Physics of Semiconductor Devices Lecture 7 I-V Characteristics

Physics of Semiconductor Devices Lecture 7. I-V Characteristics of Ideal P-N Junction A. V. Sogoyan

I-V Characteristics of Ideal P-N Junction In TE: • balance between electron and hole flows across SCR • balance between G and R in QNR’s • I =0 In forward bias: • energy barrier to minority carriers reduced • minority carrier injection • R>G in QNR’s • I ∼ exp(q. V/k. T) In reverse bias: • energy barrier to minority carriers increased • minority carrier extraction • G>R in QNR’s • I saturates to a small value

I-V Characteristics of Ideal P-N Junction Key thinking to construct model for I-V characteristics: • junction voltage sets concentration of carriers with enough energy to get injected; • rate of carrier injection set by minority carrier transport and G/R rates in quasi-neutral regions; • SCR is in quasi-equilibrium.

I-V Characteristics of Ideal P-N Junction Boundary conditions across SCR. In thermal equilibrium, Boltzmann relations: If net current inside SCR is much smaller than drift and diffusion components, then quasi-equilibrium⇒ Boltzmann relations apply:

I-V Characteristics of Ideal P-N Junction In terms of excesses:

I-V Characteristics of Ideal P-N Junction For electrons (for example):

I-V Characteristics of Ideal P-N Junction Minority carrier currents at edges of SCR(”long” diode: Wn >> Lh, Wp >> Le). Solution of diffusion equation: Excess minority carrier currents:

I-V Characteristics of Ideal P-N Junction Excess minority carrier currents: Total current: sum of electron and hole current: Define Js ≡ saturation current density (A/cm 2):

I-V Characteristics of Ideal P-N Junction

I-V Characteristics of Ideal P-N Junction Rectifying behavior arises from boundary conditions across SCR: -In forward bias: carrier concentrations at SCR edges grow up exponentially -In reverse bias: carrier concentrations at SCR edges reduced quickly to zero (can’t go below!) → I saturates

I-V Characteristics of Ideal P-N Junction Quasi-Fermi levels across long diode: Inside SCR:

I-V Characteristics of Ideal P-N Junction Quasi-neutrality in QNR’s demands n‘= p’. Consequences: In n-QNR, quasi-neutrality implies: Also, if with supplied from p-contact supplied from n-contact

I-V Characteristics of Ideal P-N Junction Looks like a capacitor ⇒ diffusion capacitance Diffusion capacitance (per unit area): If both sides are ”long”:

I-V Characteristics of Ideal P-N Junction Total diode capacitance:

Conclusions