GET 201 - Semi Conductors PDF

# Introduction To Electronic: Semiconductor properties ## Definition of Electronics The word "Electronics" deals with the sciences of electrons. The sciences of electron deals with the movement of electrons under the influence of applied electric and magnetic fields. ## Applications of Electronic...

# Introduction To Electronic: Semiconductor properties ## Definition of Electronics The word "Electronics" deals with the sciences of electrons. The sciences of electron deals with the movement of electrons under the influence of applied electric and magnetic fields. ## Applications of Electronics Today electronics has invaded every walk of life and its applications are increasing at a very fast rate. Life today without any electronic gadget become a cra.t. Applications of electronics are extensive and varied, so it is fully listed However, applications of electronics may be broad into the following categories: * **Communication:** Medical Electronics * **Entertainment:** _Instrumentation_ * **Industrial Electronics:** Navigation & Airsafting * **Defense Electronics:** Telemetry ## Electron Electron is the most fundamental and the lightest charged particle. It has a negative charge of magnitude q = 1.6 x 10^-19 coulomb and a mass m = 9.11 x 10^-31 kilogram. ## Electron is Also Observed to Behave as a Wave The wave properties are associated with moving electrons and the wavelength is related with the velocity: $$x= \frac{mv}{h}$$ where h is the planck's constant and equals 6.626 x 10^-34 joule-second. m is the mass in kilograms, v is the velocity measured in meters/second. ## Hole Hole is the deficiency created by the removal of an electron from a semiconductor atom. A hole moves within the semiconductor in a manner similar to an electron and contributes to electric current. Since an electron carries a charge of -1.6 coulombs, hole carries a charge of +1.6 coulombs. ## Electron Volt (eV) An electron volt is defined as the rise in kinetic energy of an electron in rising through a potential difference of 1 volt. 1 eV = 1.60 * 10^-19 joule ## Electronic Configuration of Carbon, Silicon, and Germanium - **Element:** Carbon - **Atomic Number:** 6 - **Electronic Configuration:** 1s^2 2s^2 2p^2 - **Element** Silicon - **Atomic Number:** 14 - **Electronic Configuration:** 1s^2 2s^2 2p^6 3s^2 3p^2 - **Element:** Germanium - **Atomic Number:** 32 - **Electronic Configuration:** 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^2 ## Energy Band Theory Of Crystals Any crystal consists of a space array of atoms (or molecule) formed by regular repetition in three dimensions of some fundamental building block. In gasses, the atoms are soxapart as to have negligible influence on each other, so electronic energy levels for each gas are the same as for the single free atom. In the case of a crystal, the atoms are closely packed; hence the energy levels for the crystal are not the same as for the free atoms. In crystalline atom, the energy levels in a crystal get modified due to interaction between the atoms. ## Energy Band Structure of Insulators, semiconductors, and conductors - **Insulators:** An insulator is a material that has extremely poor electrical conductivity. The energy band diagram of a typical insulator gives us the understanding of the forbidden energy gap between the valence band and the conduction band. An attempt to cross the energy gap by an electron is very difficult because the energy gap is too large for an electron. - **Semiconductors:** In semiconductors, the energy gap is smaller, and an electron requires a very small amount of energy to jump to the conduction band. - **Conductors:** In a conductor, the valence band and conduction band overlap, as the electrons may acquire enough energy to shift to the conduction band by even a very small amount of energy. Thus, the conductivity of metal is excellent. ## Pure Semiconductors A semiconductor has conductivity much greater than that of an insulator but much smaller than that of a metal. Typically, a semiconductor has forbidden energy gap of about 1 eV. Thus, Germanium and Si have 0.785 eV and 1.21 eV, respectively, at 0 deg C. Germanium and silicon in their pure form behave as insulators at low temperatures (300K), but at higher temperatures (360K), a few valence electrons acquire enough thermal energy to cross the forbidden energy gap and enter into the conduction band called conduction electrons and are free to move about under the influence of even a weak applied force. There exist vacant states in the conduction band. Thus, these conduction electrons are indicated by dots. Outer electrons get shifted to the conduction band. The small number of valence band electrons get shifted to the conduction band, thus reducing the conductivity of the material. There is a small vacant space created at the point where the electron has been removed. This is called a hole. ## Donor Type Impurities On adding a pentavalent impurity in a small amount of a pure Germanium or Silicon, a new allowable state results at level ED just below the conduction band as shown in Fig. 2.9. This new state resumes a very small energy (ED-EC) of the order of on e-V, which is very small compared to the forbidden gap. This allows shift of an electron from the level ED into the conduction band, and a positive charge is created in the impurity atom, thus increasing the conductivity. Hence, each impurity contributes one conduction electron. Since each impurity has donated one conduction electron, thus the impurity is said to be a donor or a donor-type impurity. ## Acceptor Type Impurities On adding a trivalent impurity in a small amount to a pure Ge or Si, allowable energy states result at level EA just below the conduction band as shown in Fig 1.26. This shift of energy (EA-EC) requires a very small amount of energy for an electron to shift from the valence band to level FA, resulting in a hole at the valence band. Since each trivalent impurity atom contributes one hole, which carries a positive charge, each trivalent impurity is said to be an acceptor type or a p-type impurity. ## Covalent Bond in Pure Or Intrinsic Semiconductor Ge and Si are the two materials popularly used in the manufacture of transistors and other semiconductor electronic devices. They are crystalline in structure and have a crystal lattice similar to diamond. A two-dimensional representation of a diamond lattice for Ge is shown in Fig 1.3. Here every Ge atom surrounded by 4 other Ge atoms, which are bound by covalent bonds. Ge has all 32 electrons in its atomic structure confined to different shells as shown in the table. Each atom in Germanium crystal contributes four valence electrons so that the atom is tetravalent. In Fig 1.3, each shaded circle represents the core of a Germanium atom and carries a positive charge of +4. Each of the four valence electrons is shared by one of the four nearest neighboring atoms, resulting in a covalent bond or electron pair represented by a curved line connecting the atoms. All the four valence electrons get tightly bound to the nucleus. Hence, the semiconductor has extremely low conductivity; the pure semiconductor behaves as an insulator at zero degree Kelvin. The structure depicted in Fig 1.3 is extremely stable and electrically neutral. ## Formation of Holes The amount of energy required to break a covalent bond is about 1 ev for Germanium, 1.8 ev for silicon, and 7 ev for diamond. This means that in silicon, the covalent bond in the crystal can be broken by supplying thermal energy in the form of photons in the visible range and bombardment of semiconductors by alpha particles, x-rays, and other particles. On breaking of a covalent bond, one of the electrons leaves the bound leaving behind an empty place or vacancy. This vacancy constitutes a hole and is represented by a small circle as shown in Fig 1.36. Hole carries a charge +q. ## Extrinsic Semiconductors Pure semiconductors are not used in the construction of semiconductor devices, since conductivity is extremely small at room temperature. A small amount of impurity, trivalent or pentavalent, is added to the pure Ge or Si to increase the conductivity. ## Donor Type Impurity Donor impurities (n-type) are arsenic and bismuth. Impurity atoms generally have the same size as the Germanium (or Silicon) atom, and it dislodges a Germanium atom in the crystal lattice, as shown in Fig 1.6. Free conduction electrons and donor energy level are present at the valence band. ## Acceptor Type Impurity Acceptor impurities (p-type) are Indium, Gallium, and Aluminium. The proportion of acceptor impurity atoms are also very small; typically one impurity atom per 10^7 Ge atoms. Each impurity atom has only three valence electrons, each of which forms a covalent bond with one of the Ge atoms showing in Fig 1.6. The remaining hole tends to move randomly in crystal lattice. ## Mass Action Law In pure semiconductor, the concentration of holes p is equal to the concentration of electrons n, or this may be expressed as the intrinsic concentration. The addition of n-type impurities to the pure semiconductor results in a reduction in the concentration of holes below the intrinsic value. Similarly, the addition of p-type impurity results in the reduction in the concentration of electrons. Theoretical analysis reveals that under thermal equilibrium, the product of the concentration n of free electrons and the concentration p of holes is constant and is independent of the amount of doping by donor and acceptor impurities. The symbol ni is used as the intrinsic concentration. This law, known as the *mass action law*, can be expressed as: $$ np= ni^2 $$ This equation gives the mass action law. We can understand doping of either n-type or p-type semiconductor. In a semiconductor, either free electrons or holes must dominate the situation. In a n-type semiconductor, electrons form the majority carriers while holes form the minority carriers. In a p-type semiconductor, holes form the majority carriers while electrons form the minority carriers. ## Charge Densities The charge density is an electric field that comes into existence in semiconductors from the movement of electrons and holes. The charge density is related to the electron density and the hole density by the charge neutrality law: $$n + Na = p + Nd $$ The above equation applies to any semiconductor. The concentration of n-type impurity must be equal to the magnitude of negative charge density. Now let n be the electron density, p be the hole density, Nd be the density of donor atoms, and NA be the density of acceptor atoms. ## Conductivity of Semiconductor The conductivity of any semiconductor, whether intrinsic or extrinsic, is given by: $$ \sigma = q(n\mu_n + p \mu_p) $$ where: * $\mu_n $ and $\mu_p$ are the mobilities of holes and electrons, respectively. - **In n-type semiconductor**: n >> p. Further p = Na. Hence conductivity of n-type semiconductor is given by: $$ \sigma_n = qN_d\mu_n $$ ## Conductivity of Semiconductor Semiconductors at room temperature (300 K) have electrical conductivity in the range of 10^7 to 10^5 ohm/metre. **Example.** Find the conductivity of Germanium under dominant acceptor conditions at 300 K. Given that for Ge, ni (at 300 K) is 2.5 x 10^13 cm^-3, and μ and μp are 3800 cm²/V-s and 1800 cm²/V-s, respectively. Given that Na is 2 x 10^15 cm^-3 (assumed). **Solution**: $$n = p = ne $$ $$ \sigma = qn(\mu_n + \mu_p) $$ $$ = 1.6 x 10^{-19} (2.5 x 10^{13})^2 (3800 + 1800) $$ $$ = 0.049 \ (ohm/cm)^{-1}$$ - **Number of Ge atoms/cm^3** = 4.4 x 10^22 - **Number of acceptor atoms/cm^3** = 2 x 10^15 - **n = p = n^2 = (2.5 x 10^13)^2 = 2.84 x 10^{10} holes/cm^3** - **Nd = 2.2 x 10^5** ## Conductivity of Silicon at 300K **Example.** Find the conductivity of silicon at 300 K: 1. Under Intrinsic Condition. 2. With donor impurity of 1 part in 5 x 10^16. 3. With acceptor impurity of 1 part in 5 x 10^16. **Solution**: Given that ni for Silicon at 300 K is 1.5 x 10^10/cm^3, and mobilities of electrons and holes in Silicon are 1300 cm²/V-s and 500 cm²/V-s, respectively. No of Silicon atoms/cm^3 = 5 x 10^22 **(a)** $$ n = p = ni $$ $$ \sigma = qni (\mu_n + \mu_p) $$ $$ = 15 \times 10^{22} \ (1.6 * 10^{-19} ) (1300 + 500) $$ $$ = 4.32 \ \times \ 10^5 \ ohm/cm $$ **(b)** - **Number of Silicon atoms/cm^3** = 5 x 10^22 - **Number of Donor Atoms/cm^3** = 5 x 10^22 / 5 x10^16 - **The number of donor atoms** = 10^6 - **Hence, n = N_d** - **p = n^2 = (1.5 x 10^10)^2 = 2.25 x 10^5** - **We may neglect p in calculating conductivity.** Hence, $$ \sigma = qn\mu_n $$ $$ =(10^6)(1.6 x 10^{-19})(1300) $$ $$ = 0.208 \ ohm/cm$$ **(c)** - **Number of acceptor atoms/cm^3** = 5 x 10^22 / 5 x 10^16 = 10^6 - **NA = 10^6** - **n = ni^2 / NA = (1.5 x 10^10)^2/ 10^6 = 2.25 x 10^5** - **Since n << p, we may neglect n in calculating the conductivity.** Hence, $$ \sigma = q p \mu_p $$ $$ = (10^6)(1.6 x 10^{-19} )(500) $$ $$ = 0.08 \ ohm/cm $$