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Semiconductors Band Structure

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Semiconductors Band Structure Semiconductors Basic Properties Band Structure • Eg = energy gap • Silicon ~ 1.17 eV • Ge ~ 0.66 eV 1 Intrinsic Semiconductors • Pure Si, Ge are intrinsic semiconductors. • Some electrons elevated to conduction band by thermal energy. Fermi-Dirac Distribution • The probability that a particular energy state ε is filled is just the F-D distribution. • For intrinsic conductors at room temperature the chemical potential, µ, is approximately equal to the Fermi Energy, EF. • The Fermi Energy is in the middle of the band gap. 2 Conduction Electrons • If ε - EF >> kT then • If we measure ε from the top of the valence band and remember that EF lies in the middle of the band gap then Conduction Electrons • A full analysis taking into account the number of states per energy (density of states) gives an estimate for the fraction of electrons in the conduction band of 3 Electrons and Holes • When an electron in the valence band is excited into the conduction band it leaves behind a hole. Holes • The holes act like positive charge carriers in the valence band. Electric Field 4 Holes • In terms of energy level electrons tend to fall into lower energy states which means that the holes tends to rise to the top of the valence band. Photon Excitations • Photons can excite electrons into the conduction band as well as thermal fluctuations 5 Impurity Semiconductors • An impurity is introduced into a semiconductor (doping) to change its electronic properties. • n-type have impurities with one more valence electron than the semiconductor. • p-type have impurities with one fewer valence electron than the semiconductor. Impurities • For silicon § n-type is pentavalent: As, P § p-type is trivalent: Al, Ga, B 6 Impurity Semiconductors • n-type Impurity Semiconductors • p-type 7 Band Structure of N-type Conduction band Fermi Energy Donor impurity levels For Si(As): Valence band Econduction - Edonor = 0.049 eV T = 0K Band Structure of N-type Conduction band Fermi Energy Donor impurity levels For Si(As): Valence band Econduction - Edonor = 0.049 eV T = 300 K Remember kT = 0.025 eV 8 Band Structure of P-type Conduction band Acceptor impurity levels Fermi Energy For Si(Ga): Valence band Eacceptor - Edvalence = 0.065 eV T = 0 K Band Structure of P-type Conduction band Acceptor impurity levels Fermi Energy For Si(Ga): Valence band Eacceptor - Edvalence = 0.065 eV Remember kT = 0.025 eV T = 300 K 9 The pn junction Forming a pn junction • p-type and n-type semiconductors are placed in contact. • electrons in the conduction band in the n-type diffuse across the junction into the p-type. Conduction band Conduction band p n Valence band Valence band 10 Forming a pn junction • p-type and n-type semiconductors are placed in contact • electrons in the conduction band in the n-type diffuse across the junction into the p-type. Conduction band Conduction band p n Valence band Valence band Forming a pn junction • once in the p-type they can drop down into the valence band and to fill up one of the hole states. Conduction band Conduction band p n Valence band Valence band 11 Forming a pn junction • once in the p-type they can drop down into the valence band and to fill up one of the hole states. Conduction band Conduction band p n Valence band Valence band Forming a pn junction • Electrons continue to diffuse across the junction. • The area of the p-type near the junction becomes more negative due to the excess electrons while the n-type becomes more positive due to the excess of holes (or deficit of electrons). • This creates an electric field in the region of the junction that eventually prevents any further significant diffusion of electrons. • This region is essentially free of mobile charge carriers and is called the depletion region. 12 Depletion Region • The depletion region is free of mobile charge carriers. • The typical thickness of the depletion region is about 1 micron or 10-4 cm. - - - + + + - - - + + + - - - + + + - - - + + + Depletion region: Mobile holes and electrons have combined leaving charged ions. Formation of the depletion region 1 2 3 4 13 Depletion Region Characteristics • The fixed charges in the depletion region create an electric field that points from the n-type to the p-type. This field tends to sweep any mobile electrons in the region back to the n-type and any mobile holes back to the p-type. Depletion region = mobile hole - - - - - + + + + + = mobile electron - - - - - + + + + + - = fixed ionized Ed donor atom - - - - - + + + + + + = fixed ionized - - - - - + + + + + acceptor atom p n Energy Diagram for pn junction • In equilibrium the Fermi energy must be the same everywhere, otherwise electrons could reduce the energy of the system by flowing to unoccupied states in a region of lower Fermi energy. Electron Energy Conduction band - - E - + F - + + + Valence band p n 14 Energy Diagram for pn junction • The potential energy difference between the two sides of the junction is given by electric field in the depletion region. Electron Energy Conduction band - - E - + F - + + E + Δ Valence band p d n Equilibrium Currents for pn junction • In equilibrium there are still small currents flowing across the junction though there is no net electron current. Electron Thermal Current Energy Recombination Current Conduction band - - E - + F - + + + Valence band p n 15 Thermal Current • Electrons in the valence band of the p-type can acquire enough thermal energy to jump into the conduction band. They diffuse into the depletion region and are swept into n-type by the E-field. Electron Energy Conduction band - - E - + F - + + + Valence band p n Recombination Current • Electrons in the conduction band of the n-type can acquire enough thermal energy to rise higher in the conduction band. They can then diffuse across the depletion region to the p-type and drop into the valence band filling a hole. Electron Energy Conduction band - - E - + F - + + + Valence band p n 16 Currents in equilibrium pn junctions • The thermal current cancels out the recombination current in the equilibrium state. • The thermal current is dependent on the width of the energy gap in the semiconductor and the temperature. • The recombination current is dependent on ΔE, the size of energy difference between the p-type and n-type bands and the temperature. Biasing pn junctions • Apply a voltage across a pn junction: p n p n + + V V Forward Bias Reverse Bias 17 Reverse bias • A negative voltage is applied to the p-region. The energy of the electrons in the p-region will increase. • The potential energy difference between the two regions will increase by (-e)(-V) = eV • This will reduce the recombination current which depends on the potential difference but leave the thermal current unchanged. • A small net electron current will flow from p to n. Reverse bias • The increase in the potential energy difference reduces the recombination current. Electron Energy Thermal current Conduction band Recombination current - - - + EF - + + ΔE + eV + Valence band p d n 18 Forward bias • A positive voltage is applied to the p-region. The energy of the electrons in the p-region will decrease. • The potential energy difference between the two regions will be reduced: (-e)(V) = -eV • This will greatly increase the recombination current which depends on the potential difference but leave the thermal current unchanged. • A large net electron current will flow from n to p. Forward bias • The increase in the potential energy difference greatly increases the recombination current. Electron Thermal current Energy Recombination current Conduction band - E - + F - + - + + ΔE - eV Valence band p d n 19 Diodes Diodes • The pn junction is used an electronic circuit element called the diode or rectifier. • The diode is the most basic electronic component. • An ideal diode would have zero resistance when forward biased and an infinite resistance when reverse biased. 20 Practical Diode Model • A somewhat more realistic model incorporates the “turn- on voltage” or knee voltage. I • There is a minimum voltage required across the diode in the forward direction before it conducts an appreciable amount of current. • The turn-on voltage is approximately 0.5 to 0.7 Volts V in Si and about 0.3 volts in Ge. Vturn-on Realistic Model • In forward bias the diode has a resistance on the order of 10 Ω. • In reverse bias the resistance is on the order of 108 Ω. 21 Biased pn junction • In terms of positive current the current vs. voltage graph for a biased pn junction: I = I (e+eV/kT 1) 0 − Breakdown • In sufficiently large reverse bias is applied to a diode an “avalanche” occurs. • At the breakdown voltage charge carriers gain enough energy (from the reverse bias electric field) between collisions to break a covalent bond in the lattice and create another charge carrier. • These two charge carriers are accelerated and create more charge carriers leading to an “avalanche” of charge carriers. • This occurs very sharply at a certain voltage. • Ordinary diodes usually fail in these conditions. 22 The Diode Curve Real Diodes • The schematic symbol for a diode is • Diodes come in many shapes, each designed for a specific set of applications. 23 Diodes and Temperature • As temperature increases, more thermal energy is available to electrons enabling them to escape their binding atoms more readily. This causes the knee voltage (the voltage at which the diode turns on) to decrease. Zener Diodes • The p-n junction diode that operates in the reverse breakdown region is usually destroyed by the excess current and the heat it produces. The zener diode is designed to successfully operate in this region. 24 Zener Diode • The characteristic curve of the zener operating in the reverse breakdown region shows that the voltage dropped across the zener diode remains relatively constant while current through the zener current is allowed to increase dramatically.
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