We derive a value d=2.49 nm (3 s.f.), the required InGaN quantum well width, to produce a â€˜trueâ€™ green laser of ~530 nm, using a simple infinite well model. â€˜True greenâ€™ semiconductor lasers are the next generation of lasers for use in HD disc-reading devices

Anand, Jasdeep

Buccheri, Alexander

Gorley, Michael

Weaver, Iain

English

University of Leicester Open Journals

Journal of Special Topics  1  P2_12 InGaN quantum-well width w.r.t λ  Jasdeep Anand, Alexander Buccheri, Michael Gorley, Iain Weaver  Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH. November 16, 2009 Abstract We derive a value d=3.87 nm (3 s.f.). This is the required InGaN quantum well width to produce a ‘true’ green laser of ~530 nm, derived using a simple infinite well model. ‘True green’ semiconductor lasers are the next generation of lasers for use in HD disc-reading devices and as such are of interest.  Introduction Semiconductor quantum wells lie at the heart of semiconductor lasers for example, current ‘Blu-ray’ players are based on InGaN quantum wells that generate laser wavelengths in the range of λ =360-480 nm.   True green InGaN lasers in the range λ =515-530 nm have great potential, being more compact, offering greater temperature stability and capable of higher modulation capacity than their current frequency doubling counterparts [1]. A true green laser of λ =530nm has still not been achieved. In this paper we look at the size of the InGaN well required to produce a 530 nm laser.  GaN-InGaN-GaN Hetrostructure  The light emitted by a semiconductor laser is determined by the energy gap of the quantum well within the hetrostucture. This is modified by size quantisation: A layer of semiconductor with a small band gap is sandwiched between layers of a large band gap semiconductor producing a quantum well that can confine both electrons and holes. Blu-ray devices use a GaN-InGaN-GaN structure so we will assume that this structure is most suitable for a true green laser.        The band gap of a quantum well, Ewell  within a simple infinite 1D quantum box approximation is given as,   (1.0) [4]  where  is the bulk band gap in InGaN, d is the quantum well width,   is the mass of an electron and ,  are the effective electron and hole masses in InGaN.   Rearranging with respect to  d  gives:   (1.1)  Determining  The energy gap in bulk InGaN is both a function of the doping and the temperature.     w.r.t the doping, X, is given by the expression [2]:     (2.0)   where  is the band gap energy of  InN,  is the band gap energy of GaN, b is the bowing parameter of ; set to  2 eV [5] and X is the In doping relative to Ga.   The bowing parameter is a coefficient inferred from the form of the band gap energy of the semiconductor material. Sources vary between ~2 eV and ~4eV [2,5]. b varies w.r.t. the lattice constant and the mismatch between the InN and GaN lattices [5]. Given that we’re not accounting for strain in the lattice and b is difficult to theoretically GaN GaN InGaN Figure 1.  GaN-InGaN-GaN hetrostructure.   P2_12 InGaN quantum-well width w.r.t λ, November 16, 2009. 2  calculate, it is assumed that an approximate value will suffice.   Jih-Yuan Chang et al is concerned with blue InGaN quantum-well lasers of . They used   X=0.2 doping for their InGaN wells and found  however, values for  vary between crystal types and values for  vary between sources. Here we’ve used values w.r.t. zincblende GaN which is why our values may vary somewhat from Jih-Yuan Chang et al.  Compound Energy gap (eV) (at 300K) GaN 3.2    InN 2.0    Table 1. [3]  Considering the doping range   we assume an average doping of X=0.5, 50/50 In/Ga to achieve   Using (2.0),   Calculating the Effective Mass Values [2] The effective mass of the electrons and holes in InGaN are also a function of the doping therefore before we calculate d we must calculate the corresponding masses for X=0.5.   (3.0)    (3.1)         (3.2)  Compound Effective mass (   0.13 [3]  0.11 [3]  0.12 (3.0) Table 2. Effective masses.  The assumption is made here that . Since  , we can neglect   in our calculations. This is probably a good approximation as the heavy hole state is the lowest hole energy, located closest to the top of the valence band and the device could be set up in such a way that by filling the light hole state with electrons, only transitions with these heavy hole states will  occur. Therefore, substituting values from table 2 into (3.0) and (3.2) give 10/1/111()( NGaInhNGaIne xxxxmm  (3.3)  Results and Discussion It is assumed equation (2.0) calculates  for T=300 K as it contains no temperature dependence and the values we’ve used for GaN and InN energy gaps are both taken at T=300 K.  Therefore, substituting  into (1.1) gives d=3.87 nm (3 s.f.)   On comparison to FIG.1 [2] it can be seen that our well size is of the same order of magnitude. The accuracy of the model could be improved further by treating the quantum dot as a finite well and accounting for the strain in the lattice.   Conclusion  Using a simplified model we have shown that the width of an InGaN quantum well in a GaN/InGaN/GaN hetrostructure can be calculated to the correct order of magnitude and that further improvement of the model requires it to be treated as a finite well.   References:  [1] Direct emitting green InGaN laser, www.ledsmagazine.com/press/19464 [2] Simulation of blue InGaN quantum-well lasers, Jih Chang et al, J.Appl.Phys.,Vol 93,No.9, 1 May 2003.  [3]www.ioffe.rssi.ru/SVA/NSM/Semicond/ [4] Quantum Wells, Mervyn Roy, Journal of Special Topics. [5] Vegard’s law deviation in lattice constant and band gap bowing parameter of zincblende . Yen-Kuang Kuo et al. Science Direct   

P2_12 InGaN quantum-well width w.r.t Î»

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P2_12 InGaN quantum-well width w.r.t Î»

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