zT vs n
Thermoelectric figure of merit vs carrier concentration for Bi2Te3 based on empirical data in plot as a thermoelectric material performance indicator. Tuning for optimal involves a compromise between thermal conductivity , Seebeck coefficient and electrical conductivity . Increasing the electrical conductivity not only produces an increase in the electronic thermal conductivity but also usually decreases the Seebeck coefficient . This makes optimal difficult to achieve. Plot scales are , , .
Download
Code
LaTeX
zt-vs-n.tex (179 lines)
\documentclass[tikz]{standalone}
\usepackage{pgfplots,siunitx}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xmode=log,
domain=1e17:1e21,
ymax=1,
enlargelimits=false,
ylabel=$zT$,
xlabel=Carrier concentration $n$ (\si{\per\centi\meter\cubed}),
grid=both,
width=12cm,
height=8cm,
decoration={name=none},
]
\addplot [ultra thick, smooth, red!85!black] coordinates {
(1.174e+18, 0.2317)
(1.551e+18, 0.2787)
(2.016e+18, 0.3300)
(2.549e+18, 0.3816)
(3.171e+18, 0.4332)
(3.891e+18, 0.4842)
(4.697e+18, 0.5373)
(5.623e+18, 0.5892)
(6.714e+18, 0.6404)
(8.017e+18, 0.6923)
(9.650e+18, 0.7450)
(1.178e+19, 0.7963)
(1.461e+19, 0.8486)
(1.878e+19, 0.8964)
(2.481e+19, 0.9278)
(3.279e+19, 0.9318)
(4.334e+19, 0.9057)
(5.515e+19, 0.8571)
(6.662e+19, 0.8045)
(7.767e+19, 0.7519)
(8.859e+19, 0.7000)
(1.008e+20, 0.6476)
(1.143e+20, 0.5953)
(1.290e+20, 0.5449)
(1.447e+20, 0.4906)
(1.628e+20, 0.4374)
(1.837e+20, 0.3850)
(2.101e+20, 0.3327)
(2.436e+20, 0.2799)
(2.887e+20, 0.2281)
(3.594e+20, 0.1753)
(4.674e+20, 0.1271)
(6.178e+20, 0.08917)
(8.167e+20, 0.06240)
(1e+21, 0.05)
} node[pos=0.48, anchor=north] {$zT$};
\addplot [ultra thick, smooth, blue!70!black] coordinates {
(1.176e+18, 0.005689)
(1.554e+18, 0.008070)
(2.054e+18, 0.009285)
(2.714e+18, 0.01216)
(3.587e+18, 0.01561)
(4.740e+18, 0.02190)
(6.264e+18, 0.02984)
(8.277e+18, 0.04013)
(1.094e+19, 0.05127)
(1.445e+19, 0.06820)
(1.910e+19, 0.09120)
(2.511e+19, 0.1191)
(3.333e+19, 0.1593)
(4.344e+19, 0.2072)
(5.433e+19, 0.2587)
(6.613e+19, 0.3123)
(7.852e+19, 0.3739)
(8.925e+19, 0.4266)
(1.001e+20, 0.4779)
(1.110e+20, 0.5310)
(1.224e+20, 0.5824)
(1.335e+20, 0.6359)
(1.441e+20, 0.6893)
(1.551e+20, 0.7425)
(1.660e+20, 0.7960)
(1.767e+20, 0.8478)
(1.876e+20, 0.9009)
(1.986e+20, 0.9532)
(2.08e+20, 1)
} node[pos=0.95, anchor=east] {$\sigma$};
\addplot [ultra thick, smooth, green!70!black] coordinates {
(1.175e+18, 0.08187)
(1.553e+18, 0.08218)
(2.053e+18, 0.08379)
(2.713e+18, 0.08472)
(3.585e+18, 0.08684)
(4.738e+18, 0.08916)
(6.261e+18, 0.09142)
(8.274e+18, 0.09411)
(1.093e+19, 0.09912)
(1.445e+19, 0.1059)
(1.909e+19, 0.1145)
(2.523e+19, 0.1256)
(3.334e+19, 0.1391)
(4.405e+19, 0.1576)
(5.821e+19, 0.1830)
(7.691e+19, 0.2164)
(1.016e+20, 0.2605)
(1.302e+20, 0.3102)
(1.589e+20, 0.3629)
(1.882e+20, 0.4143)
(2.181e+20, 0.4641)
(2.472e+20, 0.5181)
(2.764e+20, 0.5714)
(3.066e+20, 0.6246)
(3.363e+20, 0.6780)
(3.669e+20, 0.7310)
(3.981e+20, 0.7826)
(4.273e+20, 0.8389)
(4.560e+20, 0.8942)
(4.868e+20, 0.9493)
(5.2e+20, 1)
} node[pos=0.95, anchor=west] {$\kappa$};
\addplot [ultra thick, smooth, orange] coordinates {
(1.65e+18, 1)
(1.931e+18, 0.9729)
(2.553e+18, 0.9248)
(3.375e+18, 0.8777)
(4.462e+18, 0.8302)
(5.899e+18, 0.7816)
(7.745e+18, 0.7351)
(1.031e+19, 0.6866)
(1.363e+19, 0.6397)
(1.802e+19, 0.5897)
(2.382e+19, 0.5412)
(3.149e+19, 0.4937)
(4.162e+19, 0.4471)
(5.503e+19, 0.3977)
(7.117e+19, 0.3500)
(9.181e+19, 0.2944)
(1.224e+20, 0.2436)
(1.618e+20, 0.2019)
(2.138e+20, 0.1687)
(2.826e+20, 0.1389)
(3.736e+20, 0.1161)
(4.938e+20, 0.09646)
(6.321e+20, 0.08022)
(8.578e+20, 0.06624)
(1e+21, 0.06)
} node[pos=0.1, anchor=south west] {$S$};
\addplot [ultra thick, smooth, cyan] coordinates {
(1.159e+18, 0.04006)
(1.532e+18, 0.04739)
(2.025e+18, 0.05790)
(2.676e+18, 0.06974)
(3.386e+18, 0.08033)
(4.675e+18, 0.09928)
(6.179e+18, 0.1176)
(8.168e+18, 0.1379)
(1.080e+19, 0.1608)
(1.427e+19, 0.1864)
(1.886e+19, 0.2142)
(2.492e+19, 0.2430)
(3.294e+19, 0.2713)
(4.353e+19, 0.2989)
(5.754e+19, 0.3230)
(7.605e+19, 0.3422)
(1.005e+20, 0.3528)
(1.314e+20, 0.3509)
(1.757e+20, 0.3326)
(2.327e+20, 0.3049)
(3.071e+20, 0.2777)
(4.061e+20, 0.2535)
(5.369e+20, 0.2304)
(7.098e+20, 0.2095)
(1e+21, 0.185)
} node[pos=0.4, anchor=south east] {$S^2 \sigma$};
\end{axis}
\end{tikzpicture}
\end{document}
Typst
zt-vs-n.typ (214 lines)
#import "@preview/cetz:0.3.2": canvas, draw
#import "@preview/cetz-plot:0.1.1": plot
#set page(width: auto, height: auto, margin: 8pt)
#canvas({
draw.set-style(
axes: (
y: (label: (anchor: "north-west", offset: -0.2), mark: (end: "stealth", fill: black)),
x: (label: (anchor: "north", offset: 0.1), mark: (end: "stealth", fill: black)),
),
)
plot.plot(
size: (12, 8),
x-label: [Carrier concentration $n$ ($"cm"^(-3)$)],
y-label: $z T$,
y-min: 0,
x-mode: "log",
x-tick-step: 1,
x-grid: true,
y-grid: true,
// x-format: "sci",
axis-style: "left",
legend: "inner-north-east",
{
// zT curve (red)
plot.add(
style: (stroke: rgb(85%, 0%, 0%) + 2pt),
(
(1.174e18, 0.2317),
(1.551e18, 0.2787),
(2.016e18, 0.3300),
(2.549e18, 0.3816),
(3.171e18, 0.4332),
(3.891e18, 0.4842),
(4.697e18, 0.5373),
(5.623e18, 0.5892),
(6.714e18, 0.6404),
(8.017e18, 0.6923),
(9.650e18, 0.7450),
(1.178e19, 0.7963),
(1.461e19, 0.8486),
(1.878e19, 0.8964),
(2.481e19, 0.9278),
(3.279e19, 0.9318),
(4.334e19, 0.9057),
(5.515e19, 0.8571),
(6.662e19, 0.8045),
(7.767e19, 0.7519),
(8.859e19, 0.7000),
(1.008e20, 0.6476),
(1.143e20, 0.5953),
(1.290e20, 0.5449),
(1.447e20, 0.4906),
(1.628e20, 0.4374),
(1.837e20, 0.3850),
(2.101e20, 0.3327),
(2.436e20, 0.2799),
(2.887e20, 0.2281),
(3.594e20, 0.1753),
(4.674e20, 0.1271),
(6.178e20, 0.08917),
(8.167e20, 0.06240),
(1e21, 0.05),
),
label: $z T$,
)
// σ curve (blue)
plot.add(
style: (stroke: rgb(0%, 0%, 70%) + 2pt),
(
(1.176e18, 0.005689),
(1.554e18, 0.008070),
(2.054e18, 0.009285),
(2.714e18, 0.01216),
(3.587e18, 0.01561),
(4.740e18, 0.02190),
(6.264e18, 0.02984),
(8.277e18, 0.04013),
(1.094e19, 0.05127),
(1.445e19, 0.06820),
(1.910e19, 0.09120),
(2.511e19, 0.1191),
(3.333e19, 0.1593),
(4.344e19, 0.2072),
(5.433e19, 0.2587),
(6.613e19, 0.3123),
(7.852e19, 0.3739),
(8.925e19, 0.4266),
(1.001e20, 0.4779),
(1.110e20, 0.5310),
(1.224e20, 0.5824),
(1.335e20, 0.6359),
(1.441e20, 0.6893),
(1.551e20, 0.7425),
(1.660e20, 0.7960),
(1.767e20, 0.8478),
(1.876e20, 0.9009),
(1.986e20, 0.9532),
(2.08e20, 1),
),
label: $sigma$,
)
// κ curve (green)
plot.add(
style: (stroke: rgb(0%, 70%, 0%) + 2pt),
(
(1.175e18, 0.08187),
(1.553e18, 0.08218),
(2.053e18, 0.08379),
(2.713e18, 0.08472),
(3.585e18, 0.08684),
(4.738e18, 0.08916),
(6.261e18, 0.09142),
(8.274e18, 0.09411),
(1.093e19, 0.09912),
(1.445e19, 0.1059),
(1.909e19, 0.1145),
(2.523e19, 0.1256),
(3.334e19, 0.1391),
(4.405e19, 0.1576),
(5.821e19, 0.1830),
(7.691e19, 0.2164),
(1.016e20, 0.2605),
(1.302e20, 0.3102),
(1.589e20, 0.3629),
(1.882e20, 0.4143),
(2.181e20, 0.4641),
(2.472e20, 0.5181),
(2.764e20, 0.5714),
(3.066e20, 0.6246),
(3.363e20, 0.6780),
(3.669e20, 0.7310),
(3.981e20, 0.7826),
(4.273e20, 0.8389),
(4.560e20, 0.8942),
(4.868e20, 0.9493),
(5.2e20, 1),
),
label: $kappa$,
)
// S curve (orange)
plot.add(
style: (stroke: orange + 2pt),
(
(1.65e18, 1),
(1.931e18, 0.9729),
(2.553e18, 0.9248),
(3.375e18, 0.8777),
(4.462e18, 0.8302),
(5.899e18, 0.7816),
(7.745e18, 0.7351),
(1.031e19, 0.6866),
(1.363e19, 0.6397),
(1.802e19, 0.5897),
(2.382e19, 0.5412),
(3.149e19, 0.4937),
(4.162e19, 0.4471),
(5.503e19, 0.3977),
(7.117e19, 0.3500),
(9.181e19, 0.2944),
(1.224e20, 0.2436),
(1.618e20, 0.2019),
(2.138e20, 0.1687),
(2.826e20, 0.1389),
(3.736e20, 0.1161),
(4.938e20, 0.09646),
(6.321e20, 0.08022),
(8.578e20, 0.06624),
(1e21, 0.06),
),
label: $S$,
)
// S²σ curve (cyan)
plot.add(
style: (stroke: aqua + 2pt),
(
(1.159e18, 0.04006),
(1.532e18, 0.04739),
(2.025e18, 0.05790),
(2.676e18, 0.06974),
(3.386e18, 0.08033),
(4.675e18, 0.09928),
(6.179e18, 0.1176),
(8.168e18, 0.1379),
(1.080e19, 0.1608),
(1.427e19, 0.1864),
(1.886e19, 0.2142),
(2.492e19, 0.2430),
(3.294e19, 0.2713),
(4.353e19, 0.2989),
(5.754e19, 0.3230),
(7.605e19, 0.3422),
(1.005e20, 0.3528),
(1.314e20, 0.3509),
(1.757e20, 0.3326),
(2.327e20, 0.3049),
(3.071e20, 0.2777),
(4.061e20, 0.2535),
(5.369e20, 0.2304),
(7.098e20, 0.2095),
(1e21, 0.185),
),
label: $S^2 sigma$,
)
},
)
})