This document discusses techniques for characterizing electronic devices, focusing on electrical and electrochemical methods. It provides an overview of Ohm's law and how resistance is established through current-voltage relationships. Resistivity and resistance are defined, and their relationship illustrated through common formulas. Conductance is also introduced. Voltage-current characteristics are described for different materials, including how they can be used to measure conductivity. The 4-probe technique for resistance measurement is compared to the 2-probe method, highlighting how it overcomes limitations like contact resistance and ensures more accurate resistivity measurements.

1. Characterization Techniques
for Electronic Devices
Electrical and Electrochemical Techniques
BY HAMED Y. Mohammed

2. Ohm’s Law and Resistance
Ohm’s law states that the voltage or potential
difference between two points is directly proportional
to the current or electricity passing through the
resistance, and directly proportional to the resistance of
the circuit. The formula for Ohm’s law is V=IR. This
relationship between current, voltage, and relationship
was discovered by German scientist Georg Simon Ohm.
Let us learn more about Ohms Law, Resistance, and its
applications.

4. How do we establish the current-voltage relationship?
 In order to establish the current-
voltage relationship, the ratio V
/ I remains constant for a given
resistance, therefore a graph
between the potential difference
(V) and the current (I) must be a
straight line.


5. Resistivity
 Resistivity (ρ) is a fundamental
property of a material that
quantifies how strongly it resists
the flow of electric current. It is
specific to each material and is an
intrinsic characteristic that
depends on factors such as
temperature and the material's
chemical composition. The
resistivity of a material
determines how much resistance
it will offer to the flow of electric
current.

6. Resistance and Resistivity:
 Resistance (R) is a measure of how difficult it is for electric current to
pass through a given object or material. It depends on both the resistivity
of the material and its dimensions. The relationship between resistance,
resistivity, and the physical dimensions of the material is described by the
following formula:
R = ρ * (L / A)
 Where: R is the resistance of the material (measured in ohms, Ω), ρ (rho)
is the resistivity of the material (measured in ohm-meters, Ω·m), L is the
length of the material (measured in meters, m), A is the cross-sectional
area of the material (measured in square meters, m²).
 From this formula, we can see that resistance is directly proportional to
the resistivity of the material and the length (L) of the material, and
inversely proportional to its cross-sectional area (A). Therefore, materials
with higher resistivity or longer lengths will have higher resistance, while
materials with larger cross-sectional areas will have lower resistance.

7. Conductance:
Where: G is the conductance (measured in siemens, S), R is the
resistance (measured in ohms, Ω).
G = 1 / R
Conductance (G) is the reciprocal of resistance. It is a measure of how easily electric
flow through a material. The concept of conductance is used to quantify the opposite
of resistance, which is the ease of electric flow. The formula for conductance is:

8. Conductivity by Voltage-Current (I-V)
Characteristics
 he Voltage-Current (I-V) characteristics describe the relationship between the voltage applied across a
material and the resulting current flowing through it. This relationship is crucial in understanding the
behavior of different materials concerning their electrical conductivity. The I-V curve can provide insights
into how a material responds to changes in voltage and how it conducts electricity.
 For different materials, the I-V characteristics can be broadly classified into three types:
1. Ohmic Conductors: Ohmic conductors, also known as linear conductors, exhibit a linear
relationship between voltage and current. In other words, their I-V curves are straight lines passing through
the origin (0, 0) on a graph. The resistance of ohmic conductors remains constant, regardless of the
magnitude of the applied voltage. The conductivity (σ) of an ohmic conductor can be determined by
measuring the slope of its I-V curve:
σ = ΔI / ΔV
 Where: σ is the conductivity (measured in siemens per meter, S/m), ΔI is the change in current (measured in
amperes, A), ΔV is the change in voltage (measured in volts, V).
 Example: Most metallic conductors like copper, aluminum, and silver exhibit ohmic behavior under normal
operating conditions.

9. 2.Non-Ohmic Conductors: Non-ohmic conductors, also known as
non-linear conductors, do not follow a linear relationship between voltage and current.
The I-V curves for these materials are curved rather than straight lines. The resistance
of non-ohmic conductors varies with the magnitude of the applied voltage. As a result,
the conductivity of non-ohmic conductors cannot be determined directly from a single I-
V curve. Instead, it requires more complex mathematical models or separate
measurements at different voltage levels to assess their conductance accurately.
 Example: Semiconductor devices, such as diodes and transistors, are classic examples of
non-ohmic conductors.
3.Insulators: Insulators are materials with extremely high resistivity, resulting in
very low conductivity. In their I-V curves, insulators typically have a flat or nearly flat
region at low applied voltages, indicating that very little current flows through them.
However, when the applied voltage exceeds a certain threshold (known as the
breakdown voltage), the insulator suddenly starts conducting significantly.
 Example: Materials like rubber, glass, and plastics act as insulators under normal
conditions.

10. Real-world Examples of Using I-V Characteristics to
Measure Conductivity:
1.Semiconductor Characterization: In semiconductor device testing and manufacturing, I-V
characteristics are used to understand and optimize the performance of electronic
components. By analyzing the I-V curves of transistors and diodes, engineers can determine
important parameters such as the threshold voltage, saturation current, and on/off
characteristics of these devices.
2.Electrical Power Transmission: In power distribution systems, I-V characteristics are
critical for assessing the conductivity of power transmission lines and cables. These curves
help identify resistive losses and ensure efficient power delivery.
3.Battery Testing: I-V curves are used to characterize the behavior of batteries. They provide
valuable information about the battery's internal resistance, capacity, and overall health,
which is essential in battery testing and development.
4.Solar Cell Efficiency: For solar cells, I-V characteristics help evaluate their efficiency and
performance under different lighting conditions. The curves indicate the maximum power
point and efficiency of the solar cell.
In summary, I-V characteristics provide valuable insights into the
electrical conductivity of different materials and devices. By analyzing
these curves, engineers and scientists can optimize electronic
components, assess material behavior, and enhance the efficiency of
various electrical systems.

11. Advantages of 4-Probe over 2-Probe
Technique
Resistance measurements are essential in various fields, such as electronics, materials science, and
electrical engineering. Two common techniques used to measure resistance are the 2-probe
method and the 4-probe method. Let's explore each method and understand their differences, as
well as the limitations of the 2-probe technique and how the 4-probe technique overcomes them.
2-Probe
Method:
In the 2-probe method, a voltage (V) is applied across the
sample, and the resulting current (I) is measured using two
probes. The resistance (R) of the sample is then calculated
using Ohm's law:
R = V / I
The two probes serve both to apply the voltage and to
measure the resulting current. While the 2-probe method is
straightforward and simple to implement, it has limitations
due to the presence of contact resistances.

12. Limitations of the 2-Probe Method (Contact
Resistance):
1. Contact Resistance: The main limitation of the 2-
probe method is the presence of contact resistances
at the points where the probes make contact with the
sample. These contact resistances can be
significant, especially when measuring small or
highly resistive samples. The contact resistances
add to the measured resistance, leading to
inaccurate results and underestimation of the true
resistivity of the sample.
2. Current Shunting: In the 2-probe technique, the
current passes through the same points where the
voltage is applied, leading to potential current
shunting through the contact resistances. This
results in an uneven current distribution through the

13. 4-Probe Method:
The 4-probe method, also known as
the Kelvin method or 4-point probe
method, is a more accurate and
reliable technique for measuring
resistivity, especially in highly resistive
materials or samples with small
dimensions.
It overcomes the limitations of the 2-
probe method by using four separate
probes for voltage application and
current measurement.

14. How the 4-Probe Technique Overcomes
Limitations:
 1- Elimination of Contact Resistance: In the 4-probe method, two of the probes are used
for applying a known voltage across the sample, while the other two probes are used for
measuring the resulting current. The current measurement probes are spaced at a fixed
distance, much smaller than the size of the sample. Since the current measurement probes
are separate from the voltage application probes, the contact resistances do not affect the
measurement. The measured current is not distorted by the contact resistances, leading to
accurate resistance measurements.
 2- Even Current Distribution: With the 4-probe technique, the current is injected into the
sample through the current application probes and collected by the current measurement
probes, creating a well-defined current path within the sample. This ensures an even
current distribution, eliminating current shunting and providing more accurate resistivity
measurements. The 4-probe technique is commonly used for measuring the resistivity of
various materials, including semiconductors, thin films, and nanomaterials, where accurate
and reliable resistance measurements are crucial. It has found applications in research,
quality control, and materials characterization due to its capability to measure resistivity
independently of contact resistances, making it a powerful tool in the study of electrical
properties of materials.

15. Hall effect
The Hall effect is a fundamental phenomenon in physics that describes
the behavior of charged particles, such as electrons or holes (positively
charged vacancies in semiconductors), when they move through a
magnetic field and an electric current is present. It was first discovered
by the American physicist Edwin Hall in 1879.

16. Relationship to Magnetic Fields:
When a charged particle, carrying an electric current, moves through a magnetic field perpendicular
to the direction of the current, it experiences a force called the Lorentz force. This force acts
perpendicular to both the direction of the current and the magnetic field. As a result, the charged
particles are deflected to one side of the conductor, creating an electric field in the perpendicular
direction to the current flow. This phenomenon is known as the Hall effect.
The Hall effect is based on the principles of electromagnetism and can occur in various conductive
materials, including metals and semiconductors.

17. Hall Effect Setup
and
Measurement of
Charge Carriers'
Mobility and
Concentration:
The Hall effect is typically studied using a setup called the
Hall effect apparatus. It consists of a thin conducting plate
or a semiconductor sample through which a known current
is passed along its length. The plate is placed in a magnetic
field directed perpendicular to the current flow and the
plate's surface. The setup includes voltage probes at the
sides of the plate to measure the Hall voltage.
To measure charge carriers' mobility and concentration in the
material, researchers vary the current, the magnetic field strength, or
both. By measuring the Hall voltage across the sample and knowing
the current and magnetic field values, the following parameters can
be determined:
Hall Coefficient (RH): The Hall coefficient quantifies the
magnitude and direction of the Hall voltage produced by a
unit magnetic field and current density. It is given by:
RH = VH / (B * I)
Where: RH is the Hall coefficient, VH is the Hall voltage, B
is the magnetic field strength, and I is the current passing
through the sample.

18. Applications
of the Hall
Effect:
Determining Material Properties: The Hall effect is commonly used to study the electrical properties of materials, including their carrier concentration, mobility, and type of
charge carriers.
Semiconductor Characterization: In semiconductor devices, the Hall effect is
used to determine the carrier concentration and mobility, providing valuable
information for device design and optimization.
Magnetic Field Sensing: Hall effect sensors are widely used to measure
magnetic fields in applications like compasses, current sensors, and proximity
switches.
Magnetic Imaging: Hall effect sensors can be utilized to create two-dimensional
images of magnetic fields for non-destructive testing and imaging applications.
Hall Effect Thrusters: In space propulsion systems, Hall effect thrusters utilize
the Hall effect to produce thrust by ionizing a propellant gas and accelerating
the ions using magnetic fields.
Current Measurement: The Hall effect is employed in current sensing
applications, especially in electronic circuits and power systems.

19. Capacitance-Voltage
(CV) Characteristics
 Capacitance is a fundamental property
of electronic components that
measures their ability to store an
electric charge when a voltage is
applied to them. It is an essential
parameter in electronic devices and
plays a crucial role in various
applications.
 Capacitance (C) is defined as the ratio
of the electric charge (Q) stored on a
component's plates to the voltage (V)
applied across the component:
 C = Q / V
 The unit of capacitance is the farad (F),
where 1 farad is equal to 1 coulomb per
volt. However, in practical electronic
devices, capacitance is often measured
in microfarads (µF) or picofarads (pF)
due to their small sizes.
Capacitors are electronic components designed to store and
release electric charge. They consist of two conductive plates
separated by an insulating material called a dielectric. When a
voltage is applied across the capacitor, electrons accumulate on
one plate while an equal number of electrons are drawn from the
other plate. The capacitance value determines the amount of
charge the capacitor can store for a given voltage.

20. Capacitance-Voltage (CV) characteristics
1
Experimental Setup:
Set up the
semiconductor device
for measurement. This
may involve placing
the device in a test
fixture or mounting it
on a probe station.
Ensure that the
connections are made
correctly to apply the
desired voltage to the
device and measure
its capacitance.
2
Biasing the Device:
Apply a small DC bias
voltage (usually in
reverse bias for diodes
or in sub-threshold
region for MOSFETs)
to the device to
establish a starting
point for the CV
measurement.
3
Applying AC Signal:
Superimpose a small
AC signal on top of
the DC bias voltage.
The AC signal's
frequency is typically
in the range of a few
kHz to MHz,
depending on the
device and the
measurement
requirements.
4
Measuring
Capacitance: Measure
the current flowing
through the
semiconductor device
due to the AC signal
using a current-
sensitive
measurement
instrument, such as a
lock-in amplifier or an
impedance analyzer.
Simultaneously
measure the voltage
applied to the device
using a voltage
measurement
instrument.
5
Varying Voltage:
Slowly vary the DC
bias voltage while
keeping the AC signal
constant. Start from
the initial bias point
and move towards the
desired voltage range
for the measurement.
6
Plotting the Data:
Record the current
and voltage data for
each bias point. Plot
the measured current
(or capacitance) as a
function of the
applied voltage
To obtain Capacitance-Voltage (CV) characteristics and interpret them, you typically perform a
measurement on a semiconductor device, such as a diode or a MOSFET, while varying the
voltage applied to the device. The CV characteristics provide valuable insights into the
behavior and properties of the semiconductor device. Here's a step-by-step explanation of the
process:

21. Interpretation of CV
Characteristics:
Capacitance-Voltage Plot:
• The resulting plot is called the CV curve or CV
characteristic.
• The x-axis represents the applied voltage, and the y-axis
represents the measured capacitance (or current).
• Capacitance is inversely proportional to the width of the
depletion region in the semiconductor device. As the bias
voltage changes, the depletion region width changes,
affecting the capacitance.
Analysis for Diodes:
• For diodes, the CV curve shows the abrupt transition
from the reverse-biased to the forward-biased region.
• The capacitance is relatively constant in the reverse-
biased region, while it drops sharply in the forward-
biased region due to the reduction in the depletion
region width.

22. applications of CV characteristics in semiconductor
device characterization:
1. Threshold Voltage Determination (MOSFETs):
• CV measurements are commonly used to determine the threshold voltage (Vth) of Metal-Oxide-
Semiconductor Field-Effect Transistors (MOSFETs).
• The threshold voltage represents the point at which the MOSFET switches from the off-state to the on-
state.
• Knowing Vth is essential for proper circuit design and optimization, as it affects the MOSFET's behavior
in different operating regions.
2. Capacitance and Doping Concentration Estimation:
• CV measurements are used to determine the capacitance of the depletion region in semiconductor
devices.
• By analyzing the capacitance values at different bias voltages, researchers can estimate the doping
concentration in the semiconductor material.
• This information is critical for understanding device performance and optimizing the doping profile to
achieve specific electrical characteristics.

23. Cont..
3. Interface State Density Measurement:
• Interface state density refers to the number of charge traps present at the
semiconductor-insulator interface in MOSFETs.
• CV measurements can be used to extract information about interface state density,
which directly impacts device performance, such as leakage currents and subthreshold
behavior.
• Characterizing and reducing interface state density is crucial for enhancing device
performance and reliability.
3. Oxide Thickness and Quality Assessment:
• For MOSFETs and other devices with an oxide layer, CV measurements can provide
insights into the oxide thickness and quality.
• Changes in capacitance with different bias voltages can reveal variations in the oxide
layer's thickness, which is essential for ensuring consistent device performance.
3. Barrier Height Determination (Schottky Diodes):
• CV measurements are widely used to determine the barrier height in Schottky diodes,
which are metal-semiconductor junctions.
• The barrier height affects the diode's rectifying properties and is essential for optimizing
diode performance in various applications.

24. Cont..
6. Mobility Extraction (MOSFETs and Bipolar Transistors):
• CV measurements, along with other electrical characterization techniques,
are used to extract carrier mobility in both MOSFETs and bipolar
transistors.
• Understanding carrier mobility is crucial for designing high-speed and low-
power devices.
6. Quality Control and Process Monitoring:
• CV measurements are valuable tools for quality control and process
monitoring during semiconductor device fabrication.
• By comparing measured CV characteristics to expected values,
manufacturers can detect process variations and identify potential issues
in the production line.
6. Device Modeling and Simulation:
• The data obtained from CV measurements are used in device modeling
and simulations to accurately predict device behavior under different
conditions.
• Device models are essential for circuit designers to optimize circuit
performance and analyze complex circuits.