Characterization of Semiconductor

Contact resistance

Introduction

Electrical contact resistance (ECR, or simply contact resistance) is resistance to the flow of electric current caused by incomplete contact of the surfaces through which the current is flowing, and by films or oxide layers on the contacting surfaces. It occurs at electrical connections such as switches, connectors, breakers, contacts, and measurement probes. Contact resistance values are typically small (in the microohm to milliohm range). ^[1]

Measurement method

Four-terminal measurement

In a four-terminal measurement, the current used to make the measurement is injected using a second, separate pair of leads, so the contact resistance of the measurement probes and their leads is not included in the measurement.^[1:1]

TLM (Transmission line model)

Graphical description of the transfer length method (TLM)

$$R_{Tot}={\frac {R_{S}}{Z}d+2R_{C}}$$

Circular TLM

Pad structure for circular transmission line measurements (c-TLM)

$$R_{Tot}\approx {\frac {R_{S}}{2\pi }}\left[\ln \left({\frac {r_{o}}{r_{o}-d}}\right)+L_{T}\left({\frac {1}{r_{o}-d}}+{\frac {1}{r_{o}}}\right)\right]$$

$$d = r_{o} - r_{i}$$

Current–voltage characteristic

Introduction

Current–voltage characteristic, usually is IV curve, is an important metric of semiconductor lasers.

A current–voltage characteristic or I–V curve (current–voltage curve) is a relationship, typically represented as a chart or graph, between the electric current through a circuit, device, or material, and the corresponding voltage, or potential difference, across it.^[2]

Materials^[3]

LEDs are made from a variety of inorganic semiconductor materials. The following table shows the available colors with wavelength range, voltage drop, and material(s):

Color	Wavelength [nm]	Voltage drop [ΔV]	Semiconductor material
Infrared	λ > 760	ΔV < 1.63	Gallium arsenide (GaAs) Aluminium gallium arsenide (AlGaAs)
Red	610 < λ < 760	1.63 < Δ_V_ < 2.03	Aluminium gallium arsenide (AlGaAs) Gallium arsenide phosphide (GaAsP) Aluminium gallium indium phosphide (AlGaInP) Gallium(III) phosphide (GaP)
Orange	590 < λ < 610	2.03 < Δ_V_ < 2.10	Gallium arsenide phosphide (GaAsP) Aluminium gallium indium phosphide (AlGaInP) Gallium(III) phosphide (GaP)
Yellow	570 < λ < 590	2.10 < Δ_V_ < 2.18	Gallium arsenide phosphide (GaAsP) Aluminium gallium indium phosphide (AlGaInP) Gallium(III) phosphide (GaP)
Green	500 < λ < 570	1.9 < Δ_V_ < 4.0	Traditional green: Gallium(III) phosphide (GaP) Aluminium gallium indium phosphide (AlGaInP) Aluminium gallium phosphide (AlGaP) Pure green: Indium gallium nitride (InGaN) / Gallium(III) nitride (GaN)
Blue	450 < λ < 500	2.48 < Δ_V_ < 3.7	Zinc selenide (ZnSe) Indium gallium nitride (InGaN) Synthetic sapphire, Silicon carbide (SiC) as substrate with or without epitaxy, Silicon (Si) as substrate—under development (epitaxy on silicon is hard to control)
Violet	400 < λ < 450	2.76 < Δ_V_ < 4.0	Indium gallium nitride (InGaN)
Ultraviolet	λ < 400	3 < Δ_V_ < 4.1	Indium gallium nitride (InGaN) (>360 nm) Diamond (235 nm) Boron nitride (215 nm) Aluminium nitride (AlN) (210 nm) Aluminium gallium nitride (AlGaN) Aluminium gallium indium nitride (AlGaInN)—down to 210 nm

Evaluation

We can consider a semiconductor laser as diode plus resistance($R$),

$$I=I_{s}(e^{\frac{V-IR}{n V_{T}}}-1),$$

where $I_{s}$, $n$ is ideal factor ($n\geq1$, a $n$ close to 1 means more diffusion current and less combination and recombination of carrier^[4]),

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1. Contact resistance - Wikipedia ↩︎ ↩︎

2. Current–voltage characteristic - Wikipedia ↩︎

3. Light-emitting diode physics - Wikipedia ↩︎

4. 《涨知识啦13》—二极管IV特性的进化_二极管理想因子-CSDN博客 ↩︎