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What is the energy range for the conduction band in conductors?
What is the energy range for the conduction band in conductors?
There is overlapping of CB and VB.
Which of the following are examples of semiconductors?
Which of the following are examples of semiconductors?
What is the formula that represents the mass action law in semiconductors?
What is the formula that represents the mass action law in semiconductors?
ni^2 = np
In n-type semiconductors, the majority carrier is the hole.
In n-type semiconductors, the majority carrier is the hole.
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The mobility of electrons is greater than the mobility of holes.
The mobility of electrons is greater than the mobility of holes.
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What is the resistivity equation in relation to conductivity?
What is the resistivity equation in relation to conductivity?
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What is the unit of mobility?
What is the unit of mobility?
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What is true for intrinsic semiconductors?
What is true for intrinsic semiconductors?
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What is the intrinsic carrier concentration of Germanium at room temperature?
What is the intrinsic carrier concentration of Germanium at room temperature?
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The equation for drift current in semiconductors is I = ___
The equation for drift current in semiconductors is I = ___
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What happens to the depletion region in a p-n junction when the donor impurity concentration increases?
What happens to the depletion region in a p-n junction when the donor impurity concentration increases?
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Calculate the intrinsic conductivity of Silicon given ni = 1.5 x 10^10 and its mobilities.
Calculate the intrinsic conductivity of Silicon given ni = 1.5 x 10^10 and its mobilities.
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What is the current density formula with respect to conductivity?
What is the current density formula with respect to conductivity?
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Study Notes
Semiconductor Theory
- Semiconductor theory centers on the energy band diagrams of atoms.
- Inner energy levels are less energized, while outer energy levels are more energized.
Insulators
- Conduction band (CB): 6-7 eV
- Forbidden gap
- Valence Band (VB)
Semiconductors
- Conduction band (CB): 0.1-2 eV
- Valence band (VB)
- Examples: Si, Ge
Conductors
- Overlapping of CB and VB
- Examples: Al, Cu, Si
Properties of Semiconductors
- The conductivity of a semiconductor can be controlled.
- In pure semiconductors, electron formation results in hole formation.
- These characteristics are temperature-dependent.
- Free electrons: ni - Intrinsic carrier concentration
- p holes: pi - Intrinsic carrier concentration
- Electron concentration equals hole concentration: ni = pi
Extrinsic Semiconductors
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n-type semiconductors (extrinsic):
- Have a donor impurity concentration (ND)
- Donor impurity concentration exceeds hole concentration (n > p)
- The majority carrier is the electron, and the minority carrier is the hole
- The concentration of majority carriers depends on doping.
-
p-type semiconductors (extrinsic):
- Have an acceptor impurity concentration (NA).
- Acceptor impurity concentration exceeds electron concentration (p > n).
- The majority carrier is the hole, and the minority carrier is the electron.
- Mass action law: ni2= np. This law applies to both intrinsic and extrinsic semiconductors.
Conduction of Current in Semiconductors
-
Drift Velocity:
- An external electric field applied to a semiconductor causes charge carriers to form a current called drift current.
- Under steady-state conditions, each charge carrier attains a drift velocity proportional to the applied electric field.
- Velocity equation: V = μE, where μ - mobility
- μh = mobility of hole,
- μe= mobility of electron,
- μe> μh
- Mobility unit: m2/Vs
-
Drift current:
- N number of electrons move across length l in time t.
- I = dq/dt = Nq/τ
- Drift velocity: vd = l/τ = I/Nq = V/L = I/nqA (Ampere (A))
- Current density J = I/A = nqv
- J = nqv = nμE = σE (σ- conductivity)
Resistivity
- Resistivity: ρ = 1/ σ = (ohm.m)
Case of Intrinsic Semiconductors
- Conductivity of intrinsic semiconductors: σi = σn + σp
- Since n=p in intrinsic semiconductors: σi = nqμn + pqμp
- Therefore, σi = (nqμn + pqμp).E
Case of Extrinsic Semiconductors
-
n-type:
- J = Jn + Jp = ngμnE + pqμpE
- As n >> p
- J ≈ Jn
- J = nqμnE
- The majority concentration is equal to the donor concentration: n = ND
- Applying mass action law: p = ni2/ND
- Current density: J = NDqμnE
-
p-type:
- J = Jn + Jp = ngμnE + pqμpE
- As p >> n
- J ≈ Jp
- J = pqμpE
- The majority concentration is equal to the acceptor concentration: p = NA
- Applying mass action law: n = ni2/NA
- Current density: J = NAqμpE.
Majority and Minority Carrier Concentration
-
At room temperature:
- Germanium: μn = 3800, μp = 1800, ni = 2.5 x 1013
- Silicon: μn = 1300, μp = 500, ni = 1.5 x 1010
Example:
- Calculate the conductivity of intrinsic Silicon at room temperature and find current density with applied electric field of 10 V/cm.
- To this intrinsic Silicon, if a donor impurity of 1018/cm3 is added, what will be the conductivity and current density when the electric field is 10 V/cm? 1.Intrinsic Silicon: - ni = pi = 1.5 x 1010/cm3 - σi = ni qμn + piqμp - σi = 1.5 x 1010 x 1.6 x 10-19 x 1300 + 1.5 x 1010 x 1.6 x 10-19 x 500 - σi = 208 + 80 = 288 - ρi = 1/σi = 1/288 - ρi = 3.12 x 10-6 - Ji = σi E = 4.32 x 10-5 A / m2. 2.Extrinsic Silicon: - n = ND = 1018/cm3 - σ = ngμn + pqμp - σ = 1018 x 1.6 x 10-19 x 1300 + 1010 x 1.6 x 10-19 x 500 - σ = 2080 - J = σE = 2.08 x 103 A/ m2.
P-N Junctions
- A p-n junction comprises an n-type semiconductor joined to a p-type semiconductor.
- The p-side has a positive charge, while the n-side has a negative charge.
- The junction contains a depletion region with an electric field pointing from the n-side to the p-side.
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Carrier concentration:
- Abrupt junction: The depletion region is narrow, with high carrier concentration on either side.
- Graded junction: The depletion region is wide, and the concentration changes gradually on both sides.
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Depletion region width:
- The depletion region width depends on doping concentration on both sides and the intrinsic carrier concentration.
- A higher donor impurity concentration leads to a narrower depletion region width on the n-side and vice versa.
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Barrier potential:
- ...
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Description
This quiz explores the fundamental concepts of semiconductor theory, including energy band diagrams, the properties of conductors, insulators, and the distinction between intrinsic and extrinsic semiconductors. Test your knowledge on topics such as conduction bands, valence bands, and carrier concentrations.
