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/C0 and the corresponding VG for US=ΦS/(kT/q) stepped in one-unit or less increments from US=UF-21 to UF+21.UF=ΦF/(kT/q) Employ KS= 11.8 and K0= 3.9; Let T =300 K. Only NA and x0 are to be considered input variables. Setting NA =1015/cm3, use your program to plot out the low-frequency C/C0 versus VG curves for x0 =0.1 µm, 0.2 µm, and 0.3 µm

Description of the experimentCapacitance-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 Inputformat compactcloseclears= 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 parameterse0 =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 ConstantsUF =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 Computationif 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 d=(exp(US(ii))-US(ii)-1)./(F(ii).*exp(UF).*INTG);

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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 endelseend%plotting the resultif 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]);endaxis([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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