Electronics The basics of semiconductor physics Prof. Márta Rencz, Gergely Nagy BME DED September 16, 2013
The basic properties of semiconductors Semiconductors conductance is between that of conductors and insulators. They conduct current and have a negative thermal coefficient (NTC), which means that their conductivity decreases when temperature rises. This is exactly the opposite behaviour of metals. At the moment semiconductors are the basic materials of electronic devices.
The most important semiconductors The most important semiconductors: Monocristalline or single-cristal materials: Semiconductor elements: Si (silicon), Ge (germanium) They are used in integrated circuits and semiconducting devices. Compound semiconductors: GaAs (gallium arsenide), GaAsP (gallium arsenide phosphide) They are used to create LEDs. Amorphous semiconductors: amorphous Si mainly TFTs, solar cells are made of them. Organic semiconductors: OLEDs (Organic LEDs)
The band structure I. The electron s energy is a quantized quantity there are certain energy levels that are allowed for electrons, the rest of the levels are forbidden. When electrons take part in a system (atom or a crystalline consisting of many atoms), every electron has to be at a different level. The electrons take energy levels very close to the allowed levels thus in large systems the electrons take place in energy bands that are seperated by band gaps. The energy bands of electrons in a large insulator/semiconductor structure. The bands are shown in grey, the band gaps are white.
The band structure II. Conductance band: electrons that can move freely. Valence band: electrons that take part in bonds and thus are bound to atoms. From the viewpoint of conductance the important bands: The highest band that contains electrons (valence band). The band above the valence band, which is almost empty (conductance band). The band gap between them.
Insulators and conductors Conductors: the valence band and the conductance bands overlap. Insulators and semiconductors: there are bandgaps the width of the bandgap (W g ) decides whether a material is an insulator or a semiconductor. Si (semiconductor): W g = 1.12 ev SiO 2 (insulator): W g = 4.3 ev 1 ev = 0.16 aj = 0.16 10 18 J
The charge carriers I. Electrons: at the bottom of the conductance band, Holes: at the top of the valence band a hole is an absence of electron. Both electrons and holes take part in conductance! Generation: happens when an electron gets to the conductance band from the valence band. This means that two charge carriers are created: an electron in the conductance band and a hole in the valence band. Recombination: the opposite of generation when an electron falls back to the valence band.
The charge carriers II. Charge and mass of charge carriers Electrons: have a negative charge and a positive mass. Holes: have a positive charge and a positive mass (!). This can be explained in solid state physics we re not going into such depth.
The crystal structure of silicon 3D crystal structure (diamond lattice) Simplified, 2D crystal structure Silicon has four electrons that take part in the bond between its atoms. Density: ϱ = 2.33 g cm 3 Lattice constant: a = 0.543 nm
The intrinsic silicon If the temperature is above 0 K, some electrons become thermally activated and get into the conductance band. Intrinsic charge carrier concentration n i = p i = 10 10 /cm 3 n i : electron concentration (1/cm 3 ) p i : hole concentration (1/cm 3 ) The charge carrier density is very low: a cube with edges of 10 µm contains 10 electrons. The crystalline is doped in order to increase the charge carrier density.
Doping A small number of atoms of a different kind is injected into the crystal structure. This is done in a way that the dopants are placed on positions where normally Si atoms are located. Typical doping density: 10 15 10 19 / cm 3 this is indeed doping and not alloying (the density is very low). The atom density of silicon is 5 10 22 /cm 3, so a typical doping of 10 17 /cm 3 means that two atom is changed to a dopant out of every one million, which leaves us with a purity of 99.9998 %.
The n-type semiconductors Donor dopants: dopants that inject atoms that have one extra electrons at their valence band (P (phosporus), As (arsenic), Sb (antimony)). The extra electron is easier to raise into the conductance band, because it cannot take part in a strong bond. Thus its energy level is in the band gap, close to the conductance band. Electrons are the majority charge carriers Holes are the minority charge carriers donor concentration: N d electron concentration: n n hole concentration: p n Concentrations in n-type Si n n N n n n > p n
The p-type semiconductors Acceptor dopants: dopants that inject atoms that have one less electrons at their valence band (B (boron), Al (aluminium), In (indium)). Less electrons result in extra holes, that are easier to bring down to the valence band, because they cannot take part in a strong bond. Thus their energy level is in the band gap, close to the valence band. Electrons are the minority charge carriers Holes are the majority charge carriers acceptor concentration: N a electron concentration: n p hole concentration: p p Concentrations in p-type Si p p N p p p > n p
Drift current I. When a semiconductor is placed into an electric field, the electrons start to drift in the opposite direction of the field. No external field External field is present
Drift current II. Drift current is the movement of charge carriers due to an external electric field. Drift velocity is the speed of the charge carriers in the drift current: Drift velocity v d = µ n E v d = µ p E where v d : is the drift velocity µ n : is the mobility of electrons (Si: µ n = 1500 cm2 V s ) µ p : is the mobility of holes (Si: µ p = 475 cm2 V s )
Diffusion current Diffusion current: is the movement of charge carriers due to an inhomogeneity in their density. The movement is due to thermally induced movement of the electrons that is always present at temperatures above 0 K.
The pn-junction: a semiconductor diode I. A pn-junction is a monocrystalline transitional area where a p-type and an n-type semiconductor is next to each other. The diode is a device that consists of one single pn-junction. The figure is distorted: the n-type layer is much shallower in reality.
The pn-junction: a semiconductor diode II. We will be concerned with the area at the center of the structure (physical distortions at the borders result in special effects that we re not dealing with).
Most important properties of the diode When a forward voltage is applied to it, its current is an exponential ( ) function of the voltage. I exp V VT Forward direction: the p side is at a higher potential. In the reverse direction its current is very low and is independent of the voltage: I 10 12 A/mm 2 The current-voltage characteristic of the diode:
The electrostatic conditions in the pn-junction The majority carriers at the proximity of the junction diffuse across the junction to the other side. This is because there are a lot of electrons on the n side, and a lot of holes on the p, while each side has a very low density of the minority charge carriers. There is a huge gradient in the densisty of charge carriers. This results in a depleted area / space charge region an area at the junction which is empty of majority charge carriers. The dopants left by their extra electrons/holes become charged ions that create an electric field, which prevents further diffusion by generating a drift current of minority carriers in the opposite direction.
The operation of the diode Equilibrium: the diffusion of the majority carriers is in equilibrium with the drift current of the minority carriers (I = 0). Forward direction: the forward voltage lowers the electric field of the dopant ions thus increasing the drift current of the majority carriers (big I F ). Reverse direction: the reverse voltage enlarges the electric field of the dopant ions thus lowering the diffusion current of the majority carriers and increasing that of the minority carriers moved by the drift current (small I R ).
The characteristic equation of the ideal diode The characteristic equation of the ideal diode ( ) I = I 0 e V V T 1 where I 0 is the reverse current (saturation current) of the diode (I 0 10 14..15 A) V T is the thermal voltage: V T = kt q 26 mv T =293 K This is clearly a non-linear device its characteristic equation is exponential. In the forward direction the current is an exponential function of the voltage. The current is multiplied by ten at every increase of the voltage by 60 mv.
The characteristic equation of a real diode Due to secondary effects the equation in the forward direction: ( ) I = I 0 e V m V T 1 where m is the ideality factor (a.k.a. quality factor or emission coefficient) it represents several secondary effects and ranges from 1 to 2. In the reverse direction: the reverse current of the diode starts to increase steeply with the voltage at the breakdown voltage (V BR ). If the diode s current is limited by external means, the breakdown state does not harm the structure.
The application of the breakdown voltage As a very small change in the reverse voltage results in a big change in the reverse current at the breakdown state, it can be used to stabilize voltage. The diode is placed in a negative feedback configuration. Zener diode: special diode created to serve as a voltage stabiliser in the breakdown state.
The operating point of a diode I. The characteristic equation of a diode gives all the voltage-current pairs that a diode can have. In operation the diode usually works at a certain operating point, i.e. at one of the voltage-current pairs of its equation. This point is determined by the elements surrounding the device. DC analysis: the calculations performed to find the DC operating point of a non-linear device. The quantities describing the DC operating point are usually denoted with capital letters (V, I).
The operating point of a diode II. The KVL for the circuit is: V t = I R t + V which gives the equation of a line: I = V t V R t The line is called the load line it is the characteristic equation of the other element in the circuit (R t ) as a function of the diode s voltage.
The operating point of a diode III. The operating point (denoted with M in the figure) is at the intersecion of the two functions. If the graphical representation of the equations is given, this is easy to find.
The approximation of the operating point I. current Vd voltage We take advantage of the fact that the exponential function is very steep. The diode is substituted: with a voltage source when it is switched on, with an open circuit when it is switched off. The value of the voltage source (V D ) can be looked up in the datasheet of the diode (V D 0.7 V).
The approximation of the operating point II. We assume that the diode is switched on. The terminals of the resistor: left-hand side: supply voltage (V s ), right-hand side: the voltage of the diode (V D ). According to Ohm s law: I = V s V D R l If V s = 5 V, V D = 0.7 V, R l = 1 kω then I = 5 0.7 10 3 = 4.3 ma.
Small-signal analysis I. It is important to investigate what happens when there are small changes in the input voltage e.g. when the supply voltage changes slightly during operation. For small changes the exponential function can be approximated with a linear equation around the operating point. In terms of the electric model, this means that the diode is substituted with its differential resistance. The differential resistance r d = V I = m V T I
Small-signal analysis II. The differential resistance r d = V I = m V T I I in the equation of the differential resistance is the operating point current. Thus the value of the differential resistance has a very strong dependence on the operating point.
The small-signal operation of diodes I. Let s investigate what happens when small changes occur at the equilibrium state. Changes around the operating are usually denoted with lower case letters. V s = V s0 + v s sin (ωt) If the changes are small, the diode s voltage and current are sinusoidal functions around the operating point.
The small-signal operation of diodes II. The calculation is performed in three steps: 1 the DC operating point is determined, 2 the AC analysis is performed by substituting the non-linear device with its small-signal model and calculating the effects of the changes on this model, 3 the two results are added. DC analysis equilibrium AC analysis small changes It is important that only small changes can be calculated this way!
The small-signal operation of diodes III. The calculation of the small signal operation: The small-signal changes: i = v s R l + r d and v = r d i = r d v t R l + r d If R l = 1 kω, V t = 5 V and v t = 1 V: The differential resistance: r d = V T 26 mv = I 4.3 ma = 6 Ω The change (amplitude) of the diode s current: 1 i = 1.006 k 1mA the change (amplitude) of the diode s voltage: v = 6 Ω 1mA = 6 mv
The Zener diodes I. Supply voltages can be stabilized using Zener diodes. Consider the circuit on the left. Let s find the voltage and current of the Zener diode. V in = 12 V, R = 150 Ω and V BR = 3.3 V. As the input voltage is larger than the breakdown voltage: the diode is in the breakdown state. I V in V BR R = 12 3.3 0.15 = 60 ma
The Zener diodes II. How much does the output voltage change if the input changes by 1 V? The differential resistance is: 3 Ω. v out = v in r d = 3 = 20 mv r d + R t 153 Thus the change at the input is reduced to 1/50 of its value!