Experiment 4 Aim of the experiment : Employing the exact-charge relationships found in write a MATLAB program that can be used to calculate and plot low frequency C/C0 versus VG characteristics. The program is to calculate C/C 0 and the corresponding VG for US=ΦS/(kT/q) stepped in one-unit or less increments from US=UF-21 to U F+21.UF=ΦF/(kT/q) Employ KS= 11.8 and K 0= 3.9; Let T =300 K. Only 15 3 NA and x0 are to be considered input variables. Setting N A =10 /cm , use your program to plot out the low-frequency C/C0 versus VG curves for x 0 =0.1 µm, 0.2 µm, and 0.3 µm
Description of the experiment Capacitance-voltage plot is used for characterizing mos capacitor. The applied voltage is varied, and the capacitance is measured and plotted as a function of voltage.
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Matlab Code
%Low and/or HIGH-frequency p-typeMOS-C C_V CHARACTERISTICS %Subprogram CVintegrad is arun time requirement %INItialization and Input format compact close clear s= menu('choose the desird plot','Low-f C-V','High-f C-V','Both'); NA=input('Please input the bulk doping in /cm3,NA='); xo=input('Please input the oxide thickness in cm,xo='); xmin=input('Specify VGmin(volts),VGmin='); xmax=input('SpecifyVGmax(volts),VGmax='); global UF %Constants and parameters e0 =8.85e-14; q =1.6e-19; k=8.617e-5; KS=11.8; KO=3.9; ni=1.0e10; T=300; kT=k*T; %Computed Constants UF =log(NA/ni); LD =sqrt((kT*KS*e0)/(2*q*ni)); %Gate voltage computation US =UF-21:0.5:UF+21; F=sqrt(exp(UF).*(exp(-US)+US-1)+exp(-UF).*(exp(US)-US-1)); VG= kT*(US+(US./abs(US)).*(KS*xo)/(KO*LD).*F); % low-frequency capacitance computation DENOML=exp(UF).*(1-exp(-US))+exp(-UF).*(exp(US)-1); WL =(US./abs(US)).*LD.*(2*F)./DENOML; cL=1.0./(1+(KO*WL)./(KS*xo)); %High-frequency Capacitance Computation if s~=1, jj=length(US); nn=0; for ii=1:jj, if US(ii)<3, elseif nn==0, INTG=QUAD('CVintgrd',3,US(ii),0.001); nn =1; else INTG =INTG+QUAD('CVintgrd',US(ii-1),US(ii),0.001); end if US(ii)<3, cH(ii)=cL(ii); else
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d=(exp(US(ii))-US(ii)-1)./(F(ii).*exp(UF).*INTG); DENOMH=exp(UF).*(1-exp(-US(ii)))+exp(-UF).*((exp(US(ii))1)./(1+d)); WH =LD.*(2*F(ii))./DENOMH; cH(ii)=1.0/(1+(KO*WH)./(KS*xo)); end end else end %plotting the result if s==1, plot(VG,cL); elseif s==2, plot(VG,cH); else plot(VG,cL,'--',VG,cH); text(0.8*xmin,.17,'-Low-f','color',[1,1,0]); text(0.8*xmin,.12,'-High-f','color',[1,0,1]); end axis([xmin,xmax,0,1]); text(0.8*xmin,.27,['NA=',num2str(NA),'/cm3']); text(0.8*xmin,.22,['xo=',num2str(xo),'cm']); xlabel('VG(volts)');ylabel('C/CO');grid
waveforms
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Result:
Low-frequency C/C0 versus VG curves for x0 =0.1 µm, 0.2 µm, and 0.3 µm was plotted and studied.
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