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University Of Windsor Electrical and Computer Engineering W2019

ELEC-2250: 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 p-type and n-type doping. Similarly review the slides on the empirical equations to determine the carrier motilities for both p-type and

n-type carriers. 

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 

1NNRef 

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

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 5x10¹⁴ /cm³, 10¹⁶ /cm³, and 4x10¹⁷ /cm³ for both n-type 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_ELEC2250-W2019.

6.    Submit your report along with the modified m-file through the Blackboard. 

Matlab code

% ELEC-2250 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 n-type

% rp - resistivity of p-type

% mun -  Electron Mobility

% mup - Hole mobility

% Resistivity calculation using empirical method; Equation (1) q=1.6e-19       % Electron charge

N = logspace(14,20);    %Doping concentration

rn = (3.75e15 + N.^0.91)./(1.47e-17*N.^1.91 + 8.15e-1*N); %Empirical equation for n type resitivity

rp = (5.86e12 + N.^0.76)./(7.63e-18*N.^1.76 + 4.64e-4*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 (ohm-cm)') xlabel('Doping Concentration cm-3') text(1.1e14,12,'N-type') text(3.0e14,50,'P-type')

% 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 cm-3') 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 (ohm-cm)') xlabel('Doping Concentration cm-3') text(1.1e14,12,'N-type') text(3.0e14,50,'P-type')