Doping, Charge Carriers and Conductivity

Doping, Charge Carriers and Conductivity

The direction of conventional current in a forward-biased diode is:

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. In forward bias, current flows from p-side (positive) to n-side (negative) conventionally, as indicated by the diode symbol’s arrow, due to the flow of majority carriers. Substituting values gives P-side to n-side, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

Which of the following is NOT a pentavalent dopant?

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. Pentavalent dopants (valency 5) include P, As, and Sb. Indium (In) is trivalent (valency 3) and used for p-type doping, not n-type. Substituting values gives Indium (In), which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

A p-type semiconductor is doped with:

**Doping** is adding impurity to pure semiconductor to increase carriers, pentavalent (P, As, Sb) donates extra electron, 1 ppm doping in Ge with 4×10²⁸ atoms/m³ gives donor density N_d = 4×10²⁸×10⁻⁶ =4×10²² m⁻³ for 1 ppm, acceptor atoms p-type trivalent B, Al, Ga. Overall charge neutrality maintained because donor ion core positive but electron negative, net neutral. A p-type semiconductor is created by doping a tetravalent semiconductor (e.g., Si) with a trivalent impurity (e.g., B, Al, In), which accepts electrons and creates holes as majority carriers. Substituting values gives Trivalent atoms, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

The maximum number of electrons that can occupy the outer orbit of a Si atom is:

**Number of carriers** from doping: Ge crystal 4×10²⁸ atoms/m³ doped 2 ppm trivalent gives acceptor atoms 8×10²² m⁻³, holes ≈ that, for 1.5 ppm 6×10²² m⁻³, for 0.5 ppm pentavalent Si 5×10²⁸ atoms/m³ gives 2.5×10²² donors/m³. Acceptor atom effectively negative when accepts electron, donor positive when donates, but crystal neutral. The outer orbit of Si (third shell) can hold 8 electrons (2s + 6p), though Si has only 4 valence electrons naturally forming covalent bonds. Substituting values gives 8, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

A pure Si crystal is doped with 1 ppm of pentavalent impurity. If the Si atom density is \( 5 \times 10^{28} \, \text{m}

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. 1 ppm = 1 part per million = 10⁻⁶ . Number of donor atoms = 10⁻⁶ × 5 × 10²⁸ = 5 × 10²² m⁻³ . These contribute electrons, assuming full ionization at room temperature. Substituting values gives 5 × 10²² m⁻³, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

In a p-type semiconductor, the acceptor impurities create:

**Doping** is adding impurity to pure semiconductor to increase carriers, pentavalent (P, As, Sb) donates extra electron, 1 ppm doping in Ge with 4×10²⁸ atoms/m³ gives donor density N_d = 4×10²⁸×10⁻⁶ =4×10²² m⁻³ for 1 ppm, acceptor atoms p-type trivalent B, Al, Ga. Overall charge neutrality maintained because donor ion core positive but electron negative, net neutral. Trivalent acceptor impurities (e.g., B, Al) in a p-type semiconductor lack one electron per atom, creating holes that act as majority carriers by accepting electrons from the lattice. Substituting values gives Holes, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

In an extrinsic semiconductor, the minority carrier concentration is reduced due to:

**Doping** is adding impurity to pure semiconductor to increase carriers, pentavalent (P, As, Sb) donates extra electron, 1 ppm doping in Ge with 4×10²⁸ atoms/m³ gives donor density N_d = 4×10²⁸×10⁻⁶ =4×10²² m⁻³ for 1 ppm, acceptor atoms p-type trivalent B, Al, Ga. Overall charge neutrality maintained because donor ion core positive but electron negative, net neutral. Doping increases majority carriers (electrons in n-type, holes in p-type), enhancing recombination with minority carriers, thus reducing their concentration indirectly. Substituting values gives Increased recombination, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

A Si crystal with \( 5 \times 10^{28} \, \text{atoms} \, \text{m}^{-3} \) is doped with 0.5 ppm of pentavalent impurity.

**Number of carriers** from doping: Ge crystal 4×10²⁸ atoms/m³ doped 2 ppm trivalent gives acceptor atoms 8×10²² m⁻³, holes ≈ that, for 1.5 ppm 6×10²² m⁻³, for 0.5 ppm pentavalent Si 5×10²⁸ atoms/m³ gives 2.5×10²² donors/m³. Acceptor atom effectively negative when accepts electron, donor positive when donates, but crystal neutral. 0.5 ppm = 0.5 × 10⁻⁶ . Number of donor atoms = 0.5 × 10⁻⁶ × 5 × 10²⁸ = 2.5 × 10²² m⁻³ , each contributing one electron. Substituting values gives 2.5 × 10²² m⁻³, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

The majority carriers in a p-type semiconductor are:

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. In a p-type semiconductor, trivalent doping creates holes as majority carriers, while electrons are minority carriers ( n_h gg n_e ). Substituting values gives Holes, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

Which of the following is a trivalent dopant used in p-type semiconductors?

**Number of carriers** from doping: Ge crystal 4×10²⁸ atoms/m³ doped 2 ppm trivalent gives acceptor atoms 8×10²² m⁻³, holes ≈ that, for 1.5 ppm 6×10²² m⁻³, for 0.5 ppm pentavalent Si 5×10²⁸ atoms/m³ gives 2.5×10²² donors/m³. Acceptor atom effectively negative when accepts electron, donor positive when donates, but crystal neutral. Trivalent dopants (valency 3) like Boron (B), Aluminium (Al), and Indium (In) are used in p-type semiconductors to create holes. Phosphorus (P) is pentavalent. Substituting values gives Aluminium, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

In an n-type semiconductor, the number of electrons contributed by donors is:

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. In an n-type semiconductor, each pentavalent donor atom contributes one extra electron, making the electron concentration dependent on doping level, not just intrinsic generation. Substituting values gives Dependent on doping level, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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Doping, Charge Carriers and Conductivity

The process of adding impurities to a pure semiconductor is called:

**Charge carriers** in n-type majority electrons, minority holes, in p-type majority holes, minority electrons, minority concentration reduced due to recombination n_e n_h = n_i², doping increases majority, conductivity σ = e(n_e μ_e + n_h μ_h), increases with doping. Donor ionization energy small ~0.01 eV, electrons easily promoted to conduction band at room temperature. Doping is the deliberate addition of impurities (e.g., pentavalent or trivalent atoms) to a pure semiconductor to increase its conductivity by providing additional charge carriers. Substituting values gives Doping, which matches expected behaviour for this semiconductor device configuration, confirming doping, depletion and rectifier principles.

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