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\title{Equivalent Circuit-Level Characterization of 1.55 µm Ingan Laser}
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             \author[1]{Md. Jahirul  Islam}

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\date{\small \em Received: 7 December 2016 Accepted: 4 January 2017 Published: 15 January 2017}

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\begin{abstract}
        


InGaN is one of the most promising group III-V nitride materials recently focused for semiconductor based device fabrication. The advent of long haul optical communication system requires sophisticated and reliable lasing device. InGaN based lasers composited to have 0.8 eV bandgap energy produce coherent light of 1.55 ?m. In this paper, the output characteristics of a heterostructured laser with InGaN as active layer is presented systematically. The circuit-level laser modeling is developed by solving the respective rate equations. This includes the conversion of the complete laser system into its equivalent electrical circuits. Thereafter, simulation was carried out using PSPICE to evaluate the electrical quantities e.g. output power, I-V characteristics, slope efficiency and transient response. A bias voltage of 1.2 volts, threshold current of approximately 6 mA, turn on delay time of 3 ns and slope efficiency of 0.368 W/A are found. The findings are summarized in graphical representation and found to be consistent with numerical simulation of the system model.

\end{abstract}


\keywords{equivalent circuit modeling, rate equations, hetero structure, quantum well laser (QWL), pspice.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
erhapse, the invention of lasers has been proven to be one of the most significant breakthroughs for technology in the last century \hyperref[b1]{[1]}. Their applications extend to high speed communications, optical storage (e.g. CDs, DVDs, optical memories), barcode scanners in industrial machines, printers and even in medical science for spectroscopy and imaging, and also in destroying cancer tissues and unnecessary cells in human bodies \hyperref[b1]{[1]}\hyperref[b2]{[2]}. In addition, modern technology facilitates with distance learning, online education and high speed online entertainment as well as instant communication from each corner of the world. This requires enormously data to be transported within a short period of time. Optical fiber communication system is one of the strongest candidates to overcome the associated problems.\par
The issues with the constraints of noise, bulk volume of data, amount of signal power transmission, interference with other networks and nearby RF electromagnetic fields are greatly settle down with optical fiber system \hyperref[b3]{[3]}\hyperref[b4]{[4]}. Ideally, 1.55 ?m lasers are well suited for long haul communication at higher data rates due to minimal loss \hyperref[b5]{[5]}.\par
A growing interest on the group III-IV nitride based semiconductor materials has recently been prompted towards light emitting diodes, lasers and solar cells \hyperref[b9]{[9]}\hyperref[b10]{[10]}\hyperref[b11]{[11]}. The wider (0.7 -6.2 eV) and direct bandgap, low electron effective mass, and high theoretical mobilities of these materials made them suitable for device applications \hyperref[b12]{[12]}. A small amount of Ga in InN results in InGaN composite with 0.8 eV bandgap energy which is compatible with 1.55 ?m wavelength.\par
The equivalent circuit modeling (ECM) is required to clearly understanding the lasers' working conditions and to verify compatibility with associated electrical driver circuits. The ECM using Shockley equation transfers the carrier and photonics numbers into current and voltage quantities, respectively. Numbers of studies investigated the ECM for quantum dot and quantum cascaded lasers \hyperref[b13]{[13]}\hyperref[b14]{[14]}\hyperref[b15]{[15]}. However, to the best of authors' knowledge, the ECM of the proposed In GaN based laser is still unreported, and thus requires attention. 
\section[{P}]{P}\par
In this paper, we investigate the electrical equivalent circuit characteristics of a previously proposed \hyperref[b16]{[16]} InGaN based heterostructure laser diode. The static current-voltage (I-V), output power-input current (L-I), output voltage, and transient conditions are discussed briefly. PSPICE circuit simulator has been used to demonstrate the lasers' electrical characteristics.\par
A number of semiconductor alloys such as ternary, quaternary and quintuplet elements are used to fabricate 1.55 ?m laser diodes. For instance, materials including AlGaInAs, GaInNAsSb/GaAs, InGaAs/ InGaAs P, and GaInN AsSb/GaNAs \hyperref[b6]{[6]}\hyperref[b7]{[7]}\hyperref[b8]{[8]} are the choices for the active layer of the lasers. However, often these ternary, quaternary and quintuplet materials are difficult to grow, and results in lasing problem. II. 
\section[{PROPOSED LASER STRUCTURE}]{PROPOSED LASER STRUCTURE}\par
The schematic structure of the proposed 1.55 ?m quantum-well hetero structure lasers using InGaN is shown in Fig. \hyperref[fig_0]{1}. A c-plane sapphire wafer is used as the substrate. The LD structure consists of 0.6 µm thick n-In 0.15 Ga 0.85 N contact layer, 0.1 µm thick GaN cladding layer, 0.2 µm thick In 0.15 Ga 0.85 N guiding layer, and a 0.1 µm thick InGaN active layer. 
\section[{III.}]{III.} 
\section[{MATHEMATICAL MODEL}]{MATHEMATICAL MODEL}\par
The rate equations for quantum well lasers are given by \hyperref[b17]{[17]}\hyperref[b18]{[18]} ( )  3 , where A, B, and C are the unimolecular, radiative, and Auger recombination coefficients, respectively; S = photon density = S tot /V a , where, S tot is again the total number of photons in the active volume; ? = ? A AN+? B BN 2 +? C CN 3 , where ? A , ? B , and ? C are coupling coefficients; P f = the output power, V a = is the volume of a single QW; ? i = is the currentinjection efficiency; Î?" c = is the optical confinement factor of one QW; g 0 = is the carrier dependent gain coefficient; ? p = is the photon lifetime; ?= is the lasing wavelength; ? c = is the output-power coupling coefficient; and ( )( ) ( ) ( ) ( ) ( ) i 0 a n d N t I t N t N t S t ? g dt eV ? 1 ?S t = ? ? +\textbf{(1)}1 1 ?S t = +\par
the gain saturation term. ? dI I eV dt = and the stimulated emission component I 2 . The p-n heterojunction voltage V j can be represented by one ohmic resistance R e , series-connected with Shockley p-n junction diode (shown in Fig. \hyperref[fig_2]{2}). 
\section[{IV.}]{IV.} 
\section[{MODEL IMPLEMENTATION}]{MODEL IMPLEMENTATION}1 2 j d 0 d V C C 1 V ? ? ? = ? ? ? ? ?\par
, a junction depletion capacitance is added to the circuit, where C 0 is the zero bias depletion capacitance, V j is the junction voltage, V d is the build-in potential. Now, multiplying Eqn. (  {\ref 2}) by eV a we get,( ) ( ) ( ) ( ) ( ) ( ) 0 a a a c a c p n d S t S t ?N t g N t S t eV eV eV Î?" eV Î?" dt ? ? 1 ?S t = ? + + +\textbf{(6)}\par
which later reduces to( ) ( ) ( ) ( ) ( ) p 0 c n c p d S t S t N t S t C G Î?" ?I Î?" dt R 1 ?S t + = + + (7)\par
Rearranging Eqn. \hyperref[b7]{(7)}, one can get( ) ( ) ( ) ( ) p 0 n c p c C S t d St N t S t G ?I Î?" R Î?" dt 1 ?S t + = + + (8)\par
Where the parameters R p and G 0 are defined by \hyperref[b19]{[19]},p p p ? R C = , (\textbf{)}2 13 0 nom G D J 2 10 = ? × .\par
Also, D= a constant andn nom a I J V = . stimulated component ( ) ( ) ( ) 0 N t S t G 1 ?S t +\par
. These two components are modeled by two (I 3 and I 2 ) current sources as shown in Fig. \hyperref[fig_3]{3}. Thus, the light output is proportional to the output node in voltage representation. The voltage representation is applicable if transmission channel and receiver circuit are included in the simulation. Now from Eqns. (  {\ref 4}) and (  {\ref 8}), the total equivalent circuit for a single QW laser has been illustrated in Fig. 4.\par
V.    Input Current (mA)   The results of PSPICE circuit model for InGaN based laser developed according to the electrical equivalent circuit discussed in section IV, is presented in this section. The parameters used for the PSPICE simulation are listed in Table \hyperref[tab_1]{1}. 
\section[{PSPICE CIRCUIT SIMULATION RESULTS}]{PSPICE CIRCUIT SIMULATION RESULTS}\par
Output Power (mW)  
\section[{CONCLUSION}]{CONCLUSION}\par
A detailed electrical equivalent circuit model of 1.55 ?m InGaN based laser has been studied numerically. The characteristics are realized through the development of the equivalent circuit modeling of the quantum well laser. The electrical circuit modeling of the laser is important to find out the electrical parameters. The PSPICE circuit simulation resulted in an increase in output power with the increase of input current. Threshold current of approximately 6 mA, bias voltage of 1.20 volts, slope efficiency of 0.368 W/A and turn on delay of 3 ns have been found from this circuit analysis. These electrical properties present the richness of InGaN based lasers, and are in agreement with the results of numerical simulations of the same model. Attention on ECM for the laser is important to understanding the electrical mechanism, and requires exhaustive investigation to be matched with electrical automatic power control, modulation scheme, level shifter and slow start circuits.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}=}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Fig. 3 :}\end{figure}
      \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.27172131147540984\textwidth}P{0.22991803278688525\textwidth}P{0.3483606557377049\textwidth}}
Parameter\tabcellsep Unit\tabcellsep Value\\
R e\tabcellsep ?\tabcellsep 0.468\\
R p\tabcellsep ?\tabcellsep 29.4\\
R s\tabcellsep ?\tabcellsep 2.0\\
? ns\tabcellsep ns\tabcellsep 2.25\\
? np\tabcellsep ns\tabcellsep 3\\
C p\tabcellsep pF\tabcellsep 0.102\\
C d\tabcellsep pF\tabcellsep 10\\
S c\tabcellsep m -3\tabcellsep 10 18\\
D\tabcellsep V -1 A -1 m 6\tabcellsep 1.79x10 -29\\
? s\tabcellsep -\tabcellsep 10 -5\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 			\footnote{© 2017 Global Journals Inc. (US)Equivalent Circuit-Level Characterization of 1.55 µm Ingan Laser} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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\bibitem[Yavari and Ahmadi ()]{b14}\label{b14} 	 		‘Circuit-Level Implementation of Semiconductor Self-Assembled Quantum Dot Laser’.  		 			M H Yavari 		,  		 			V Ahmadi 		.  	 	 		\textit{Journal of Quantum Electronics}  		2009. 15  (3)  p. .  	 	 (Selected Topics in IEEE) 
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\end{document}
