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.
THEORY
The equation used in this experiment is-Id=(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 CODE-a) When µn is varied-clc; 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
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)--->');
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 (Vgs-Vth).
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
are-1) 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 CODE-1) 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--->'); 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--->');
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--->');
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.
ABSTRACT-
The 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 below-Qd(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 used-Vx=(Vgs-Vth)-(Qd/WCox) V. MATLAB CODE- clc; 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--->');
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<Vgs<Vt, the gated region between the source and drain is depleted. No carrier flow can be observed in the channel. As the gate voltage is increased beyond the threshold voltage (Vgs > Vt), an inversion layer is formed.
Thus, in linear region operation, the channel region acts as a voltage-controlled resistor.
The output current Id for the triode region id given by: Id= (0.5*Un*Cox*W)/L*[2*(Vgs-Vt)*Vds-Vds2]
b) Saturation region:
For Vds = Vdsat, the inversion charge at the drain is reduced to zero, which is called the pinch-off point. Beyond the pinch-off point, a depleted surface region forms adjacent to the drain, and this depletion region grows toward the source with increasing drain voltages. This operation mode of the MOSFET is called the saturation mode or the saturation region. In the saturation region the current equation for Id is given by:
Id= (0.5*Un*Cox*W)/L*(Vgs-Vt)2 MATLAB CODE: c) Triode region: clc; clear all; u=500*10^(-4);
Eox=3.9*8.85*10^-12; Cox=Eox/(1*10^(-9)); Vg=3:1:5; Vt=0.7; Vd=0:0.05:10; W=10^(-9); L=20*10^(-9); Vg1=0:0.5:10; for j=1:length(Vg) for i=1:length(Vd) if Vd(i)<(Vg(j)-Vt) Id(i)=u*Cox*(W/L)*((Vg(j)-Vt)*Vd(i)-0.5*Vd(i)^2); k=Id(i); else Id(i)=k; end end subplot(2,1,1) plot(Vd,Id);grid; hold on; Id1(j)=u*Cox*(W/L)*((Vg(j)-Vt)*1-0.5*(1)^2); Id2(j)=u*Cox*(W/L)*((Vg(j)-Vt)*0.5-0.5*(0.5)^2); R(j)=(1-0.5)/(Id1(j)-Id2(j)) end for i=1:length(Vg1) Id3(i)=u*Cox*(W/L)*(Vg1(i)-Vt)^2; end subplot(2,1,2) plot(Vg1,Id3); OUTPUT:
d) Saturation Region: clc; clear all; close all; U=500*10^(-4); Eox=3.9*8.85*10^-12; Cox=Eox/(2*10^-9); Vg=0:0.5:10; W=10^(-9); Vt=1 L=20:20:100; for j=1:length(L) for i=1:length(Vg) Id(i)=0.5*U*Cox*W/(L(j)*10^(-9))*((Vg(i)-Vt)^2); end y1=log(0.5*U*Cox*W/(L(j)*10^(-9))*((2-Vt)^2)); y2=log(0.5*U*Cox*W/(L(j)*10^(-9))*((3-Vt)^2)); m(j)=1/(y2-y1) plot(Vg,log(Id));grid on; hold on; end OUTPUT:
CONCLUSION:
The expected outcome has been accomplished using MATLAB. The required graph has been generated by the MATLAB code.
The graph for both the triode region and the saturation region has been plotted and obtained as expected.
Lab Assignment No 5
AIM: To implement the CS configuration Abstract:
In this experiment we have study the behavior of transconductance, output impedance, intrinsic gain and output voltage with respect to the input voltage and plotted the graph correspondingly.
Theory:
We know that the equation of drain current is Id=0.5*Un*Cox*WL*(Vin-Vt)^2
Equation of output voltage is given as-Vo=Vdd-Rd*Id1
Equation of transconductance
is-gm=
√
(2∗ Un∗ Cox ∗(W / L)∗Id)Equation of output impedance is-ro=1/(Un*Cox*WL*(Vin-Vt)) MATLAB CODE:
c) To draw the graph of gm,Id and Vout with respect to Vin Rd=1000; MnCox=50*10^-6; WL=10; for i=1:length(Vin) if Vin(i)<=Vt Vo(i)=Vdd;
elseif ((Vin(i)>Vt) && (Vin(i)<4)) Id1(i)=0.5*MnCox*WL*(Vin(i)-Vt)^2; Vo(i)=Vdd-Rd*Id1(i);
elseif (Vin(i)>=4) % Id2(j)=0.5*u*Cox*((2*Vin(i)-Vt)*Vo(i-1)-Vo(i-1)^2); %Vo(i)=Vdd-Rd*Id2(j); % j=j+1; Ron(i)=1/(MnCox*WL*(Vin(i)-Vt)); Vo(i)=(Vdd*Ron(i))/(Ron(i)+Rd); Id1(i)=Vdd/(Rd+Ron(i)); gm(i)=(MnCox*WL*Vo(i-1)); end end subplot(3,1,1) plot(Vin,Vo); grid on; xlabel('Vin--->'); ylabel('Vout---->'); subplot(3,1,2) plot(Vin,Id1); grid on; xlabel('Vin---->'); ylabel('Id--->'); subplot(3,1,3) plot(Vin,gm); grid on; xlabel('Vin---->'); ylabel('gm--->');
d) To obtain the graph between ro vs L and Id vs Vds clc;
close all; Vds=[0:0.05:2.5]; Vt=0.7; Vgs=3; Mn=1000*10^(-4); Eox=3.9*8.854*10^(-12); tox=10^(-9); Cox=Eox/tox; L=[2*10^(-8):2*10^(-8):10*10^(-8)]; W=10^-6; subplot(2,1,1); for j=1:length(L) for i=1:length(Vds) Id(i)=(Mn*Cox*W*(((Vgs-Vt)*Vds(i))-(Vds(i)^(2)/2))/L(j)); end plot(Vds,Id); grid; hold on; end for m=1:length(L) Vds=2.3 Id1(m)=(Mn*Cox*W*(((Vgs-Vt)*Vds)-(Vds^(2)/2))/L(m)); Vds=2.29 Id2(m)=(Mn*Cox*W*(((Vgs-Vt)*Vds)-(Vds^(2)/2))/L(m)); end for k=1:length(L) R(k)=0.01/(Id1(k)-Id2(k)); end subplot(2,1,2); plot(L,R); grid; hold on;
Simulation and Result: (a)
Lab Assignment No. 6
AIM: TO STUDY THE CHARACTERISTICS OF SHORT CHENNEL EFFECT OF MOS TRANSISTOR.
ABSTRACT-
The aim of this experiment is to plot the characteristics of Vgs v/s Id and see observe the effect of the short channel when Vgs is varied.
The equation used in this experiment is-Id= (W/L)*µn*Cd*Vt2 * e ( Vgs − Vt
nVt ) *(1- e-( Vds
Vt ))
Where Vt= Vto * η*Vds + ϒ ( ❑√Øs+Vsb - ❑√Qs )
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, Cd= depletion η=chain induced barrier lowering, ϒ=body effect factor.
MATLAB CODE-clc; clear all; close all; VT=.02585; Vto=.7; Esi=3.9*8.854*10^-12; q=1.6*10^-19; Nsub=10^15; cd=sqrt(q*Esi*Nsub/(4*.65)); Y=.35; w=10^-6; l=10^-8; n=.08; u=.05; Qs=.2; cox=Esi/(2*10^-2); N=1+(cd/cox); vds=5; vsb=[0:.5:2] vgs=[0:.1:5] for i=1:length(vsb) for j=1:length(vgs)
vt=(Vto*n*vds) + Y*(sqrt(vsb(i)+Qs)+sqrt(Qs)); Id(j)=(w/l)*u*cd*(VT)^2*(exp((vgs(j)-vt)/(N*VT)))*(1-exp((vds)/VT)); end subplot(2,1,1) plot(vgs,Id);grid hold on; subplot(2,1,2) plot(vgs,log(Id));grid hold on; end
ylabel('Id---> for short channel subthreshold conduction'); xlabel('Vgs--->for gate to source voltage');
SIMULATED OUTPUT:
CONCLUSION:
Hence we have shown the characteristics of short channel effect in the mos transistor when varies the gate to source voltage then the drain current is increases linirly.
