Question bank — Recombination and generation mechanisms

False — recombination $R$ and generation $G$ are both nonzero and equal, so only the net rate $U=R-G$ is zero. The traffic never halts; it just balances.

False — $U=0$ only means the system sits at equilibrium ($np=n_i^2$). Electrons and holes are still being created and destroyed continuously at rate $R=G\ne 0$.

False — excess ($np>n_i^2$) means too many pairs, so net recombination ($U>0$) kicks in to drag $np$ back down. Net generation ($U<0$) only fires when $np<n_i^2$.

Roughly true but "exactly" is wrong — the electron may sit slightly above $E_c$ and the hole slightly below $E_v$, so photon energy is $\approx E_g$ (a small spread), which is why LED emission is a band, not a single line.

False — the block is band structure, not purity. Si is indirect-gap, so band-to-band recombination needs a phonon for momentum and is intrinsically slow; SRH wins and dumps energy as heat regardless of cleanliness.

False — it is the most harmful. Mid-gap traps minimise the SRH denominator, maximising $U$; they are "lifetime killers." Off-centre traps re-emit a captured carrier easily and waste the recombination event.

False — the energy goes to a third carrier as kinetic energy, which then relaxes by giving off phonons (heat). No photon leaves the crystal, which is why Auger reduces LED/solar efficiency.

False — the rates add because channels act in parallel, so $1/\tau =\sum 1/{\tau }_i$. The fastest path (smallest ${\tau }_i$) dominates the total.

False — in low injection $\tau$ is a fixed material property (e.g. $1/(B{n}_0)$ or $1/(\sigma v_{th}{N}_t)$), independent of $\Delta n$. Only at high injection does the effective lifetime shift.

The generation term is missing. Correct is $U_{rad}=B(np-n_i^2)$; at equilibrium the $n_i^2$ exactly cancels $np$ so $U=0$. Writing $U=R$ forgets thermal generation $G_0=B{n}_i^2$.

The lifetime is set by the majority concentration the minority meets, so ${\tau }_p=1/(B{n}_0)$. A hole recombines by finding one of the abundant electrons; $p_0$ is tiny and irrelevant.

It falls as $1/N_D^2$ (from ${\tau }_{Auger}=1/(C_n{n}_0^2)$) because Auger needs two like carriers plus one opposite — the rate scales with the square of the majority density.

They move oppositely: raising $E_t$ increases $n_1$ but decreases $p_1$ (their exponents have opposite signs). Their product $n_1{p}_1=n_i^2$ stays fixed while their sum is minimised only at $E_t=E_i$.

The numerator is always $np-n_i^2$, independent of $E_t$. Trap position only enters the denominator (through $n_1,p_1$), which is why it sets the strength but not the sign of $U$.

The clean exponential only follows when the continuity equation reduces to $d\Delta p/dt=-\Delta p/\tau$ — i.e. no drift, no external generation. Add a field or light and drift/generation terms reappear and the decay is no longer a pure exponential.

Both are driven by the same distance-from-equilibrium factor $np-n_i^2$ once you subtract equilibrium generation. The bare $Bnp$ is only $R$, not the net $U$.

Instruments see only changes above the constant equilibrium background; the ceaseless balanced traffic $R=G$ produces no observable, so the excess-driven net $U=R-G$ is what governs decay, current, and light output.

It measures how far the carrier product sits from its equilibrium value $n_i^2$; every channel is a restoring process, so its net rate must vanish exactly at equilibrium — a factor $(np-n_i^2)$ guarantees that.

A single $E_g$ transition must shed both a large energy and (in indirect Si) crystal momentum simultaneously — improbable. A mid-gap trap splits it into two smaller, individually likely capture events, so trap-assisted recombination dominates.

It requires three carriers to meet at once, so its rate scales like $n^{2}p$ or $n{p}^2$; at low carrier density this triple coincidence is rare, but at high density it overwhelms the two-body channels.

Its conduction-band minimum and valence-band maximum share the same crystal momentum, so an electron can drop and emit a photon without needing a phonon — making radiative recombination fast (ns lifetimes) and efficient.

Because rates add in parallel, the largest $1/{\tau }_i$ dominates $\sum 1/{\tau }_i$; the process that removes carriers quickest sets the pace, exactly like the smallest resistance carrying most current in parallel.

$G_0$ comes from lattice heat lifting electrons across the gap and depends only on temperature, not on injected carriers; $R\propto np$ climbs immediately when you inject, so injecting shifts the balance toward net recombination.

Zero — $U_{rad}=B(n_0{p}_0-n_i^2)=B(n_i^2-n_i^2)=0$, since $n_0{p}_0=n_i^2$ by the Law of Mass Action. Perfect cancellation, no net loss.

A carrier-depleted region ($np<n_i^2$), such as inside a reverse-biased depletion zone, where the crystal generates pairs to refill toward equilibrium — the origin of reverse saturation current in a PN Junction Diode.

${\tau }_{SRH}=1/(\sigma v_{th}{N}_t)\to \infty$, so SRH switches off entirely and the (slower) radiative or Auger channels take over — this is why ultra-pure Si has very long minority-carrier lifetimes.

Auger dominates, since ${\tau }_{Auger}\propto 1/N_D^2$ collapses fastest with doping — it caps the achievable lifetime and open-circuit voltage in heavily doped Solar Cells.

It becomes $\approx ({\tau }_p+{\tau }_n)\Delta n$, so $U\approx \Delta n/({\tau }_p+{\tau }_n)$ — the effective lifetime is the sum of capture times, larger than the low-injection value; the material effectively recombines more slowly per carrier.

The excess decays as $\Delta p(t)=\Delta p(0)e^{-t/\tau }$, the field-free Continuity Equation with no source — the same $\tau$ that sets Minority Carrier Diffusion lengths controls how fast the crystal forgets the light.

SRH vanishes and radiative is intrinsically weak, so lifetimes become very long and are ultimately set by Auger at high doping — precisely the regime that makes efficient silicon LEDs and Lasers essentially impossible.