Extrinsic Semiconductors
Now, let’s spice things up! We introduce doping — intentionally adding impurities to the semiconductor. This is where the real fun begins! When you dope a semiconductor, you create either an n-type semiconductor (with extra electrons) or a p-type semiconductor (with extra “holes,” which are essentially missing electrons). The type and concentration of dopants significantly affect the Fermi level position.
3. N-Type Semiconductors
In an n-type semiconductor, we add donor impurities, such as phosphorus or arsenic, to silicon. These donors have extra electrons that aren’t tightly bound to the atoms and can easily move into the conduction band. This means that the Fermi level shifts closer to the conduction band. The higher the concentration of donor atoms, the closer the Fermi level gets to the conduction band edge.
The key equation here involves the donor concentration (Nd) and the intrinsic carrier concentration (ni). The Fermi level (Ef) can be estimated using the following relation: Ef = Ei + kT ln(Nd/ni), where Ei is the intrinsic Fermi level, k is Boltzmann’s constant, and T is the temperature. Notice that as Nd increases, the Ef moves closer to the conduction band. This increased concentration of electrons makes the semiconductor more conductive, as there are more charge carriers available to carry current. Remember that the higher the donor concentration, the easier it is for electrons to freely move.
Think of it like this: imagine a stadium where the seats represent energy levels. In an intrinsic semiconductor, only a few seats are occupied. In an n-type semiconductor, we’ve flooded the lower seats with electrons from the donor atoms, so the “Fermi level” rises up. This “rising up” of the Fermi level is a direct consequence of the increased electron concentration. Because there are now more available electrons, the material becomes much more conductive — that’s the whole point of doping!
Understanding this effect is critical for designing transistors. The precise control of the Fermi level in different regions of the transistor enables us to switch the device on and off, control the flow of current, and amplify signals. All the magic of modern electronics relies on this careful manipulation of electron concentrations and the corresponding shift in the Fermi level.
4. P-Type Semiconductors: Hole-y Goodness!
On the other hand, in a p-type semiconductor, we add acceptor impurities, such as boron, to silicon. These acceptors “accept” electrons from the valence band, creating holes. This means the Fermi level shifts closer to the valence band. The higher the concentration of acceptor atoms, the closer the Fermi level gets to the valence band edge.
The Fermi level (Ef) in a p-type semiconductor can be estimated using the following relation: Ef = Ei – kT ln(Na/ni), where Na is the acceptor concentration. As Na increases, the Ef moves closer to the valence band edge. In this case, the increased concentration of holes makes the semiconductor more conductive to positive charge carriers (holes), allowing current flow in a different way.
Continuing the stadium analogy, we are now emptying the lower seats, creating “holes.” This results in the “Fermi level” dropping down. The increased concentration of holes makes the material more conductive to positive charge carriers. These “holes” are not physical particles, but rather the absence of an electron. It’s easier for electrons to move into these empty spaces, and this movement effectively constitutes positive charge flowing through the semiconductor.
In p-type semiconductors, the Fermi level is crucial for determining the barrier height in metal-semiconductor junctions. When a metal is brought into contact with a p-type semiconductor, the difference between the metal’s work function and the semiconductor’s Fermi level dictates the type of contact formed (Ohmic or Schottky). This property is vital in designing various semiconductor devices. The type and quality of contacts determines the efficiency of current injection and extraction, ultimately dictating device performance.