LAB IX. METAL OXIDE SEMICONDUCTOR
FIELD EFFECT TRANSISTORS
1. OBJECTIVE
In this lab, you will study the I-V characteristics and small signal model of Metal Oxide
Semiconductor Field Effect Transistors (MOSFET).
2. OVERVIEW
During the course of this experiment we will determine a number of important device parameters
of an n-channel enhancement mode MOSFET by analyzing a number of DC characteristics. The
DC characteristics will be split up into three ranges: the sub threshold region (VGS < VT), the
linear region (VT < VGD, VGS > VT), and the saturation region (VT > VGD, VGS > VT). You will
learn the relevance of the current pre-factor ( nCi Z / L ), the channel transconductance (gm), the
channel conductance (gDS), and the channel resistance rd.
Information essential to your understanding of this lab:
1. Theoretical background of the MOSFET (Streetman 6.4.1-6.4.4 & 6.5.1-6.5.2)
Materials necessary for this Experiment:
1. Standard testing station
2. One MOSFET (Part: 2N4351)
3. 1kΩ resistor
3. BACKGROUND INFORMATION
3.1 CHART OF SYMBOLS
Here is a chart of symbols used in this lab manual. This list is not all inclusive; however, it does
contain the most common symbols and their units.
Table 1. Chart of the symbols used in this lab.
Symbol
Symbol Name
Units
Qi
Qd
Ci
iDS
total charge in the insulator
total charge in the depletion region
insulator capacitance
total drain to source current
DC drain to source current
AC drain to source current
saturation drain current
Intrinsic energy level
Fermi energy level
potential difference between intrinsic
energy level and the Fermi-level
metal-semiconductor work function
difference
voltage applied to the semiconductor
material
Pinch-off voltage
total drain to source voltage
DC drain to source voltage
C
C
Farads
mA
mA
mA
mA
eV
eV
DS
ids
IDSAT
Ei
EF
F
MS
VA
VP
vDS
VDS
10-1
V
V
V
V
V
V
vds
vGS
VGS
Vgs
gm
gDS
L
Z
WMax
n
AC drain to source voltage
Total gate to source voltage
DC gate to source voltage
AC gate to source voltage
Transconductance
channel conductance
length of channel
width of channel
max distance the depletion width induced
by the gate can extend
V
V
V
V
scale factor
-1
siemens (S) or mhos ()
Cm
Cm
cm
2
cm / V-sec
average electron mobility
3.2 CHART OF EQUATIONS
All of the equations from the background portion of the manual are shown in the table below.
Table 2. Chart of the equations used in this lab.
Equation Name
1
Square law approximation
of drain to source current
2
3
4
5
6
Saturation voltage for a
MOSFET
Square law approximation
of saturated drain to source
current
Channel conductance
Transconductance in the
linear region
Transconductance in the
saturation region
Formula
I DS 
VDSAT
 n ZCi
2
L
 VGS  VT
I DSAT 
g DS 
gm 
[(VGS  VT )VDS  .5  VDS ]
 n ZCi
2L
(VGS  VT ) 2
I DS
I
 CZ
 DS  ( n i )(VGS  VT  VDS )
VDS VDS
L
I DS
VGS
g m sat. 

VDS const.
I DS
VGS
I DS sat.
VGS V
(
VDS  const.
(
DS  const.
 n Ci Z
L
 n Ci Z
L
)VDS
)VGS  VT 
3.3 CURRENT IN A MOSFET
When solving for the current in a MOSFET the first step is to find the conductivity between the
source and the drain. To do this you must integrate each of the differential conductance elements
in the channel from drain to source. After integrating the differential conductance elements the
current in the channel of a MOSFET reduced to,
I DS 
 n ZCi
[(VGS  VT )VDS  0.5  VDS ]
2
(1)
L
where  n is the average electron mobility at the Si-SiO2 interface in the channel area, Z is
the width of the channel, Ci is the capacitance of the oxide layer under the gate, and L is
the length of the channel.
The above equation holds true until pinch-off is reached. When the channel is pinched off,
the drain to source voltage is said to be saturated. The saturation voltage can be found by the
following:
10-2
VDSAT  VGS  VT .
(2)
When the drain to source voltage saturates, the drain to source current is also saturated and it is
given by:
I DSAT 
n ZCi
2L
(VGS  VT )2
(3)
When the current saturates, it is no longer a linear function of the drain voltage.
3.4 DEVICE PARAMETERS OF MOSFETS
There are several ways of representing the drain current response of the MOSFET as a function of
VDS and VGS. Each method of representation gives unique perspective of the device performance.
Of those, Figure 1 is the most common representation.
Figure 1. IDS vs. VDS characteristic of an n-channel MOSFET.
Another commonly used representation is IDS1/2 vs. VGS as shown in Figure 2 which was obtained
by biasing the device so that the gate and the drain are at the same potential. Connecting the gate
and the drain contacts together and connecting these leads to the drain power supply does this. In
this connection, saturation condition is satisfied for all applied voltages where VGS > VT. Taking the
square root of both sides of equation (3) yields a linear relationship between IDS1/2 and VGS – VT.

The dependence of  n ZCi / 2 L

1/ 2
on the gate voltage is also shown in Figure 2. The values are

obtained from the derivative of the IDS1/2 vs. VGS dependence. The max value of  n ZCi / 2 L
0.04 A1/2/V at VGS = 3 V.
10-3

1/ 2
is
Figure 2. The IDS1/2 as a function of VGS for the case of VGS = VDS.
In the linear I-V region, the MOSFET acts as a resistive load and its conductance is linearly
dependent upon the gate voltage. The channel conductance, gDS, in the linear region is given by:
g DS 
I DS
VDS

VGS cons tan t
I DS
VDS
(
VGS  cons tan t
 n Ci Z
L
)(VGS  VT  VDS ) 
1
rd
(4)
`
The channel conductance is an important parameter used in the design of analog switching circuits.
It makes possible MOSFET switching circuits without the use of resistors. Note that at the
saturation condition the channel conductance is (theoretically) zero.
Experimentally, the channel conductance in the linear region is measured by holding VDS to a value
of 50 mV to ensure linear operation. The gate voltage is varied from 0 V to 10 V as the drain
current is measured. The value of gDS can then be plotted by use of (4). Figure 3 shows the
measured dependence of gDS as a function of VGS. It indicates that the channel conductance
increases nearly linearly with VGS above threshold. It is also instructive to note that the slope of this
curve is given by  n ZCi / L in the equation (4).
The channel resistance, rd, can be found by the inverse of the channel conductance gDS. However,
while the channel conductance gDS of the MOSFET is of interest in the linear region, the channel
resistance rd is of interest typically in the saturation region. Theoretically the channel resistance at
the saturation condition is expected to be infinite. However, realistic MOSFET have finite values
of the channel resistance. The channel resistance is an essential component of the small signal
model of a MOSFET (Figure 4). By knowing the channel resistance of a MOSFET, you can match
the load resistance and the MOSFET channel resistance. As a result, you can maximize the gain of
your amplifier. Experimentally you may find the slope of the IDS vs VDS characteristic in the
saturation region and invert it to find the channel resistance rd.
As indicated in the equation (4), the channel resistance rd is given by the inverse of the channel
conductance. Figure 5 shows the measured channel resistance rd as a function of VDS with VGS
ranging from 2.5V to 5V in 0.5 V increments.
10-4
Figure 3. The measured drain conductance as a function of VGS, for VDS = 0.050 V.
Figure 4. Small signal model of the MOSFET.
Figure 5. The channel resistance, rd, as a function of VDS for several values of VGS.
10-5
The transconductance, gm is typically utilized in the saturation region in conjunction with the small
signal model of a MOSFET to build an amplifier circuit. The transconductance describes the effect
the gate has on the conductivity of the MOSFET at a certain operating point. The transconductance
of a MOSFET in the linear region is:
gm 
I DS
VGS

VDS const.
I DS
VGS
(
 n Ci Z
VDS  const.
L
)VDS .
(5)
In the saturation region the equation (5) may be used if you substitute the VD,SAT for VDS where
VD,SAT =VGS-VT.
g m sat. 
I DS sat.
VGS V
(
DS  const.
 n Ci Z
L
)VGS  VT  .
(6)
The Figure 6 shows the measured gm as a function of VGS which was obtained by measuring the
amount of the drain current change versus the gate voltage change with a fixed VDS. It can be seen
that there is essentially no current flow and gm is zero when VGS < VT (before threshold). For 0 <
VGS – VT < VDS , the MOSFET operates in the saturation region and the gm is increasing linearly
with increasing VGS – VT. At higher values of VGS (VGD > VT), the MOSFET operates in the linear
region and the gm levels off corresponding to operation in the linear region.
Figure 6. The transconductance, gm, as a function of VGS for various fixed VDS values.
If you know the geometry of your MOSFET, you can find the value of the prefactor,  n ZCi / 2L . L
is the length of the channel; Z is the width of the channel. Ci is the capacitance of the SiO2
insulating layer and is given by: Ci=r/toxide, where toxide is the thickness of the oxide layer.  n is
the average electron mobility in the channel area. The average electron mobility in the channel
area of the average silicon MOSFET is about 650 cm2/V-sec. These values can be used to calculate
the drain current at a given gate voltage.
4. PRE-LAB REPORT
Study sections 3.3 – 3.4 of the lab manual then do the following pre-lab. If you have read and
understood the background material, then this prelab should take you no longer than 30 minutes so
do not be intimidated by the number of questions. Many will take less than a minute.
10-6
IDS1/2 dependence on VGS
Use the 2N4351 IDS1/2 – VGS data, Figure 2, to obtain the following parameter values.
a. Estimate the value of VT.
b. Estimate the value of the prefactor, nCi Z/(2L), from the derivative curve at
VGS = 3V.
2. Channel conductance (gDS) dependence on VGS
Use the 2N4351 gDS – VGS data, Figure 3, to obtain the following parameter values.
a. Estimate the value of VT.
b. Estimate the value of 2x the prefactor, nCi Z/(L), from the derivative slope
between VGS = 2V and VGS = 4V using (4).
1.
3. Transconductance (gm) dependence on VGS
Use the 2N4351 gm – VGS data, Figure 6, to obtain the following parameter values.
a. Estimate the value of VT.
b. Estimate the value of 2x the prefactor, nCi Z/(L), from the derivative slope
between VGS = 2V and VGS = 4V using (6).
4.
Drain resistance (rd) dependence on VGS
Use the 2N4351 rd – VDS data, Figure 5, to obtain the following parameter values.
a. Use the slope of the drain characteristic, IDS vs. VDS data, Figure 1, to estimate
the value of rd at VDS = 5V for the VGS = 2.5V and 3.5V curve.
b. Use the drain resistance curves, rd vs. VDS data, Figure 5, to estimate the value
of rd at VDS = 5V for the VGS = 2.5V and 3.5V.
c. Compare these values of the drain resistance, rd.
5. PROCEDURE
5.1
IDS-VDS CHARACTERISTICS
Identify the leads of the MOSFET 2N4351 using the Figure 7 and construct a circuit shown
in Figure 8. Be sure the substrate (or case or bulk) terminal is connected to the source
terminal and both are connected to the grounded side of the circuit as shown in Figure 8.
The lower Keithley is used to supply VGS and the upper Keithley is used to supply VDS. Use
the LabView program, FET_ivcurve.vi, to obtain IDS-VDS characteristic curves. Perform
both (a) and (b) below. Use estimated VT found in the prelab. These characteristics are
used to determine the parameters of the transistor in your report, so accurate measurements
are needed.
a. VDS = 0V to 10V in 0.2V steps with VGS = VT – 0.5V to VT + 0.5V in 0.2V steps.
b. VDS = 0V to 10V in 0.2V steps with VGS = VT to 5V in 0.5V steps.
Figure 7. Identification of the leads on the MOSFET 2N4351.**
**In some cases the device will have an antistatic wire wrapped around all four leads. This wire should be
removed prior to using the device as it will short all four leads together.
10-7
Figure 8. A circuit for obtaining the IDS-VDS, gm-VGS, gDS-VGS, and rd-VGS characteristics.
5.2
gDS DEPENDANCE ON VGS
Use the circuit shown in Figure 8 and the LabView program, FET_gds.vi, to measure the
gDS dependence on VGS in the linear region. Set VDS to 100 mV and the gate voltage is to be
varied from 0.0 V to 10.0 V. The value of gDS is obtained by dividing the measured current
IDS by the constant VDS = 100 mV.
5.3
rd DEPENDANCE ON VGS
Use the circuit shown in Figure 8 and the LabView program, FET_rds.vi, to measure the
rd dependence on VGS in the saturation region. Set VDS to vary from 0.0 V to 10.0 V in 0.1 V
steps with VGS = 2.5 V, 3.0 V, 3.5V, 4.0 V, 4.5V, and 5.0 V.
5.4
gm DEPENDANCE ON VGS
Use the same circuit of Figure 8 and the LabView program, FET_gm.vi to measure the gm
dependence on VGS. Set VGS to vary from 0.0 V to 10.0 V in 0.1 V steps with VDS = 1.0V,
3.0 V, and 5.0 V.
5.5
IDS1/2-VGS CHARACTERISTIC
Use the circuit of Figure 9, and the LabView program, FET_ivcurve.vi, to obtain a set of
IDS – VGS characteristics curves. Set VDS = 0.0 V to 10.0 V in 0.2V steps. Note that the only
difference between this measurement and the first measurement is the addition of a wire.
This additional wire causes VDS = VGS so that IDS – VGS data may be extracted for this
device. Manipulate this data to obtain curves similar to Figure 2 using the i array method


1/ 2
1/ 2
of numeric differentiation with the following equation: I DS (i  1)  I DS (i  1) . For the
VGS (i  1)  VGS (i  1)
report, you will obtain the values of VT and nCiZ/2L from this data.
10-8
Figure 9. A circuit for obtaining the IDS1/2-VGS characteristics.
6. LAB REPORT



Write a summary of the experiment.
IDS-VDS characteristics
o Plot the IDS vs. VDS characteristic. Show the pinch-off locus in the plot. Make sure both
axes are labeled and the graph is appropriately titled.
gDS dependence on VGS
o Show the plot of the gDS vs. VGS curves. Make sure both axes are labeled and the graph
is appropriately titled.
o Mark your plot to show VT.
o Report the values you obtained for VT and  n ZCi / 2 L from this data.


rd dependence on VGS
o Plot the rd vs. VGS characteristic. Make sure both axes are labeled and the graph is
appropriately titled.
o Calculate the value of rd using the derivative method with
rd (i) 


VDS (i  1)  VDS (i  1)
I DS (i  1)  I DS (i  1)
from the IDS vs. VDS characteristic. Compare the
calculated values and the measured values of rd.
gm dependence on VGS
o Show the plot of the gm vs. VGS curves. Make sure both axes are labeled and the graph
is appropriately titled.
o Mark your plot to show VT.
o Report the values you obtained for VT and  n ZCi / 2 L from this data.
o Using the IDS vs. VDS characteristics, calculate the value of gm using the following
equation:

g m (i) 
I DS (i  1)  I DS (i  1)
VGS (i  1)  VGS (i  1)
.

Compare the calculated values and the
measured values of gm.

IDS1/2-VGS characteristic
o Show the plot of the IDS1/2 vs. VGS curves. Make sure both axes are labeled and the
graph is appropriately titled.
10-9
o
o

Mark your plot to show VT.
Report the values you obtained for VT and  n ZCi / 2 L from this data.
Conclusions:
o Compare the different values you found for VT and  n ZCi / 2 L from the various



o

characteristics.
In your opinion which characteristic is the best one to use to find VT
and  n ZCi / 2 L ? Explain your answer.
10-10