Finished work

.gitignore

@@ -0,0 +1,4 @@
+.venv/
+.vscode/
+.~lock*
+ОТЧЕТЫ/

README.md

@@ -1,253 +0,0 @@
-МИНОБРНАУКИ РОССИИ
-
-Санкт-Петербургский государственный
-
-электротехнический университет
-
-«ЛЭТИ» им. В.И. Ульянова (Ленина)
-
-Кафедра Микрорадиоэлектроники и технологии радиоаппаратуры
-
-(МИТ)
-
-ОТЧЕТ
-
-**по ИДЗ**
-
-**по дисциплине «ОЭиР»**
-
-****Тема: Исследование контактных явлений в структуре
-металл-полупроводник****
-
-****Вариант 14,6,3****
-
-https://www.meme-arsenal.com/memes/4598e00877a721c55a46dc4aafb78719.jpg
-
-  ------------------ -- -------------
-  Студент гр. 1181      Шишков Д.А.
-  Преподаватель         Филипюк И.А
-  ------------------ -- -------------
-
-Санкт-Петербург
-
-2023
-
-Задание:
-
-Для заданной пары металл-полупроводник оценить кинетические свойства
-заданных материалов, рассчитать и построить энергетическую диаграмму и
-вольт-амперную характеристику контакта в заданном диапазоне температур,
-дать рекомендации по применению исследуемого контакта.
-
-Таблица 1. Некоторые свойства металлов
-
-<table>
-<tbody>
-<tr class="odd">
-<td><p>No</p>
-<p>ВАР.</p></td>
-<td>Элемент</td>
-<td>Структура</td>
-<td>Атомная масса</td>
-<td>Параметр решетки, Å</td>
-<td>Плотность, г/см3</td>
-<td>Удельное сопротивление, мкОм·см</td>
-<td>Температура, К</td>
-<td>Работа выхода φ, эВ</td>
-<td></td>
-<td></td>
-</tr>
-<tr class="even">
-<td>Дебая (TD)</td>
-<td>Ферми (TF·10<sup>-4</sup>)</td>
-<td>плавления (Tпл)</td>
-<td></td>
-<td></td>
-<td></td>
-<td></td>
-<td></td>
-<td></td>
-<td></td>
-<td></td>
-</tr>
-<tr class="odd">
-<td>14</td>
-<td>Au</td>
-<td>ГЦК</td>
-<td>196.9</td>
-<td>4.08</td>
-<td>19.28</td>
-<td>2.2</td>
-<td>165</td>
-<td>6.39</td>
-<td>1337</td>
-<td>4.58</td>
-</tr>
-</tbody>
-</table>
-
-1\) Определить класс симметрии заданных материалов, построить прямую и
-обратную элементарные ячейки заданных материалов. Определить размеры
-Зоны Бриллюэна в направлениях X, L, К.
-
-Гранецентрированная Кубическая решётка
-
-Формула симметрии: 3L~4~4L~3~6L~2~9PC
-
-Класс симметрии: m3m
-
-Так как формулы симметрии ГЦК и простой кубической решётки совпадают,
-приведём на рис. 1-3 изображения осей, плоскостей и центра симметрии для
-последнего
-
-![](pictures/Pictures/100000010000015E00000147D7C1BAAC07F91159.png){width="3.4504in"
-height="2.9512in"}
-
-Рис. 1 Изображение осей симметрии кубической решётки
-
-![](pictures/Pictures/10000001000001CC00000131EEA170A8799B8110.png){width="4.5437in"
-height="3.0126in"}
-
-Рис. 2 Изображение плоскостей симметрии куба
-
-![](pictures/Pictures/10000001000000DC00000100F9B19430CB57B85C.png){width="2.0882in"
-height="2.4307in"}
-
-Рис. 3 Изображение центра симметрии куба
-
-Базисные вектора:
-
-$$a_{1} = \begin{bmatrix}
-\frac{1}{\sqrt{2}} \\
-\frac{1}{\sqrt{2}} \\
-0 \\
-\end{bmatrix}$$, $$a_{2} = \begin{bmatrix}
-\frac{1}{\sqrt{2}} \\
-0 \\
-\frac{1}{\sqrt{2}} \\
-\end{bmatrix}$$, $$a_{3} = \begin{bmatrix}
-0 \\
-\frac{1}{\sqrt{2}} \\
-\frac{1}{\sqrt{2}} \\
-\end{bmatrix}$$, считая, что постоянная решётки = 1
-
-Построим кристаллическую решётку по заданным векторам (рис. 4)
-
-![](pictures/Pictures/1000000100000102000000EC388FD10724EFA862.png){width="2.6874in"
-height="2.4583in"}
-
-Рис. 4 ГЦК
-
-Объём элементарной ячейки:
-
-$$V = {|{\overrightarrow{a_{1}} \cdot \left\lbrack {\overrightarrow{a_{2}} \times a_{3}} \right\rbrack}|} = \frac{1}{\sqrt{2}}$$
-
-Базисные вектора обратной решётки:
-
-$${a_{i}^{\ast} = \frac{2\pi}{V}}\left\lbrack {a_{j} \times a_{k}} \right\rbrack,{i \neq j \neq k}$$
-
-$$a_{1}^{\ast} = \begin{bmatrix}
-{\sqrt{2}\pi} \\
-{{- \sqrt{2}}\pi} \\
-{{- \sqrt{2}}\pi} \\
-\end{bmatrix}$$, $$a_{2}^{\ast} = \begin{bmatrix}
-{{- \sqrt{2}}\pi} \\
-{\sqrt{2}\pi} \\
-{{- \sqrt{2}}\pi} \\
-\end{bmatrix}$$, $$a_{3}^{\ast} = \begin{bmatrix}
-{{- \sqrt{2}}\pi} \\
-{{- \sqrt{2}}\pi} \\
-{\sqrt{2}\pi} \\
-\end{bmatrix}$$
-
-Изобразим её на рис. 5
-
-![](pictures/Pictures/10000001000002D0000003619A2670E62D0CE93C.png){width="4.128in"
-height="3.6374in"}
-
-Рис. 5 Обратная решётка ГЦК
-
-Первая зона Бриллюэна (рис. 6):
-
-![](pictures/Pictures/10000001000001C20000011D0C7FC81F7FC396D5.png){width="4.6874in"
-height="2.9689in"}
-
-Рис. 6 Первая зона Бриллюэна
-
-Размеры зоны Бриллюэна по направлениям X, L, K:
-
-$$X = \begin{bmatrix}
-0 \\
-0 \\
-1 \\
-\end{bmatrix}$$ - центр верхнего квадрата
-
-$$L = \begin{bmatrix}
-0.5 \\
-0.5 \\
-0.5 \\
-\end{bmatrix}$$ - центр шестиугольника
-
-$$K = \begin{bmatrix}
-0.75 \\
-0.75 \\
-0 \\
-\end{bmatrix}$$ - середина грани соединяющей два шестиугольника
-
-2\) Определить концентрацию электронов для заданного металла из условия
-касания зоны Бриллюэна и сферы Ферми и сделать суждение о применимости
-теории свободных электронов.
-
-В момент касания волновой вектор kф, соответствующий радиусу сферы
-Ферми, равен волновому вектору kз, при котором в направлении,
-перпендикулярном отражающим плоскостям, выполняется уравнение
-Вульфа-Брэггов. Условия касания для двумерной модели можно записать в
-виде $$k_{ф} = k_{з}$$ или, поскольку $${k = 2}\frac{\pi}{\lambda}$$, то
-$$\lambda_{ф} = \lambda_{з}$$.
-
-Объем сферы Ферми в пространстве импульсов равен
-$$\frac{4}{3}\pi p_{ф}^{3}$$ , где $$p_{ф}$$ -- импульс электронов на
-поверхности Ферми. С другой стороны, этот же объем равен
-$$\frac{N}{2}\frac{h^{3}}{V}$$, где N -- число электронов в объеме V.
-Таким образом:
-
-$$\frac{4}{3}\pi{p_{ф}^{3} = \frac{N}{2}}\frac{h^{3}}{V}$$
-
-Откуда находим:
-
-$${p_{ф} = h}\left( \frac{3N}{8\pi V} \right)^{1/3}$$
-
-Поскольку по соотношению де-Бройля $$\lambda = \frac{h}{p}$$, то
-$$\lambda_{ф} = \left( \frac{8\pi V}{3N} \right)^{1/3}$$
-
-Найдем теперь λз. Из всех граней первой зоны Бриллюэна для
-гранецентрированной решетки ближе всего к началу координат находятся
-грани, обусловленные отражением электронов от плоскостей {111}. Поэтому
-сфера Ферми впервые коснется именно этих граней. Таким образом, для
-определения условий касания сферы с первой зоной Бриллюэна необходимо
-найти длину волны, при которой электроны взаимодействуют с плоскостями
-{111}. Из уравнения Вульфа -- Бреггов
-$${\mathit{n\lambda} = 2}d\mathit{sin\theta}$$ находим:
-
-3
-
-$${\lambda_{з} = 2}{d = 2}{\frac{a}{\sqrt{H^{2} + K^{2} + L^{2}}} = 2}\frac{a}{\sqrt{3}}$$
-
-(здесь θ = 90°, так как в точке касания волновой вектор перпендикулярен
-к плоскостям {111}; п = 1, так как λ--наибольшее)
-
-Если в объеме V число атомов Na, то число элементарных ячеек будет
-$$\frac{N_{a}}{4}$$, так как на одну ячейку гранецентрированной решетки
-приходится четыре атома, тогда $${V = a^{3}}\frac{N_{a}}{4}$$
-
-Откуда $$a = \left( \frac{4V}{N_{a}} \right)^{1/3}$$, следовательно
-$${\lambda_{з} = \frac{2}{\sqrt{3}}}\left( \frac{4V}{N_{a}} \right)^{1/3}$$
-
-Возводя обе части этого тождества в куб и произведя необходимые
-сокращения, получаем:
-
-$$\frac{N}{N_{a}} = \frac{\pi\sqrt{3}}{4} = 1.36$$
-
-Список литературы:
-
-Астанин В.В. Физика твёрдого тела

direct.svg

@@ -0,0 +1,295 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="210mm"
+   height="297mm"
+   viewBox="0 0 210 297"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="direct.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="true"
+     showguides="false"
+     inkscape:zoom="256"
+     inkscape:cx="1.4824219"
+     inkscape:cy="17.152344"
+     inkscape:window-width="1920"
+     inkscape:window-height="1011"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1">
+    <inkscape:grid
+       type="xygrid"
+       id="grid19748"
+       units="mm"
+       spacingx="0.01"
+       spacingy="0.01"
+       empspacing="10"
+       color="#000000"
+       opacity="0.14901961"
+       empcolor="#000000"
+       empopacity="0.30196078" />
+  </sodipodi:namedview>
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="TriangleStart"
+       refX="3.0780001"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="TriangleStart"
+       markerWidth="5.3240752"
+       markerHeight="6.1550002"
+       viewBox="0 0 5.3244081 6.1553851"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.5)"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:1pt"
+         d="M 5.77,0 -2.88,5 V -5 Z"
+         id="path135" />
+    </marker>
+    <inkscape:path-effect
+       effect="powerstroke"
+       id="path-effect16530"
+       is_visible="true"
+       lpeversion="1"
+       offset_points="0,4.9921382"
+       not_jump="false"
+       sort_points="true"
+       interpolator_type="CubicBezierJohan"
+       interpolator_beta="0.2"
+       start_linecap_type="zerowidth"
+       linejoin_type="extrp_arc"
+       miter_limit="4"
+       scale_width="1"
+       end_linecap_type="zerowidth" />
+    <inkscape:path-effect
+       effect="powerstroke"
+       id="path-effect16522"
+       is_visible="true"
+       lpeversion="1"
+       offset_points="0,4.9921382"
+       not_jump="false"
+       sort_points="true"
+       interpolator_type="CubicBezierJohan"
+       interpolator_beta="0.2"
+       start_linecap_type="zerowidth"
+       linejoin_type="extrp_arc"
+       miter_limit="4"
+       scale_width="1"
+       end_linecap_type="zerowidth" />
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00795313, 0.00795313;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.5813255 H 0.45"
+       id="path7778" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5461472 H 0.95"
+       id="path7778-3-5-6-2" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6014777 H 0.95"
+       id="path7778-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.6064878"
+       id="text473"><tspan
+         sodipodi:role="line"
+         id="tspan471"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.6064878">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10489">Fпп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10485">i</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.5574546"
+       id="text473-9"><tspan
+         sodipodi:role="line"
+         id="tspan471-1"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.5574546">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10475">d</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.6922479"
+       id="text616"><tspan
+         sodipodi:role="line"
+         id="tspan614"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.6922479">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10501">v</tspan> </tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.5155053"
+       id="text616-5"><tspan
+         sodipodi:role="line"
+         id="tspan614-6"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.5155053">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10465">с</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.00443677"
+       y="5.0054002"
+       id="text799"><tspan
+         sodipodi:role="line"
+         id="tspan797"
+         style="stroke-width:0.264583"
+         x="0.00443677"
+         y="5.0054002">0.115 эВ = e*U = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10513">Fпп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10515">i</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10517">мe</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.66805112"
+       y="4.5167785"
+       id="text1054"><tspan
+         sodipodi:role="line"
+         id="tspan1052"
+         style="stroke-width:0.264583;fill:#000000"
+         x="0.66805112"
+         y="4.5167785" /></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.17028902"
+       y="4.6055279"
+       id="text419-3"><tspan
+         sodipodi:role="line"
+         id="tspan417-6"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.17028902"
+         y="4.6055279">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10509">Fме</tspan> = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10511">ме</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95820701"
+       y="4.5351515"
+       id="text616-5-7"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-5"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95820701"
+         y="4.5351515">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10469">F</tspan><tspan
+   id="tspan10523"
+   style="font-size:65%;baseline-shift:super">n</tspan></tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6861446 H 0.95"
+       id="path7778-3-5" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5161446 H 0.95"
+       id="path7778-3-5-6" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5311472 H 0.94999996"
+       id="path7778-3-9" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265105;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.3263255 H 0.45"
+       id="path7778-3-5-1" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265105;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.49782902,4.1763255 h 0.45"
+       id="path7778-3-5-1-3" />
+    <path
+       style="fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264999;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.39878057,4.754264 0.50412376,4.838957"
+       id="path14621" />
+    <path
+       style="fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;stroke-width:0.003;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0121123, 0.00605613, 0.00302808, 0.00605613;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.40502615,4.7667513 Z"
+       id="path16520"
+       inkscape:path-effect="#path-effect16522"
+       inkscape:original-d="M 0.40502615,4.7667513 Z" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.38217625"
+       y="4.3144484"
+       id="text616-5-2-6-9"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1-2"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.38217625"
+         y="4.3144484">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16759">0ме</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16757">0</tspan></tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00273861;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;marker-start:url(#TriangleStart);marker-end:url(#TriangleStart);paint-order:markers stroke fill"
+       d="M 0.09852112,4.7 V 4.8"
+       id="path16532-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176151px;fill:#000000;stroke-width:0.264226"
+       x="0.10490404"
+       y="4.7626786"
+       id="text419-3-6"
+       transform="scale(1.0013509,0.99865093)"><tspan
+         sodipodi:role="line"
+         id="tspan417-6-1"
+         style="font-size:0.0176151px;stroke-width:0.264226"
+         x="0.10490404"
+         y="4.7626786">= 0.1 эВ</tspan></text>
+    <path
+       style="fill:none;stroke-width:0.003;stroke-dasharray:none;stroke:#000000;stroke-opacity:1"
+       d="m 0.44978277,4.5807323 c 0.0530168,-0.051568 0.0513858,-0.049549 0.0513858,-0.049549"
+       id="path61187" />
+  </g>
+</svg>

main.py

@@ -0,0 +1,54 @@
+# %%
+import numpy as np
+
+def dr(*x, p = 3):
+    print(np.round(x, p))
+
+def vol(x):
+    return np.dot(x[0], np.cross(x[1], x[2]))
+
+# %%
+A_metal = 4.08
+# a_general = np.array(((1/np.sqrt(2), 1/np.sqrt(2), 0), (1/np.sqrt(2), 0, 1/np.sqrt(2)), (0, 1/np.sqrt(2), 1/np.sqrt(2))))
+a_metal = A_metal/2 * np.array(((0, 1, 1), (1, 0, 1), (1, 1, 0)))
+
+dr(a_metal)
+
+a = a_metal
+V_metal = np.dot(a[0], np.cross(a[1], a[2]))
+
+dr(V_metal, A_metal**3/4)
+
+a_ = 2*np.pi/V_metal * np.array((np.cross(a[1],a[2]), np.cross(a[0], a[2]), np.cross(a[0], a[1])))
+
+dr(a_)
+
+dr(a_[0][0], 2*np.pi/A)
+
+X = np.array((0, 0, 1)) * A
+L = np.array((0.5, 0.5, 0.5)) * A
+K = np.array((0.75, 0.75, 0)) * A
+
+dr(X, L, K)
+
+dr(vol(a_))
+
+# %%
+
+A_diel = 6.48
+
+a_diel = a_general * A_diel
+
+dr(a_diel)
+
+a = a_diel
+V_diel = np.dot(a[0], np.cross(a[1], a[2]))
+
+dr(V_diel)
+
+a_ = 2*np.pi/np.abs(V_diel) * np.array((np.cross(a[1],a[2]), np.cross(a[0], a[2]), np.cross(a[0], a[1])))
+
+dr(a_)
+# %%
+a = a_general
+dr(2*np.pi/(np.dot(a[0], np.cross(a[1], a[2])))*np.cross(a[1], a[2]))

me-sem.svg

@@ -0,0 +1,406 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="210mm"
+   height="297mm"
+   viewBox="0 0 210 297"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="me-sem.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="true"
+     showguides="false"
+     inkscape:zoom="256"
+     inkscape:cx="1.2890625"
+     inkscape:cy="17.179688"
+     inkscape:window-width="1920"
+     inkscape:window-height="1011"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1">
+    <inkscape:grid
+       type="xygrid"
+       id="grid19748"
+       units="mm"
+       spacingx="0.01"
+       spacingy="0.01"
+       empspacing="10"
+       color="#000000"
+       opacity="0.14901961"
+       empcolor="#000000"
+       empopacity="0.30196078" />
+  </sodipodi:namedview>
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="TriangleStart"
+       refX="3.0780001"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="TriangleStart"
+       markerWidth="5.3240752"
+       markerHeight="6.1550002"
+       viewBox="0 0 5.3244081 6.1553851"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.5)"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:1pt"
+         d="M 5.77,0 -2.88,5 V -5 Z"
+         id="path135" />
+    </marker>
+    <inkscape:path-effect
+       effect="powerstroke"
+       id="path-effect16530"
+       is_visible="true"
+       lpeversion="1"
+       offset_points="0,4.9921382"
+       not_jump="false"
+       sort_points="true"
+       interpolator_type="CubicBezierJohan"
+       interpolator_beta="0.2"
+       start_linecap_type="zerowidth"
+       linejoin_type="extrp_arc"
+       miter_limit="4"
+       scale_width="1"
+       end_linecap_type="zerowidth" />
+    <inkscape:path-effect
+       effect="powerstroke"
+       id="path-effect16522"
+       is_visible="true"
+       lpeversion="1"
+       offset_points="0,4.9921382"
+       not_jump="false"
+       sort_points="true"
+       interpolator_type="CubicBezierJohan"
+       interpolator_beta="0.2"
+       start_linecap_type="zerowidth"
+       linejoin_type="extrp_arc"
+       miter_limit="4"
+       scale_width="1"
+       end_linecap_type="zerowidth" />
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00795313, 0.00795313;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.5813255 H 0.45"
+       id="path7778" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5961472 H 0.95"
+       id="path7778-3-5-6-2" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6514777 H 0.95"
+       id="path7778-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.6564879"
+       id="text473"><tspan
+         sodipodi:role="line"
+         id="tspan471"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.6564879">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10489">Fпп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10485">i</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan13632">б</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.6074548"
+       id="text473-9"><tspan
+         sodipodi:role="line"
+         id="tspan471-1"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.6074548">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10475">d</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan13630">б</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.7422481"
+       id="text616"><tspan
+         sodipodi:role="line"
+         id="tspan614"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.7422481">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10501">v</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan13634">б</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.5655055"
+       id="text616-5"><tspan
+         sodipodi:role="line"
+         id="tspan614-6"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.5655055">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10465">с</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan13626">б</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.00443677"
+       y="5.0054002"
+       id="text799"><tspan
+         sodipodi:role="line"
+         id="tspan797"
+         style="stroke-width:0.264583"
+         x="0.00443677"
+         y="5.0054002">0.115 эВ = e*U = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10513">Fпп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10515">i</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10517">мe</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.66805112"
+       y="4.5167785"
+       id="text1054"><tspan
+         sodipodi:role="line"
+         id="tspan1052"
+         style="stroke-width:0.264583;fill:#000000"
+         x="0.66805112"
+         y="4.5167785" /></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.17028902"
+       y="4.6055279"
+       id="text419-3"><tspan
+         sodipodi:role="line"
+         id="tspan417-6"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.17028902"
+         y="4.6055279">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10509">Fме</tspan> = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10511">ме</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95820701"
+       y="4.5851517"
+       id="text616-5-7"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-5"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95820701"
+         y="4.5851517">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10469">F</tspan><tspan
+   id="tspan10523"
+   style="font-size:65%;baseline-shift:super">n</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan13628">б</tspan></tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.7361446 H 0.95"
+       id="path7778-3-5" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5661446 H 0.95"
+       id="path7778-3-5-6" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.5811472 H 0.94999996"
+       id="path7778-3-9" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265105;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.3263255 H 0.45"
+       id="path7778-3-5-1" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265105;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.49782902,4.2263255 h 0.45"
+       id="path7778-3-5-1-3" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:0.079375px;font-family:sans-serif;-inkscape-font-specification:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.00264583;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00265105, 0.00530209;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       x="0.4590115"
+       y="4.4511046"
+       id="text10426"><tspan
+         sodipodi:role="line"
+         id="tspan10424"
+         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:0.079375px;font-family:sans-serif;-inkscape-font-specification:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.00264583"
+         x="0.4590115"
+         y="4.4511046">...</tspan></text>
+    <path
+       style="fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264999;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.33112482,4.7903648 0.10534319,0.084693"
+       id="path14621" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00302807;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.44977371,4.3264682 c 0.0212738,0.00229 0.0108773,-0.1018684 0.0499472,-0.099928"
+       id="path14623-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00302807;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.45016204,4.6664682 c 0.0212738,0.00229 0.0108773,-0.1018684 0.0499472,-0.099928"
+       id="path14623-6-0"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00302807;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0121123, 0.00605614, 0.00302807, 0.00605614;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.4507384,4.7513755 c 0.0212738,0.00229 0.0108773,-0.1018684 0.0499472,-0.099928"
+       id="path14623-6-0-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00302807;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.45016204,4.8364682 c 0.0212738,0.00229 0.0108773,-0.1018684 0.0499472,-0.099928"
+       id="path14623-6-0-2"
+       sodipodi:nodetypes="cc" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.46278834"
+       y="4.8620062"
+       id="text616-5-2-6"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.46278834"
+         y="4.8620062">W<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16459">пп</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.43761128"
+       y="4.8788462"
+       id="text616-5-2-6-7"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1-9"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.43761128"
+         y="4.8788462">W<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16514">ме</tspan></tspan></text>
+    <path
+       style="fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;stroke-width:0.003;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0121123, 0.00605613, 0.00302808, 0.00605613;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.40502615,4.7667513 Z"
+       id="path16520"
+       inkscape:path-effect="#path-effect16522"
+       inkscape:original-d="M 0.40502615,4.7667513 Z" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.002;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.501,4.735 v 0.12"
+       id="path16532" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.002;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="m 0.45599163,4.835 v 0.02"
+       id="path16532-0" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.002;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.451,4.837 V 4.855"
+       id="path16532-0-2" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.48745891"
+       y="4.2763157"
+       id="text616-5-2-6-3"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1-7"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.48745891"
+         y="4.2763157">Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16747">б</tspan> = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16745">ме</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan17572">пп</tspan><tspan
+   id="tspan17578"
+   style="font-size:65%;baseline-shift:super">n</tspan> = -0.1 эВ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.38217625"
+       y="4.3144484"
+       id="text616-5-2-6-9"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1-2"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.38217625"
+         y="4.3144484">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16759">0ме</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16757">0</tspan></tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.50209939"
+       y="4.2177706"
+       id="text616-5-2-6-9-8"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7-1-2-9"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.50209939"
+         y="4.2177706">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16749">0пп</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16751">0</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan16755">б</tspan></tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00273861;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;marker-start:url(#TriangleStart);marker-end:url(#TriangleStart);paint-order:markers stroke fill"
+       d="M 0.09852112,4.7 V 4.8"
+       id="path16532-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176151px;fill:#000000;stroke-width:0.264226"
+       x="0.10490404"
+       y="4.7626786"
+       id="text419-3-6"
+       transform="scale(1.0013509,0.99865093)"><tspan
+         sodipodi:role="line"
+         id="tspan417-6-1"
+         style="font-size:0.0176151px;stroke-width:0.264226"
+         x="0.10490404"
+         y="4.7626786">= 0.1 эВ</tspan></text>
+  </g>
+</svg>

me-vac-sem.svg

@@ -0,0 +1,289 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="210mm"
+   height="297mm"
+   viewBox="0 0 210 297"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="me-vac-sem.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="true"
+     showguides="false"
+     inkscape:zoom="256"
+     inkscape:cx="1.7480469"
+     inkscape:cy="16.992188"
+     inkscape:window-width="1920"
+     inkscape:window-height="1011"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1">
+    <inkscape:grid
+       type="xygrid"
+       id="grid26957"
+       spacingx="0.01"
+       spacingy="0.01"
+       empspacing="10"
+       units="mm"
+       color="#000000"
+       opacity="0.14901961"
+       empcolor="#000000"
+       empopacity="0.30196078" />
+  </sodipodi:namedview>
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="TriangleStart"
+       refX="3.0780001"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="TriangleStart"
+       markerWidth="5.3240752"
+       markerHeight="6.1550002"
+       viewBox="0 0 5.3244081 6.1553851"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.5)"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:context-stroke;stroke-width:1pt"
+         d="M 5.77,0 -2.88,5 V -5 Z"
+         id="path135" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00249942;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00749828, 0.00749828;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.5813255 H 0.4"
+       id="path7778" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00265104,0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6963255 H 0.95"
+       id="path7778-3-5-6-2" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.751656 H 0.95"
+       id="path7778-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.7566662"
+       id="text473"><tspan
+         sodipodi:role="line"
+         id="tspan471"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.7566662">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10489">Fпп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10485">i</tspan> = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10491">пп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10493">i</tspan> = 4.75 эВ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.707633"
+       id="text473-9"><tspan
+         sodipodi:role="line"
+         id="tspan471-1"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.707633">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10475">d</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10477">c</tspan> + E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10479">g</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10481">c</tspan> + E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10483">d</tspan> = 4.695 эВ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.8424263"
+       id="text616"><tspan
+         sodipodi:role="line"
+         id="tspan614"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.8424263">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10501">v</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10503">F</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10505">i</tspan> + E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10507">G</tspan>/2= 4.835 эВ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.6656837"
+       id="text616-5"><tspan
+         sodipodi:role="line"
+         id="tspan614-6"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.6656837">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10465">с</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10463">F</tspan><tspan
+   id="tspan10499"
+   style="font-size:65%;baseline-shift:super">i</tspan> - E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10467">G</tspan>/2 = 4.665 эВ = X</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.35252184"
+       y="4.6306996"
+       id="text799"><tspan
+         sodipodi:role="line"
+         id="tspan797"
+         style="stroke-width:0.264583"
+         x="0.35252184"
+         y="4.6306996">e*U = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan33327">мe</tspan> - Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan33329">пп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan33465">n</tspan> = -0.1 эВ </tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.66805112"
+       y="4.5167785"
+       id="text1054"><tspan
+         sodipodi:role="line"
+         id="tspan1052"
+         style="stroke-width:0.264583;fill:#000000"
+         x="0.66805112"
+         y="4.5167785" /></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176616px;fill:#000000;stroke-width:0.264924"
+       x="0.24197295"
+       y="4.5786605"
+       id="text419-3"
+       transform="scale(1.001288,0.99871366)"><tspan
+         sodipodi:role="line"
+         id="tspan417-6"
+         style="font-size:0.0176616px;stroke-width:0.264924"
+         x="0.24197295"
+         y="4.5786605">E<tspan
+   style="font-size:0.0114801px;baseline-shift:sub;stroke-width:0.264924"
+   id="tspan10509">Fме</tspan> = Ф<tspan
+   style="font-size:0.0114801px;baseline-shift:sub;stroke-width:0.264924"
+   id="tspan10511">ме</tspan> = 4.58 эВ</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95820701"
+       y="4.6853299"
+       id="text616-5-7"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-5"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95820701"
+         y="4.6853299">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10469">F</tspan><tspan
+   id="tspan10523"
+   style="font-size:65%;baseline-shift:super">n</tspan> = E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10471">c</tspan> - E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10473">g</tspan>/2 = 4.68 эВ = Ф<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10461">пп</tspan><tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan10459">n</tspan></tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.8363229 H 0.95"
+       id="path7778-3-5" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6663229 H 0.95"
+       id="path7778-3-5-6" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00265104;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.0106042, 0.00530208, 0.00265104, 0.00530208;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0.5,4.6813255 H 0.94999996"
+       id="path7778-3-9" />
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00385188;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       d="M 0,4.3263255 H 0.95"
+       id="path7778-3-5-1" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176389px;fill:#000000;stroke-width:0.264583"
+       x="0.95828903"
+       y="4.3301716"
+       id="text616-5-2"><tspan
+         sodipodi:role="line"
+         id="tspan614-6-7"
+         style="font-size:0.0176389px;stroke-width:0.264583"
+         x="0.95828903"
+         y="4.3301716">E<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan10584">0</tspan> = 0</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:0.079375px;font-family:sans-serif;-inkscape-font-specification:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.00264583;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:0.00265105, 0.00530209;stroke-dashoffset:0;stroke-opacity:1;paint-order:markers stroke fill"
+       x="0.46828499"
+       y="4.4363971"
+       id="text10426"><tspan
+         sodipodi:role="line"
+         id="tspan10424"
+         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:0.079375px;font-family:sans-serif;-inkscape-font-specification:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.00264583"
+         x="0.46828499"
+         y="4.4363971">...</tspan></text>
+    <path
+       style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:0.00273861;stroke-linecap:butt;stroke-linejoin:bevel;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1;marker-start:url(#TriangleStart);marker-end:url(#TriangleStart);paint-order:markers stroke fill"
+       d="m 0.09842807,4.7002955 v 0.1"
+       id="path16532-3" />
+    <text
+       xml:space="preserve"
+       style="font-size:0.0176151px;fill:#000000;stroke-width:0.264226"
+       x="0.10481112"
+       y="4.7629743"
+       id="text419-3-6"
+       transform="scale(1.0013509,0.99865093)"><tspan
+         sodipodi:role="line"
+         id="tspan417-6-1"
+         style="font-size:0.0176151px;stroke-width:0.264226"
+         x="0.10481112"
+         y="4.7629743">= 0.1 эВ</tspan></text>
+  </g>
+</svg>

media/phermi_sphere_and_brillouin_zone.svg

@@ -0,0 +1,137 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="500"
+   height="500"
+   viewBox="0 0 132.29166 132.29166"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="phermi_sphere_and_brillouin_zone.svg"
+   inkscape:export-filename="phermi_sphere_and_brillouin_zone.png"
+   inkscape:export-xdpi="96"
+   inkscape:export-ydpi="96"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#000000"
+     borderopacity="0.25"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="1"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="px"
+     showgrid="false"
+     inkscape:zoom="1.3177789"
+     inkscape:cx="159.35905"
+     inkscape:cy="235.24432"
+     inkscape:window-width="1920"
+     inkscape:window-height="1011"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1" />
+  <defs
+     id="defs2">
+    <rect
+       x="354.36109"
+       y="227.3227"
+       width="55.208311"
+       height="92.486793"
+       id="rect2699" />
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <rect
+       style="fill:#ffffff;fill-opacity:1;stroke:none;stroke-width:0.79375;stroke-dasharray:none"
+       id="rect4355"
+       width="132.29166"
+       height="132.29166"
+       x="0"
+       y="0" />
+    <rect
+       style="fill:none;stroke:#000000;stroke-width:0.001"
+       id="rect165"
+       width="23.8125"
+       height="23.8125"
+       x="2.0095859"
+       y="2.0703168" />
+    <rect
+       style="fill:none;stroke:#000000;stroke-width:1.3229166;stroke-dasharray:none"
+       id="rect847"
+       width="119.0625"
+       height="119.0625"
+       x="6.6145835"
+       y="6.6145835" />
+    <circle
+       style="fill:none;stroke:#000000;stroke-width:1.3229166;stroke-dasharray:none"
+       id="path1686"
+       cx="66.145836"
+       cy="66.145836"
+       r="59.134377" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1.3229166;stroke-dasharray:none"
+       d="M 125.67708,66.136077 H 66.145833"
+       id="path2643" />
+    <text
+       xml:space="preserve"
+       transform="scale(0.26458333)"
+       id="text2697"
+       style="font-size:14px;white-space:pre;shape-inside:url(#rect2699);display:inline;fill:none;stroke:#000000;stroke-width:3;stroke-dasharray:none" />
+    <text
+       xml:space="preserve"
+       style="font-size:3.70417px;fill:none;stroke:#000000;stroke-width:0.79375;stroke-dasharray:none"
+       x="90.692299"
+       y="48.238441"
+       id="text2705"><tspan
+         sodipodi:role="line"
+         id="tspan2703"
+         style="stroke-width:0.79375"
+         x="90.692299"
+         y="48.238441" /></text>
+    <g
+       id="g1332"
+       transform="matrix(0.99999424,0,0,1,-1.4357607,-0.15224842)">
+      <text
+         xml:space="preserve"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:7.40834px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.793778;stroke-dasharray:none"
+         x="94.470284"
+         y="63.990917"
+         id="text2709"><tspan
+           sodipodi:role="line"
+           id="tspan2707"
+           style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:7.40834px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.793778"
+           x="94.470284"
+           y="63.990917">k</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23334px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.793778;stroke-dasharray:none"
+         x="98.149872"
+         y="64.505356"
+         id="text2763"><tspan
+           sodipodi:role="line"
+           id="tspan2761"
+           style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:4.23334px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';stroke-width:0.793778"
+           x="98.149872"
+           y="64.505356">f</tspan></text>
+    </g>
+    <text
+       xml:space="preserve"
+       style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:7.40833px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.79375;stroke-dasharray:none"
+       x="61.778629"
+       y="131.77359"
+       id="text2767"><tspan
+         sodipodi:role="line"
+         id="tspan2765"
+         style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:7.40833px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Italic';stroke-width:0.79375"
+         x="61.778629"
+         y="131.77359">a*</tspan></text>
+  </g>
+</svg>