Читать книгу Semiconductor Basics - George Domingo - Страница 29

Now consider the situation where the valence band is full (case 1), but there is a small gap between the conduction and valence bands (case 3). At absolute zero, all the electrons are in the valence band, the lowest allowed energy, and thus the valence band is completely full. But at room temperature, there is enough thermal energy in the system that, statistically, a few electrons can make the jump from the valence band to the conduction band. I show this in Figure 2.8.

In pure silicon, as I said earlier, there are 5 × 10²² silicon atoms per cm³; but only a tiny number (1.45 × 10¹⁰ electrons per cm³) have, statistically, sufficient energy at room temperature to jump from the valence band to the conduction band. Although 10¹⁰ electrons per cm³ looks very large, this is only a single solitary electron out of 3.4 × 10¹² silicon atoms (1 out of 3 400 000 000 000) that gain the energy needed to jump to the conduction band. This situation is exemplified in Figure 2.8. Note that as the very few electrons jump to the conduction band, they leave behind an empty spot, which we call a hole. The holes are called p‐particles (p for positive) because they appear to have a positive charge. (Remember, each silicon atom is neutral, that is, it has as many protons – positive charges – in the nucleus as it has electrons in the orbits. If you remove one electron, the atom becomes positively charged.) Notice also that in an intrinsic (i.e. perfectly pure) semiconductor, the number of electrons, n_i, and the number of holes, p_i, have to be exactly the same, since every electron that jumps to the conduction band leaves behind an empty space (a hole) in the valence band. We refer to these intrinsic electrons and holes using the subscript i.

Figure 2.8 The valence band in a semiconductor is completely full, the conduction band is empty, and the separation between the two bands is small, but at room temperature, which is what I show here, there is sufficient energy to kick a few electrons from the valence band to the conduction band, thus generating a small current when we apply a voltage.

Consider what happens when we apply a voltage, as I show on the right in Figure 2.8. Electrons move left toward the positive side: both the electrons in the conduction band and those electrons in the valence band that have an empty space to their left. We like to say, and you will see why later, that the hole (the empty space) is moving in the opposite direction – to the right, toward the negative side – so the hole acts like a positive particle moving to the negative terminal.

Since it is the thermal energy that determines how many electrons can jump to the conduction band and are free to move, and how many holes are left behind, you can expect that the current in a semiconductor is highly dependent on the temperature, that is, the thermal energy. Figure 2.9 shows the number of free electrons in silicon and gallium‐arsenide (GaAs) in the conduction band as a function of temperature.

Note that the number of intrinsic electrons and holes in the plot (the vertical y axis) is logarithmic, and the temperature (T, on the horizontal x‐axis) is not the temperature but 1000/temperature in absolute units (Kelvin). The actual temperature in degrees Celsius is at the right side of the plot. The advantage of plotting it this way is that the change in the number of free electrons versus 1/T is very linear. For convenience, I mark the values at room temperature (27 °C), at freezing (0 °C) and at the boiling point of water (100 °C).

Figure 2.9 Electron and hole concentrations in Si and GaAs change drastically as a function of temperature. Temperature is an indication of the energy of the system, and the more energy in the system, the more electrons can move from the valence band to the conduction band, leaving behind the same number of holes.

The number of free charges is also dependent on the light. Photons can hit the silicon crystal and give their energy to an electron that can use this energy to jump to the conduction band.

Looking at Figure 2.9, at room temperature (27 °C, 300 K), the number of electrons and holes in silicon is 1.45 × 10¹⁰ cm⁻³, as I said earlier; but if we cool it down to 0 °C (the temperature of ice water), the number decreases rapidly to 2 × 10⁹ cm⁻³, a factor of 10 lower. If we do the opposite and immerse a semiconductor in boiling water (100 °C), the number of free charges increases to 3 × 10¹² cm⁻³, 300 times larger than at room temperature. As a rule of thumb, the number of free charges in silicon doubles every 7°C.

In the same graph, I have the number of free charges in GaAs, the next‐most‐used semiconductor. Because the separation between the valence and conduction bands (Eg) in GaAs is larger than that of Si (1.43 eV vs. 1.12 eV), the number of free carriers in pure GaAs material is much lower than that of silicon, 1.79 × 10⁶ cm⁻³.

Remember this temperature dependence when we talk about the operation and use of semiconductor devices. When we turn on an electronic device, the temperature increases, and its electronic properties change. In Chapter 9, I discuss some of the tricks that designers use to stabilize circuits.