Iowa state University

EE 330 Lab Report Lab 6: Models for MOS Devices

Chongli Cai 2/20/2012

EE 330 Lab Report

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Introduction The objective of this lab is to find out the relationship between the square law model of a

MOS transistor and the BSIM model. In this lab we compared these two models and

show the reason for the square law model is relative less accurate. In this lab, we also

created a schematic circuit in Cadence and measure some data as well as calculate the

model parameters.

Procedure, Result and Analysis

Part 1: Square-law Parameter Extraction

MOS transistor with W=12µm, L=3µ

I. Derive the process parameter VT0

Keeping the VDS constant and used the different VGS to get the two current

values.

Figure (1)

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Measure date:

VGS=2V, ID1=265.2µA; VGS=2.5V, ID1=479.6µA;

From the equation:

211 1

1

212 2

1

( ) (1 )2

( ) (1 )2

D OX GS T DS

D OX GS T DS

WI C V V V

L

WI C V V V

L

Getting the Result:

00

0

2265.20.5498

479.6 2.5

TT

T

VV V

V

II. Derive the process parameter

Keeping the VGS constant and used the different VDS to get the two current

values.

Measure date:

VDS=4V, ID1=265.2µA; VDS=3V, ID2=263.3µA;

From the equation:

211 1

1

212 2

1

( ) (1 )2

( ) (1 )2

D OX GS T DS

D OX GS T DS

WI C V V V

L

WI C V V V

L

Getting the Result:

265.2 1 40.00737

263.3 1 3

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III. Derive the process parameter OXC

Using the circuit shown in Figure (1) and the measurement value derived

in previous two steps to calculate the process parameter OXC

Measurement and derived parameter value from previous:

VGS=2V, VDS=4V, ID=265.2µA, 0.00737 , 0 0.5498TV V

From the equation:

21

1

( ) (1 )2

D OX GS T DS

WI C V V V

L

Getting the result

21

1

( ) (1 )2

DOX

GS T DS

IC

WV V V

L

261.36 /OXC A V

IV. Derive the process parameter

Considering the Bulk Effect, we using the equation:

0 ( )T T BSV V V

Changing the voltage BSV three times (including the condition BSV =0), we can

getting three groups data (because we have three unknown variables)

Figure (2)

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Measurement data:

When VBS=0, VT=744.3mV;

When VBS=-2V, VT=1.212V;

When VBS=-4V, VT=1.46V;

Getting the result:

Using the calculator the solve the equation system

=0.4347

MOS transistor with W=1.5µm, L=0.6µ

To derive the process parameter for another MOS (W=1.5µm, L=0.6µ) transistor,

using the same procedures and calculation method as the previous one.

So, getting the following result:

VT0=0.8147; =0.1861; 264.8 /OXC A V ; =0.6425

Part 2: Comparison with BSIM Model MOS transistor with W=12µm, L=3µ

For the different VGS value, sweeping the VDS from 0 to 5V and measure the

current and getting the following transfer characteristics (Figure (4))

Figure (3)

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Figure (4)

Figure (5)

This is the operating point for the MOS transistor (VDS=4 V, VGS=2Vand VBS=0). AS shown

above, the operating current (ID) is 269.17µA, which is really near to the value

calculated by using the parameters extracted in the previous part. ( The corresponding

value derived in the previous part is 265.2µA. Also, we can measure the slop of this

curve, which is the value of . The value is 1.869µ which has a big difference with the

value derived in the previous part (The value derived in previous part is 0.00737).

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Next, setting the VDS to the operating point and sweeping the VGS from 0 to 5V, we can

the following plot

Figure (6)

Figure (7)

The threshold voltage of this MOS transistor in BSIM model is 733.2mV. The

corresponding value in the square-law model is 549.8mV. The error percentage

approximately is 20.92%. (a little bit difference).

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MOS transistor with W=50µm, L=1um

For the different VGS value, sweeping the VDS from 0 to 5V and measure the

current and getting the following transfer characteristics (Figure (9))

Figure (8)

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Figure (9)

Figure (10)

This is the operating point for the MOS transistor (VDS=5 V, VDS=5Vand VBS=0). AS

shown above, the operating current (ID) is 12.7831mA.

Using the model parameters extracted in the previous part to calculate the operating point:

21

1

50( ) (1 ) 61.36 * (4 0.8)(1 75.17 *5) 9.8

2 1D OX GS T DS

WI C V V V mA

L

12.7831 9.823.34%

12.7831Error

This error is a little bit large.

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Comparing the error calculated for the two different MOS transistor, we can find out that

the error between BSIM model and square-law model when operating near the operating

point and with device dimension close to those used to extract the parameter is relatively

smaller than that of the MOS which is operating at distant operating point with device

dimensions that are substantially different than those used to extract the model parameter.

In my measurement, the error for two different conditions is 20.94% and 23.34%

respectively.

Part 5: Output Conductance Extraction

Using the small signal model to find the

From the equation : 0 DQg I

The equation is shown as Figure (11)

Figure (11)

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Relationship between L and

L I dq(µ) g ds(s) lamada

2.5u 1550 6.886 0.004442581

3.5u 1217 5.106 0.004195563

4.5u 972.9 3.88 0.003988077

5.5u 810.1 3.101 0.003827922

6.5u 708.4 2.632 0.003715415

7.5u 617.9 2.228 0.003605761

8.5u 547.8 1.924 0.003512231

Table (1)

Figure (12)

0.003

0.0032

0.0034

0.0036

0.0038

0.004

0.0042

0.0044

0.0046

0 2 4 6 8

lamada (um)

L (um)

L VS lamada

lamada

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The relationship between L and VDS

Vds (V) Idq (µ) g ds (s) lamada

2.2 261.7 2.212 0.008452

2.4 262.1 2.092 0.007982

2.6 262.5 2.012 0.007665

2.8 262.9 1.956 0.00744

3 263.3 1.916 0.007277

3.2 263.7 1.886 0.007152

3.4 264.1 1.863 0.007054

Table (2)

Figure (13)

Analysis

From the figure (12) and figure (13), the channel length modulation constant of the

MOS transistor is inversely proportional to both the Vds and length L of it.

0.0068

0.007

0.0072

0.0074

0.0076

0.0078

0.008

0.0082

0.0084

0.0086

2 2.5 3 3.5

Vds (v)

L (um) Vds VS lamada

lamada

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Conclusion This lab is useful to make sense about the difference between BSIM model and square-

law model. That is useful for practicing the formula and parameter. The square-law

model has a relatively lager error when comparing with the BSIM model. BSIM model

has 95 process parameters while the square-law model only has 6 process parameters.