Semiconductor Devices Prof Zbigniew Lisik Department of Semiconductor
Semiconductor Devices Prof. Zbigniew Lisik Department of Semiconductor and Optoelectronics Devices room: 116 e-mail: zbigniew. lisik@p. lodz. pl lectures 30 hours lab. exercises 30 hours IFE T&CS
Fundamentals of Semiconductor Physics Metal Semiconductor Isolator T T T very low medium very large Chapter 1 -1
Fundamentals of Semiconductor Physics What are semiconductors ? 1. They are crystals 2. They can be: ● atom crystals like: Si, Ge, C-diamond ● compound crystals like: Ga. As, In. Sb, Si. C, Ga. N 3. When they are pure, their resistivity is in a middle range Chapter 1 -2
Fundamentals of Semiconductor Physics Basic semiconductors: Si Ge Ga. As Si. C Ga. N - silicon germanium gallium arsenide silicon carbide gallium nitride Chapter 1 -3
Fundamentals of Semiconductor Physics Structure of silicon crystal – so called diamond structure Crystal bond between 2 atoms The bond arises when 2 atoms are so close that two of their valance electrons become common, which results in quantum nature attraction electrons atom A atom B Chapter 1 -4
Fundamentals of Semiconductor Physics Structure of silicon crystal – so called diamond structure Crystal bond between 2 atoms The bond arises when 2 atoms are so close that two of their valance electrons become common, which results in quantum nature attraction two electron bond two atoms molecula Chapter 1 -5
Fundamentals of Semiconductor Physics Structure of silicon crystal – so called diamond structure Si 3 D 2 D Si Si Chapter 1 -6
Fundamentals of Semiconductor Physics Structure of silicon crystal – 2 D representation Si Si Si Si Chapter 1 -7
Fundamentals of Semiconductor Physics Structure of crystal – energy band model Pauli restriction – elektrons must be recognisable W single atom + ● ● W 3 ● W 2 ● W 1 ● - electron atoms in crystal W + ● ● R W 3 ● ● W 2 ● ● W 1 R Chapter 1 -8
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T=0 K Si Si If the temperature of crystal T = 0 K all the valance electrons take part in the atom bonds Conduction Band Si Si Si W 3 Si Si Valence Band ● ● W 2 ● ● W 1 Chapter 1 -9
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T=0 K If the crystal temperature T = 0 K all the valance electrons take part in the atom bonds Si Si The crystal temperature can, however, increase and then T> 0 K. Si Si If the sufficient energy is delivered to the valance electron, it can leave its position in the interatom bond and can become a free electron. Chapter 1 -10
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T>0 K Si Si Si Si The valance electron taking sufficient energy leaves its position in the bond and becomes free electron. Such a free electron can move in the crystal without any restriction and is called conduct electron in contrast to the electrons in bonds called valance electrons Chapter 1 -11
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T>0 K Si Si Si Si The valance electron taking sufficient energy leaves its position in the bond and becomes free electron. The empty place in the bond structure is called hole and can also move through the crystal as the result of valance electrons hopping from one bond to another. Chapter 1 -12
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T>0 K Conduct electrons are not connected Si Si Si Si with any bonds and can freely move inside the crystal. Since they are negative charge –q their movement can create an electric current Holes are not connected with any particular bond and can freely move inside the crystal. Since the hole means the lack of an electron, it is connected with the local excess of positive charge +q. This charge moves together with the hole creating an electric current. Chapter 1 -13
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal T>0 K Si Si Si The presented process is called electron-hole pair generation and has its energy band model: WC Conduction Band WV Valence Band Si Si Wg = W c - W v Chapter 1 -14
Fundamentals of Semiconductor Physics 2 D Structure of silicon crystal Electrons – fermions fulfilling the Pauli restriction Conduction band The presented process is called electron-hole pair generation and has its energy band model: WC WC Band gap Valance band WV WV Wg = W c - W v Chapter 1 -15
Fundamentals of Semiconductor Physics Dopands in Silicon T = 0 K Si Si Si Ga Si Si As Si Ga acceptors III Mendeleiew group Ga, B, Al As donors V Mendeleiew group As, Sb, P Chapter 1 -16
Fundamentals of Semiconductor Physics Dopands in Silicon T > 0 K Si Si Si Ga- Si Si As+ Si Ga acceptor As donor Ionization energy of dopands is very low Chapter 1 -17
Fundamentals of Semiconductor Physics Dopands in Silicon T > 0 K Energy band model: Si Si Si Ga- Si Si As+ Si WC WD WA WV Ionization energy of dopands is very low Wi << Wg Chapter 1 -18
Fundamentals of Semiconductor Physics Carrier concentration in doped semiconductor Charge balance: nd + N a + n T = p. T + N d + p a n 0 + N a = p 0 + N d Types of semiconductors Na > Nd pp 0 > np 0 p-type Na < Nd pn 0 < nn 0 n-type Na = Nd p 0 = ni i-type Chapter 1 -19
Fundamentals of Semiconductor Physics Equilibrium carrier concentration n 0 , p 0 Thermodynamic equilibrium state The state of the system being in constant temperature without any energy exchange with surroundings - so called adiabatic conditions. The equilibrium densities of electrons and holes, n 0 and p 0, result from the balance of generation and annihilation processes: gd. T=rd. T and g. T=r. T Type n gd. T rd. T g. T r. T WC WD WA WV Chapter 1 -20
Fundamentals of Semiconductor Physics Statistical physics ● It is used to describe physical phenomena that are created by huge number of elements – e. g. properties of gases that can be considered as the set of molecules. ● The phenomenon is described by the parameters that represent the behaviour of the set of elements being related to the average value of particular element feature Temperature – average kinetic energy of molecules Pressure – average momentum of molecules Chapter 1 -21
Fundamentals of Semiconductor Physics Statistical physics ● The set of elements is characterised by the probability function that determines the probability that the considered parametr of an element has particular magnitude. ● In the classical approach, the probability function has a bell-like shape with the maximum value corresponded to the average value of parameter (energy in the figure). Boltzman distribution f(W) Wav W Chapter 1 -22
Fundamentals of Semiconductor Physics Statistical physics ● If we want to know how many particles (e. g. electrons) have their energy in the range <W 1, W 2>, it is enough to calculate the integral: where: N(W) – state density function (in classical approach, total number of particles N(W) = N) f(W) – probability that the state of energy W is occupied Chapter 1 -23
Fundamentals of Semiconductor Physics Statistical physics Classical approach – Bolzmann distribution f(W) Wśr W Quantum approach – Fermi-Dirac distribution f(W) 1 0. 5 WF W WF – Fermi energy (Fermi lavel) Chapter 1 -24
Fundamentals of Semiconductor Physics Statistical physics Classical approximation – (W – WF) > 2 k. T Quantum approach – Fermi-Dirac distribution WF – Fermi energy (Fermi lavel) Chapter 1 -25
Fundamentals of Semiconductor Physics Statistical physics Classical approximation – (W – WF) > 2 k. T If this approach can be used to estimate the electron and hole density in semiconductor, such a semiconductor is called non-degenerated Only such semiconductors will be considered in our lectures Chapter 1 -26
Fundamentals of Semiconductor Physics Equilibrium carrier concentration Classical aproximation for electrons Wc 1 Concentration of electrons in conduction band: Conduction band Wc states occupied by electrons Under the assumption: WC 1 NC – effective density of states in the conduction band Chapter 1 -27
Fundamentals of Semiconductor Physics Equilibrium carrier concentration Classical aproximation for holes states occupied by holes Wv Concentration of holes in valance band: Valance band Wv 1 Under the assumption: WV 1 - NV – effective density of states in the valance band Chapter 1 -28
Fundamentals of Semiconductor Physics Equilibrium in intrinsic semiconductor n 0 = p 0 From the equilibrium condition: one can calculate WFi, the Fermi energy for intrinsic semiconductor : WC 0. 5 (WC – WV) WFi WV Chapter 1 -29
Fundamentals of Semiconductor Physics Equilibrium in doped semiconductor n 0 ≠ p 0 Transformation of electron equation: Chapter 1 -30
Fundamentals of Semiconductor Physics Equilibrium in doped semiconductor n 0 ≠ p 0 Transformation of hole equation: Chapter 1 -31
Fundamentals of Semiconductor Physics Equilibrium in doped semiconductor n 0 ≠ p 0 Product of hole and electron concentration: At constant temperature n 0 p 0 is constant independently on the dopand concentration Chapter 1 -32
Fundamentals of Semiconductor Physics Equilibrium in doped semiconductor n 0 ≠ p 0 Transformation of hole and electron product: ni = f(T) Chapter 1 -33
Fundamentals of Semiconductor Physics Carrier concentration in doped semiconductor ln n 0 ln p 0 Typ n n 0 = n d + n T p 0 = p T ni p 0 Ts T Ti Ts – saturation temperature Ti – intrinsic temperature WC WD WV Chapter 1 -34
Fundamentals of Semiconductor Physics Carrier concentration in doped semiconductor ln n 0 ln p 0 Type n n 0 ni p 0 Ts T ρ Ti Ts – saturation temperature Ti – intrinsic temperature T Ts Ti Chapter 1 -35
Fundamentals of Semiconductor Physics Thermal limitation for semiconductor devices If semiconductor devices are to keep their data sheet ratings, the concentration of majority carriers cannot change considerably. Condition 1: It is true when Tmin not lower than Ts. For Si Tmin ≈ -50 °C Recommended area Ts[ C] ln n 0 ln p 0 ni p 0 Ts T Ti Chapter 1 -36
Fundamentals of Semiconductor Physics Thermal limitation for semiconductor devices If semiconductor devices are to keep their data sheet ratings, the concentration of majority carriers cannot change considerably. Condition 2: It is true when Tmax lower than Ti. For Si Tmax < 400 °C Recommended area ln n 0 ln p 0 ni p 0 Ts T Ti Chapter 1 -37
Fundamentals of Semiconductor Physics Thermal limitation for semiconductor devices If semiconductor devices are to keep their data sheet ratings, the concentration of majority carriers cannot change considerably. Typical ranges defined for silicon devices in catalogues: Range Commercial [ C] 0 – 70 Industrial -25 – 85 Extended industrial -40 – 125 Military -55 – 125 Recommended area ln n 0 ln p 0 ni p 0 Ts T Ti Chapter 1 -38
Fundamentals of Semiconductor Physics Current filamentation – hot spot If T inside <Ts, Ti>, the negative thermal feedback occurs: Silicon chip Safe area J Q T Ti Current is pushed out from warmer area and heat dissipation decreases ρ T Ts Ti Chapter 1 -39
Fundamentals of Semiconductor Physics Current filamentation – hot spot If T inside <Ts, Ti>, the negative thermal feedback occurs: Silicon chip Safe area J Q ρ T Current is pushed out from warmer area and heat dissipation decreases T Ts Ti Chapter 1 -40
Fundamentals of Semiconductor Physics Current filamentation – hot spot If T outside <Ts, Ti>, the positive thermal feedback occurs: Silicon chip Safe area J Q T Ti Current is squeezed in warmer area and heat dissipation increases ρ T Ts Ti Chapter 1 -41
Fundamentals of Semiconductor Physics Current filamentation – hot spot If T outside <Ts, Ti>, the positive thermal feedback occurs: Silicon chip Safe area J Q ρ T Current is squeezed into small area and hot spot is generated T Ts Ti Chapter 1 -42
Fundamentals of Semiconductor Physics Nonequilibrium carrier concentration Dn Equilibrium concentrations n 0 , p 0 WC h Nonequillibrum concentrations n = n 0 + Dn p = p 0 + Dp Δn, Δp – excess concentrations Dp WV usually: Dn = Dp Chapter 1 -43
Fundamentals of Semiconductor Physics Nonequilibrium carrier concentration Quasi-Fermi level n = n 0 + Dn p = p 0 + Dp Chapter 1 -44
Fundamentals of Semiconductor Physics Nonequilibrium carrier concentration Quasi-Fermi level Wc n-type WF WFh Wv Wc p-type WFe – quasi-Fermi level for electrons WFh – quasi-Fermi level for holes WFe WF WFh Wv Chapter 1 -45
Phenomena in Semiconductors Recombination processes n 0 WC g. T p 0 r. T WV Equillibrum state: g. T – rate of electron-hole pairs thermal generation r. T – rate of electron-hole pairs thermal anihilation g. T = r. T Steady state constant carrier concentrations Chapter 2 -1
Phenomena in Semiconductors Recombination processes n 0 + Δn h gr p 0 + Δn WC g. T r WV Non-equillibrum state: g. T – rate of electron-hole pairs thermal generation gr – rate of electron-hole pairs radiative generation r – rate of electron-hole pairs anihilation Steady state gr + g. T = r constant carrier concentrations Chapter 2 -2
- Slides: 48