This report consists of the analysis of results of evaluation of a 3inch diameter silicon wafer that was fabricated in the clean room at USC under Professor. Kaviani. The wafer consists of resistors, capacitors, MOSFETs and diodes. The device was tested and the results are used to characterize the device. The whole process was done in 100 class clean room, the Powell Foundation Instructional Laboratory. This report will show the calculations performed to do an analysis of the results and will aim to offer an insight into the theory behind the operation of these devices.

1. I
UNIVERSITY OF SOUTHERN CALIFORNIA
DEPARTMENT OF ELECTRICAL ENGINEERING
FABRICATION OF MOSFETS
PREPARED UNDER DR. KIAN KAVIANI
REPORT BY
AKSHATHA SURESH
asuresh@usc.edu
SPRING 2013

2. II
TABLE OF CONTENT:
1. ABSTRACT..........................................................................................................................................1
2. INTRODUCTION............................................................................................................................... 2
3. THEORY............................................................................................................................................. 3
3.1 Resistor ............................................................................................................................................... 3
3.2 Diode....................................................................................................................................................7
3.3 CAPACITANCE.................................................. ..............................................................................10
3.4 MOSFET............................................... .............................................................................................15
4 RESULTS........................................................... ......................................... ....................................... 20
4.1 Resistance...........................................................................................................................................21
4.1.1 Sheet resistance measurement using average method......................................................................21
4.1.2 Sheet resistance measurement using Transmission Line Measurement(TLM) ............................. .22
4.2 PN Diodes...........................................................................................................................................22
4.2.1 The extraction of Vbi( Build-in potential)........... ........................................................................... 22
4.2.2 The extraction of n................................... .............................................................................. ........ 25
4.2.3 The extraction of I0 ......................................... .............................................................................. 25
4.3 Capacitor............................................................................................................................................ 26
4.3.1 The extraction of Tox( The thickness of Gate Oxide): ..........……………………………………..27
4.3.2 The extraction of N sub ................................................................................................................... 27
4.3.3 The extraction of Qss ...................................................................................................................... 27
4.3.4 The extraction of N...........................................................................................................................27
4.4 Mosfet.................................................................................................................................................28
4.4.1 Saturation region, Sqrt(ldss) vs . V gs ............................................................................................ 29
4.4.2 Ids Vs. Vgs ...................................................................................................................................... 30
4.4.3 gm/W VS. Vgs ................................................................................................................................ 31
4.4.4 gd/W VS. Vgs ................................................................................................................................. 31
4.4.5 gm / gd VS . Vgs ............................................................................................................................. 32
5 DISCUSSION ...................................................................................................................................... 33
5.1 Resistance ...........................................................................................................................................36
5.2 PN Diode ............................................................................................................................................ 36
5.3 Capacitor............................................................................................................................................. 36
5.4 Mosfet ................................................................................................................................................ 36
6 CONCLUSION ....................................................................................................................................37
7 REFERENCES ....................................................................................................................................37
8 APPENDICES ..................................... ............................................................................................... 38

3. III
LIST OF FIGURES:
Figure1: Top and cross sectional view of resistor.....................................................................................3
Figure2: Top view of an IC resistor............................................................................................................4
Figure3: Cross sectional view of an IC resistor Resistance ........................................................................4
Figure4: Test structure for transfer line method..........................................................................................5
Figure5: Plot of Distance vs Resistance…………………….......................................................................6
Figure6: IC Resistors…………………....................................................................................................6
Figure7: PN Junction Diode…........................ ......................... ................................................................7
Figure8: PN Diode I-V Characteristics…………........................................................................................8
Figure9: Diode I-V characteristics (Theoretical)………..... .......................................................................8
Figure10: Ideal plot of Ln(I) vs Vf…….....................................................................................................9
Figure11: Non-Ideal plot of Ln(I) vs Vf obtained in the lab……................................................................9
Figurel2: MOS capacitor...........................................................................................................................10
Figure13: MOS capacitor energy band structure………….........................................................................10
Figure14: Flat Band Condition………………………...............................................................................11
Figure15: Accumulation..........................................................................................................................11
Figurel6: Depletion.................................................................................................................................. 12
Figurel7: Inversion..................................................................................................................................12
Figurel8: MOS capacitor C-V characteristics.............................................................................................13
Figure19: Graph for calculation of oxide charges in MOS capacitor...........................................................14
Figure20: Plot of I-V characteristics of MOSFET...................................................................................15
Figure21: Plot of Vgs vs Sqrt(Idss)…….....................................................................................................17
Figure22: Plot of Idss vs Vgs…….…….....................................................................................................17
Figure23: Plot of gm/W vs Vgs ….…........................................................................................................18
Figure24: Plot of (gd/W) vs Vgs ..……......................................................................................................19
Figure25: Plot of gc vs Vgs ……...............................................................................................................19
Figure26: Plot of Distance vs Resistance ……...........................................................................................20
Figure27: Plot of If vs Vf ………..…….....................................................................................................22
Figure28: Plot of ln(If) vs Vf …….............................................................................................................23
Figure29: Plot of ln(If) vs Vf …….............................................................................................................23
Figure30: Plot of ln(If) vs Vf …….............................................................................................................24
Figure31: Plot of ln(If) vs Vf …….............................................................................................................25

4. IV
Figure32: C-V plot of MOS capacitor …................... ................................................................................26
Figure33: Ids vs Vds for MOSFET in saturation and linear......................................................................28
Figure34: Graph of Sqrt (Idss) vs Vgs(volts)..........................................................................................30
Figure35: Plot of Idss Vs Vgss …......................................................................................................31
Figure36 Plot of gm/W Vs Vgs ….....................................................................................................32
Figure37 Plot of gd/W Vs Vgs ….....................................................................................,................33
Figure38 Plot of gm / gd vs Vgs (volts).......... ....................................................................................34
Figure39 Plot of gc vs Vgs …..............................................................................................................35

5. V
LIST OF NOMENCLATURES :
Rsh: Sheet Resistance [ohm/square]
Rc: Ohmic Contact Resistance [ohm/square]
Vbi: Built-in Potential [V]
K: Bolzman Constant =8.617 x 10-5 [e V K^-1]
n: Ideality factor
ε0: Permittivity of the free space = 8.85 *10 14 [F /cm]
Cox: Oxide (Si02) relative permittivity =3.9
tox: Oxide thickness [cm]
Nsub: Doping density of body [cm^-3]
Φf: Fermi Potential [V]
Ld: Deby Length [cm]
Qss: Oxide Charge [F]
Cfb: Flat band capacitance [F]
Vfb: Flat band voltage [V]
Nf: The number of charges per unit area of the capacitor [F/cm2
W: Mosfet width [um]
L: Mosfet channel length [um]
Vth: Threshold Voltage [V]
u(sat): Average mobility of carriers in the channel in saturation region [cm^2/ V.sec]
Vs: Saturation Velocity [cm/sec]
Gm: Transconductance at saturation [mS]
Gd: Output transconductance [mS]
Gc: Channel Conductance [mS]
u(lin): Average mobility of carriers in the channel in linear region [cm^2/V.sec]

6. VI
LIST OF TABLES :
Table1: Extraction of Rsh from R vs Distance(µm) plot... ........................................................................20
Table2: Extraction of Rsh from IC resistors......... ....................................................................................21
Table3: Table of Iteration values to find Nsub........................................................................................27
Table4: Idss Vs Sqrt (Idss).....................................................................................................................29
Table5: gm/W (mS/mm)............................................................................................................................31
Table6: gd/W (mS/mm).............................................................................................................................33
Table7: Channel Conductance gc in Linear region................................................................................35

7. 1
Abstract
This report consists of the analysis of results of evaluation of a 3inch diameter silicon wafer that was
fabricated in the clean room at USC under Professor. Kaviani. The wafer consists of resistors, capacitors,
MOSFETs and diodes. The device was tested and the results are used to characterize the device. The whole
process was done in 100 class clean room, the Powell Foundation Instructional Laboratory. This report will
show the calculations performed to do an analysis of the results and will aim to offer an insight into the
theory behind the operation of these devices.

8. 2
2. Introduction
The transistor was the breakthrough for a new and large family of materials used in technology and
manufacturing. Semiconductors are a special type of crystal whose electrical properties put them between
conductors and insulators.
Initially some uncertainties remained with respect to the manufacture of transistors and diodes with three
and two electrodes, respectively. The factors determining how and why a transistor worked were only
partially understood. The component's surface and surface properties, for example, played an important
role. The same applied to the structure of the material itself, meaning the crystal structure.
Theoretical advances and the development of manufacturing methods therefore went hand-in-hand. An
important advance was achieved in the early 1960s, when silicon replaced germanium as the dominant
material. At first it had been difficult to manufacture silicon crystals. Now it was instead possible to exploit
that material's superior heat-handling properties. Much later, another material, gallium arsenide, would be
used, most often in optical applications. Today, silicon carbide is increasingly used, but silicon is still the
dominant material.
Over the years, manufacturers have learned to produce purer materials and much larger crystals, and
manufacturing methods have been developed that exploit these properties. Crystals can be grown one layer
of atoms at a time, and it is possible to inject the substances that determine the component's characteristics
using ionizing radiation. This makes it possible to precisely specify component characteristics, to achieve
better production economy, and to fit more functions on the same chip.
The ability to combine many functions in the same circuit is based on a breakthrough made independently
around 1960 by Jack Kilby at Texas Instruments and Robert Noyce at Fairchild Semiconductors. The
technology behind this invention has been variously called microelectronics, integrated circuits and planer
technology.
Instead of just making one transistor at a time, it was now possible, using the same piece of silicon and the
same manufacturing process, to create many different components, including not only transistors, but also
diodes (rectifiers) and resistors. This method would make possible such component combinations that
would allow a whole computer to be put on a single chip of silicon as a microprocessor.
In addition to larger and better silicon crystals, another prerequisite for semiconductor development was
continuous improvement in photographic techniques. Integration of many components on a single chip of
silicon was achieved by photographic exposure of layer after layer with a pattern that could later be etched

9. 3
out to form the various components, which now number in the millions on each chip. This rapid and
continuous development was characterized at an early stage by one of the pioneers, Gordon Moore, who
together with Robert Noyce started Intel in 1968. What is now called Moore's Law states that the cost for
raw computing power drops by 50 percent every 18 months – a trend that has held true for several decades.
3. Theory
3.1 Resistors
A linear resistor is a linear, passive two-terminal electrical component that implements electrical
resistance as a circuit element. The current through a resistor is in direct proportion to the voltage across
the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's terminals to the intensity of
current through the circuit is called resistance. This relation is represented by Ohm’s Law:
Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in most
electronic equipment. Practical resistors can be made of various compounds and films, as well as resistance
wire (wire made of a high-resistivity alloy, such as nickel-chrome). Resistors are also implemented
within integrated circuits, particularly analog devices, and can also be integrated into hybrid and printed
circuits.
Figure 1: Cross Sectional view of resistor
The resistance R of a rectangular block of uniformly doped material is given by:
R = ρ.L/A
R = (ρ.L)/(W.t)
R = Rsh (L / W) effective
ρ : Resistivity of the material (ohm – cm)
L : Length of the block (cm)
W: Width of the block (cm)
A : Area of cross section of the block (cm2)

10. 4
t : Thickness of the block (cm)
Rsh : Sheet Resistance of the block (ohm/square)
(L/W) effective: Effective Number of squares
= (L/W) length + (L/W) pads + (L/W) bends
The most commonly used techniques in industrial environment are
 Transmission Line Measurement (TLM)
 Transfer Line Method (also TLM).
3.1.1Transmission Line Method
Figure 2: Top view of an IC resistor
Figure 3: Cross sectional view of an IC resistor
The total Resistance (RT) measured on the scope is sum of the Resistance due to the wire& probe tips
(usually small and neglected) +Resistance due to the contact metal (Rm) + Resistance due to the metal-
semiconductor contact (Ohmic Contact : Rc) and the resistance of the doped layer (Rs).
RT = 2Rm + 2Rc + Rs
Rm value compared to Rc & Rs is small and we usually neglect that, that results in:
RT = 2Rc + Rs
Where:
Rs= Rsh .d / A

11. 5
Using d1 & d2 and their corresponding measured total resistance of RT1 & RT2 we obtain:
RT1 = 2Rc + Rsh.d1 / A
RT2 = 2Rc + Rsh.d2 / A
If we solve the above system for Rc, we obtain:
Rc = (RT1.d2 – RT2.d1)/2(d1 – d2)
Rsh = A(RT1 – RT2)/(d1 – d2)
The disadvantage of this method for finding Rsh is that the “A” or the cross sectional area of the carrier
flow in the IC resistor is needed and that depends on the junction depth (t) of the diffused layer at the end
of the process, and we usually do not have this number available. That is why the Transmission Line
Measurement (TLM) is used more commonly in which we can extract both Rc & Rm simultaneously
without much trouble.
3.1.2 Transfer Line Measurement
Figure4: Test structure for transfer line method
In the transfer line method we measure the resistances across the distances d1, d2, d3, d4, d5, d6.After
obtaining the resistances we plot a graph of distance vs. resistance. From the graph we can extract Rc and
Rsh.

12. 6
Figure 5: Plot of Distance vs Resistance
3.1.3 IC Resistors
Figure 6: IC Resistors
These are the three types of resistors fabricated on the 3” wafer.

13. 7
R400, R800 & R5400. Resistance values are measured for each of these resistors. Using the below
mentioned formula we can calculate the sheet resistance.
R = Rsh (L/W) effective
Here for making the pad corrections in R400, R800 and R5400, we just add 40 micrometers to the nominal
lengths to have 440, 840, and 5440 micrometers accordingly. In the R5400 we need to make the correction
for bends.
3.2 PN DIODES
A pn junction is formed by diffusing a p-type material to an n-type wafer .Vbi is the built in voltage in a pn-
junction diode in equilibrium. VA is the voltage that is applied to the diode terminals.
Figure 7: PN Junction Diode
Applying Va > 0, the diode is forward biased. Reverse bias is when Va < 0. The diode is in equilibrium
when Va = 0. Va is considered positive when the higher potential is applied to the p-side of the diode.
When Va= 0, the Fermi level is constant and we can determine that the diode is in equilibrium. If we reverse
bias the diode, apply Va < 0, we increase the potential hill by lowering then-side of the diode with respect
to the p-side, increasing the barrier to diffusion. If we forward bias the diode, apply Va > 0, we decrease
the potential hill by lowering the p-side of the diode with respect to the n-side, making it almost flat.

14. 8
Figure 8: PN Diode I-V Characteristics
In forward bias operation, the diode will not conduct significant current until the voltage reaches about
0.7V. After that point large increases in current cause little change in voltage.
In reverse bias operation, the diode will not conduct significant current until some breakdown threshold
voltage which is typically quite large (e.g. 200V). This voltage must be somewhat greater than the peak
input voltage (PIV) rating of the diode.
Built in Potential: Vbi
Vbi = (KT/q)ln(Nn.Pp/ni^2)
Figure 9: Diode I-V characteristics (Theoretical)
Using the above assumptions, following a lengthy derivation we can derive the following equation which
describes the current – voltage
(I – V) characteristics of a PN diode:
I = Io [exp (q V/n KT) – 1]
Where:
: V represents the applied bias (V > 0 for forward bias, and V < 0 for reverse bias)

15. 9
: n is a correction factor which takes into account all non – ideal effects and is called ideality
factor and in most cases it is usually between 1 & 2
: Io is the reverse saturation current, (usually in the micro – pico Ampere value).
In the Diode I-V formula, for all practical purposes in the forward bias regime we can rewrite the equation
as:
I = Io exp(qV/nKT)
Taking the natural logarithm of the above relation results in a linear relation for Ln(I) Vs. V;
Ln (I) = Ln(Io) + (q/nKT) V
Values of Io, n and Vbi are extracted from the graphs given below.
Figure 10: Ideal plot of Ln(I) vs Vf
Figure 11: Non-Ideal plot of Ln(I) vs Vf obtained in the lab.

16. 10
3.3 Metal – Oxide – Semiconductor (MOS) Capacitors
Figure 12: MOS capacitor
The MOS capacitor consists of a Metal-Oxide-Semiconductor structure as illustrated by the Figure. It
consists of a semiconductor substrate with a thin oxide layer and a top metal contact, referred to as the gate.
A second metal layer forms an Ohmic contact to the back of the semiconductor and is called the bulk
contact. The structure shown has a p-type substrate. We will refer to this as an n-type MOS or nMOS
capacitor since the inversion layer contains electrons.
3.3.1 MOS Capacitors: Band Structure
Figure 13: MOS capacitor energy band structure

17. 11
Flat Band Condition
Figure 14: Flat Band Condition
The term flat band refers to fact that the energy band diagram of the semiconductor is flat, which implies
that no charge exists in the semiconductor. The flat band voltage is obtained when the applied gate voltage
equals the work function difference between the gate metal and the semiconductor. If there is a fixed charge
in the oxide and/or at the oxide-silicon interface, the expression for the flat band voltage must be modified
accordingly.
MOS Capacitors (V < 0): Accumulation
Figure 15: Accumulation
Accumulation occurs when we apply a voltage less than the flat band voltage. The negative charge on the
gate attracts holes from the substrate to the oxide-semiconductor interface. Only a small amount of band
bending is needed to build up the accumulation charge so that almost all of the potential variation is within
the oxide

18. 12
MOS Capacitors (V > 0): Depletion
Figure 16: Depletion
When we apply higher positive voltages than the flat band voltage, negative charges build up inside the
semiconductor. Initially this charge is due to the depletion of the semiconductor starting from the oxide-
semiconductor interface. The depletion layer width further increases with increasing gate voltage.
MOS Capacitors (V >> 0): Inversion & Threshold
Figure 17: Inversion
As the potential across the semiconductor increases beyond twice the bulk potential, another type of
negative charge emerges at the oxide-semiconductor interface: this charge is due to minority carriers, which
form a so-called inversion layer. As one further increase the gate voltage, the depletion layer width barely
increases further since the charge in the inversion layer increases exponentially with the surface potential.
3.3.2 MOS Capacitors C – V Characteristics

19. 13
Figure 18: MOS capacitor C-V characteristics
Extraction of Oxide Thickness from the C – V data
Cmax=Csio2
Where ε0x: Oxide (SiO2) relative permittivity = 3.9
ε0: Permittivity of the free space = 8.85 X10^-14 (F / cm)
A: Area of the Capacitor (either square with the side of
400mm, or circle with the diameter of 400 mm)
tox: Oxide Thickness (cm)
Csi=(εSiε0A)/W
Csf= CSiCSiO2/(CSi+CSiO2)
Calculation of Nsub

20. 14
• ɸf = (KT/q) ln (NA / ni) > 0 p – type semiconductor (V)
• ɸf = (KT/q)ln(ni/ND)< 0 n – type semiconductor (V)
• Nsub = 4ɸf Csf
2
/(qεSiε0A2
)
Extraction of Oxide Charges
Figure 19: Graph for calculation of oxide charges in MOS capacitor
VFB= ɸMS + Qss/CSiO2
Where ɸMS = ɸM - ɸs
ɸM: Metal work function, for Al gate, 4.10 V
ɸs: Semiconductor work function
ɸs = XSi + Eg/2+ ɸf
Where XSi: Electron Affinity of Silicon = 4.05 V
Eg: Bang gap of Si at T = 300 K = 1.12 V
Ld= (εSiε0KT/q2
NA)1/2
: Deby Length
Flat band capacitance CFB= 1/((1/Cox)+ (Ld/εSiε0A))
The number of charges per unit area of the capacitor ( Nf ) can be found by:
Nf = Qss /(q. Area of the capacitor)
3.4 Metal–oxide–semiconductor Field Effect Transistor (MOSFET)

21. 15
A MOSFET structure comprises of a silicon substrate on which an oxide layer (SiO2) is grown and further
depositing a metal or polycrystalline silicon on the oxide. The SiO2 layer acts as the dielectric thereby
making the structure equivalent to a capacitor, with one of its electrodes replaced by a semiconductor.
A voltage applied across the oxide layer creates a current channel of charges between the source and the
drain. The voltage difference between the source & drain controls the current flow in the structure.
Depending on the kind of charges flowing in the channel it can be categorized as a p-type MOSFET or n-
type MOSFET. This structure can be used for amplifying current or as a switching circuit.
3.4.1 Assumptions made for MOSFET Model
 We assume that we have long channels (L > 5 micrometer)
 We assume the mobility of electrons is constant in the channel.
 We assume that the shape of the channel (same as the MOS inversion layer) as a function of the
drain – source bias changes linearly (gradual– channel approximation, GCA).
 Furthermore, we assume the electric along the channel is the dominant electric field and the
component of electric perpendicular to the channel inside the semiconductor is negligible.
For long channel MOSFETs this is a fairly good approximation.
3.4.2 I-V Characteristics of MOSFET
Figure 20: Plot of I-V characteristics of MOSFET
MOSFET operates in three regions

22. 16
1. Cutoff Regime: When the input voltage Vgs < Vth (threshold voltage) the transitor does not turn
on and hence there is no current flow in the channel.
2. Linear Regime: In this regime the current varies linearly with the applied input bias i.e Drain-
Source voltage and the current equation is given as follows. The MOSFET operates in this region
as long as Vds < Vgs-Vth.
Square Law Model: Linear Regime
Ids= µC0W/L [(Vgs-Vth)Vds-Vds2
/2]
3. Saturation Regime
The MOSFET operates in the saturation region once Vds > Vgs-Vth. During this phase the drain current
saturates. Saturation regime is the most important part of transistors operating regime where
a flat characteristics (at least theoretically) allows the circuit designers use the transistors over a wide
operating voltages. Therefore, most of our device parameter extraction is done in the saturation regime.
Square Law Model - Saturation Region
In order to find Vdss , we realize that the onset of the saturation is where the relationship defined
as square law model has a maximum Ids, therefore in order to find Vds = Vdss, all we need to do is to
differentiate Ids with respect to Vds and solve for Vds. We then find:
Vds = Vdss = Vgs – Vth
Replacing Vds in the square law formula above
we can find an expression for Vdss as:
Square Law Model – Saturation Region
Idss= µC0W/2L (Vgs-Vth)2
The above equation represents the drain current (Idss) in the saturation region. This equation is a function
of Vgs and not Vds.
Extraction of Threshold Voltage
If we take square root of the above relationship we find:
Sqrt(Idss)= Sqrt(µCoW/2L [(Vgs-Vth)2
])

23. 17
Figure 21: Plot of Vgs vs Sqrt(Idss)
From the above plot using the slope value we can extract the average channel mobility at saturation and
from the X-intercept we obtain the threshold voltage.
Saturation Velocity (Vs)
There is also another way of looking at the saturation regime, and that is to attribute the saturation of the
drain current to the carriers in the channel have reached their saturation velocity (Vs).
Modifying the square law model to implement Vs in this equation, we need to replace Vs with:
Vs = μ (Vgs – Vth ) /2L
and rewrite the square law model as:
Idss = VsCoW(Vgs – Vth )
Extraction of Saturation Velocity
Figure 22: Plot of Idss vs Vgs
Using the slope from the above graph, capacitance per unit area and MOSFET width we can extract
saturation velocity.

24. 18
3.4.3 Figures of Merit of MOSFETs for DC characterization:
3.4.3.1 Transconductance : gm
The most important figure of merit of MOSFETs is transconductance (gm) which represent the conductance
(inverse of the resistance) of the channel and is defined as:
gm = ( δIds / δVgs ) at constant Vds.
The units of conductance is [1/ohm] or “mho”, but a more common unit used for gm is Siemens
[S = A/V].
We are usually interested in the transconductance for the saturation regime; therefore, we approximate δIds
/ δVgs with ΔIds / ΔVgs.
Where ΔIds / ΔVgs = (Ids2 – Ids1) / (Vgs2 – Vgs1), we can find values of transconductance at a fixed large
Vds (i.e. Vds > 6 V).
Figure 23: Plot of gm/W vs Vgs
For large values of Vds gm is calculated for different values of Ids and Vgs values. From the above plot we
can get the maximum value of gm and the corresponding Vgs.
3.4.3.2 Output Conductance: gd
The second most important figure of merit for DC characterization of a Field Effect
Transistor is output conductance, gd which is defined as:
gd = ( δIds / δVds ) at constant Vgs
gd ~ ΔIds / ΔVds
gd ~ (Ids2 – Ids1) / (Vds2 – Vds1) at constant Vgs
Now we calculate various gd values for different values of Ids & Vds.

25. 19
Figure 24: Plot of (gd/W) vs Vgs
Now we need to plot a graph of gm/gd against Vgs(V).
From this we need to obtain the maximum value of gm/gd and the voltage swing. The voltage swing is 90%
of the maximum value of gm/gd.
3.4.3.3 Channel Conductance (gc) and Extraction of Mobility in Linear Regime
• Channel conductance is defined as:
gc = ( δIds / δVds ),at constant Vgs
gc = µC0W/L[(Vgs-Vth)-Vds]
In the linear regime Vds values are very small (i.e. Vds < 0.2 V), and therefore we can approximate
the above equation as:
gc = µC0W/L(Vgs-Vth)
Figure 25: Plot of gc vs Vgs
gc ~ ΔIds / ΔVds
gc ~ (Ids2 – Ids1) / (Vds2 – Vds1),at constant Vgs
From the above graph we can extract the mobility in the linear regime using the slope of the graph.

26. 20
4. Results
4.1 Resistors
4.1.1 Rsh measurement using Transfer Line Method
The following values are obtained from the transfer line method.
Transfer Line Method measurements
Table 1: Extraction of Rsh from R vs Distance(µm) plot.
No Distance (µm) Resistance (Ω)
5,4 60 32.82
6,5 100 46.9
7,6 200 85.2
8,7 300 123.7
9,8 380 158.7
Figure 26: Plot of Distance vs Resistance
y = 0.3916x + 8.0032
0
20
40
60
80
100
120
140
160
180
0 50 100 150 200 250 300 350 400
Resistance(Ohm)
Distance(um)
Plot of distance vs resistance
Series1
Linear (Series1)

27. 21
Slope = Rsh/Z, Z=20µm, Rsh = 7.832 ohms
The Y-intercept of this graph gives 2Rc. Therefore, Rc=4 ohms. The slope of the graph is Rsh/Z.
4.1.2 IC Resistors
Table 1: Extraction of Rsh from IC resistors
Length(µm) Effective length(µm) (L/W)effective Resistance(Ω) Rsh = R/(L/W)effective
400 440 22 400 9.091
800 840 42 800 9.523
5400 5440 272 5.4 k ohms 9.9264
Rsh(400) = 9.091 Ω/sq Rsh(5400) = 9.9264 Ω/sq
Rsh(800 )= 9.523 Ω/sq Rsh(avg) = 9.513 Ω/sq.
4.2 PN DIODE
4.2.1 Extraction of Vbi
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
If(Amp)
Vf(V)
Plot of If vs Vf
Series1

28. 22
Figure 27: Plot of If vs Vf
Extracted Vbi value from lab = 0.68 V
4.2.2 Calculation of Ideality Factor (n)
Figure 28: Plot of ln(If) vs Vf
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
ln(If)Amps
Vf(Volts)
Plot of Vf vs ln(If)
Series1
y = 1.318x - 6.6037
-4.69
-4.68
-4.67
-4.66
-4.65
-4.64
-4.63
-4.62
1.45 1.46 1.47 1.48 1.49 1.5 1.51
ln(If)Amps
Vf(Volts)
Region 1
Series1
Linear (Series1)
Slope1 =1 .318

29. 23
Figure 29 Plot of ln(If) vs Vf
Figure 30 Plot of ln(If) vs Vf (volts)
y = 6.5072x - 12.694
-14
-12
-10
-8
-6
-4
-2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
ln(If)Amps
Vf(Volts)
Region 2
Series1
Linear (Series1)
Slope2 = 6.5072
y = 22.367x - 19.974
-12.7
-12.6
-12.5
-12.4
-12.3
-12.2
-12.1
-12
-11.9
-11.8
ln(If)Amps
Vf(Volts)
Region 3
Series1
Linear (Series1)

30. 24
Figure 31 Plot of ln(If) vs Vf (volts)
From the graph we get Slope1 = 1.8812, Slope 2 = 3.3944 , Slope 3 = 29.12
Slope of region 3 SLOPE (3) = 22.367 => n3 = (38.46) / (22.367) => n1 = 1.719
Slope of region 2 SLOPE (2) = 6.5072 => n2 = (38.46) / (6.5072 ) => n2 = 5.91
Slope of region 1 SLOPE (1) = 1.3180 => n1 = (38.46) / (1.318) => n3 = 29.18
The leakage current is found by extending the third slope backwards to intersect
with the Y axis. The value of Y intercept is ln(Io).
From the graph the value of IO can be found out as IO= exp (-19.974)
Leakage current IO = 2.115 uAmps
4.3. MOS Capacitor
All capacitor calculations were carried out on a circular capacitor of diameter 400μm.
0.00E+00
5.00E-11
1.00E-10
1.50E-10
2.00E-10
2.50E-10
-1.20E+01 -1.00E+01 -8.00E+00 -6.00E+00 -4.00E+00 -2.00E+00 0.00E+00 2.00E+00 4.00E+00
Capacitance(F)
Vbias(V)
CV plot of capacitor
Series1

31. 25
Figure 32: C-V plot of MOS capacitor
From the above graph we can extract the maximum & minimum values of capacitance which gives us the
CSiO2 & CSi values.
4.3.1 Extraction of Oxide Thickness
From the graph, CSiO2 = Cmax = 218 pF and CSi = 27.7 pF = Cmin
Cross sectional area of the circular capacitor of diameter 400µm is given as A = π * r2
, r = 200µm
A = 1.256E-3 cm2
CSiO2= εoxε0A/tox
218 pF= 3.9*8.85*10-14
*1.256 * 10-3
/ tox
From above calculations, tox = 198.85 Å.
4.3.2 Calculation of Nsub
Csf = CSiCSiO2 / (CSi+CSiO2) = 24.57 pF
ɸf = (KT/q) ln (NA / ni)
Nsub = 4ɸf Csf
2
/(qεSiε0A2
)
Table 2: Calculation of Nsub by iteration
NA(cm-3
) ɸf(V) Nsub(cm-3
)
1016
0.3855 1.068 x 1016
1.068 x 1016
0.34868 9.66494 x 1015
9.66494 x 1015
0.3461 9.593314 x 1015
9.593314 x 1015
0.3459 9.587979 x 1015
9.587979 x 1015
0.34589 9.587978 x 1015
In the above calculations we start with Nsub = NA = 10E16 cm-3
Thus, NA= 9.587979 x 1015
cm-3
, ɸf = 0.34589V

32. 26
4.3.3 Extraction of Oxide charges
Deby Length Ld = (εSiε0KT/q2
NA)1/2
= 2.4128 E-6 cm
Here Cox = Cmax = 218 pF
CFB= 1/((1/Cox)+ (Ld/εSiε0A)) = 98.54 pF
From the C-V plot we can extract VFB ≈0.4V
VFB= ɸMS + Qss/CSiO2 ɸM = 4.10 V, ɸs = XSi + Eg/2+ ɸf, XSi= 4.05 V, Eg= 1.12 V
0.4 = 4.1-(4.05+(1.12/2)+ 0.34589 )+ Qss/218pF
From the above equation, we get Qss= 2.73784 E-10 C
The number of charges per unit area of the capacitor ( Nf ) can be found by
Nf = Qss /(q. Area of the capacitor) = 1.3624 E 12 cm-2
4.4 MOSFET Calculations
4.4.1 Calculation of Threshold voltage & Channel Mobility in Saturation
The electrical parameters calculated below were extracted from a MOSFET device with channel width W
= 40 µm and channel length L=16 µm.
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
0 2 4 6 8 10 12 14 16
Ids(A)
Vds(V)
Vds vs Ids Curve
Series1
Series2
Series3
Series4
Series5
Series6
Series7
Series8
Series9
Series10
Series11

33. 27
Figure 33a. Vds vs Ids curve in saturation for MOSFET W = 40 µm
Figure 33 (b) Ids vs Vds for MOSFET in linear
Vgs (Volts) Idss Amps Sqrt (Idss) Amps
0 3.15 E-04 0.017748239
1 6.33 E-04 0.025159491
2 1.16 E-03 0.034058772
3 1.86 E-03 0.043127717
4 2.74 E-03 0.052345009
5 3.75E-03 0.061237243
6 4.89 E-03 0.069928535
7 6.10 E-03 0.078102496
8 7.39 E-03 0.085965109
9 8.71 E-03 0.093327380
10 1.01 E-02 0.100498756
11 1.14 E-02 0.106770782
12 1.27 E-02 0.112249722
Table4 Idss Vs Sqrt (Idss)
-5.00E-05
0.00E+00
5.00E-05
1.00E-04
1.50E-04
2.00E-04
0 0.02 0.04 0.06 0.08 0.1
Ids(A)
Vds(V)
Vds vs Ids
Series1
Series2
Series3
Series4
Series5
Series6
Series7
Series8
Series9
Series10
Series11

34. 28
Figure 34 Graph of Sqrt (Idss) vs Vgs(volts)
From the graph the value of Vth is Vth = -2.2 volts
Co= CSiO2/A = 218*10-12
/1.256*10-3
= 17.35668 x 10-8
F / cm2
The slope of the above graph is SQRT(µC0W/2L) = 0.0081
(µ)saturation = 256.934 cm2
/(V.s)
4.4.2 Extraction of Saturation Velocity
y = 0.0081x + 0.0191
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
-4 1 6 11 16
Sqrt.Idss(A)
Vgs(V)
Sqrt. Idss vs Vgs
Sqrt. Idss
Linear (Sqrt. Idss)
Vth = -2.2V
y = 0.0011x - 0.0009
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
0 2 4 6 8 10 12 14
Idss(A)
Vgs(V)
Idss vs Vgs
Series1
Linear (Series1)
Slope = 0.0011

35. 29
Figure 35 Plot of Idss Vs Vgss
Slope = Vs Co W slope = 0.0011
Hence Vs = 0.15844 E6 cm/s
4.4.3 Extraction of Transconductance (gm)
Vgs1(V) Ids1(A) Ids2(A) Vgs2(V) Ids2-Ids1 gm(mS) gm/W(mS/mm)
0 3.15 E-04 6.33 E-04 1 3.18E-04 0.318 7.95
1 6.33 E-04 1.16 E-03 2 5.27E-04 0.527 13.175
2 1.16 E-03 1.86 E-03 3 0.7E-03 0.7 17.5
3 1.86 E-03 2.74 E-03 4 0.88E-03 0.88 22
4 2.74 E-03 3.75E-03 5 1.01E-03 1.01 25.25
5 3.75E-03 4.89 E-03 6 1.14E-03 1.14 28.5
6 4.89 E-03 6.10 E-03 7 1.21E-03 1.21 30.25
7 6.10 E-03 7.39 E-03 8 1.29E-03 1.29 32.25
8 7.39 E-03 8.71 E-03 9 1.32E-03 1.32 33
9 8.71 E-03 1.01 E-02 10 1.39 E-03 1.39 34.75
10 1.01 E-02 1.14 E-02 11 0.13 E-02 1.3 32.5
11 1.14 E-02 1.27 E-02 12 0.13 E-02 1.3 31.9
12 1.26 E-02 1.39E-02 13 0.13E-02 1.3 31.1
Table 5 gm/W (mS/mm)

36. 30
Figure 36.(gm/W) vs Vgs
From the graph we get maximum value of (gm/w) = 33.75 mS/mm at Vgs = 9V
4.4.4 Calculation of output conductance (gd)
In the saturation region gd is defined as ΔIds / ΔVds which is further equal to (Ids2 – Ids1) / (Vds2 –Vds1)
at constant Vgs.
Vds = 10V & Vds = 11V for the calculation of gd are considered.
Vgs(V) Ids1(A) Ids2(A) gd(mS) gd/W(mS/mm)
0 3.15E-04 3.31E-04 0.016 0.4
1 6.33E-04 6.57E-04 0.024 0.6
2 1.16E-03 1.19 E-03 0.03 0.75
3 1.86 E-03 1.91 E-03 0.06 1.5
4 2.74 E-03 2.78 E-03 0.04 1
5 3.75 E-03 3.8 E-03 0.05 1.25
6 4.89 E-03 4.93 E-03 0.04 1
7 6.10 E-03 6.14 E-03 0.04 1
8 7.39 E-03 7.42 E-03 0.03 0.75
9 8.71 E-03 8.75 E-03 0.04 1
y = 1.9067x + 14.646
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14
gm(mS)/W(mm)
Vgs(Volt)
gm(mS)/W(mm) vs Vgs
Series1
Linear (Series1)

37. 31
10 1.01 E-02 1.01 E-02 0.0 0
11 1.14E-02 1.15 E-02 0.1 2.5
12 1.26E-02 1.28 E-02 0.2 5
Table 6 gd(mS)/W(mm)
Figure 37 gd(mS)/W(mm) vs Vgs
From the graph the maximum value of gd is obtained as gd max = 5
4.4.5 Extraction of maximum (gm/gd ) & the voltage swing (ΔVgs)
Figure 38.Plot of gm / gd vs Vgs (volts)
0
1
2
3
4
5
6
0 2 4 6 8 10 12 14
gd(mS)/W(mm)
Vgs(V)
plot of gd(mS)/W(mm) vs Vgs
Series1
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12
gm/gd
Vgs(volts)
gm/gd
Series1

38. 32
The above plot gives a (gm/gd) max = 16.85, 0.9*(gm/gd) max = 15.165. From this we get voltage swing
= 1 V.
4.4.6 Channel Conductance (gc) & Extraction of Mobility in Linear Regime
In linear regime, gc = ΔIds / ΔVds = (Ids2 – Ids1) / (Vds2 – Vds1) at Vgs = constant.
The value of Vds2 = 0.09 and Vds1 = 0.08 are taken for calculating gc
Vgs(volts) Ids2 Ids1 gc
0 1.92E-05 1.71E-05 2.1E-04
1 4.64E-05 4.15E-05 4.9E-04
2 6.77E-05 6.08E-05 6.9E-04
3 8.69E-05 7.76E-05 9.3E-04
4 1.04E-04 9.35E-05 1.05E-03
5 1.2E-04 1.07E-04 1.3E-03
6 1.34E-04 1.21E-04 1.3E-03
7 1.47E-04 1.32E-04 1.5E-03
8 1.58E-04 1.41E-04 1.7E-03
9 1.67E-04 1.49E-04 1.8E-03
10 1.74E-04 1.56E-04 1.8E-03
Table 7 Channel Conductance gc in Linear region
Figure.39.Plot of gc vs Vgs
slope = µCoW/L, slope = 0.0002
(µ)linear = 201.34 cm2
/ ( V.s )
y = 0.0002x + 0.0004
0.00E+00
5.00E-04
1.00E-03
1.50E-03
2.00E-03
2.50E-03
0 2 4 6 8 10 12
gc
Vgs(V)
gc vs Vgs
Series1
Linear (Series1)
Slope =

39. 33
5. DISCUSSION
5.1. Resistors
The resistances were calculated from three different resistors of length 400 µm , 800 µm and 5400
µm. The resistance values of TLM N20 were also calculated. The Sheet resistance Rsh was
calculated from the measured resistances. The sheet resistances are as follows
Rsh(400) = 9.091 Ω/sq
Rsh(800 ) = 9.523 Ω/sq
Rsh(5400) = 9.9264 Ω/sq
Rsh(avg) = 9.513 Ω/sq.
The sheet resistance of TLM N20 and Rc were calculated as Rc = 4 ohms and Rsh (TLM N20
) = 7.832 ohms / square.
5.2 PN DIODE
The extracted values of PN diode are as follows Vbi = 0.68 volts , n1 = 1.718 , n2 = 5.91, n3 = 29.18.
The Vbi is built potential and is usually in the order of 0.58 and here the value of Vbi
is in orders of 0.6 volts. The ideality factor n obtained is little far from each other.
The leakage current is in order of micro amperes here. But in industry with billion transistors
the leakage current is order of nano amperes.
5.3. MOS CAPACITORS
The value of MOS capacitors calculated are as follows
Vth = -2.5 volts
(µ)saturation = 256.934 cm2
/(V.s)
Saturation velocity Vs = 0.15844E06 cm/s
(gm/W)max = 33.75 mS/mm
(gd/W)max = 5 mS/mm
(gm/gd) max = 16.85 voltage swing = 1 V
(µ)linear = 201.34 cm2
/(V.s)
The ionic charges trapped because of dangling bonds or unsatisfied bonds cause a negative shift
in threshold voltage. The threshold voltage is negative because of that. In industry usually a
threshold adjustment is done to compensate for the negative shift in threshold voltage. Also
here the value of saturation velocity in linear regime is little less that the saturation
velocity in saturation region.

40. 34
6. CONCLUSION
This course provides a in depth understanding of the fabrication process starting from cleaning
the wafer and all the way until testing. The CMOS lectures provides a knowledge about how
the structure looks in actual process. This provides insight in to some concepts of Solid state
devices. The clean room experience was invaluable and one of few rare opportunities to get hands
on training on fabrication of a wafer. The testing of fabricated wafer gives a profound
knowledge of the testing IC in industry. IC testing is one of the areas to get good chips
and to make reliability of chips manufactured. This course provides a full overview and
knowledge of all such process.
7. REFERENCES
[1]http://www.eecs.berkeley.edu/~hu/Chenming-Hu_ch5.pdf.
[2]http://ecee.colorado.edu/~bart/book/book/chapter6/ch6_2.htm.
[3]Donald.A.Neamen "Semconductor Physics and Devices - Basic Principles" McGraw Hill third
edition.
[4] http://cc.ee.ntu.edu.tw/~lhlu/eecourses/Electronics1/Electronics_Ch5.pdf.
[5] EE 504L-Solid State Processing and Integrated Circuit Laboratory Lecture notes by Dr. Kian Kaviani,
Summer 2012,Viterbi School of Engineering, University of Southern California.