Electrical Sciences
(EEE F111)
Lecture No – 26
Dr. Sudeep Baudha
Electrical and Electronics Engineering Department
BITS Pilani KK Birla Goa Campus
From Last Lecture (Recap)
➢ LR – C CKTs
➢ Practice Problems
➢ Conceptual Derivation
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Next Segment
➢ Semiconductors
➢ Diodes
➢ Transistors
➢ Op-Amps (Operational Amplifiers)
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Metal, Insulator and
Semiconductor
Metal (or Conductor): Any material that support a flow of
charge when a voltage source of finite magnitude is applied
across its terminal.
Insulator: Any material that offers a very low level of
conductivity.
Semiconductor: A material that has a conductivity level
somewhere between the extremes of an insulator or
conductor.
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Semiconductor
• Two famous semiconductor
materials are Silicon and
Germanium
• Figure shows crystal lattice structure
of silicon (Si) or germanium (Ge)
• Si-Si or Ge-Ge bond is covalent
bond
• At low temperature, Si and Ge
behaves as a insulator material as
no free electron is available for
conduction
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Semiconductor
• At room temperature (T = 300 K), thermal energy can break
the covalent bond
• If the bond is broken, a
vacate space is created,
which is known as a hole
• Hole can be visualized as
absence of electron
• The hole and resulting
free electron is known a
electron-hole pair
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Semiconductor
• In a semiconductor, flow of current can be visualized as
movement of hole (hole current) or movement of electron
(electron current or current)
•
Semiconductors can be classified as Intrinsic (pure) and
Extrinsic (Doped)
• In intrinsic semiconductor,
number of free electrons (n) = number of free holes (p)
or n = p = ni ; where ni is the intrinsic carrier concentration
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Current Density in Semiconductor
• Current density (J) in semiconductor:
𝐽 = 𝑛𝑞m𝑛𝐸 + 𝑝𝑞m𝑝𝐸
𝐽 = (𝑛m𝑛 + 𝑝m𝑝)𝑞𝐸
𝐽 = σ𝐸 ; where σ = (𝑛m𝑛 + 𝑝m𝑝)𝑞
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Doped or (Extrinsic) Semiconductors
• The conductivity of the semiconductor can be increased
significantly by adding small amount of appropriate impurity.
• Doping: The process of adding impurity to a intrinsic (or pure)
semiconductor. The added impurity, either trivalent or
pentavalent, is known as dopant.
• Trivalent impurity (or Acceptor impurity): Element having 3
electrons in the valence band. Example: Boron
• Pentavalent impurity (or Donor impurity): Element having 5
electrons in the valence band. Example: Arsenic or
phosphorous
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Doped or (Extrinsic) Semiconductors
• N-type (Majority carriers are electrons) and P-type
semiconductor (Majority carrier are electrons)
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Mass Action Law
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PN-Junction
Formation of pn-junction
• Assume that the n-type and p-type semiconductors are
separated by a distance D
• Once the semiconductors are placed in contact, junction
formation takes place
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PN-Junction:
Depletion Layer Formation
(a)
(b)
Hole -ve ion
electron +ve ion
Diffusion current
(c)
Drift current
Depletion region or space charge region or transition region
“The region of uncovered positive and negative ions is called the
depletion region due to the depletion of carriers in this region”
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Insights into the Depletion Layer
• When pn junction is formed, electrons diffuses from n-type to ptype semiconductor and holes diffuses from p-type to n-type
semiconductor due to concentration gradient (Fig. b).
• Diffusion current: It flows due to the diffusion of the carriers from
higher to lower concentration. The direction of diffusion current is
opposite to the direction of moving electrons (Fig. b).
• During the diffusion of the carriers, recombination of the electrons
and holes takes place. Once the electron recombine with the hole,
ionized atoms are left on the either side of the junction i.e.
negative ions on the p-side and positive ions on the n-side
• These ions are immobile and results in an electric field (E).
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Insights into the Depletion Layer
• The flow of minority carriers in the presence of electric field
across the depletion region is known as drift current (Fig. c).
• At equilibrium, Diffusion current = Drift current, which leads to net
current = 0 A.
• The depletion region (or depletion width) is the region where free
electrons and holes are not available. This region is depleted of
the free carriers.
• Depletion width changes with the change in applied voltage
across the pn-junction.
• The magnitude of the electric field can be evaluated if the voltage
across the depletion layer (built-in-voltage) and depletion width is
known
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PN-Junction: Built in Voltage
• Built in voltage (Vbi or Vo or VT): The potential difference
across the depletion region is known as built in voltage or cutin voltage or knee voltage.
𝑘𝑇
𝑁𝐴 𝑁𝐷
𝑉𝑏𝑖 =
ln( 2 )
𝑞
𝑛𝑖
k = Boltzmann Constant = 1.38×10-23 J/K
T = Temperature in Kelvin
q = Electronic Charge = 1.6×10-19 C
𝑘𝑇
𝑇
= 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 =
; it is specified in volts;
𝑞
11600
𝑘𝑇
= 26 mV at T = 300 K
𝑞
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PN-Junction
• The barrier potential, Vo depends on
• Doping level
• Temperature
• Acceptor concentration
• Donor concentration
• Type of semiconductor
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PN-Junction Diode
• Schematic view of a pn-diode
(Va )
p-side
n-side
(Vn )
If the metal (or ohmic) contacts to a pn-junction, the resulting
in a circuit element is known as pn-diode or junction diode
• Depending on the applied bias, pn-diode operates in two
modes
• Forward bias mode (Va > Vn)
• Reverse bias mode (Va < Vn)
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PN-Junction Diode
Current-Voltage characteristics of a pn-diode
i = Is (𝑒
ʋ
ɳ𝑉𝑇
− 1)
Is : Reverse saturation current
VT : Volt equivalent of temperature = T/11600
ɳ (eta): Emission coefficient ; for Si ɳ = 2 and for Ge ɳ = 1
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Impact of Applied Voltage (Bias) on
Depletion Width
Forward Bias Mode (Va > Vn)
• Electric field across the depletion layer reduces, which
leads to flow of current in a diode.
• The current flows due to majority carriers
Reverse Bias Mode (Va < Vn)
• Electric field across the depletion layer increases,
which restricts the flow of the electrons (or current).
• The current flows due to minority carriers
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Diodes : Si and Ge
Ge
Si
Current-Voltage characteristics of Silicon (Si) and Germanium
(Ge) diode.
• VT,Ge < VT,Si
• IGe > Isi
• The higher current and lower built in voltage in Ge diode is
due to the lower bandgap of Ge material
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Lecture Ends….
Thank you for your Attention
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