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 physicswiki:semiconductors:nbasedled:nbasedled [2019/04/09 06:15]zoltan.jehn created physicswiki:semiconductors:nbasedled:nbasedled [2019/04/09 06:38]zoltan.jehn 2019/04/09 11:53 zoltan.jehn 2019/04/09 06:38 zoltan.jehn 2019/04/09 06:15 zoltan.jehn created 2019/04/09 11:53 zoltan.jehn 2019/04/09 06:38 zoltan.jehn 2019/04/09 06:15 zoltan.jehn created Last revision Both sides next revision Line 3: Line 3: === Structure === === Structure === - We simulation we used the following LED structure in figure ​\ref{fig:​LEDstr}. The doping for donor concentration is $N_d^+ = 2E24\frac{1}{m^3}$,​ while the acceptor concentration is  $N_a^- = 7E25\frac{1}{m^3}$. The growth direction was in the $c \uparrow$ axis of the crytal structure, which means, the pyro, and piezo effects are also should be considered. + We simulation we used the following LED structure in figure ​1. The doping for donor concentration is $N_d^+ = 2E24\frac{1}{m^3}$,​ while the acceptor concentration is  $N_a^- = 7E25\frac{1}{m^3}$. The growth direction was in the $c \uparrow$ axis of the crytal structure, which means, the pyro, and piezo effects are also should be considered. + <​figure>​ + ;#; + <​latex>​ + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​str.tex} + ​ + ;#; + <​caption>​ **Figure 1.** Structure of the LED​ + ​ - \begin{minipage}[b]{0.99\textwidth} - \centering - \begin{tikzpicture} - \draw [fill =  lightgray] (0,0) rectangle (3,3); - \draw [fill =  red] (3,0) rectangle (3.5,3); - \draw [fill =  gray] (3.5,0) rectangle (5.5,3); - \draw [fill =  lightgray] (5.5,0) rectangle (7.5,3); - \draw (1.5,1.0) node[above] {GaN}; - \draw (6.5,1.0) node[above] {GaN}; ​ - \draw (4.5,1.0) node[above] {Al$_{0.2}$Ga$_{0.8}$N}; ​ - \draw [dashed] (3.25, 1.0) to[out=-100] (5, -0.5) node[align=left,​ below] {Ga$_{0.6}$In$_{0.4}$N};​ - \draw [fill =  darkgray] (-0.5,-0.2) rectangle (0,3.2); - \draw [fill =  darkgray] (7.5,-0.2) rectangle (8,3.2); - \draw (8.0,1.5) [thick,​rounded corners] ​ --  (8.5, 1.5) -- (8.5, -0.5)  node[align=left,​ below] {Anode} ; - \filldraw (8, 1.5) circle (2pt); - \draw (-0.5,1.5) [thick,​rounded corners] ​  ​-- ​ (-1, 1.5) -- (-1, -0.5)  node[align=left,​ below] {Cathode}; - \filldraw (-0.5, 1.5) circle (2pt); - \draw (1.5,0.5) node[above] {N$_d^{+}$};​ - \draw (4.5,0.5) node[above] {N$_a^{-}$};​ - \draw (6.5,0.5) node[above] {N$_a^{-}$};​ - \draw (0.1,3.2) [<​->​] ​  ​-- ​ (2.9, 3.2); - \draw (3.1,3.2) [<​->​] ​  ​-- ​ (3.4, 3.2); - \draw (3.6,3.2) [<​->​] ​  ​-- ​ (5.4, 3.2); - \draw (5.6,3.2) [<​->​] ​  ​-- ​ (7.4, 3.2); - \draw (1.5,3.2) node[above] {100nm}; - \draw (3.25,3.2) node[above] {3.5nm}; - \draw (4.5,3.2) node[above] {50nm}; - \draw (6.5,3.2) node[above] {50nm}; - \draw (5,-1) node[below] {active region}; - %\draw [fill =  gray] (0,1) rectangle (1.5,1.5); - %\draw [fill =  gray] (5.5,1) rectangle (7,1.5); - %\draw [fill =  white] (1.75,1.5) rectangle (5.25,​1.75);​ - %\draw [fill =  gray] (1.75,1.75) rectangle (5.25,​2.25);​ - %\draw [dashed,​rounded corners](0,​0.8) -- (1.7,0.8) -- (1.7, 1.3) -- (5.3, 1.3) -- (5.3, 0.8) -- (7,0.8); - %\draw (3.5,0.25) node[above] {p }; - %\draw (3.5,1.75) node[above] {n++  }; - %\draw (0.75, 1.0) node[above] {n }; - %\draw (6.25, 1.0) node[above] {n }; - %\filldraw (3.5,3) [thick] ​ node[align=left,​ above] {Gate} ​ --  (3.5, 2.25) circle (2pt); - %\draw (-0.0,2) [thick,​rounded corners] ​ node[align=left,​ above] {Source} ​ --  (0.75, 2) -- (0.75, 1.5) ; - %\filldraw (0.75, 1.5) circle (2pt); - %\draw (7.0,2) [thick,​rounded corners] ​ node[align=left,​ above] {Drain} ​ --  (6.25, 2) -- (6.25, 1.5) ; - %\filldraw (6.25, 1.5) circle (2pt); - %\draw [dashed] (2, 1.675) to[out=-250] (1, 3) node[align=left,​ above] {SiO$_2$}; - %\draw (5,0.25) node[above] {Substrate }; - %\draw [dashed, thick] (1.7, 1.4) -- (5.3, 1.4); - %\draw [dashed] (4.5, 1.4) to[in=-100] (6, 3) node[align=left,​ above] {Channel}; - %\draw [dashed] (2.5, 1.3) to[out=+10] (3, -1) node[align=left,​ below] {Depletion region}; - \end{tikzpicture} - \captionof{figure}{Structure of the LED} - \label{fig:​LEDstr} - \end{minipage} - %\begin{minipage}[b]{0.35\textwidth} - % \centering - % \begin{tabular}{l|ll} - % Donor concentration&​ N$_d^+$ &​ 2E24$\frac{1}{m^3}$ ​ \\ - % Acceptor concentration &​N$_a^-$&​7E25$\frac{1}{m^3}$\\ - % \end{tabular} - %\captionof{table}{Parameters of the simulated FET} - %\label{table:​parameterstable} - %\end{minipage} - \section{Bandstructure at zero bias} + === Bandstructure at zero bias === - The bandstructure of the device is plotted in figure \ref{fig:​0vcb}. ​ - It shows that the polarization charges band the profile to the opposite direction as the pn junction would do. For clarification built in potential with, and without polarization charges is depicted in figure \ref{fig:​pot},​ while the polarization charges are depicted in figure \ref{fig:​polarization}. + The bandstructure of the device is plotted in figure 2. + It shows that the polarization charges band the profile to the opposite direction as the pn junction would do. For clarification built in potential with, and without polarization charges is depicted in figure 3, while the polarization charges are depicted in figure 4. - \begin{minipage}[t]{0.99\textwidth} - \centering - \input{images/​bandstr.tex} - \captionof{figure}{Bandstructure at zero bias.} - \label{fig:​0vcb} - \end{minipage} + <​figure>​ + ;#; + <​latex>​ + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​bandstr.tex} + ​ + ;#; + <​caption>​ **Figure 2.** Bandstructure at zero bias.​ + ​ + <​figure>​ + ;#; + <​latex>​ + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​potcomp.tex} + ​ + ;#; + <​caption>​ **Figure 3.** Built-in potential​ + ​ - \begin{minipage}[t]{0.5\textwidth} - \centering - \input{images/​potcomp.tex} - \captionof{figure}{Built-in potential} - \label{fig:​pot} - \end{minipage} - \begin{minipage}[t]{0.5\textwidth} - \centering - \input{images/​polarizationcharges.tex} - \captionof{figure}{Piezo and Pyro charges in the structure} - \label{fig:​polarization} - \end{minipage} - \section{Active region} + <​figure>​ + ;#; + <​latex>​ + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​polarizationcharges.tex} + ​ + ;#; + <​caption>​ **Figure 4.** Piezo and Pyro charges in the structure​ + ​ + === Active region=== - The active of th device is built from InGaN alloy, due its lower bandgap, which results higher carrier concentration in that region. It is a quantum-well region, which creates a confinement for both electron and hole state. The ground state eigenfunctions for this confinement is plotted in figure ​\ref{fig:​WFS} ​for electrons, and the heavy-holes. ​ + The active of th device is built from InGaN alloy, due its lower bandgap, which results higher carrier concentration in that region. It is a quantum-well region, which creates a confinement for both electron and hole state. The ground state eigenfunctions for this confinement is plotted in figure ​5. for electrons, and the heavy-holes. ​ - \begin{minipage}[t]{0.99\textwidth} + <​figure>​ - \centering + ;#; - \input{images/​eigenvalues.tex} + <​latex>​ - \captionof{figure}{Active region of the device with plotted electron and hole eigenfunctions in the quantum well.} + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​eigenvalues.tex} - \label{fig:​WFS} + ​ - \end{minipage} + ;#; + <​caption>​ **Figure 5.** Active region of the device with plotted electron and hole eigenfunctions in the quantum well.​ + ​ - + === Voltage Characteristics ​=== - \section{Voltage Characteristics} + If we apply bias on the device, we inject carriers to the Quantum well, and those could recombine which process results a photon. The radiative recombination process can be included in the solution of the carrier transport equations, alongside with other non-radiative recombination processes, such as SRH and Auger recombination in our simulation. ​ If we apply bias on the device, we inject carriers to the Quantum well, and those could recombine which process results a photon. The radiative recombination process can be included in the solution of the carrier transport equations, alongside with other non-radiative recombination processes, such as SRH and Auger recombination in our simulation. ​ Line 124: Line 78: which means we should integrate the full recombination and radiative recombinations in the device. And the ratio is the efficiency factor. ​ which means we should integrate the full recombination and radiative recombinations in the device. And the ratio is the efficiency factor. ​ - The internal quantum efficiency is plotted in figure ​\ref{fig:​IQE} ​around its maximum. + The internal quantum efficiency is plotted in figure ​6. around its maximum. - \begin{minipage}[t]{0.99\textwidth} + - \centering + - \input{images/​IQEplot.tex} + - \captionof{figure}{Internal quantum efficiency maximum} + - \label{fig:​IQE} + - \end{minipage} + - \section{Gain spectrum} + <​figure>​ + ;#; + <​latex>​ + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​IQEplot.tex} + ​ + ;#; + <​caption>​ **Figure 6.** Internal quantum efficiency maximum​ + ​ - For various bias voltages we can calculate absorption, emission, and gain spectrum of the active region in the device. For various bias voltages it is plotted in figure ​\ref{fig:​gainsp}. here we neglected the imperfections in the quantum well, which would round down the edge of the emission/​absorption curves. ​ + + + === Gain spectrum === + + For various bias voltages we can calculate absorption, emission, and gain spectrum of the active region in the device. For various bias voltages it is plotted in figure ​7. here we neglected the imperfections in the quantum well, which would round down the edge of the emission/​absorption curves. ​ - \begin{minipage}[t]{0.99\textwidth} + - \centering + <​figure>​ - \input{images/​gainsp.tex} + ;#; - \captionof{figure}{Gain spectrum of the device for various bias voltages.} + <​latex>​ - \label{fig:​gainsp} + \input{/​var/​www/​dokuwiki/​data/​media/​physicswiki/​nbasedled/​gainsp.tex} - \end{minipage} + ​ + ;#; + <​caption>​ **Figure 7.** Gain spectrum of the device for various bias voltages.​ +
• physicswiki/semiconductors/nbasedled/nbasedled.txt