Introduction

Electronic circuits are built using components that allow for the precise control of electron flow. Historically, such control was achieved using vacuum tubes (also known as valves), like diodes, triodes, tetrodes, and pentodes. These devices consisted of multiple electrodes placed within an evacuated glass enclosure. Electrons were typically emitted from a heated cathode and moved through the vacuum, their flow controlled by voltages applied to other electrodes (grids and anodes).

Vacuum tubes were characterized by their large size, significant power consumption, requirement for high operating voltages (often hundreds of volts), and limited lifespan and reliability. The vacuum was essential to prevent collisions between electrons and air molecules, which would impede their motion.

The advent of modern solid-state electronics began in the 1930s with the realization that certain solid materials, known as semiconductors, and structures made from them (like junctions), could also effectively control the flow of charge carriers. Unlike vacuum tubes, semiconductor devices utilize charge carriers that move within the solid material itself. Simple external stimuli such as light, heat, or small applied voltages can significantly alter the number and direction of these charge carriers.

Semiconductor devices offer numerous advantages over vacuum tubes: they are much smaller, consume less power, operate at lower voltages (typically a few volts), and are highly reliable with a long operational life. Their solid-state nature eliminates the need for heating filaments or large evacuated spaces. This shift from vacuum tubes to semiconductor devices, particularly the invention of the transistor in 1948, revolutionized electronics and led to the development of integrated circuits (ICs), which are the backbone of modern technology.

Even before their full theoretical understanding, natural semiconductor crystals were used. For instance, a contact point on a galena (Lead sulfide, PbS) crystal served as a detector for radio waves in early radio receivers.

This chapter will introduce the fundamental concepts of semiconductor physics, focusing on the behavior of materials like silicon (Si) and germanium (Ge). We will then discuss basic semiconductor devices such as the p-n junction diode (a two-terminal device) and the bipolar junction transistor (a three-terminal device). Finally, we will explore some basic circuits demonstrating their applications, particularly the use of a diode in rectification.

Classification Of Metals, Conductors And Semiconductors

Solid materials can be broadly categorized into three types based on their ability to conduct electricity, which is quantified by their electrical conductivity ($\sigma$) or its reciprocal, resistivity ($\rho = 1/\sigma$):

1. Metals: These materials are excellent conductors of electricity. They have very high conductivity or very low resistivity. Their resistivity is typically in the range of $10^{-2}$ to $10^{-8}\ \Omega \text{ m}$, corresponding to a conductivity range of $10^2$ to $10^8\ \text{S m}^{-1}$.

2. Insulators: These materials are poor conductors of electricity. They have very low conductivity or very high resistivity. Their resistivity is typically in the range of $10^{11}$ to $10^{19}\ \Omega \text{ m}$, corresponding to a conductivity range of $10^{-11}$ to $10^{-19}\ \text{S m}^{-1}$.

3. Semiconductors: These materials have electrical conductivity properties that lie between those of metals and insulators. Their resistivity is typically in the range of $10^{-5}$ to $10^6\ \Omega \text{ m}$, corresponding to a conductivity range of $10^5$ to $10^{-6}\ \text{S m}^{-1}$.

The conductivity of semiconductors is generally much lower than that of metals but significantly higher than that of insulators. Furthermore, the conductivity of semiconductors is highly sensitive to factors like temperature and the presence of impurities, a property that distinguishes them from metals and insulators.

Semiconductors can be broadly classified into:

• Elemental Semiconductors: Composed of a single element, primarily Silicon (Si) and Germanium (Ge), which are in Group 14 of the periodic table.
• Compound Semiconductors: Formed by combining two or more elements. These can be inorganic (e.g., Cadmium Sulfide (CdS), Gallium Arsenide (GaAs)) or organic (e.g., anthracene, conducting polymers like polypyrrole).

While elemental and inorganic compound semiconductors form the basis of most current electronic devices, organic semiconductors and polymers are an area of active research for future technologies like flexible electronics and molecular electronics. This chapter focuses mainly on inorganic semiconductors, particularly Si and Ge, whose properties provide a general framework for understanding many other semiconductors.

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On The Basis Of Energy Bands

A more fundamental way to classify solids is based on their energy band structure. In an isolated atom, electrons occupy discrete energy levels. However, when atoms come together to form a solid, their valence electrons interact with the electric fields of neighboring atoms. These interactions cause the discrete energy levels of individual atoms to split and broaden, forming continuous ranges of allowed energies called energy bands.

In solids, the electrons occupy these energy bands. The two most important bands for electrical conduction are:

1. Valence Band (VB): This band contains the energy levels of the outermost (valence) electrons of the atoms. At absolute zero temperature and without external energy input, this band is typically completely filled with valence electrons.

2. Conduction Band (CB): This band lies above the valence band and contains energy levels where electrons can move freely throughout the crystal, contributing to electrical conduction. At absolute zero, this band is typically empty.

The region between the top of the valence band ($E_V$) and the bottom of the conduction band ($E_C$) where no electron energy levels exist is called the energy band gap ($E_g$) (

Figure 14.1). The size of this energy gap determines whether a material is a metal, insulator, or semiconductor ( Figure 14.2):

• Metals: In metals, the conduction band is either partially filled or overlaps with the valence band [Figure 14.2(a)]. With no energy gap or a very small effective one, electrons can easily move from the valence band to the conduction band or to higher levels within the partially filled valence band, making a large number of free electrons available for conduction. This results in high conductivity.
• Insulators: In insulators, there is a large energy band gap ($E_g > 3$ eV) between the valence band and the conduction band [Figure 14.2(b)]. At room temperature, the thermal energy is insufficient to excite electrons from the filled valence band across this large gap into the empty conduction band. Consequently, very few free electrons are available, leading to extremely low conductivity.
• Semiconductors: In semiconductors, there is a finite but relatively small energy band gap ($E_g < 3$ eV) [Figure 14.2(c)]. At absolute zero (0 K), the valence band is filled, and the conduction band is empty, similar to an insulator. However, at temperatures above 0 K, some valence electrons gain enough thermal energy to overcome the small energy gap and move into the conduction band. These electrons become free charge carriers, and their movement contributes to conductivity. The number of these thermally excited electrons, and hence the conductivity, increases with temperature.

For Si, $E_g \approx 1.1$ eV, and for Ge, $E_g \approx 0.7$ eV at room temperature. For carbon (diamond), $E_g \approx 5.4$ eV, which is why diamond is an excellent insulator, despite having the same crystal structure as Si and Ge.

Intrinsic Semiconductor

A pure semiconductor material, like crystalline Silicon (Si) or Germanium (Ge), is called an intrinsic semiconductor. Si and Ge crystallize in a diamond-like structure where each atom is covalently bonded to four nearest neighbors (

Figure 14.3). Each Si or Ge atom has four valence electrons, and these are shared with the four neighboring atoms to form stable covalent bonds ( Figure 14.4).

At absolute zero temperature (0 K), all valence electrons are tightly bound in these covalent bonds, and there are no free charge carriers. The intrinsic semiconductor behaves like an insulator (

Figure 14.6(a)).

As the temperature increases, thermal energy can cause some of the covalent bonds to break. When a covalent bond breaks, an electron is released from its bound state and becomes a free electron that can move through the crystal lattice, contributing to electrical conduction. The absence of the electron in the broken bond creates a vacancy with an effective positive charge, called a hole (

Figure 14.5(a)). This electron-hole pair generation is a thermal process.

The hole can also contribute to conduction. When an electron from a neighboring covalent bond moves to fill the hole, the hole appears to have moved to the site where the electron originated (

Figure 14.5(b)). Thus, the movement of holes can be visualized as the movement of positive charge carriers.

In an intrinsic semiconductor, the number of free electrons ($n_e$) generated by thermal excitation is always equal to the number of holes ($n_h$) created. This carrier concentration is denoted by $n_i$, the intrinsic carrier concentration:

$$n_e = n_h = n_i$$

Under an applied electric field, free electrons move towards the positive terminal (electron current $I_e$), while holes move towards the negative terminal (hole current $I_h$). The total current ($I$) in an intrinsic semiconductor is the sum of the electron and hole currents:

$$I = I_e + I_h$$

At any given temperature, there is a balance between the generation of electron-hole pairs and their recombination (when a free electron falls back into a hole). The intrinsic carrier concentration $n_i$ increases significantly with temperature, leading to an increase in conductivity.

The energy band diagram for an intrinsic semiconductor at $T > 0$ K shows some electrons in the conduction band and an equal number of holes in the valence band, indicating the presence of charge carriers available for conduction (

Figure 14.6(b)).

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Extrinsic Semiconductor

The conductivity of intrinsic semiconductors at room temperature is often too low for practical electronic applications. To increase their conductivity significantly, a controlled amount of specific impurity atoms is added to the pure semiconductor crystal. This process is called doping, and the resulting material is an extrinsic semiconductor or impurity semiconductor. The impurity atoms are called dopants.

The dopant concentration is typically very small, on the order of parts per million (ppm), but it drastically alters the number of charge carriers. For the dopant to fit into the semiconductor lattice without causing significant distortion, its atomic size should be similar to that of the host semiconductor atoms (Si or Ge).

For tetravalent semiconductors like Si and Ge (Group 14), dopants are usually chosen from Group 15 (pentavalent) or Group 13 (trivalent) elements. This gives rise to two types of extrinsic semiconductors:

(i) n-type semiconductor:

When a pentavalent impurity atom (like Arsenic (As), Antimony (Sb), or Phosphorous (P)) is added to a pure Si or Ge crystal, it replaces a host atom in the lattice (

Figure 14.7(a)). Four of the five valence electrons of the dopant atom form covalent bonds with the four neighboring Si or Ge atoms. The fifth valence electron is loosely bound to the dopant atom because it is screened by the positively charged core formed by the nucleus and inner electrons of the dopant atom plus the four bonding electrons it shares with neighbors. This fifth electron is only weakly attracted to the core.

The energy required to free this extra electron from the dopant atom and make it available for conduction is very small (e.g., about 0.01 eV for Ge, 0.05 eV for Si), much less than the intrinsic band gap energy ($E_g$). At room temperature, most of these extra electrons are easily ionized and move into the conduction band, becoming free charge carriers. Since the pentavalent impurity atoms donate electrons, they are called donor impurities.

In an n-type semiconductor, the number of conduction electrons ($n_e$) is predominantly determined by the number of donor atoms ($N_D$), as these contribute far more electrons than the intrinsic thermal generation. While electron-hole pairs are still generated intrinsically, the large number of electrons from the dopant increases the recombination rate, reducing the number of holes ($n_h$). Consequently, in n-type semiconductors, electrons are the majority carriers, and holes are the minority carriers:

$$n_e \gg n_h$$

(ii) p-type semiconductor:

When a trivalent impurity atom (like Indium (In), Boron (B), or Aluminium (Al)) is added to a pure Si or Ge crystal, it also replaces a host atom (

Figure 14.8(a)). The dopant atom has only three valence electrons, which form covalent bonds with three neighboring Si or Ge atoms. To complete the covalent bond with the fourth neighbor, the dopant atom needs one more electron. This results in a vacancy or deficit of an electron in the bond, which is a hole.

The trivalent impurity atom accepts an electron from a neighboring Si or Ge atom to complete its fourth bond, effectively creating a mobile hole in the valence band of the host atom. Since the trivalent impurity atoms accept electrons, they are called acceptor impurities.

The energy required for an electron from the valence band to move into an acceptor site (creating a hole in the valence band) is very small (similar to donor ionization energy). At room temperature, most acceptor atoms readily create holes. In a p-type semiconductor, the number of holes ($n_h$) is primarily determined by the number of acceptor atoms ($N_A$), as these create far more holes than intrinsic generation. The presence of extra holes increases the recombination rate with intrinsic electrons, reducing $n_e$. Consequently, in p-type semiconductors, holes are the majority carriers, and electrons are the minority carriers:

$$n_h \gg n_e$$

In both n-type and p-type semiconductors, the crystal as a whole remains electrically neutral. The extra majority carriers are balanced by the fixed charges of the ionized donor or acceptor impurity atoms in the lattice. The number of free electrons and holes in thermal equilibrium in any semiconductor (intrinsic or extrinsic) is related by the mass action law:

$$n_e n_h = n_i^2$$

where $n_i$ is the intrinsic carrier concentration. This law holds true even in doped semiconductors. For example, in an n-type semiconductor with $n_e \approx N_D$, the hole concentration is $n_h = n_i^2 / N_D$. Since $N_D \gg n_i$, $n_h$ is much smaller than $n_i$.

Doping introduces additional energy levels in the band structure. In n-type semiconductors, donor levels ($E_D$) are created just below the conduction band minimum ($E_C$) (

Figure 14.9(a)). In p-type semiconductors, acceptor levels ($E_A$) are created just above the valence band maximum ($E_V$) ( Figure 14.9(b)). These shallow levels allow carriers to move into the conduction or valence bands with minimal thermal energy, significantly increasing conductivity compared to intrinsic semiconductors.

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P-n Junction

A p-n junction is formed when a p-type semiconductor material is joined to an n-type semiconductor material. This junction is a fundamental component of most semiconductor devices, including diodes, transistors, and integrated circuits. Understanding its behavior is crucial for analyzing how these devices work.

A p-n junction is not created by simply physically pressing together a piece of p-type and a piece of n-type semiconductor. The contact achieved this way would be irregular at the atomic level and would not form a continuous crystal structure required for controlled charge flow. Instead, p-n junctions are typically fabricated by special techniques like diffusion or ion implantation, where impurity atoms are introduced into a specific region of a semiconductor wafer of the opposite type, converting that region into p-type or n-type material and creating a continuous metallurgical junction.

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P-n Junction Formation

When a p-n junction is formed, two primary processes occur due to the differences in charge carrier concentrations on either side of the junction:

1. Diffusion: Initially, there is a very high concentration of free electrons in the n-region and a very high concentration of holes in the p-region. Due to this concentration gradient, electrons diffuse from the n-side to the p-side, and holes diffuse from the p-side to the n-side (

Figure 14.10). This movement of charge carriers constitutes a diffusion current.

2. Drift: As electrons diffuse from the n-side into the p-side, they leave behind positively charged, immobile donor ions in the n-region near the junction. Similarly, as holes diffuse from the p-side into the n-side, they leave behind negatively charged, immobile acceptor ions in the p-region near the junction. These layers of immobile positive charge on the n-side and negative charge on the p-side create a region around the junction that is depleted of free charge carriers (electrons and holes). This region is called the depletion region or depletion layer (

Figure 14.10).

Within the depletion region, an internal electric field is established, directed from the positive ions on the n-side towards the negative ions on the p-side. This electric field opposes the further diffusion of majority carriers (electrons from n-side, holes from p-side). Instead, it causes minority carriers that wander into the depletion region (electrons from p-side, holes from n-side) to be swept across the junction. This movement of charge carriers due to the electric field is called drift, and it constitutes a drift current, which flows in the opposite direction to the diffusion current.

Initially, the diffusion current is large, and the drift current is small. As diffusion proceeds, the depletion region widens, the internal electric field strengthens, and the drift current increases. This process continues until the diffusion current equals the drift current. At this point, a state of equilibrium is reached, and there is no net flow of charge across the junction. The established electric field across the depletion region creates a potential difference called the barrier potential ($V_0$) or built-in potential (

Figure 14.11). The n-side becomes positive relative to the p-side due to the accumulation of positive donor ions, effectively forming a potential barrier that prevents further majority carrier flow.

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Semiconductor Diode

A semiconductor diode is a two-terminal electronic component fundamentally consisting of a p-n junction. Metallic contacts are attached to the p-type and n-type regions to allow for the application of an external voltage (

Figure 14.12(a)). The symbolic representation of a p-n junction diode is shown in Figure 14.12(b), where the arrow indicates the conventional direction of current flow when the diode is forward biased (from p-side to n-side).

The behavior of a p-n junction diode is determined by how an external voltage (bias) affects the built-in potential barrier ($V_0$) formed during the junction formation at equilibrium (zero bias) (

Figure 14.11).

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P-n Junction Diode Under Forward Bias

A p-n junction diode is said to be forward biased when an external voltage $V$ is applied such that the positive terminal of a battery is connected to the p-side and the negative terminal to the n-side (

Figure 14.13(a)). The majority of the applied voltage drops across the depletion region, as its resistance is much higher than the p- and n-regions which contain abundant charge carriers. The direction of the applied voltage is opposite to that of the built-in barrier potential ($V_0$).

This applied forward bias voltage reduces the effective potential barrier height to $(V_0 - V)$ (

Figure 14.13(b)). As the barrier height decreases, it becomes easier for majority carriers to overcome the barrier. Electrons from the n-side and holes from the p-side gain enough energy to cross the depletion region.

This movement of majority carriers across the junction is called minority carrier injection, as electrons crossing to the p-side become minority carriers there, and holes crossing to the n-side become minority carriers there (

Figure 14.14). These injected minority carriers diffuse away from the junction into the bulk of the p- and n-regions, respectively, where they eventually recombine with majority carriers.

The diffusion of injected minority carriers creates a significant diffusion current flowing across the junction. In forward bias, this diffusion current is the dominant component of the total diode current. For small forward voltages, the current is small, but as $V$ increases and the barrier is significantly reduced, the current increases rapidly, typically exponentially, with the applied voltage. The magnitude of the forward current is usually in the milliamps (mA) range.

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P-n Junction Diode Under Reverse Bias

A p-n junction diode is reverse biased when an external voltage $V$ is applied such that the positive terminal of a battery is connected to the n-side and the negative terminal to the p-side (

Figure 14.15(a)). The direction of the applied voltage is the same as that of the built-in barrier potential ($V_0$).

This applied reverse bias voltage increases the effective potential barrier height to $(V_0 + V)$ (

Figure 14.15(b)). The depletion region widens further. This increased barrier strongly opposes the flow of majority carriers (electrons from n-side, holes from p-side) across the junction, effectively reducing the diffusion current to almost zero.

However, there is still a small current that flows under reverse bias. This current is due to the movement of minority carriers. Minority carriers (electrons in the p-side, holes in the n-side) that are thermally generated within or near the depletion region are swept across the junction by the internal electric field, which is strengthened by the reverse bias. This forms a small drift current flowing in the direction opposite to the forward current. The magnitude of this reverse drift current is very small, typically in the microamps ($\mu$A) or nanoamps (nA) range.

The reverse drift current is limited by the rate of thermal generation of minority carriers, which is relatively insensitive to the applied voltage. Hence, the reverse current remains almost constant as the reverse bias voltage increases, up to a certain critical voltage called the breakdown voltage ($V_{br}$). At breakdown voltage, the reverse current increases dramatically due to processes like Zener breakdown or avalanche breakdown. Operating a general-purpose diode beyond its breakdown voltage can cause it to overheat and be permanently damaged.

The current-voltage (V-I) characteristics of a typical silicon p-n junction diode (

Figure 14.16(c)) summarize its behavior: negligible current under reverse bias (until breakdown) and significant current under forward bias (above a certain threshold voltage). The experimental circuit arrangements for measuring these characteristics are shown in Figure 14.16(a) (forward bias) and Figure 14.16(b) (reverse bias). In forward bias, current is measured in mA; in reverse bias, it is measured in $\mu$A.

The V-I curve shows that in forward bias, current is very small until the voltage reaches the threshold voltage (or cut-in voltage) (around 0.7 V for Si, 0.2 V for Ge). Beyond this voltage, the current rises steeply. In reverse bias, the current remains very low (reverse saturation current) until the breakdown voltage is reached.

The resistance of a diode is not constant but varies with the operating point. The dynamic resistance ($r_d$) is defined as the change in voltage across the diode divided by the resulting change in current at a specific operating point:

$$r_d = \frac{\Delta V}{\Delta I}$$

In the steep region of the forward characteristic, the dynamic resistance is low. In the reverse bias region (before breakdown), the resistance is very high.

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Application Of Junction Diode As A Rectifier

One of the most important applications of a p-n junction diode is its ability to act as a rectifier. Rectification is the process of converting alternating current (AC) or voltage into direct current (DC) or voltage. Since a diode allows current to flow easily in the forward direction (when forward biased) but blocks current significantly in the reverse direction (when reverse biased), it can be used to shape an AC waveform into a unidirectional (though not necessarily steady) DC form.

A simple circuit using a single diode to achieve rectification is the half-wave rectifier. In this circuit (

Figure 14.18(a)), an AC voltage is applied across a diode and a load resistor ($R_L$) connected in series. During the positive half-cycle of the input AC voltage, the p-side of the diode becomes positive relative to the n-side, forward biasing the diode. The diode conducts, and current flows through the load resistor, producing an output voltage across $R_L$ that follows the shape of the positive half-cycle of the input.

During the negative half-cycle of the input AC voltage, the p-side of the diode becomes negative relative to the n-side, reverse biasing the diode. The diode ideally blocks current flow (only a negligible reverse saturation current exists). Therefore, there is no current through the load resistor, and the output voltage across $R_L$ is zero for this half-cycle (

Figure 14.18(b)).

The output voltage waveform is a series of positive pulses with gaps in between, corresponding to the original positive half-cycles. This output is unidirectional (it only flows in one direction) but is not a steady DC voltage; it is called a pulsating DC. It's a "half-wave" rectifier because it only uses half of the input AC waveform to produce output.

To utilize both half-cycles of the input AC, a full-wave rectifier circuit can be used. A common type of full-wave rectifier uses two diodes and a center-tapped transformer (

Figure 14.19(a)). The center-tapped transformer provides two AC voltages that are equal in magnitude but 180° out of phase. The p-sides of the two diodes ($D_1$ and $D_2$) are connected to the ends of the transformer's secondary winding (A and B), and their n-sides are connected together to one end of the load resistor $R_L$. The other end of $R_L$ is connected to the center tap of the transformer.

During the positive half-cycle of the AC voltage at point A (relative to the center tap), point B is negative (relative to the center tap) (

Figure 14.19(b)). Diode $D_1$ is forward biased and conducts, while diode $D_2$ is reverse biased and blocks current. Current flows through $D_1$ and $R_L$.

During the negative half-cycle of the AC voltage at point A, point B becomes positive. Diode $D_1$ is now reverse biased and blocks, while diode $D_2$ is forward biased and conducts. Current flows through $D_2$ and $R_L$. Note that in both half-cycles, the current flows through the load resistor $R_L$ in the same direction (from the common connection of the n-sides to the center tap).

The output voltage across $R_L$ is a series of positive pulses, corresponding to both the positive and negative half-cycles of the input AC waveform (

Figure 14.19(c)). This pulsating DC output is more continuous than that of a half-wave rectifier.

To convert the pulsating DC output into a smooth, steady DC voltage, a filter circuit is usually added. A common filter is a large capacitor connected in parallel with the load resistor ($R_L$) (

Figure 14.20(a)). The capacitor charges up when the rectified voltage pulses rise. When the rectified voltage starts to fall, the capacitor discharges through the load resistor, maintaining the voltage across $R_L$. Since the capacitor charges rapidly to the peak voltage and discharges relatively slowly through the load, the output voltage remains close to the peak value of the rectified pulses, with only a small ripple ( Figure 14.20(b)). The larger the capacitance and the larger the load resistance, the slower the discharge, and the smoother the DC output (larger time constant $RC$). Inductors can also be used in filter circuits, often in combination with capacitors.

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