To generate gain in a laser medium, you need to create population inversion.

http://en.wikipedia.org/wiki/Population_inversion

To do this you pump the medium, in case of Germanium you pump with current. Since Ge is a 3-level system (see the description in the above mentioned article as well) you need to pump hard to achieve population inversion. This is the main reason of the lasing threshold. To start laser laser operation the gain should be high enough to compensate the losses of the cavity. Therefore low loss cavity can reduce lasing threshold, but not below a certain level.

Hi, Gabor, thanks a lot for your answer and suggested article. They are very helpful for me.

I read the article and know that "Because at least half the population of atoms must be excited from the ground state to obtain a population inversion, the laser medium must be very strongly pumped. This makes three-level lasers rather inefficient. And four-level lasers are favored."

But it is still not clear for me: what are level 2 and 3 in Ge? and is it possible to be a 4-level system?

Thanks!

I don't know the energy levels of the Ge, but you can find out which is the 3rd level from the wavelength (photon energy) of the laser. It can happen that it is not even a single level, but a band with many levels separated by small energy gaps. It is common in solid state mediums. The 2nd can be another level (or band) above the 3rd with fast, non-radiative energy transfer to the 3rd or even can be the highest level of the band of the 3rd. Basically the spectroscopic properties of each medium are given, however in case of semiconductors you can use p or n type doping to change it. Good luck :) You can start with studying the spectroscopy of 4-level systems like Nd:YAG or Ti:Sapphire and understand what makes them to have 4-levels.

Hi, Gabor, many thanks!

Based on your description and my knowledge of Ge's band-gap structure, the physic picture for 3-lever is clear for me.

Also thanks for your suggestion of studying the examples to understand better 4-lever systems.

Thanks for your time and kind help!

I also posted this question on linkedin, and Dr. Fang-Zheng Lin suggested me two helpful books: "Diode Lasers and Photonic Integrated Circuits" by L. A. Coldren and "Physics of Optoelectronic Devices" by S. L. Chuang.

the levels in Ge are: Gamma valley, L-valley and valence band.

Hi Philippe,

I am very happy to have you join this discussion. Thanks a lot!

I have a question to ask you: Since the tensile strain splits the valance band into light hole band and heavy hole band, why it is not a 4-level system? I mean: Gamma valley, L-valley, light hole band and heavy hole band.

Thank you very much!

Best regards,

Min

Hi Min Xie,

The threshhold gain is given by the loss in the lasing waveguide added to the loss due to the mirrors (1/L*ln(1/R^2), where L is the laser length and R is the mirror reflectivity). For III-VsThere are some models (see Coldren) that relate current to charge carrier density and then to gain, for Germanium this needs to be measured. The high doping you need in the Germanium lasers leads to substantial optical absorption in the active waveguide. It is, therefore, intrinsically hard to make a really low loss cavity even if your mirrors are perfect. I would estimate the lower limit of material gain due to losses in doping at something like 50/cm. This number (which might be lower) needs to be reached regardless of cavity and laser design and constitutes a hard boundary.

Regarding the bands, I disagree that the three levels are Gamma valley, L-valley and valence band, as the L-valley is not the the only level feeding the gamma valey. It is more: level 1 and 4 are the Fermi levels in the ohmic contacts on n and p-side, the lasing levels are the conduction and valence band in the active region (Germanium). Filling the L-valley just eliminates a loss channel but is not the 'feeder' level for the gamma valley. In semiconductor lasers the limiting factors are quite different from Ti:Sapphires or YAGs, so I am not sure if studying traditional 4-level laser systems will help so much here. But Coldrens book is an excellent introduction to waveguide based lasers and really to be recommended.

Cheers, Dominik

I think Dominik is probably right about the levels you could consider. I also think that the emission mechanism in Germanium is not as trivial as the MIT/Stanford model describes it. Recent measurements from J. Faist's group (one contribution in 2012 and one last month) shows that the emission from Ge can not be attributed only to the mechanism describe by the MIT as the Free Carrier Absorption is too high to explain any lasing. From my personal experience, the best emitters I got working were not p-i-n structures as suggested by the MIT/Stanford model.

At the moment I strongly believe that nobody got it totally right.

Dear Dominik,

Thank you so much for the very nice and patient explanation to me. I think I understand point 1. But still should search for a band diagram for the 4 levels you described.

Sorry for my late reply, cause I have an important interview related to this topic today, though failed, I really appreciate all of your help.

Thank you very much for your time and discussion.

With best regards,

Min

Feb 26, 2014

Dear Philippe,

As a freshman in this topic, I could not give any judgement for the emission mechanism in Germanium. I will keep following the groups you have mentioned. And also good luck for you. Wish you make it lasing!

Best regards,

Min

Feb 26, 2014

Hi Min,

the attached link has a nice picture explaining the simlest instance of a semiconductor light source (I hope the author Dieter Bimberg doesnt mind and it reproduces nicely here). The Fermi levels (Efc, Efv) are marked and serve as injection levels, the band edges in conduction and valence band (Ec, Ev) serve as recombination levels. In the case of a siomple pn-junctionyou have something similar to a 3-level laser (a) as the Bandgap energy for the electrons at the point of highest hole concentration is close to the fermilevel and vice versa. This structire does not work to well as a laser, maybe as LED. In (b) you see a heterostructure i.e. a pin-diode where the intrinsic material has a lower bandgap (in this case GaAs between AlGaAs, typical would also be InGaAs(P) between InP). This resembles more the 4 level case, as fermi levels (injection) are separate from band edges in the low bandgap material (recombination). The carrier distribution is more uniform and the laser/LED will perform better.

I am sorry my answer is so late, I dont check here to often and hope this helps clarify the ideas.

Cheers, Dominik

http://photonicssociety.org/newsletters/jun13/images/Radiant-Swan_01.jpg

I have some study on Ge LED and Laser. Besides the concepts similar to direct band gap materials, the indirect band gap nature of Ge also plays an important role. The competitiveness between radiative recombination and non-radiative recombination (SRH, Auger, and surface recombination) as well as phonon-assistant indirect band gap transition are important for population inversion condition. The elevated junction temperature also contributes to carrier distribution in k space and alters the transition mechanism. The cavity design for optical confinement and related selected resonant mode. I think the most important things are defect/impurity density and surface/interface recombination.