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Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Basic semiconductor physics.

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Presentation on theme: "Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Basic semiconductor physics."— Presentation transcript:

1 Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Basic semiconductor physics

2 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Summary of the physics required ► Charge carriers in semiconductors ► Currents in semiconductors ► Generation, recombination; continuity equation

3 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Energy bands ► Resulting from principles of quantum physics Discrete energy levels: The discrete (allowed) energy levels of an atom become energy bands in a crystal lattice More atoms – more energy levels of electrons: There are so many of them that they form energy bands:

4 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET conductance band valance band Valance band, conductance band ► Valance band – these electrons form the chemical bonds  almost full ► Conductance bend – electrons here can freely move  almost empty v – valance band / uppermost full c – conductance band / lowermost empty

5 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Electrons and holes ► Generation: using the average thermal energy ► Electrons: in the bottom of the conduction band ► Holes: in the top of the valance band ► Both the electrons and the holes form the electrical current conduction band valance band recombination generation Electron: negative charge, positive mass Hole:positive charge, positive mass

6 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Conductors and insulators semiconductor insulator metal forbidden gap band gap For Si: W g = 1.12 eV for SiO 2 : W g = 4.3 eV 1 eV = 0.16 aJ = 0.16  J

7 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Band structure of semiconductors Valance band conduction band GaAs: direct band  opto-electronic devices (LEDs) Si: indirect band indirect direct

8 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Generation / recombination ~~~~> = W g /h Direct recombination may result in light emission (LEDs) W g Light absorption results in generation (solar cells) Experiment Spontaneous process: thermal excitation – jump into the conduction band / recombination  equilibrium

9 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Crystalline structure of Si ► SiN=14 4 bonds, IV-th column of the periodic table ► Diamond lattice, lattice constant a=0.543 nm ► Each atom has 4 nearest neighbor real 3D simplified 2D undoped or intrinsic semiconductor

10 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET valance dopant: donor (As, P, Sb) ► Electron: majority carrier ► Hole: minority carrier conduction band valance band n-type semiconductor

11 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET valance dopant: acceptor (B, Ga, In) ► Electron: minority carrier ► Hole: majority carrier conduction band valance band p-type semiconductor

12 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Calculation of carrier concentration possible energy states occupation probability concentrations electrons holes FD statistics:

13 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Calculation of carrier concentration ► The results is: ► If there is no doping: n = p = n i  it is called intrinsic material = W i W F : Fermi-level

14 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET The Fermi-level ► Formal definition of the Fermi-level: the energy level where the probability of occupancy is 0.5: ► In case of intrinsic semiconductor this is in the middle of the band gap: ► This is the intrinsic Fermi-level W i electrons holes

15 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Carrier concentrations ► Depends on temperature only, does not depend on doping concentration For silicon at 300 K absolute temperature n i = /cm 3 (10 electrons in a cube of size 0.01 mm x 0.01 mm x 0.01 mm) Mass action law

16 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Carrier concentrations ► Si, T = 300 K, donor concentration N D = /cm 3 ► What are the hole and electron concentrations?  Donor doping  n  N D = /cm 3  Hole concentration:p = n i 2 /n = /10 17 = 10 3 /cm 3 ► What is the relative density of the dopants?  1 cm 3 Si contains 5  atoms  thus, / 5  = 2   The purity of doped Si is Problem

17 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Carrier concentrations ► Just re-order the equations kT = 1.38  VAs/K  300 K =4,14  J = eV = 26 meV Thermal energy In doped semiconductors the Fermi-level is shifted wrt the intrinsic Fermi- level

18 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Temperature dependence ni2 =ni2 = Problem ► How strong is it for Si?  15% / o C

19 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Temperature dependence of carrier concentrations Problem Si, T = 300 K, donor dopant concentration N D = /cm 3 n  N D = /cm 3 p = n i 2 / n = /10 17 = 10 3 /cm 3  How do n and p change, if T is increased by 25 degrees? n  N D = /cm 3 – unchnaged n i 2 =  = 33   p = n i 2 / n = 33  /10 17 = 3.3  10 4 /cm 3 Only the minority carrier concentration increased!  T=16.5 o C  10 

20 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Currents in semiconductors ► Drift current ► Diffusion current Not discussed:  currents due to temperature gradients  currents induced by magnetic fields  energy transport besides carrier transport  combined transport phenomena

21 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Drift current No electrical field Thermal movement of electrons  = mobility m 2 /Vs There is E electrical field

22 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Drift current  charge density v velocity (average) Differencial Ohm's law Specific electrical conductivity of the semiconductor Specific resistance

23 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Carrier mobilities Si  n = 1500 cm 2 /Vs  p = 350 cm 2 /Vs Electric field [V/cm] Drift velocity [cm/s] electrons holes

24 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Carrier mobilities ► Mobility decreases with increasing doping concentration ► At around room temperature mobilities decrease as temperature increases 300 K Si, holes  ~ T -3/2 Mobility

25 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Diffusion current ► Reasons:  concentration difference (gradient)  thermal movement ► Proportional to the gradient ► D: diffusion constant [m 2 /s]

26 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Total currents Einstein's relationship Thermal voltage

27 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Generation, recombination ► Life-time: average time an electron spends in the conduction band ► Generation rate: g [1/m 3 s] ► Recombination rate: r [1/m 3 s] conduction band valance band recombination generation  n,  p 1 ns … 1  s

28 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET  N electron  V volume A surface Continuity equation

29 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Diffusion equation

30 Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Basic semiconductor physics © András Poppe & Vladimír Székely, BME-EET Example for the solition of the diff. eq.: p diffusion length


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