Band Overlap in Metals

The overlap of the 3s-band and 3p-band allows conduction electrons to be present, making metals conductive despite expectations.

The energy band diagram consists of a conduction band (Ec) and a valence band (Ev), separated by a band gap energy (Eg).

Common elemental semiconductors include Silicon (Si) and Germanium (Ge), while compound semiconductors include GaAs and CdTe.

<p>Eg can be determined by the minimum photon energy (hn) that the semiconductor absorbs.</p> Signup and view all the answers

<p>Semiconductors typically have four electrons in their outer valence orbit, which enables them to form crystal lattices.</p> Signup and view all the answers

<p>The longest wavelength absorbed by Silicon is approximately 1 mm.</p> Signup and view all the answers

<p>A metal’s conduction band contains more energy levels than available electrons, allowing for electrical conductivity.</p> Signup and view all the answers

<p>Direct band gap semiconductors can absorb and emit light efficiently, while indirect band gap semiconductors require a phonon interaction for transitions.</p> Signup and view all the answers

<p>Fermions must obey Pauli's exclusion principle, which states that no two electrons can occupy the same quantum state.</p> Signup and view all the answers

<p>At 0 K, the Fermi-Dirac distribution function is a rectangular shape, meaning all states below the Fermi energy (Ef) are filled, and those above Ef are empty.</p> Signup and view all the answers

<p>As temperature rises above 0 K, the probability of occupancy for states above the Fermi level increases, while some states below it may become empty.</p> Signup and view all the answers

<p>The probability of occupancy f(E) equals ½ at the Fermi energy level (Ef).</p> Signup and view all the answers

<p>In an intrinsic semiconductor at 0 K, the Fermi energy level lies midway between the filled valence band and the empty conduction band.</p> Signup and view all the answers

<p>As temperature increases, the Fermi-Dirac probability allows some occupancy of energy states above the Fermi level, while states below may be emptied.</p> Signup and view all the answers

<p>Fermions are indistinguishable because they are identical in nature and cannot be distinguished from one another in a quantum state.</p> Signup and view all the answers

<p>The Fermi-Dirac distribution function is given by $f(E) = \frac{1}{1 + e^{(E - E_F) / kT}}$.</p> Signup and view all the answers

<p>Complete ionization is reached when $n_n = N_D$.</p> Signup and view all the answers

<p>In the extrinsic region, the electron concentration remains essentially constant over a wide temperature range.</p> Signup and view all the answers

<p>A semiconductor transitions to intrinsic when the intrinsic carrier concentration becomes comparable to the donor concentration.</p> Signup and view all the answers

<p>No, Si doped with $10^{15}$ atoms/cm³ of As is not useful at 400 K as its electron concentration is only $10^{13}$ cm⁻³.</p> Signup and view all the answers

<p>Yes, Ge doped with $10^{15}$ cm⁻³ of Sb can be used, as its electron concentration is $5 imes 10^{15}$ cm⁻³.</p> Signup and view all the answers

<p>Carrier motion is caused by the application of an electric field and a difference in carrier concentration between two points.</p> Signup and view all the answers

<p>The mean free path is the average distance between collisions that the carriers experience.</p> Signup and view all the answers

<p>The electron concentration varies linearly from $1 imes 10^{18}$ to $7 imes 10^{17}$ cm⁻³.</p> Signup and view all the answers

<p>The electron concentration in the conduction band is given by the product of the density of allowed quantum states, $N(E)$, and the Fermi-Dirac probability function, $F(E)$: $n(E) = N(E) F(E)$.</p> Signup and view all the answers

<p>The upper limit is taken as infinity because it allows for the consideration of all possible energy states in the conduction band that electrons can occupy.</p> Signup and view all the answers

<p>The Fermi-Dirac distribution can be approximated by the Boltzmann distribution when the condition $(E - E_f) &gt; 3kT$ is satisfied, which implies that significant energy levels are well above the Fermi level.</p> Signup and view all the answers

<p>When an energy level $E &lt; E_f$, the probability of occupancy can exceed 1, which is physically meaningless and invalidates the distribution.</p> Signup and view all the answers

<p>The total hole concentration, $p_0$, is calculated by integrating the product of the density of allowed quantum states in the valence band and the probability that a state is not occupied by an electron over the entire valence band energy.</p> Signup and view all the answers

<p>As donor concentration increases, the Fermi level moves closer to the conduction band, reflecting a higher probability of finding electrons in that band.</p> Signup and view all the answers

<p>$N_c$ represents the effective density of states in the conduction band, influencing the carrier concentration when calculating intrinsic carrier concentrations.</p> Signup and view all the answers

<p>Restricting energy levels to values greater than $E_f$ prevents the calculation of probabilities that exceed 1, which would be non-physical.</p> Signup and view all the answers

<p>Radiative recombination occurs when an electron from the conduction band recombines with a hole in the valence band, resulting in the emission of a photon.</p> Signup and view all the answers

<p>The photon energy must be at least equal to the band-gap energy, $E_g$, of the semiconductor.</p> Signup and view all the answers

<p>The mean lifetime is the average time a hole or electron exists before recombination occurs.</p> Signup and view all the answers

<p>The three mechanisms are Auger recombination, recombination by defects, and surface recombination.</p> Signup and view all the answers

<p>Thermal agitation continuously generates new electron-hole pairs while also enabling existing pairs to recombine.</p> Signup and view all the answers

<p>In n-type semiconductors, electrons are abundant, so the percentage increase in holes, which are less plentiful, can be substantial.</p> Signup and view all the answers

<p>When a free electron fills an empty covalent bond, it results in the loss of a charge carrier pair, creating a hole.</p> Signup and view all the answers

<p>In a pure semiconductor, the number of holes is equal to the number of free electrons.</p> Signup and view all the answers