Semiconductor Physics and Carrier Transport

Flashcards for reviewing carrier transport, semiconductor physics, band theory, doping statistics, and historical milestones.

The first point-contact bipolar transistor was demonstrated at Bell Labs in December 1947 by John Bardeen, Walter Brattain, and __________.

William Shockley

The integrated circuit was independently developed by Jack Kilby at Texas Instruments using germanium and by __________ at Fairchild Semiconductor using silicon.

Robert Noyce

According to __________ Law, the number of transistors on a microchip doubles approximately every two years.

Moore's

Intel's $10\,nm$ FinFET technology node features a Fin Pitch of $34\,nm$ and a Fin Height of __________.

$$53\,nm$$

Solids with a regular, periodic arrangement of atoms extending throughout the material are classified as __________ solids.

crystalline

In a simple cubic (SC) unit cell there is $1$ atom, in a body-centered cubic (BCC) cell there are $2$ atoms, and in a face-centered cubic (FCC) cell there are __________ atoms.

$$4$$

To determine the Miller indices of a crystallographic plane, take the axis intercepts, calculate their __________, and clear fractions to obtain the smallest set of integers.

reciprocals

Silicon has a __________ crystal structure, which consists of two interpenetrating face-centered cubic sublattices with a coordination number of $4$.

diamond

A crystal defect created when a host atom is displaced into an interstitial site leaving behind a vacancy is called a __________ defect.

Frenkel

When a covalent bond breaks in silicon at temperatures above absolute zero, a free electron is generated along with a vacant electronic state in the valence band called a __________.

hole

Doping intrinsic silicon with Group V donor impurities such as Arsenic or Phosphorus creates an __________ semiconductor.

n-type

The effective mass $m^*$ of an electron in a crystal lattice is inversely proportional to the second derivative of its energy-momentum relation, expressed as $m^* = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{\hbar^2}{\frac{d^2E}{dk^2}}$$

The density of allowed quantum states per unit volume in the conduction band is given by $g_c(E) = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{4\pi (2m_n^*)^{3/2}}{h^3} \sqrt{E - E_c}$$

The probability $f(E)$ that an available energy state $E$ is occupied by an electron under thermal equilibrium is defined by the __________ function.

Fermi-Dirac

The Maxwell-Boltzmann distribution approximates the Fermi-Dirac function when the energy state satisfies $E - E_F \gg \text{\_\_\_\_\_\_\_\_\_\_}$.

$$kT$$

At $T = 300\,K$, the effective density of states in the conduction band $N_c$ for silicon is equal to __________.

$$2.8 \times 10^{19}\,cm^{-3}$$

The thermal-equilibrium hole concentration $p_0$ expressed in terms of the valence band effective density of states $N_v$ is $p_0 = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$N_v \exp\left[\frac{-(E_F - E_v)}{kT}\right]$$

The Law of Mass Action states that for any non-degenerate semiconductor in thermal equilibrium, the product $n_0 p_0$ equals __________.

$$n_i^2$$

The energy difference between the intrinsic Fermi level $E_{Fi}$ and the midgap energy $E_{\text{midgap}}$ is given by $E_{Fi} - E_{\text{midgap}} = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{3}{4} kT \ln\left(\frac{m_p^*}{m_n^*}\right)$$

Under complete ionization, the condition of charge neutrality in a doped semiconductor requires that $n_0 + N_a^- = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$p_0 + N_d^+$$

In an extrinsic n-type semiconductor where $N_d \gg N_a$ and $N_d \gg n_i$, the thermal-equilibrium electron concentration $n_0$ simplifies to $n_0 \approx \text{\_\_\_\_\_\_\_\_\_\_}$.

$$N_d$$

At very low temperatures, donor electrons lack thermal energy to jump to the conduction band and remain bound to donor atoms in the __________ region.

partial ionization

In non-equilibrium conditions, separate energy levels called __________-Fermi levels are used to calculate electron and hole concentrations.

Quasi

The drift current density of holes in a semiconductor under an applied electric field $E$ is given by $J_{p|drf} = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$e p \mu_p E$$

Matthiessen's rule combines lattice scattering mobility $\mu_L$ and ionized impurity scattering mobility $\mu_I$ as $\frac{1}{\mu} = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{1}{\mu_I} + \frac{1}{\mu_L}$$

In Gallium Arsenide (GaAs), the electron drift velocity decreases at high electric fields due to the __________ mechanism.

inter-valley transfer

The diffusion current density for electrons flowing along a concentration gradient $\frac{dn}{dx}$ is $J_{nx|dif} = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$e D_n \frac{dn}{dx}$$

The Einstein relation relates carrier diffusivity $D$ to mobility $\mu$ via $\frac{D_n}{\mu_n} = \frac{D_p}{\mu_p} = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{kT}{e}$$

In a non-uniformly doped n-type semiconductor, a spatial variation in donor doping $N_d(x)$ induces an internal electric field $E_x = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$-\left(\frac{kT}{e}\right) \frac{1}{N_d(x)} \frac{dN_d(x)}{dx}$$

The Hall Effect establishes a transverse electric field $E_H$ and voltage $V_H$ when a current $I_x$ passes through a semiconductor in the presence of a perpendicular magnetic field $B_z$, where for a p-type semiconductor $V_H = \text{\_\_\_\_\_\_\_\_\_\_}$.

$$\frac{I_x B_z}{e p d}$$