Notes on Semiconductor Diodes - Comprehensive Study

13.1 SEMICONDUCTOR MATERIALS

• Semiconductors possess conductivity between conductors and insulators at room temperature. Their electrical properties are highly responsive to external factors.

• Common examples: Germanium (Ge), Silicon (Si), Boron (B), Selenium (Se).

• Conductivity and resistivity ranges:

  • Conductors: high conductivity, low resistivity, allowing easy electron flow.

  • Insulators: very low conductivity, strongly resisting electron flow.

  • Semiconductors: conductivities between these extremes, highly modifiable by small amounts of carefully controlled impurities.

• Temperature dependence (negative temperature coefficient): Resistance decreases with increasing temperature (conductivity increases with T). This is because thermal energy liberates more charge carriers.

  • At very low temperatures: behave like insulators, as there is insufficient thermal energy to create free carriers.

  • At higher temperatures: become conductive, as more energy is available to break atomic bonds and create electron-hole pairs.

• Illumination affects resistivity: Light (photons) can supply energy to electrons, lowering resistivity and thus increasing conductivity, a principle used in photodiodes.

• Nonlinearity: Semiconductors are nonlinear resistors; unlike ohmic resistors, the current is not directly proportional to voltage, enabling their use in rectifiers and switches.

• Impurity sensitivity: Small amounts of certain impurities significantly alter conductivity and conduction mechanisms. These impurities are called dopants.

  • Donors: typically pentavalent elements like arsenic (As), antimony (Sb), phosphorus (P), which donate free electrons to the crystal lattice.

  • Acceptors: typically trivalent elements like boron (B), gallium (Ga), indium (In), which create 'holes' in the crystal lattice by accepting electrons.

• Significance of impurities: The controlled introduction and gradient of impurities (doping) at junctions are fundamental to creating active electronic devices such as diodes, transistors, SCRs, UJTs, varistors, and thermistors.

• Elemental semiconductors: Ge, Si, grey crystalline tin, Se, Te, B, etc.

  • Silicon and germanium are most widely used due to the relatively small energy required to break their covalent bonds, making them practical for thermal generation of carriers at room temperature.

• Advantages of semiconductor devices:

  • Compact size, low cost, light weight, ruggedness compared to vacuum tubes.

  • Instantaneous operation (no warm-up time), low operating voltage and power consumption.

  • High efficiency, long life, minimal aging (when operated within specified limits).

• Key takeaway: The electrical conductivity of semiconductors is highly tunable via external factors like temperature, illumination, and especially through controlled introduction of impurities (doping), which is the basis for active electronic device functionality.

13.2 ENERGY LEVELS

• Electrons occupy fixed shells (K, L, M, N, O, P, Q) around a nucleus; the K shell is closest to the nucleus and has the lowest energy.

• Maximum electrons per shell given by the formula $2n^2$, where n is the shell number:

  • K ($n=1$): $2 imes 1^2 = 2$ electrons

  • L ($n=2$): $2 imes 2^2 = 8$ electrons

  • M ($n=3$): $2 imes 3^2 = 18$ electrons

  • N ($n=4$): $2 imes 4^2 = 32$ electrons

• Outer electrons (valence electrons): These electrons determine the electrical and chemical characteristics of an atom. They may be fully or partially filled, influencing bonding behavior.

• Energy diagrams: Energy levels correspond to a particular orbit radius; a larger orbit implies electrons at a higher energy state, further from the nucleus.

• Energy units: Measured in electron volts (eV), a convenient unit for atomic and molecular energy scales.

  • $1\text{ eV} = q_e \times 1\text{ V}$ (the energy needed to move an electron through a 1-volt potential difference, where $q_e$ is the elementary charge of an electron, approximately $1.602 imes 10^{-19}\text{ J}$).

• Forbidden regions (gaps): Exist between allowed discrete energy levels; electrons cannot stably occupy these states but can pass through them if they acquire sufficient energy (e.g., from thermal or photon excitation).

• Bound electrons: Electrons in inner shells are tightly bound to the nucleus and require significant energy to be dislodged.

• Excited electrons:

  • Can temporarily leap to higher, unoccupied energy levels by acquiring energy from external sources (e.g., heat or light).

  • If sufficient energy is absorbed, an electron may leave the atom entirely, becoming a free electron.

  • Excited electrons tend to quickly return to lower, more stable energy levels, releasing the excess energy, typically as heat (phonons) or light (photons).

13.3 ENERGY BANDS IN SOLIDS

• In a solid material, due to the close proximity and interaction between a large number of atoms, the discrete energy levels of individual isolated atoms merge into continuous energy bands. This phenomenon is governed by the Pauli Exclusion Principle.

• Two main bands relevant to conduction:

  • Valence band: The highest range of electron energies in which electrons are typically found at absolute zero temperature, involved in atomic bonding. It is the highest occupied energy band in its ground state.

  • Conduction band: A higher range of energies where electrons are free to move throughout the material, contributing to electrical current. Electrons in this band are delocalized.

• Forbidden energy gap (band gap) $E_g$: The energy region between the valence and conduction bands where no allowed electron states exist. It defines the minimum energy an electron needs to jump from the valence band to the conduction band.

• Distinguishing materials by $E_g$ width:

  • Insulators: Characterized by a very large band gap (e.g., $E_g \gtrsim 5\text{ eV}$). It requires an extremely high amount of energy (or electric field) for electrons to cross this gap, making them very poor conductors.

  • Semiconductors: Possess a moderate band gap (e.g., $\approx 1\text{ eV}$). This intermediate gap allows some electrons to jump to the conduction band under thermal excitation at room temperature, making their conductivity tunable.

  • Conductors: Essentially have no band gap; the valence and conduction bands either overlap significantly or the conduction band is partially filled. This allows electrons to move freely with very little energy input.

• Insulators at room temperature:

  • Almost no electrons are in the conduction band because $E_g$ is too large for thermal energy to easily overcome.

  • The valence band is completely filled, preventing electron movement within it. Consequently, electrical conduction is negligible.

  • Electrons can only cross the gap by applying extremely high temperatures or very strong electric fields, which can lead to dielectric breakdown.

• Conductors:

  • Valence and conduction bands overlap or the conduction band is naturally incomplete. Electrons are effectively free to move across the entire solid with minimal energy input, making them excellent conductors.

• Intrinsic semiconductors:

  • At absolute zero (0 K): The valence band is completely full, and the conduction band is entirely empty. The material behaves like an insulator.

  • At room temperature: Thermal energy is sufficient to promote a small number of electrons across the band gap to the conduction band, creating an equal number of electron-hole pairs. This enables a limited amount of electrical conduction.

• Intrinsic Si and Ge band gaps at room temperature:

  • Silicon: $E_g \approx 1.12\text{ eV}$

  • Germanium: $E_g \approx 0.72\text{ eV}$

• For reference at absolute zero:

  • $E_g^{\text{Si}} \approx 1.21\text{ eV}$

  • $E_g^{\text{Ge}} \approx 0.785\text{ eV}$

• Silicon and germanium comparison: Silicon has a larger band gap than germanium. Therefore, silicon requires more energy for an electron to move from the valence band to the conduction band, resulting in typically lower conductivity than germanium at the same temperature and purity level.

• Metals: Their band structure typically involves overlapping conduction and valence bands or partially filled conduction bands, which results in a continuous availability of free electrons that can move through the lattice, leading to high electrical conductivity.

13.4 CONDUCTION IN SOLIDS

• Conduction occurs when an applied electric field causes charge carriers (electrons and/or holes) to move in a preferred direction, creating an electric current.

• Two primary mechanisms for current flow in semiconductors:

  • Motion of free electrons in the conduction band: These electrons are not bound to any specific atom and can freely accelerate under an electric field.

  • Transfer of holes in the valence band: This is a conceptual movement where an empty electron state (a hole) appears to move as electrons from adjacent atoms fill it.

• Hole concept:

  • A missing electron in the valence band represents a net positive charge and acts as a positive charge carrier. It is not an actual physical particle but a convenient way to describe the collective movement of the remaining electrons in the valence band.

  • When an electron from a neighboring covalent bond moves to fill a hole, the hole effectively shifts to the position previously occupied by that electron. Therefore, holes move in the opposite direction to electron motion.

  • In an electric field, electrons (which have a negative charge) are attracted towards the positive terminal of the field.

  • Holes (which are treated as positive charges) are attracted towards the negative terminal of the field.

  • In a semiconductor (or any conductor), current involves the movement of both electrons and holes. By convention, current direction (positive to negative) is defined as the direction of positive charge flow, which is opposite to the direction of electron motion.

  • Free electrons in the conduction band are delocalized and move relatively freely, contributing significantly to current.

  • Holes represent the absence of electrons and move as if they were positively charged particles, also contributing to the total current.

13.5 DRIFT AND DIFFUSION CURRENTS

• Two primary mechanisms of carrier transport in semiconductors:

  • Drift: The directed motion of charge carriers (electrons and holes) under the influence of an externally applied electric field.

  • Diffusion: The random motion of charge carriers from a region of higher concentration to a region of lower concentration, driven by the concentration gradient itself, not an electric field.

13.5.1 Drift Current

• With a steady electric field $E$ applied across a semiconductor, free electrons and holes experience a net force and drift with an average velocity. For electrons, this drift velocity is $v_d = -\mu_n E$ (where $\mu_n$ is electron mobility and the negative sign indicates drift opposite to the field), and for holes, it is $v_d = \mu_p E$ (where $\mu_p$ is hole mobility, in the same direction as the field). The units of mobility are typically m$^2$/(V\cdot s).

• This drift velocity is superimposed on the random thermal motion of carriers, resulting in a net movement of charge and thus an electrical current (drift current).

13.5.2 Diffusion Current

• Diffusion current occurs solely due to differences in carrier concentration across the semiconductor. Carriers move from regions where they are abundant to regions where they are scarce.

• This random motion continues until carrier concentrations become uniformly distributed throughout the material. In many semiconductor devices, diffusion and drift currents often occur simultaneously and in opposition, especially near P-N junctions, leading to a balance at equilibrium or a net current under bias.

13.6 ATOMIC BONDS

• The type of atomic bonding within a material critically determines whether it behaves as an insulator, semiconductor, or conductor.

• Primary bonds (strong): Involve strong attractive forces between atoms and require significant energy to break.

  • Metallic bonding: Occurs in metals where atoms donate their valence electrons to a shared 'sea' or 'cloud' of delocalized electrons. These electrons form an 'electron gas' that moves freely between a lattice of positively charged metal ions (e.g., copper, silver). This free electron mobility accounts for high electrical and thermal conductivity.

  • Covalent bonding: Involves atoms sharing valence electrons to achieve a stable, full outer electron shell (e.g., silicon and germanium form extensive covalent networks in their crystal structure). In pure covalent materials, all valence shells are filled by shared electrons, and there are no free carriers by default at low temperatures, making them insulators or semiconductors.

  • Ionic bonding: Characterized by the complete transfer of one or more electrons from one atom to another, leading to the formation of positively and negatively charged ions. These ions are then held together by strong electrostatic attractive forces. This bonding type is common in many insulators (e.g., NaCl).

• Secondary bonds (Van der Waals): Weaker intermolecular attractive forces, less relevant to semiconductor conductivity but important for physical properties of some materials.

13.7 INTRINSIC SEMICONDUCTORS

• Intrinsic semiconductors are materials with an extremely pure crystal structure, containing minimal impurity content. Modern manufacturing processes can achieve very low impurity levels, often less than 1 part per billion.

• Silicon and germanium are archetypal intrinsic semiconductors because the energy required to break their covalent bonds is relatively small, making them suitable for electronic applications:

  • For Silicon (Si): The bond-breaking energy at room temperature is approximately $E_{\text{bond}}^{\text{Si}} \approx 1.12\text{ eV}$.

  • For Germanium (Ge): The bond-breaking energy at room temperature is approximately $E_{\text{bond}}^{\text{Ge}} \approx 0.72\text{ eV}$.

• Crystal structure and energy bands:

  • In both Si and Ge, each atom forms four covalent bonds with four neighboring atoms in a tetrahedral lattice structure.

  • Energy band diagrams show that at 0 K, the valence band is completely full, and the conduction band is entirely empty, separated by a small energy gap.

  • At room temperature, thermal energy is sufficient to break a small number of these covalent bonds, promoting electrons from the valence band to the conduction band, thereby creating both free electrons and holes.

• Formation of electron-hole pairs (thermal generation):

  • When a covalent bond absorbs sufficient thermal energy, it can break, releasing an electron that becomes free (moves to the conduction band). This creates a vacant electron site (a hole) in the valence band.

  • In intrinsic materials, electrons and holes are always