Extrinsic Semiconductors: Doping and Types

• Intrinsic semiconductor conductivity depends on temperature and is very low at room temperature
• Impurities must be added to increase conductivity

Impure Semiconductors

• Adding a small amount (ppm) of suitable impurity increases conductivity significantly, resulting in an extrinsic semiconductor
• Deliberate addition of a desirable impurity is called doping and the impurity atoms are called dopants
• A doped semiconductor material should not distort the original pure semiconductor lattice and occupies very few of original semiconductor atom sites in the crystal
• Dopant and semiconductor atoms should be nearly the same size for minimal lattice distortion
• Silicon (Si) and Germanium (Ge) are tetravalent and belong to the fourth group in the periodic table, so dopants are chosen from the nearby fifth or third group, so the dopant atom size remains similar to Si or Ge

Types of Dopants

• Pentavalent dopants (valency - 5), such as arsenic (As), antimony (Sb), and phosphorus (P), are called donor impurities
• Trivalent dopants (valency - 3), such as indium (In), aluminum (Al), and boron (B), are called acceptor impurities
• Doping provides two types of impure semiconductors

N-Type Semiconductors

• Doping Si or Ge with a pentavalent element (arsenic, antimony, or indium) causes it to occupy an atom position in the crystal lattice
• Four of its electrons bond with the four silicon neighbors while the fifth remains weakly bound to its parent atom because the four electrons in bonding act as the effective core of the atom by the fifth electron
• Ionization energy required to free the electron is very small; it moves freely in the semiconductor lattice even at room temperature
• Energy needed to separate this electron from its atom is ~0.01 eV for germanium and 0.05 eV for silicon
• Forbidden band energy to jump is about 0.72 eV for Ge and about 1.1 eV for Si at room temperature in the intrinsic semiconductor, much less than 1.1 eV for Si
• Pentavalent dopants donate an extra electron for conduction and are known as donor impurities
• Dopant atoms determine the number of conduction electrons, independent of ambient temperature changes
• Number of free electrons and holes increases weakly with temperature, as impurity increases the number of free electrons n and electrons increase with decreasing number of holes (electron connection)
• Majority carriers electron ($n_e$) is greater, leading to the number of minority carrier holes ($n_h$) being lesser: $n_e >> n_h$
• The majority charge carrier is electrons, the charge on electrons is negative and the negative is called N in english so from the first letter it is called n-type semiconductor

P-Type Semiconductors

• Trivalent atoms (Al, B, In, etc.) are doped in small quantities during Si or Ge crystal formation
• The impurity atom arranges in place of Si or Ge atom and the four Si or Ge atoms around it form a covalent bond with three atoms
• The fourth bond has an electron deficiency (absence or empty space), so that a hole is obtained
• Holes attract electrons; electrons jump from the nearest covalent bond to fill the hole, creating a new hole
• Trivalent atoms become negatively charged when sharing the fourth electron with neighboring atoms and is treated as the the core of a negative charge along with its associated hole
• Each acceptor atom yields one hole, with the total hole count determined by impurity atoms and released electrons from intrinsic semiconductor bonds at room temperature
• In p-type semiconductors, majority charge carriers are holes and minority charge carriers are electrons
• Holes are considered positive, this semiconductor is called p-type
• For p-type semiconductors: $n_e << n_h$, $n_e$ = number of free electrons, $n_h$ = number of holes
• Both n-type and p-type semiconductors are electrically neutral because the charge of hole is equivalent to the charge in the ionised core

Band Theory and Semiconductors

• Extrinsic semiconductors feature abundant majority current carriers that increase the chances of minority carriers being destroyed, reducing intrinsic minority carrier concentration
• Doping affects a semiconductor's energy band structure. Extrinsic semiconductors have extra energy states from donor ($E_D$) and acceptor ($E_A$) impurities
• In n-type Si semiconductors, the donor energy level ($E_D$) resides slightly below the conduction band's bottom ($E_C$), enabling electrons to move into the conduction band with minimal energy
• At room temperature, most donor atoms are ionized, while only a few Si atoms are ionized (~ $10^{12}$ atoms). As a result, the conduction band mainly consists of electrons originating from the donor impurities

P-Type Semiconductors and Bands

• For p-type semiconductors, the acceptor energy level $𝐸_𝐴$ is slightly above the top $𝐸_𝑉$ of the valence band
• Very little energy is needed for an electron in the valence band to jump to the $𝐸_𝐴$ level and ionize the acceptor negatively
• With a small energy supply, the hole from level $𝐸_𝐴$ sinks into the valence band $𝐸_𝑉$, and an electron comes up
• Most acceptor atoms are ionized at room temperature, creating holes in the valence band ($E_V$)
• At room temperature, the density of holes in the valence band is mostly due to impurity in the extrinsic semiconductor

Simpified Metals, Insultators and Semiconductors

• The energy difference between $E_V$ and $E_C$ is 5.4 eV for C (diamond), 1.1 eV for Si, 0.7 eV for Ge, and 0 eV for Sn (a metal)
• Giving energy to a semiconductor creates electron-hole pairs as electrons migrate to the conduction band ($E_C$), but this state is unstable
• Electrons and holes interact and recombine following thermodynamics, with electrons reoccupying holes
• Electron-hole pair creation and recombination occur simultaneously
• In thermal equilibrium, the electron-hole pair formation and recombination rates are equal
• Recombination Rate ∝ $n_e n_h $, where $n_e$ and $n_h$ are electron and hole number densities, respectively
• The recombination rate = $R n_e n_h$ where R is known as the recombination coefficient
• For intrinsic conductors: $n_e = n_h = n_i$
• Recombination rate: $R n_i^2$

Thermal Equilibrium

• $R n_i^2$ = $R n_e n_h$
• $n_i^2$ = $ n_e n_h$

Distinctions Between P-Type and N-Type Semiconductors

• P-type semiconductors are created by adding tetravalent impurities (Al, Ga, or In), while n-type semiconductors are created by adding pentavalent impurities (P, Sb, or As)
• Majority charge carriers are holes in p-type and electrons in n-type
• Minority charge carriers are electrons in p-type and holes in n-type
• Conduction is mainly due to holes in p-type and electrons in n-type
• For p-type: $n_n > n_e$ and for n-type: $n_e > n_n$

Intrinsic vs Extrinsic Semiconductors

• N-type semiconductors have electrons as majority carriers, while p-type have holes
• In n-type semiconductors, $n_e > n_h$, and in p-type, $n_e < n_h$

Diodes and Transistors

• The primary constitutional unit for diode and transistor is the p-n junction
• p-n junction has two electrodes; it is called a p-n junction diode

P-N Junction Formation and Carrier Behavior

• A p-n junction forms when a region of a silicon wafer is doped with acceptor impurities (Al) to create a p-type semiconductor, and another region is doped with donor impurities (As) to create an n-type semiconductor
• The metallic junction between the p and n regions is formed
• Important processes during p-n junction formation include diffusion and drift
• Number density is the number of electrons or holes per unit volume
• Different densities in p and n semiconductors cause hole diffusion from p to n (p → n) and electron diffusion from n to p (n → p)
• Charge carrier motion leads to diffusion current across the junction
• Electrons diffusing from n to p leave behind ionized donors (positive charge) on the n-side, bonded to surrounding atoms, causing the development of a positively charged layer on the n-side
• Holes diffusing from p to n leave ionized acceptors (negative charge) on the p-side and they are immobile
• Space-charge region is depletion region or depletion layer
• The n-region of the depletion layer lacks majority charge carrier electrons, and the p-region lacks holes
• The thickness of depletion regions is about one-tenth of a micrometer in a p-n junction (approximately 0.5 µm)
• Positive space-charge region on the n-side and negative space-charge region on the p-side generates an electric field directed from positive to negative charge
• This field causes electrons to move to the n-side and holes to move to the p-side
• The electric field leads to the movement of charge carriers due to the electric field is called drift

Current Dynamics

• Initially, diffusion current is greater than drift current
• The space charge regions expand as diffusion continues, thereby increasing electric field strength and drift current
• The process continues until diffusion and drift currents become equal

P-N Junction Equilibrium and Potential

• A p-n junction forms once diffusion current equals drift current
• Has two connection terminals, the p-n junction is called diode
• There is no net current in a p-njunction when it is in equilibrium
• Due to charge carrier diffusion, electrons decrease in the n-section and increase in the p-section, therefore creating a potential difference across the junction
• Polarity opposes further carrier flow, establishing equilibrium
• Loss of electrons by n-material and acquisition by p generate potential that prevents electron movement from the n-region to the p-region
• The barrier obtained in the depletion region is also called depletion barrier

Diode Properties

• The two metal contacts of the junction are called semiconductor diode and have two terminals

Symbol

• p-n junction circuit symbol indicates conventional current direction in forward bias

Barrier Adjustment

• Can be altered by applying an external voltage (V) across the diode

Biasing Methods

• Two ways p-n junctions can be biased is forward bias and reverse bias

Forward Bias

• The positive terminal of the battery connects to p side of junction and negative terminal connects to n side
• Applied voltage drops across depletion region; p and n-side voltage drop is negligible due to high depletion region resistance
• Applied voltage opposes built-in potential ($V_0$), reducing depletion layer width and barrier height ($V >> V_0$)
• Effective barrier height under forward bias is Vo – V

Applied Voltage in Forward Bias

• When no external battery is connected, depletion barrier height shows as 1
• With a low applied voltage, height of effective barrier potential shows by 2
• A larger applied voltage results in a height shows by 3
• Increasing the applied voltage reduces barrier height and increases available carriers, so current rises
• Electrons cross from n-side to p-side (minority carriers) and holes cross from p-side to n-side
• The process under forward bias is known as minority carrier injection
• Minority carrier concentration increases at junction boundary compared to distant locations
• The injected electrons diffuse from the p-side junction edge to the other end of the p-side
• Injected holes simultaneously diffuse from the n-side junction edge to the other end of the n-side

Forward Bias

• Motion of charged carriers creates current
• Total diode forward current equals sum of hole diffusion current and electron diffusion current, typically in mA
• Forward biased junctions have low resistance and an external battery voltage of 1.5 V.

Reverse Bias

• Reverse bias occurs when an external voltage (V) is applied across the diode with the n-side positive and the p-side negative
• Applied voltage mostly drops across the depletion region
• Direction of applied voltage (Vo) aligns with the direction of barrier potential (V)
• Increase in barrier height and widening of depletion region occurs due to electric field modification
• Effective barrier height under reverse bias is V + Vo

Reverse Bias Detailed Dynamics

• When the battery is not connected potential barrier Vo shows as 1, shows as Vo + V when external voltage applied
• Suppresses electron flow from n → p and hole flow from p → n
• Some minority charge carriers are able to pass through the junction due to high external voltage
• The current flow has the hole in the n-region and the electron in the p-region
• However, increase in reverse current increase is reduced with large reverse voltage
• Reverse current depends on the minority concentrations on either side of the junction and does not depend on applied voltage
• Some voltage across the junction suffices for minority carriers

Breakdown

• Reverse bias voltage typically ranges from 10 V to 15 V
• The current obtained is of the order of microampere (μA)
• Static characteristic displays the relationship between current and voltage in a junction diode
• Static characteristics include forward and reverse characteristics

Forward Bias Characteristics

• In forward bias, current increases slightly until voltage crosses a threshold
• After reaching a characteristic voltage, current increases exponentially, even with small voltage increases
• Voltage is the threshold voltage or cut-in voltage
• 0.2 V happens for germanium diodes and ~ 0.7 V for silicon diodes

Diode Properties

• p-n junction diodes typically allow current flow in one direction, thus are used for alternating current (AC) rectification
• Overheating can damage the p-n junction diode if forward voltage exceeds its safety value, and there is a high current generated
• Ge or Si junction diodes are non-sensitive to 100 °C and 170 °C temperatures

Reverse Bias Characteristics

• The current remains essentially voltage independent up to a critical reverse bias voltage (known as breakdown voltage $V_{br}$)
• When reverse bias voltage is equal to breakdown voltage ($V = V_{br}$), the diode reverse current sharply increase or slight increases in bias voltage
• Without external circuit limitation below the rate value gets the p-n junction gets destroyed and it overheats

Additional Reverse Bias Properties

• For reverse bias, there is a current (of ~ μA) is direction opposite and remains almost constant with changing bias
• Also known as: reverse saturation current
• Diodes are not used beyond the reverse saturation current region for general purposes

Diode Characteristics

$r_d = \frac{\Delta V}{\Delta I}$, dynamic resistance (ratio of small change in voltage to a small change in current)

• In forward modes: 10 Ω to 100 Ω
• In reverse bias mode: of the order of 106 Ω (MΩ)

Forward Bias vs Reverse Bias

Junction Creation

Physically joining separate slabs of p-type and n-type semiconductors does not create a functional p-n junction because any slab will have roughness exceeding inter-atomic crystal spacing (~2 to 3 Å), preventing continuous contact at atomic level.

Silicon Crystal Doping

• A pure silicon (Si) crystal (5 × 10^28 atoms/m³) doped with 1 ppm concentration of pentavalent arsenic (As) can be described as,
• Thermally generated electrons: $n_i = 1.5 × 10^{16} m^{-3}$
• 1 ppm = 1 part per million = $10^6$
• Electron number density due to As atom: $N_D = \frac{5 × 10^{28}}{10^6} = 5 × 10^{22} m^{-3} $
• After doping,the the number of electrons is $n_i << N_D$
• $ n_e = N_D = 5 × 10^{22} m^{-3}$
• Now, $n_i^2 = n_e n_h$.
• $n_h = \frac{n_i^2}{n_e} = \frac{(1.5 × 10^{16})^2 }{5 × 10^{22}} = 4.5 × 10^9 m^{-3}$

Calculating Diode Resistance

• Consider diode characteristics as a straight line between I = 10 mA to I = 20 mA

Part A

• $I_2 = 20 mA$ for $V_2 = 0.8V$, (Point A)
• $I_1 = 10 mA$ for $V_1 = 0.7 V$, (Point C)
• The resistance of forward bias = $r_{fb}$
• $r_{fb} = \frac{\Delta V}{\Delta I} = \frac{V_2 - V_1}{I_2 - I_1} = \frac{0.8 - 0.7}{(20-10)*10^{-3}} = \frac{0.8 - 0.7}{(20-10)*10^{-3}} = \frac{0.1 * 10^3}{10} = 10Ω$

Part B

• At Point D: $V = -10V, I = -1 μA$
• the resistance of reverse bias = $r_{rb}= \frac{V}{I} = \frac{-10}{-1 * 10^{-6}} = 1 * 10^7Ω $