# Mosfet Matlab Code

#### Short Description

vlsi lab experiment...

#### Description

Lab Assignment No. 1 AIM: TO STUDY THE CHARACTERISTICS OF Id AND Vgs ABSTRACT The main aim of this experiment is to plot the Vgs v/s Id characteristics and observe the effect on the drain current when Vgs is varied. Further the device parameters such as the mobility and the channel length are varied to observe the effect on the characteristics. THEORYThe equation used in this experiment isId=(1/2)*µn*Cox*(W/L)*(Vgs-Vth)2 Where Id= drain current, µn = mobility of electrons, Cox= oxide capacitance,W= width of the MOSFET, L= channel length , Vgs= gate source voltage, Vth= threshold voltage. The above equation is valid when the MOSFET is in saturation where the drain current no longer depends on the drain to source voltage but it rather follows the square law. MATLAB CODEa)

When µn is variedclc; clear all; close all; Vgs=[0:.5:30]; Vt=.4; Mn1=300*(10^(-4)); Mn2=500*(10^(-4)); Mn3=700*(10^(-4)); Cox=((3.9*8.854*(10^(-3)))/2); W=10^(-9); L=(10^(-7)) for i=1:length(Vgs) Id1(i)=(0.5*Mn1*Cox*W*((Vgs(i)-Vt)^2)/L); Id2(i)=(0.5*Mn2*Cox*W*((Vgs(i)-Vt)^2)/L); Id3(i)=(0.5*Mn3*Cox*W*((Vgs(i)-Vt)^2)/L); end plot(Vgs,Id1,'Color',[.6 0 0]);grid; hold on; plot(Vgs,Id2,'Color',[0 .6 0]);grid; hold on; plot(Vgs,Id3,'Color',[0 0 .6]);grid; hold on;

xlabel ('Vgs (V)---------------->'); ylabel ('Id (A)---------------->'); Schematic matlab output-

b) L is varied clc; clear all; close all; Vgs=[0:.5:30]; Vt=.4; Mn=500*(10^(-4)); Cox=((3.9*8.854*(10^(-3)))/2); W=10^(-9); L1=(10^(-7)); L2=(3*(10^(-7))); L3=(5*(10^(-7))); for i=1:length(Vgs) Id1(i)=(0.5*Mn*Cox*W*((Vgs(i)-Vt)^2)/L1); Id2(i)=(0.5*Mn*Cox*W*((Vgs(i)-Vt)^2)/L2); Id3(i)=(0.5*Mn*Cox*W*((Vgs(i)-Vt)^2)/L3); end plot(Vgs,Id1);grid; hold on; plot(Vgs,Id2);grid; hold on; plot(Vgs,Id3);grid;

hold on; xlabel('Vgs (V)---------------->'); ylabel('Id (A)---------------->'); OUTPUT-

CONCLUSION- As observed from the two output graph that with changes in the mobility as well as the channel length, the drain current shows a variation with increase in the gate source voltage. As the mobility of carriers increases, the drain current increases. This is because, increase of mobility signifies that there are less collision and electrons can move through the channel freely and hence generate more current. With the decrease in channel length, the current increases. Because a shorter channel has more concentration of carriers and more carrier concentration will generate more current.

Lab Assignment No 2 AIM - TO OBSERVE THE VARIATION OF TRANSCONDUCTANCE W.R.T. THE DRAIN CURRENT AND THE OVERDRIVE VOLTAGE. ABSTRACT In this experiment we will determine the variation of the transconductance of the MOSFET with the drain current Id as well as the overdrive voltage (VgsVth). THEORY We all know that a MOSFET operating in saturation always produces a constant current in response to the variation of gate source voltage. That is it always behaves like a current source. Transconductance is the measure of how well the MOSFET device is able to convert the voltage into output current. The governing equations are1) gm= µn*Cox*(W/L)*(Vgs-Vth) A/V; where gm is the transconductance of the device, µn is the mobility of carriers, Cox is the oxide capacitance, W= width of the device, L=channel length, (Vgs-Vth)= overdrive voltage. 2) gm= √ 2 µ n ∗Cox ∗ ( W / L ) Id A/V; Id is the drain current. 3) gm= (2*Id)/(Vgs-Vth) A/V. MATLAB CODE1) clc; clear all; close all; Vgs=[0:0.5:10]; Vt=0.7; Mn=(500*10^(-4)); Cox=(3.9*8.854*10^(-3)/2); W=10^-9; L=10^-7; for i=1:length(Vgs) gm(i)=((Mn*Cox*W*(Vgs(i)-Vt))/L); end for i=1:length(Vgs) t(i)=Vgs(i)-Vt; end plot(t,gm);grid; title('Graph of (Vgs-Vt) v/s gm');

xlabel('Vgs-Vt---->'); ylabel('gm----->'); OUTPUT-

2) clc; clear all; close all; Ids=[0:0.5:5]; Mn=(500*10^(-4)); Cox=(3.9*8.854*10^(-3)/2); W=10^-9; L=10^-7; for i=1:length(Ids) gm(i)=(2*Mn*Cox*W*Ids(i)/L)^0.5; end plot(Ids,gm);grid; title('Graph of Id v/s gm'); xlabel('Ids------>'); ylabel('gm------>');

OUTPUT-

3) clc; clear all; close all; Vgs=[0.8:0.5:5]; Vt=0.7; Ids=0.5; for i=1:length(Vgs) gm(i)=((2*Ids)/(Vgs(i)-Vt)); end for i=1:length(Vgs) t(i)=Vgs(i)-Vt; end plot(t,gm);grid; title('Graph of (Vgs-Vt) v/s gm'); xlabel('Vgs-Vt---->'); ylabel('gm----->');

OUTPUT-

CONCLUSION- The three output curves shows the variation of the transconductance with the overdrive voltages and drain current based on the equation mentioned above. The first equation depicts a linear relationship between transconductance and overdrive whereas in the third relationship gm is inversely proportional to overdrive voltage. In the second relationship, the transconductance is proportional to the square rrot of drain current.

Lab Assignment No 3 AIM - TO STUDY THE VARIATION OF THE CHARGE IN THE DEPLETED REGION WITH VOLTAGE AT ANY POINT x ALONG THE CHANNEL. ABSTRACTThe aim of this experiment is to observe how the charge density along along the varies with the voltage at any point x along the channel and vice versa. THEORY The equations used in this experiment are given belowQd(x)=WCox(Vgs-V(x)-Vth) C; Where Qd(x) is the charge density at any point x along the channel, V(x) is the voltage at any point x. To observe the reverse case, i.e., the variation of Vx w.r.t. to Qd the following equation is usedVx=(Vgs-Vth)-(Qd/WCox) V. MATLAB CODEclc; clear all; close all; Qd=[0:10^-9:5*10^-9]; Vgs=2; Vt=0.7; W=10^(-6); Cox=(3.9*8.854*10^(-12))/(2*10^(-9)); for i=1:length(Qd) Vx(i)=((Vgs-Vt)-(Qd(i)/(W*Cox))); end subplot(2,1,1); plot(Qd,Vx);grid; xlabel('Qd (C)------->'); ylabel('V(x)(V)--------->'); subplot(2,1,2); plot(Vx,Qd); grid on; xlabel('Vx------>'); ylabel('Qd------>');

OUTPUT-

CONCLUSION As evident from the output curve above, both the curve shows negative slope. This shows that both the terms are inversely related. An increase in one term will cause a decrease in other term and vice versa.

Lab Assignment no. 4 AIM: To study the characteristics of Id with varying parameters, considering both Triode and Saturation region. ABSTRACT: In this experiment the graph of Id is plotted with varying the parameters like- length (L), Vgs in the Saturation region as well in Triode region. THEORY: a) Triode region: When the Gate voltage is in the range 0