empirical equations to determine the resistivity of a semiconductor for both ptype and ntype doping. Similarly review the slides on the empirical equations to determine the carrier motilities for both ptype and
ntype carriers.
3 75 10. 15 N091. n 17 191N_{D}. _{}8 15 10. ^{D}_{ }1N_{D }_{ }1 47 10. 12 NA076. 5 86 10. 


 (1) 
Empirical equations for Resistivity:
p 7 63 10. 18 176N_{A}. 4 64 10. 4N_{A }_{} Empirical Equations for Mobility:
From measured data, an empirical relationship between electron and hole mobilities as a function of doping concentration at 300 K is given as
^{0 }_{} (2)
_{min }
1NNRef
where is the carrier mobility (_{n }or _{p}), N is the doping concentration (N N_{D} or _{A}) and all other quantities are fitting parameters. To model the temperature dependence of mobility, each of the parameters _{min}, _{0},N_{Ref },and are modified following the general expression
A A 300 300T (3)
Where A represents _{min}, _{0},N_{Ref },and , and is the temperature exponent. The 300 K values of the parameters _{min }, _{0},N_{Ref }, and are available in Table 1 below:
Table 1
Parameter  Value at 300 K  Temperature exponent  
 Electrons  Holes 

NRef (cm3)  1.3x10^{17}  2.35x10^{17}  2.4 
_{min }(cm /Vs^{2 })  92  54.3  0.57 
_{0}(cm /Vs^{2 })  1268  406.9  2.33 electron, 2.23 holes 
 0.91  0.88  0.146 
Analytical Equations for resistivity:
q n( _{n }p _{p})
1 (4)
Assignment tasks:
1. Run the codes and observe the graphs for both resistivity and mobility.
2. Use Matlab function grid and zoom the figure windows. Mark the resistivity and mobility values for 5x10^{14} /cm^{3}, 10^{16} /cm^{3}, and 4x10^{17} /cm^{3} for both ntype and ptype doping concentrations on the graphs. Identify the graphs with your group ID.
3. Write your own codes to compare the resistivity graphs obtained following the empirical equations (1) with those obtained from the analytical equations (4).
4. Repeat step 2. Is there any change of values? What percent (if any)?
5. Summarize your observations from the lab in a text report including the graphs and a discussion. Name the report file as YOUR_LAST_NAME _lab#`5_ELEC2250W2019.
6. Submit your report along with the modified mfile through the Blackboard.
Matlab code
% ELEC2250 W2019
% Lab assignment 5
% Resistivity, Mobility calculations and verification of Einstein's relations close all clear all clc %
% N is doping concentration
% rn  resistivity of ntype
% rp  resistivity of ptype
% mun  Electron Mobility
% mup  Hole mobility
% Resistivity calculation using empirical method; Equation (1) q=1.6e19 % Electron charge
N = logspace(14,20); %Doping concentration
rn = (3.75e15 + N.^0.91)./(1.47e17*N.^1.91 + 8.15e1*N); %Empirical equation for n type resitivity
rp = (5.86e12 + N.^0.76)./(7.63e18*N.^1.76 + 4.64e4*N); %Empirical equation for p type resitivity semilogx(N,rn,'b',N,rp,'r') %Plot using a semilog scale
title('Resistivity versus Doping (Empirical)') ylabel('Resistivity (ohmcm)') xlabel('Doping Concentration cm3') text(1.1e14,12,'Ntype') text(3.0e14,50,'Ptype')
% Mobility calculation using empirical method; Equation (2)
NDref=1.3e17; %Table 1 variable NAref=2.35e17; %Table 1 variable mu_n_min=92; %Table 1 variable mu_p_min=54.3; %Table 1 variable mu_n_0=1268; %Table 1 variable mu_p_0=406.9; %Table 1 variable alpha_n=0.91; %Table 1 variable alpha_p=0.88; %Table 1 variable
mu_n=mu_n_min+mu_n_0./(1+(N/NDref).^alpha_n); %Equation (2) for electron mu_p=mu_p_min+mu_p_0./(1+(N/NAref).^alpha_p); %Equation (2) for holes figure
semilogx(N,mu_n,'b',N,mu_p,'r') text(8.0e16,1000,'Electron Mobility') text(5.0e14,560,'Hole Mobility') title('Mobility versus Doping') xlabel('Doping Concentration in cm3') ylabel('Bulk Mobility (cm2/v.s)')
%Resistivity calculation using analytical method; Equation (4) sigma=q*N.*mu_n; %Equation (4) for electrons (neglecting hole concetration) rhon=1./sigma;
sigma=q*N.*mu_p; %Equation (4) for holes (neglecting electron concetration) rhop=1./sigma; figure
semilogx(N,rhon,'b',N,rhop,'r')
title('Resistivity versus Doping (Analytical)') ylabel('Resistivity (ohmcm)') xlabel('Doping Concentration cm3') text(1.1e14,12,'Ntype') text(3.0e14,50,'Ptype')