Figure 2.1 The p-n junction diode showing metal anode and cathode contacts connected to semiconductor p-type and n-type regions respectively. There are two metal-semiconductor junctions in addition to the p-n semiconductor junction. The diode symbol and two examples of diode applications in circuit design are shown. The diode logic gate was used in early diode-transistor logic solid state computers popular in the 1960s but has been replaced by transistor-based designs that consume less power and switch faster

Figure 2.2 Band model of p-n junction in equilibrium showing constant Fermi energy and transition region to allow valence band and conduction band to be continuous

Figure 2. 3 Flow directions of the four p-n junction currents Figure 2.3 Flow directions of the four p-n junction currents. The two diffusion currents are driven by concentration gradients of electrons or holes across the junction and the two drift currents are driven by the electric field. Note that the electron currents flow in the direction opposite to the flux or flow of electrons. The electron diffusion flux is to the left and the electron drift flux is to the right

Figure 2.4 A p-n junction diode with external voltage source connected. The external bias voltage will modify the built-in electric field

Figure 2. 5 Diode band model with the application of a forward bias Figure 2.5 Diode band model with the application of a forward bias. The energy barrier across the transition region is smaller resulting in much higher currents dominated by diffusion currents. In the depletion region ε will be smaller and drift currents no longer compensate for diffusion currents. Note that the applied voltage V (in volts) must be multiplied by the electron charge q (in coulombs) to obtain energy (in joules)

Figure 2. 6 Diode band model with the application of a reverse bias Figure 2.6 Diode band model with the application of a reverse bias. Since the applied voltage V is negative, the energy barrier as well as electric field ε become larger across the transition region virtually eliminating diffusion currents

Figure 2. 7 Diode current as a function of applied voltage Figure 2.7 Diode current as a function of applied voltage. The reverse drift current saturates to a small value and is called the reverse saturation current. When V = 0 the drift and diffusion currents are equal in magnitude and the net current is zero

Figure 2.8 The equilibrium p-n junction energy barrier height E0 may be obtained from (E f − E v)n−side − (E f − E v)p−side resulting in Equation 2.5

Figure 2. 9 Depletion occurs near the junction Figure 2.9 Depletion occurs near the junction. In order to establish equilibrium conditions, electrons and holes recombine and the Fermi energy lies close to the middle of the bandgap in the strongly depleted region

Figure 2. 10 A depletion region of width W0 is assumed at the junction Figure 2.10 A depletion region of width W0 is assumed at the junction. Charge density ρ is zero outside of the depletion region. Inside the depletion region a net charge density due to ionized dopants is established. The origin of the x-axis is placed at the junction for convenience

Figure 2.11 A Gaussian surface having volume AWp0 (shaded) encloses the negative charge of magnitude Q on the p-side of the depletion region

Figure 2.12 The electric field directions for the two parts of the depletion region showing that the fields add at the junction

Figure 2.13 The equilibrium electric field ε(x) and potential V(x) for the p-n junction follow from the application of Gauss’s law to the fixed depletion charge. Note that V on the n-side is higher compared to the p-side, whereas in Figure 2.2 the energy levels on the n-side are lower. This is the case because the energy scale in Figure 2.2 is for electron energy levels; however, the voltage scale in Figure 2.13 is established for a positive charge by convention

Figure 2.14 Coordinates xp and xn define distances into the p-type and n-type semiconductor regions starting from the depletion region edges

Figure 2. 15 (a) Quasi-Fermi levels for a forward biased junction Figure 2.15 (a) Quasi-Fermi levels for a forward biased junction. (Fp)p−side and (Fn)n−side are horizontal because for low-level injection the majority carrier concentrations are approximately fixed; however, minority carrier concentrations increase towards the depletion region due to carrier injection and therefore (Fn)p−side and (Fp)n−side are tilted. The separation between quasi-Fermi levels at the depletion region edge is equal to qV. (b) Quasi-Fermi levels for a reverse biased junction with V < 0. Minority carriers drift across the depletion region. Minority carrier concentrations now decrease towards the depletion region. Therefore (Fn)p−side and (Fp)n−side are tilted. The separation between quasi-Fermi levels at the depletion region edges is equal to |qV|

Figure 2.15 (cont.)

Figure 2.16 Excess carrier concentration on either side of the p-n junction depletion region. For forward bias the excess concentration is positive and for reverse bias it is small and negative

Figure 2.17 Minority currents In(xp) and Ip(xn) as well as majority currents Ip(xp) and In(xn). The sum of the majority andminority currents is always the total current I. Each majority current is divided into two parts, one part supplying carriers to recombine with minority carriers and the other part being injected across the junction to supply the other side with minority carriers

Figure 2.18 Measured current–voltage characteristics of a diode as well as predicted characteristics based on the diode equation. A very steep increase in current as applied voltage approaches the built-in potential V0 is observed in practice as well as an abrupt onset of reverse breakdown current at Vbd

Figure 2.19 Increase in depletion region width and increase in junction field with the application of a reverse bias for the p-n junction of Figure 2.13. The equilibrium conditions with depletion width W and peak electric field ε0 are shown with dotted lines. With the application of reverse bias V (V negative) the depletion width increases to Wbias and the peak electric field increases to εbias

Figure 2.20 Tunnelling of valence-band electron from valence band on p-side to conduction band on n-side upon application of a small reverse bias voltage. Note that there is a large supply of valence band electrons on the p-side. In comparison there is only a small supply of thermally generated minority carrier electrons that result in current I0. This explains how the reverse current can be much larger than I0 as shown in Figure 2.18, when V exceeds the breakdown voltage Vbd

Figure 2.21 In a tunnel diode the depletion width is very narrow due to the use of degenerate p+ and n+ doping. In addition to the narrow depletion region, the Fermi level enters the bands on either side of the diode resulting in the alignment of electron energy states in the conduction band on the n-side with valence electron states on the p-side. Electron tunnelling occurs in either direction as shown

Figure 2. 22 Current–voltage (I–V) characteristic of a tunnel diode Figure 2.22 Current–voltage (I–V) characteristic of a tunnel diode. At low voltages, tunnelling currents result in significant current flow in both directions. At higher positive bias voltages, electrons in the conduction band on the n-side will no longer be aligned with the valence band on the p-side. This will prevent tunnelling and current flow will therefore decrease. Current flow will eventually rise upon further increase of forward bias since the potential barrier decreases as in a normal p-n junction

Figure 2.23 The quasi-Fermi levels within the depletion region are shown. Although the depletion region is created by the recombination of charges in equilibrium, once injection takes place in forward bias, excess carriers must flow through this region

Figure 2.24 Metal-semiconductor contact for an n-type semiconductor without any flow of charge between the two sides. The predicted barrier height Eb = Ec − Ef and the flat bands shown are not achieved in real devices due to charge flow and charges at the metal semiconductor interface that cause band bending and associated electric fields at the interface and in the semiconductor

Figure 2.25 Metal-semiconductor contact energy band diagrams under various conditions. The subscripts ‘b’ refer to the fact that these are ‘built-in’ and are present without the application of an external voltage. (a) If the interface is positively charged then the band-bending will be as shown. This forms an ohmic contact provided that the semiconductor doping level is high enough to make the energy barrier Eb small. (b) If the interface is negatively charged then band bending will result in a large energy barrier Eb, which blocks electron flow from the metal to the semiconductor, as well as a depletion region in the semiconductor. A Schottky diode is formed

Figure 2.25 (cont.)

Figure 2.26 Momentum space is equivalent to reciprocal space of Figure 1.11, but each axis of Figure 1.11 is multiplied by h to convert the space to momentum space in which the x-axis is marked in momentum units of h/a , the y-axis in momentum units of h/b , and the z-axis in momentum units of h/c. This is the model we use for the electrons in the vacuum adjacent to the metal surface

Figure 2.27 If the interface is negatively charged and the semiconductor is strongly doped to form an n+ region near the interface then band bending can result in a very narrow energy barrier of height Eb, which permits electron flow by tunnelling through the barrier and an ohmic contact is formed, as well as an additional built-in barrier qVb formed due to band bending in the semiconductor

Figure 2.28 Example of an ohmic contact between p-type silicon and a metal. Electrons from the metal recombine with a high concentration of holes that accumulate near the surface of the p-type semiconductor. Each hole that recombines allows another hole to take its place, resulting in continuous current flow

Figure 2.29 Example of heterojunction formed between p-type GaAs and n-type Ga1-xAlxAs