MORGAN STATE UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EEGR.2

Question

MORGAN STATE UNIVERSITY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING EEGR.215 Materials and Devices Fall 2017 Credits-4 LAB 2: Positioning of Fermi Level Flow Diagram Due: September 13, 2017: Lab Due: September 27. 2017 OBJECTIVE: In this exercise the student will use Matlab or Excel to solve problems to plot the positioning of the Fermi Level as a function of doping and temperature EQUIPMENT: Matlab and Excel. Directions: Complete the following prolem below. Use Matlab or Excel to create a program to plot the positioning of the Fermi level as a function of doping and temperature. Include your final Matlab code or Excel spreadsheet with assignment submission. Make sure to label all axes Discuss plots and summarize results, Refer to assignment submittal guideline sheet. Any copying of programs will result in a No GRADE for the copier and the person from which the work was copied (NO Exceptions)This lab will be serve as 2 lab grades! Due Date: September 27, 2017 (Please note Flow Diagram due September 13, 2017) In class, we derived quantitatively how the electron and hole concentrations change as the Fermi energy level moves through the bandap energy where, and P= N, expl kT These expressions are based upon the probability that an available state is occupied or empty. In like manner, we can apply probability statistics to obtain expressions for the number of ionized donor and acceptor energy states where 1+4exp T

Explanation / Answer

gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton', gui_Singleton, ...
                   'gui_OpeningFcn', @FermiLevel_OpeningFcn, ...
                   'gui_OutputFcn', @FermiLevel_OutputFcn, ...
                   'gui_LayoutFcn', [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT

global k J mo h gD gA;
k =8.617E-5;
J=1.602E-19;
mo=9.109E-31;
h=6.626E-34;
gD=2; gA=4;

% --- Executes just before FermiLevel is made visible.
function FermiLevel_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to FermiLevel (see VARARGIN)

% Choose default command line output for FermiLevel
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes FermiLevel wait for user response (see UIRESUME)
% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.
function varargout = FermiLevel_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;

%%ButonforSilicon
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
menuSiDon=get(handles.popupmenu1,'value');
switch menuSiDon
    case 1
        %no option available
    case 2
        ED=0.034;%Li
        DonImpu='Li';
    case 3
        ED=0.043;%Sb
        DonImpu='Sb';
    case 4
        ED=0.046;%P
        DonImpu='P';
    case 5
        ED=0.054;%As
        DonImpu='As';
    case 6
        ED=0.071;%Bi
        DonImpu='Bi';
end
menuSiAcc=get(handles.popupmenu2,'value');
switch menuSiAcc
    case 1
        %no option available
    case 2
        EA=0.044;%B
        AccImpu='B';
    case 3
        EA=0.069;%Al
        AccImpu='Al';
    case 4
        EA=0.073;%Ga
        AccImpu='Ga';
    case 5
        EA=0.16;%In
        AccImpu='In';
    case 6
        EA=0.25;%Tl
        AccImpu='Tl';
end
%Fermi_Level(mdn, mdp, ED, EA, Material, EgO, alpha, beta, guess)
Fermi_Level(1.084,0.55,ED,EA,' Silicon',1.17,4.73E-4,636,0.55)
text(611.5,0.509,'Ec'); text(611.5,-0.528,'Ev'); text(611.5,-0.029,'Ei');
text(20.26,0.215,'n-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(20.26,0.15,strcat('Donor Impurity: ',DonImpu),'FontWeight','bold');
text(20.26,-0.193,'p-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(20.26,-0.26,strcat('Acceptor Impurity: ',AccImpu),'FontWeight','bold');

% --- Executes on selection change in popupmenu1.
function popupmenu1_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu1 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu1

% --- Executes during object creation, after setting all properties.
function popupmenu1_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

% --- Executes on selection change in popupmenu2.
function popupmenu2_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu2 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu2

% --- Executes during object creation, after setting all properties.
function popupmenu2_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

%%ButtonforGe
% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
menuGeDon=get(handles.popupmenu5,'value');
switch menuGeDon
    case 1
        %no option available
    case 2
        ED=0.0093;%Li
        DonImpu='Li';
    case 3
        ED=0.0096;%Sb
        DonImpu='Sb';
    case 4
        ED=0.012;%P
        DonImpu='P';
    case 5
        ED=0.013;%As
        DonImpu='As';
    case 6
        ED=0.18;%S
        DonImpu='S';
end
menuGeAcc=get(handles.popupmenu6,'value');
switch menuGeAcc
    case 1
        %no option available
    case 2
        EA=0.01;%B
        AccImpu='B';
    case 3
        EA=0.01;%Al
        AccImpu='Al';
    case 4
        EA=0.01;%Tl
        AccImpu='Tl';
    case 5
        EA=0.011;%Ga
        AccImpu='Ga';
    case 6
        EA=0.011;%In
        AccImpu='In';
end
%Fermi_Level(mdn, mdp, ED, EA, Material, EgO, alpha, beta, guess)
Fermi_Level(0.561,0.29,ED,EA,' Germanium',0.744,4.77E-4,235,0.35)
text(610.5,0.272,'Ec'); text(610.5,-0.272,'Ev'); text(610.5,-0.03,'Ei');
text(20.26,0.115,'n-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(20.26,0.062,strcat('Donor Impurity: ',DonImpu),'FontWeight','bold');
text(20.26,-0.066,'p-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(20.26,-0.12,strcat('Acceptor Impurity: ',AccImpu),'FontWeight','bold');

% --- Executes on selection change in popupmenu5.
function popupmenu5_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu5 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu5

% --- Executes during object creation, after setting all properties.
function popupmenu5_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

% --- Executes on selection change in popupmenu6.
function popupmenu6_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu6 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu6 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu6

% --- Executes during object creation, after setting all properties.
function popupmenu6_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu6 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

%%ButtonforGaAs
% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
menuGaAsDon=get(handles.popupmenu8,'value');
switch menuGaAsDon
    case 1
        %no option available
    case 2
        ED=0.0058;%Si
        DonImpu='Si';
    case 3
        ED=0.0059;%Se
        DonImpu='Se';
    case 4
        ED=0.006;%Ge
        DonImpu='Ge';
    case 5
        ED=0.006;%S
        DonImpu='S';
    case 6
        ED=0.006;%Sn
        DonImpu='S';
    case 7
        ED=0.03;%Te
        DonImpu='Te';
end
menuGaAsAcc=get(handles.popupmenu7,'value');
switch menuGaAsAcc
    case 1
        %no option available
    case 2
        EA=0.026;%C
        AccImpu='C';
    case 3
        EA=0.028;%Be
        AccImpu='Be';
    case 4
        EA=0.028;%Mg
        AccImpu='Mg';
    case 5
        EA=0.031;%Zn
        AccImpu='Zn';
    case 6
        EA=0.035;%Si
        AccImpu='Si';
    case 7
        EA=0.035;%Cd
        DonImpu='Cd';
end
%Fermi_Level(mdn, mdp, ED, EA, Material, EgO, alpha, beta, guess)
Fermi_Level(0.068,0.47,ED,EA,' Gallium Arsenide',1.519,5.41E-4,204,0.7)
text(604.3,0.6458,'Ec'); text(604.3,-0.6458,'Ev'); text(604.3,0.08,'Ei');
text(10.66,0.18,'n-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(10.66,0.13,strcat('Donor Impurity: ',DonImpu),'FontWeight','bold');
text(8.29,-0.12,'p-type','FontWeight','bold','FontSize',12,'FontAngle','italic')
text(8.29,-0.18,strcat('Acceptor Impurity: ',AccImpu),'FontWeight','bold');

% --- Executes on selection change in popupmenu7.
function popupmenu7_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu7 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu7 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu7

% --- Executes during object creation, after setting all properties.
function popupmenu7_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu7 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

% --- Executes on selection change in popupmenu8.
function popupmenu8_Callback(hObject, eventdata, handles)
% hObject    handle to popupmenu8 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = get(hObject,'String') returns popupmenu8 contents as cell array
%        contents{get(hObject,'Value')} returns selected item from popupmenu8

% --- Executes during object creation, after setting all properties.
function popupmenu8_CreateFcn(hObject, eventdata, handles)
% hObject    handle to popupmenu8 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

%%ButtonforFermiIntegral
% --- Executes on button press in pushbutton5.
function pushbutton5_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%FERMI-DIRAC INTEGRAL
%of order 1/2
%This program compares the Fermi Integral of order 1/2 when evaluated with
%the algorithm of Ref 1, Ref 2, and Ref 3.

hand=figure;
set(hand,'Name','Fermi-Dirac Integral','NumberTitle','off','Color',[0.65 0.81 0.82]);
screen=get(0,'ScreenSize');
width=screen(4);
large=screen(3);
set(hand,'position',[50,50,large-750,width-145]);
centerfig

%Ref 1: Solid State Electronics, 25, 1067 (1982)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n=-8:0.2:8; %(Greek letter eta)
F=(exp(-n)+3*sqrt(pi/2)*((n+2.13)+((abs(n-2.13)).^2.4+9.6).^(5/12)).^(-3/2)).^-1;
Ref1=semilogy(n,F,'b','LineWidth',3); grid on, axis([-8 8 1E-4 20]),hold on
set(Ref1,'DisplayName','Ref 1');

%Ref 2: Semiconductor Physical Electronics, Sheng S. Li. pp 89
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for ind=1:length(n)
    if n(ind)<=-4
        Fermi(ind)=exp(n(ind));
    elseif n(ind)>-4 && n(ind)<1
        Fermi(ind)=1/(exp(-n(ind))+0.27);
    elseif n(ind)>=1 && n(ind)<=4
        Fermi(ind)=(4/(3*sqrt(pi)))*(n(ind)^2+(pi^2)/6)^(3/4);
    else
        Fermi(ind)=(4/(3*sqrt(pi)))*n(ind)^(3/2);
    end
end
Ref2=semilogy(n,Fermi,'r','LineWidth',2,'LineStyle','--');
set(Ref2,'DisplayName','Ref 2');

%Ref 3: Physica Status Solidi(b) vol. 188, 1995, pp 635-644
%the mfile is available at Matlab Central
%(a minor modification was made to plot the data)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

aj=1/2;
eta=-8:0.2:8;
format long e;

for cont=1:length(eta)

%==============================================================
% Evaluation of Trapezoidal sum begins
range=8.;
if eta(cont) > 0.
   range=sqrt(eta(cont)+64.);end;
h=0.5;
nmax=range/h;
sum=0.;
if aj== (-0.5)
   sum=1./(1.+exp(-eta(cont)));end;
for i=1:nmax
   u=i*h;
   ff=2.*(u^(2.*aj+1))/(1.+exp(u*u-eta(cont)));
   sum=sum+ff;end;

%Trapezoidal Summation ends
%==============================================================

% Pole correction for trapezoidal sum begins
pol=0.;
npole=0;
% Fix the starting value of BK1 to start while loop
bk1=0;
while bk1 <= 14.*pi
   npole=npole+1;
   bk=(2*npole -1)*pi;
   rho=sqrt(eta(cont)*eta(cont)+bk*bk);
   t1=1;
   t2=0;
   if eta(cont) < 0;
      tk=- aj*(atan(-bk/eta(cont))+pi);
   elseif eta(cont) ==0;
      tk=0.5*pi*aj;
   else;
      eta(cont) > 0;
      tk=aj*atan(bk/eta(cont));
   end;
   rk=- (rho^aj);
   tk=tk+0.5*atan(t2/t1);
   if eta(cont) < 0
      rk= -rk;
   end;
   ak=(2.*pi/h)*sqrt(0.5*(rho+eta(cont)));
   bk1=(2.*pi/h)*sqrt(0.5*(rho-eta(cont)));
   if bk1 <= (14.*pi)
   gama=exp(bk1);
   t1=gama*sin(ak+tk)-sin(tk);
   t2=1.-2.*gama*cos(ak)+gama*gama;
   pol=pol+4.*pi*rk*t1/t2;
   end; %ends if loop above
end; % Top while loop ends
npole=npole-1;
fdp=sum*h+pol;
% Program ends with the following output
%==========================================================================
%   disp('Fermi-Dirac Integral Value');
%   disp(fdp/gamma(1+aj));
%   disp('Number of trapezoidal points & number of poles');
%   disp([round(nmax),npole]);
fermiIntegral(cont)=fdp/gamma(1+aj);
end

Ref3=semilogy(eta,fermiIntegral,'g','LineWidth',2,'LineStyle',':');
set(Ref3,'DisplayName','Ref 3');

%Asymtotic approach
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y4=(4/(3*sqrt(pi)))*n.^(3/2);
e1=plot(n,exp(n),'k','LineWidth',2,'LineStyle',':');
e2=plot(n,y4,'k','LineWidth',2,'LineStyle',':');
set(e1,'DisplayName','e^{eta}');
set(e2,'DisplayName','4/(3sqrt(pi))eta^{3/2}');

title('Fermi-Dirac Integral, F_{1/2}(eta)','FontSize',11,'FontWeight','bold')
xlabel('eta [(E_{F}-E_{C})/kT or (E_{V}-E_{F})/kT ]','FontSize',12,'FontWeight','bold')
ylabel('F_{1/2}(eta)','FontSize',12,'FontWeight','bold')

legend('Location','NorthWest'), clc

%%ButtonforGapsvsT
% --- Executes on button press in pushbutton6.
function pushbutton6_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton6 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%Temperature Dependence of Energy Band Gap
%GaAs, Si, Ge
%The temperature dependence of the energy bandgap is determined with the
%following expression for Eg.
%Eg(T) = Eg(0)-(alfa*T^2)/(T+beta)

hand=figure;
set(hand,'Name','Energy Band Gap vs Temperature','NumberTitle','off','Color',[0.65 0.81 0.82]);
screen=get(0,'ScreenSize');
width=screen(4);
large=screen(3);
set(hand,'position',[50,50,large-750,width-145]);
centerfig

T=linspace(0,1000,300);%Temperature range (K)

EgGaAs=1.519-(5.41E-4*T.^2)./(T+204);
plot(T,EgGaAs,'g','LineWidth',3), grid on, hold on

EgSi=1.17-(4.73E-4*T.^2)./(T+636);
plot(T,EgSi,'b','LineWidth',3)

EgGe=0.744-(4.77E-4*T.^2)./(T+235);
plot(T,EgGe,'c','LineWidth',3)

legend('GaAs','Si','Ge')
title('Energy Bandgaps of GaAs, Si, and Ge as a function of temperature','FontWeight','Bold')
xlabel('T(K)','FontWeight','Bold'), ylabel('Bandgap E_{g}(eV)','FontWeight','Bold')

%%ButtonforIntrinsic
% --- Executes on button press in pushbutton7.
function pushbutton7_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton7 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%INTRINSIC CARRIER DENSITY
%GaAs, Si, and Ge

T=200:2:2000;
EgGaAs=1.519-(5.41E-4*T.^2)./(T+204);
EgSi=1.17-(4.73E-4*T.^2)./(T+636);
EgGe=0.744-(4.77E-4*T.^2)./(T+235);
mo=9.109E-31;
k=8.61E-5;
%GaAs
mdnGaAs=0.068*mo;
mdpGaAs=0.47*mo;
%Si
mdnSi=1.084*mo;
mdpSi=0.55*mo;
%Ge
mdnGe=0.561*mo;
mdpGe=0.29*mo;
%
hand=figure(4);
set(hand,'Name','Intrinsic Carrier Density','NumberTitle','off','Color',[0.65 0.81 0.82]);
screen=get(0,'ScreenSize');
width=screen(4);
large=screen(3);
set(hand,'position',[50,50,large-400,width-145]);
centerfig
%
subplot(1,2,1)
niGaAs=(2.5E19*(T/300).^(3/2))*(((mdnGaAs*mdpGaAs)/mo^2)^(3/4)).*exp(-EgGaAs./(2*k*T));
semilogy(1000./T,niGaAs,'g','LineWidth',3), grid on
axis([0.5 4.5 1E6 1E20]),
hold on
%
niSi=(2.5E19*(T/300).^(3/2))*(((mdnSi*mdpSi)/mo^2)^(3/4)).*exp(-EgSi./(2*k*T));
semilogy(1000./T,niSi,'b','LineWidth',3)
%
niGe=(2.5E19*(T/300).^(3/2))*(((mdnGe*mdpGe)/mo^2)^(3/4)).*exp(-EgGe./(2*k*T));
semilogy(1000./T,niGe,'c','LineWidth',3)
%
xlabel('1000/T (K^{-1})','FontWeight','Bold'), ylabel('Intrinsic carrier density n_{i} (cm^{-3})','FontWeight','Bold')
legend('GaAs','Si','Ge')
%
subplot(1,2,2)
semilogy(T,niGaAs,'g','LineWidth',3),axis([200 1600 10 1E20]), grid on, hold on
semilogy(T,niSi,'b','LineWidth',3)
semilogy(T,niGe,'c','LineWidth',3)
xlabel('T (K)','FontWeight','Bold'), ylabel('Intrinsic carrier density n_{i} (cm^{-3})','FontWeight','Bold')
legend('GaAs','Si','Ge','Location','NorthWest')

% --------------------------------------------------------------------
function Untitled_1_Callback(hObject, eventdata, handles)
% hObject    handle to Untitled_1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% --------------------------------------------------------------------
function Untitled_2_Callback(hObject, eventdata, handles)
% hObject    handle to Untitled_2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
box=msgbox('Help displayed in the Command Window');
pause(4)
close(box)
help FermiLevel

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