# Laser question (Confinement factor and quantum well thickness)

## Main Question or Discussion Point

1. What do we mean by the carrier number at transparency. I mean, what is carrier transparency of a laser?

2. in an IEEE paper ("Circuit Modeling of Quantum-Well Lasers for Optoelectronic Integrated Circuits (ICs) Including Physical Effect of Deep-Level Traps" IEEE J. Quantum electronics, vol. 38, No. 11, November 2002 ) by Mohammad reza Salehi,

he introduced an equation,

Gamma = 0.3 * N' * (d/d0)

where Gamma is the optical Confinement Factor, N' is the number of quantum wells of the laser and d is the thickness of a single quantum well. He said, d0=1000A(angstrom). Now my question is, Where does this d0 come from and why did they mentioned that its value is 1000. I looked at the reference of this paper, they did the same. the didn't mention this either that what is d0.

thank you

## Answers and Replies

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Cthugha
Science Advisor
1. What do we mean by the carrier number at transparency. I mean, what is carrier transparency of a laser?
If you consider a low number of carriers, lasing will not occur because the photons in the cavity will quickly be absorbed due to stimulated absorption and the photon number inside the cavity will be too low to cause efficient stimulated emission. However at higher carrier numbers the effect of stimulated absorption will be small compared to the effect of stimulated emission. The material becomes transparent. Usually the transparency current is defined as the current, where stimulated absorption and emission are exactly balanced.

2. in an IEEE paper ("Circuit Modeling of Quantum-Well Lasers for Optoelectronic Integrated Circuits (ICs) Including Physical Effect of Deep-Level Traps" IEEE J. Quantum electronics, vol. 38, No. 11, November 2002 ) by Mohammad reza Salehi,

he introduced an equation,

Gamma = 0.3 * N' * (d/d0)

where Gamma is the optical Confinement Factor, N' is the number of quantum wells of the laser and d is the thickness of a single quantum well. He said, d0=1000A(angstrom). Now my question is, Where does this d0 come from and why did they mentioned that its value is 1000. I looked at the reference of this paper, they did the same. the didn't mention this either that what is d0.
The optical confinement factor is usually defined as the ratio of the emission profile in the active medium to the complete emission profile in the structure. In QW lasers usually GaAs confinement layers are placed around the QWs (seperate confinement heterostructures). 1000A is a very common value for the size of such a SCH, so I suppose this is where this value comes from.

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Dear cthugha,

Thank you very very much for your reply. it really helped me a lot.