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In December 1947, John Bardeen and Walter Houser Brattain obtained transistor action at Bell Telephone Laboratories. William Shockley proposed the distinct bipolar junction transistor within the following month.^[ref]

Their 1948 paper describes ground, etched germanium, initially also anodized and rinsed. Surface contacts separated by $50$–$250\mu \mathrm{m}$ share a broad base contact. Positive emitter biasing injects electron holes; negative collector biasing draws them toward the collector. An input signal changes emitter electric current, and a collector electrical load converts the resulting change into voltage.^[ref]

Early electric field control experiments gave unexpectedly weak responses. John Bardeen proposed that surface states screened the interior. Surface charge could create a barrier and a hole-rich semiconductor inversion layer. Replacing an electrolyte control with a gold contact reversed the response sign, suggesting electron hole carrier injection. Closely spaced contacts made from a gold-coated wedge split with a razor then enabled power gain. The relative importance of surface and bulk transport depended on preparation and collector forming.^[ref]

The 1948 authors found that collector-current increments could exceed emitter-current increments; their current gain depended on biasing.^[ref] A terminal-current ratio alone cannot identify the microscopic path. Surface states, the local barrier, carrier injection and contact preparation prevent a single ideal modern bipolar junction transistor model from explaining every point-contact transistor.

For the conventional electric current directions drawn in the figure, $I_E$ enters the emitter, $I_C$ leaves the collector and signed $I_B$ enters the base. Kirchhoff's current law requiresThus a local current gain $\alpha >1$ requires an accompanying base-current change. The collector increment is not simply a count of injected electron holes, and it does not violate electric charge conservation.

For an experiment following the functional arrangement, first establish each contact's separate current-voltage characteristic relative to the base. Then hold collector biasing fixed, vary a small emitter signal, and compare the collector electrical load voltage with the input. A decisive power gain check measures both input electric current and voltage and the output power in a known electrical load; voltage enlargement alone is insufficient. These are proposed measurement controls, not additional claims about the 1947 laboratory record.

Repeating a setting tests drift; reversing or removing emitter biasing tests whether the response requires carrier injection. Contact motion, surface contamination, temperature, direct electrical coupling and noise can all affect the inference. A small-signal model describes measured local terminal response without deciding every microscopic mechanism.

A double heterostructure laser electrically pumps its central layer for stimulated emission. Band offsets confine charge carriers; refractive index contrast confines the optical normal mode.^[ref]

For an original bookkeeping model, let $R$ be the injected pair rate per unit area, $d$ the active-layer thickness, $N$ its excess pair number density, $\tau$ a recombination lifetime, and ${\tau }_e$ an escape time. Before appreciable stimulated emission, supposeChoose two otherwise identical devices with ${\tau }_e=\tau$ and ${\tau }_e=9\tau$. The resulting steady state populations are $R\tau /(2d)$ and $9R\tau /(10d)$: improved confinement raises the population by a factor $1.8$ at fixed injection. This linear model assumes equal excess Electron and electron hole densities, fixed lifetimes, and no laser gain clamping.

Optical confinement enters separately. For a chosen optical normal mode, define $0<\Gamma \le 1$ as its gain-overlap factor with the active layer. With material optical gain $g$, internal loss ${\alpha }_i$, and mirror loss ${\alpha }_m$, a simple laser threshold condition isFor stipulated losses ${\alpha }_i+{\alpha }_m=3$ in inverse-length units, $\Gamma =1/2$ requires $g=6$, whereas $\Gamma =3/4$ requires $g=4$. This calculation varies optical overlap only; the preceding population calculation varies carrier escape only. Their combination explains the usefulness of controlling both the energy band profile and the optical normal mode.

Herbert Kroemer proposed the double heterostructure laser in 1963; he did not participate in its 1970 experimental realization.^[ref] Zhores I. Alferov describes his group's independent 1963 proposal and later experimental program.^[ref]

George Elwood Smith reports fabricating MOS capacitors, thermally generating the first packet, and clocking it to an output that pushed it into the substrate for electric current detection. A later integrated eight-bit device demonstrated imaging. Dark or reversed-clock control traces are not specified; feasibility alone does not calibrate charge-transfer efficiency.^[ref]

A discriminating repeat would compare identical cycles with and without initial carrier injection, then suppress or reverse the transfer sequence while retaining output switching. An electric current transient synchronized with gate switching can include capacitor feedthrough; only the difference tied to initial electric charge and the expected transfer delay tests packet transport. These are proposed controls, not controls documented in the lecture. For an optical version, a blocked exposure estimates dark current and read noise; a spatially isolated illuminated optical detector pixel exposes any deferred charge in CCD readout trail. Photon shot noise persists even with ideal transfer.

A light-emitting diode is a semiconductor diode producing electroluminescence under electric current. Forward bias injects Electrons and electron holes; radiative electron-hole recombination emits photons. A double heterostructure uses band offsets to retain both charge carriers in an active layer. A sufficiently thin layer is a quantum well.^[ref]

The optical and electrical questions are different: photon energy sets a color scale, while light-emitting diode efficiency determines how much supplied energy escapes as light. The blue light-emitting diode made compact white light-emitting diodes and full-color displays practical. A modulated light-emitting diode can also supply the optical signal in a chopped-light lock-in experiment.

Ordinary doped semiconductor devices need a regime where their donor impurities or acceptor impurities supply mobile charge carriers while intrinsic thermal excitation remains sufficiently small.

At low temperature, donor impurities or acceptor impurities may no longer be ionized. Dopant freeze-out reduces the carrier density, raises electrical resistance and changes the intended carrier injection and p-n junction response. At high temperature the intrinsic carrier concentration grows aswhen band effective masses and band gap are treated as constant. Once it becomes comparable with the net doping density, it overwhelms the intended electron-hole imbalance; reverse leakage and dissipation increase and useful p/n control is lost.

The usual operating window lies between freeze-out and intrinsic conduction, with mobility and thermal management placing further practical limits. This is a statement about conventional doped-device operation, not a fundamental prohibition on engineered cryogenic or wide-bandgap devices.

An ideal diffusion-dominated p-n junction obeys the Shockley diode equationwith diode ideality factor $\eta =1$ in the simplest model. Forward bias gives exponential current growth; reverse bias gives a nearly constant $-I_s$ until diode reverse breakdown, outside this ideal expression.

For a long abrupt p-n junction in low carrier injection, the diode saturation current isHere $\mathcal{A}$ is area, $N_D,N_A$ are ionized dopant densities, and $D,L$ are minority-carrier diffusion coefficients and diffusion lengths in the appropriate regions. At each temperature, extract $I_s$ either from the reverse-saturation plateau below breakdown or from a forward exponential fit using its measured diode ideality factor.

Extracting a semiconductor band gap from diode saturation current requires correcting for the transport prefactor:A plot against $1/T$ has slope $-E_g/k_B$ when the gap and effective masses are nearly temperature-independent. Alternatively divide the measured $I_s$ by a known $C(T)$ to recover the full $n_i^2(T)$. The prefactor cannot generally be assumed constant over an arbitrarily broad range. Junction-generation or recombination-dominated current can scale as $n_i$ instead, so the diffusion regime should be identified from the current-voltage behaviour.

A p-n junction joins regions of a semiconductor with opposite majority charge carriers: Electrons on one side and electron holes on the other. It provides the junction modeled by the Shockley diode equation.

Near an unbiased p-n junction, diffusion leaves exposed ionized donor impurities and acceptor impurities. Their electric field opposes further majority-carrier transfer. At thermal equilibrium, drift and diffusion balance; there is no net electric current. Forward bias reduces the barrier to carrier injection; reverse bias enlarges it. A heavily doped tunnel diode adds a different transport route, quantum tunnelling, that the ordinary Shockley diode equation omits.

A semiconductor has an electronic band gap and a conductivity strongly affected by temperature, impurities and carrier injection. Optical absorption can create mobile electrons and holes, enabling a photodiode.

The useful feature of a semiconductor is that its charge carrier population can be controlled. Semiconductor doping changes the supply of mobile Electrons or electron holes; carrier injection changes their population away from thermal equilibrium. A transistor turns that control into an electronic amplifier: a small input signal controls a larger flow of supplied energy.

For a uniform semiconductor in a weak electric field, a simple drift model writes its electrical conductivity asHere $q>0$ is the elementary charge, $n,p$ are the number densities of mobile Electrons and electron holes, and ${\mu }_n,{\mu }_p$ their positive charge carrier mobilities. The two contributions add because opposite electric charges drift in opposite directions and therefore carry electric current in the same direction. This model assumes fixed temperature and mobilities and omits diffusion from density gradients.

An original dimensionless example isolates the effect of carrier injection. Suppose initially $p\ll n=n_0$ and ${\mu }_n=2{\mu }_p$. Adding equal excess populations $\Delta n=\Delta p=0.1n_0$ gives $\Delta \sigma /{\sigma }_0=0.15$, even though the added electron holes remain a minority carrier population. A semiconductor can respond strongly to a small injected population without changing its underlying band gap.

A tunnel diode is a p-n junction with sufficiently heavy semiconductor doping on both sides to make a thin depletion region and permit substantial interband tunnelling. The neutral regions are degenerate semiconductors. Its distinctive forward current-voltage characteristic contains a peak followed by a valley: over part of the curve, increasing the applied electric potential difference decreases the electric current. The Esaki tunnel-diode experiment made this behavior experimentally concrete.

The useful quantity is the local slope, not the ratio of total voltage to total electric current. With conventional electric current $I$ entering the positive-voltage terminal, defineNegative differential resistance means $g_d<0$, hence $r_d<0$ where defined. A forward operating point can still have $V>0$, $I>0$ and absorbed power $VI>0$. A small voltage increase then gives a negative current increment; this does not make the total electric current negative or turn the device into an unlimited source of energy. The external supply sets the operating point and supplies the energy available for an electronic amplifier.

An original idealized construction explains the shape. Put the n-type semiconductor on the left and the p-type semiconductor on the right. Take $q>0$ as the elementary charge and $V=V_p-V_n$. Increasing forward bias lowers the right-hand Electron energy levels relative to the left. Denote the two reservoir electrochemical potentials by ${\mu }_n,{\mu }_p$, so that ${\mu }_n-{\mu }_p=qV$. At zero temperature, occupied left-hand conduction band states extend up to ${\mu }_n$; empty right-hand valence band states start at ${\mu }_p$. For transfer conserving Electron energy, the available interval isIt is nonempty only when its upper endpoint exceeds its lower endpoint. Both an occupied initial quantum state and an empty final quantum state must exist at the same energy. The Pauli exclusion principle prevents transfer into an already occupied final quantum state.

For the original diagram, choose arbitrary energy units with $E_{c,n}=-0.5$, ${\mu }_n=0$, ${\mu }_p=-u$ and $E_{v,p}=0.5-u$, where $u$ is $qV$ in those units. The available interval has widthThus $L(0.25)=0.25$, $L(0.50)=0.50$, $L(0.70)=0.30$, and $L(1.15)=0$. Initially forward bias opens a transfer window; further forward bias closes it by moving the right-hand valence band edge below the left-hand conduction band edge. This is a state-counting illustration, not a formula for a measured electric current.

For reverse bias, the transfer direction changes: occupied right-hand valence band states can feed empty left-hand conduction band states. In the same construction, $u=-0.70$ opens the interval $0<E<0.70$ for this reverse transfer. A narrow depletion region allows a large reverse quantum tunnelling electric current at small electric potential difference, whereas the ordinary Shockley diode equation predicts only a small reverse saturation electric current before diode reverse breakdown. At zero biasing, equal reservoir occupations give zero net electric current; quantum tunnelling does not require a net equilibrium flow.

A finite-temperature refinement replaces sharp occupation cutoffs with the Fermi-Dirac distribution. An illustrative weak-transfer expression isHere $\mathcal{W}\ge 0$ describes allowed initial/final quantum states and their coupling, and $f_n,f_p$ are Fermi-Dirac distributions with the respective electrochemical potentials. The occupation difference follows by subtracting the reverse transfer factor from the forward one: $f_n(1-f_p)-f_p(1-f_n)=f_n-f_p$. An overlap interval alone does not determine $\mathcal{W}$: transmission probability, density of states, crystal momentum selection and phonons can matter. A complete germanium calculation is more demanding than multiplying two constant density of states factors. At larger forward bias, ordinary carrier injection and diffusion supply a rising current branch even after direct band overlap is lost.