📚 Electron Energies in Solids | 固体中的电子能量
In CIE A-Level Physics, the topic of electron energies in solids explains how the discrete energy levels of isolated atoms merge into continuous bands when atoms are packed into a crystal lattice. This band model is the key to understanding why some materials conduct electricity, some insulate, and some behave as semiconductors.
在CIE A-Level物理中，固体中的电子能量这一主题解释了孤立原子的分立能级如何在原子排列成晶格时合并为连续能带。这个能带模型是理解为什么有些材料导电、有些绝缘、有些具有半导体特性的关键。
1. From Atomic Energy Levels to Energy Bands | 从原子能级到能带
An isolated atom has sharply defined electron energy levels. When a large number of atoms are brought close together to form a solid, each atomic energy level splits into many closely spaced sub-levels, forming an energy band.
孤立原子具有分立的电子能级。当大量原子靠近形成固体时，每个原子能级分裂成许多间隔很小的子能级，形成能带。
For example, in a silicon crystal, the 3s and 3p atomic orbitals overlap and broaden into bands. The Pauli exclusion principle prevents all electrons from occupying the same state, so the levels must spread out into a range of energies.
例如，在硅晶体中，3s和3p原子轨道重叠并展宽成能带。泡利不相容原理阻止所有电子占据同一状态，因此能级必须扩展到一个能量范围。
The width of a band depends on the degree of overlap and the type of atomic orbitals involved. Inner-shell electrons are tightly bound and form very narrow bands, while outer-shell electrons form wider bands.
能带的宽度取决于重叠程度以及所涉及的原子轨道类型。内层电子被束缚较紧，形成很窄的能带；外层电子形成较宽的能带。
2. Valence Band and Conduction Band | 价带与导带
In the band model, the valence band is the highest energy band that is fully or partially occupied by electrons at absolute zero. The conduction band is the next higher band, which may be empty or partially filled.
在能带模型中，价带是绝对零度时被电子完全或部分占据的最高能带。导带是能量更高的下一个能带，它可以是空的或部分填充的。
Electrons in the valence band are bound to atoms and cannot move freely through the solid. Electrons promoted to the conduction band are delocalised and can act as charge carriers.
价带中的电子被原子束缚，不能在固体中自由移动。被激发到导带的电子是离域的，可以作为载流子。
The separation between these two bands determines the electrical behaviour of the material. If the separation is very small, electrons can be promoted easily.
这两个能带之间的间隔决定了材料的导电行为。如果间隔很小，电子就容易被激发。
3. Band Gap: The Energy Difference | 带隙：能量差
The energy difference between the top of the valence band and the bottom of the conduction band is called the band gap, often written as ΔE or simply the energy gap. It represents the minimum energy required to free a valence electron.
价带顶部与导带底部之间的能量差称为带隙，通常写作 ΔE 或简称能隙。它表示释放一个价电子所需的最小能量。
ΔE = E(conduction) − E(valence)
Band gap values are usually quoted in electronvolts (eV). For example, silicon has a band gap of about 1.1 eV, germanium about 0.7 eV, and diamond about 5.5 eV.
带隙值通常以电子伏特（eV）表示。例如，硅的带隙约为1.1 eV，锗约为0.7 eV，金刚石约为5.5 eV。
A photon with energy greater than the band gap can excite an electron across the gap. This is the basis of photoconductivity and semiconductor light sensors.
能量大于带隙的光子可以将电子激发越过带隙。这是光电导和半导体光传感器的基础。
4. Conductors: Overlapping Bands | 导体：能带重叠
In a conductor, the valence band and the conduction band overlap, or the valence band is only partially filled. There is effectively no band gap between occupied and unoccupied states.
在导体中，价带和导带重叠，或者价带只被部分填充。实际上在占据态和未占据态之间没有带隙。
Because empty states are immediately available at very similar energies, electrons can gain a small amount of energy from an electric field and move through the lattice. This explains the very high conductivity of metals such as copper and aluminium.
由于能量相近的空态可以立即被利用，电子只需从电场获得很小的能量就能在晶格中移动。这解释了铜和铝等金属具有很高的电导率。
In metals, the number of free electrons is almost independent of temperature, but lattice vibrations increase with temperature. This causes the resistance to increase slightly as temperature rises.
在金属中，自由电子数几乎与温度无关，但晶格振动随温度升高而增强。这导致电阻随温度升高而略有增大。
5. Insulators: Large Band Gap | 绝缘体：宽带隙
In an insulator, the valence band is completely filled and the conduction band is empty. The band gap is large, typically greater than about 5 eV.
在绝缘体中，价带被完全填满，导带为空。带隙很大，通常大于约5 eV。
Ordinary thermal energy at room temperature is only about 0.025 eV, far too small to promote electrons across such a large gap. An extremely high electric field is needed to make an insulator conduct, which usually causes breakdown.
室温下的普通热运动能量只有约0.025 eV，远不足以使电子越过如此大的带隙。需要极高的电场才能使绝缘体导电，这通常会导致击穿。
In an insulator, even a large applied voltage cannot produce a steady current because the filled valence band leaves no nearby empty states for electrons to move into.
在绝缘体中，即使施加很大的电压也不能产生稳定电流，因为被填满的价带没有邻近的空态可供电子移动进入。
6. Semiconductors: Small Band Gap | 半导体：窄带隙Published by TutorHao | A-Level Physics Revision Series | aleveler.com
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