Diffusion Capacitance¶
Forward-injected carrier charge in a pn junction gives a bias-dependent incremental capacitance distinct from depletion capacitance.
Core Idea¶
Forward bias injects minority carriers into a pn diode's quasi-neutral regions. Their stored charge changes with voltage, giving incremental diffusion capacitance \(C_d=dQ_{\mathrm{stored}}/dV\) at an operating point. It is distinct from depletion-layer junction capacitance \(C_j\).[ref-396edd14d93c][ref-fe3c219c59fc]
Scope of Application¶
In the cited narrow-base small-signal model, stored hole charge on the n-side is \(Q_p=\tau_{Tp}I_p\) and electron charge on the p-side is \(Q_n=\tau_{Tn}I_n\). With fixed transport times and ideal forward exponential currents, \(C_d\simeq(q/kT)(\tau_{Tp}I_p+\tau_{Tn}I_n)\). UCLA distinguishes wide-base lifetime from narrow-base transit time. Strong forward bias can make \(C_d\) dominant; reverse/small forward bias often leaves \(C_j\) dominant.[ref-396edd14d93c][ref-fe3c219c59fc]
Clarity¶
Specify which charge \(Q\) counts, bias, geometry, temperature and frequency regime. \(C_d\) is a derivative, not \(Q/V\). The shortcut \(C_d=\tau g_d\) requires a fixed appropriate storage time; if \(\tau\) varies with voltage, differentiate \(\tau(V)I(V)\) fully. A single universal “charge in transit” rule for any device exceeds the sources.[ref-396edd14d93c][ref-fe3c219c59fc]
Manages Complexity¶
The charge derivative packages a distributed carrier profile into a local equivalent-circuit branch, useful for small slow perturbations. It does not replace full dynamic diffusion admittance at high frequency. Shockley's original 1949 work discusses carrier diffusion and frequency-dependent junction response, not an unconditional compact formula.[^ref-1d3d5bb0064a]
Abstract Reasoning¶
Calculate each neutral-region excess charge, differentiate with respect to terminal voltage and add the side contributions. Compare the result with \(C_j\) at the same bias. For strong forward operation, more injected current improves conduction while also raising stored charge and capacitance; switching or high-frequency analysis must account for that burden, not attribute all circuit speed to \(C_d\) alone.[^ref-396edd14d93c]
Knowledge Transfer¶
The hole and electron sides share the same derivative relation but have different currents and time scales. The logic extends to another electronic charge-control model only after its stored charge and transport law are identified. Generic delayed inventory is an analogy, not automatically diffusion capacitance. This entry currently has no strict parent edge; a generic delayed-inventory relation is not asserted.
[^ref-396edd14d93c]: J. del Alamo, MIT 6.012 Lecture 16, The pn Junction Diode (II) (2005), pp.11–18, charge and two-capacitance derivation. [^ref-fe3c219c59fc]: UCLA, Basic Semiconductor Devices for Electrical Engineers, chapter 3, equations 3.127–3.137, wide- and narrow-base diode charge. [^ref-1d3d5bb0064a]: William Shockley, “The Theory of p–n Junctions in Semiconductors and p–n Junction Transistors,” Bell System Technical Journal (1949), original abstract on diffusion and dynamic admittance.
Neighborhood in Abstraction Space¶
Diffusion Capacitance sits in a sparse region of the domain-specific corpus (68th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Condensed Matter & Physical Chemistry Models (26 abstractions)
Nearest neighbors
- Su–Schrieffer–Heeger model — 0.85
- Mott–Schottky Equation — 0.84
- Dynamic logic (digital electronics) — 0.84
- Single Vegetative Obstruction Model — 0.83
- Rooted product of graphs — 0.83
Computed from structural-signature embeddings · 2026-10-08