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- 1. Solid State Physics UNIST, Jungwoo Yoo 1. What holds atoms together - interatomic forces (Ch. 1.6) 2. Arrangement of atoms in solid - crystal structure (Ch. 1.1-4) - Elementary crystallography - Typical crystal structures - X-ray Crystallography 3. Atomic vibration in solid - lattice vibration (Ch. 2) - Sound waves - Lattice vibrations - Heat capacity from lattice vibration - Thermal conductivity ---------------------------------------------------------------------------------------------------------(Midterm I) 4. Free electron gas - an early look at metals (Ch. 3) - The free electron model, Transport properties of the conduction electrons 5. Free electron in crystal - the effect of periodic potential (Ch. 4) - Nearly free electron theory - Block's theorem (Ch. 11.3) - The tight binding approach - Insulator, semiconductor, or metal - Band structure and optical properties 6. Waves in crystal (Ch. 11) - Elastic scattering of waves by a crystal - Wavelike normal modes - Block's theorem - Normal modes, reciprocal lattice, brillouin zone --------------------------------------------------------------------------------------------------------(Midterm II) 7. Semiconductors (Ch. 5) - Electrons and holes - Methods of providing electrons and holes - Transport properties - Non-equilibrium carrier densities 8. Semiconductor devices (Ch. 6) - The p-n junction - Other devices based on p-n junction - Metal-oxide-semiconductor field-effect transistor (MOSFET) ---------------------------------------------------------------------------------------------------------------(Final) All about atoms backstage All about electrons Main character Main applications
- 2. Solid State Physics UNIST, Jungwoo Yoo Semiconductors Device - The p-n junction - Other devices based on p-n junction - Metal-oxide-semiconductor field effect semiconductor (MOSFET) To understand the great majority of semiconductor devices it is necessary to consider the behavior of charge carriers near a surface or interface. Of particular importance are the boundary detween an n-type region and a p-type region, the boundary between a semiconductor and an insulator, and the boundary between two different semiconductors. This chapter will focus on the understanding the physics of the devices, rather than the technical applications.
- 3. Solid State Physics UNIST, Jungwoo Yoo The junction between two metals If two metals of different work function are brought into contact, 1 1FE 2FE 2 Electron will cross from left to right to occupy the lower energy states available. However, as electrons cross over there will be an excess of positive charge on the left-hand side and an excess of negative charge on the right-hand side. Consequently, an electric field is set up with a polarity that hinders the flow of electrons from left to right and encourages the flow of electron from right to left. A dynamic equilibrium is established when equal numbers of electrons cross in both directions. The potential difference between the two metals, called the contact potential is equal to the difference between the two work functions; the potential difference may be obtained by equating the Fermi levels of the two media in contact 1 FE 2 12
- 4. Solid State Physics UNIST, Jungwoo Yoo p The p-n Junction with Zero Bias n vE cE p vE cE n Particle flow Hole diffusion Hole drift Electron diffusion Electron drift Current flow p n E - - - + + + w p n Electrostatic potential pne 0
- 5. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The behavior of p-n junction results from the effect on the electron energy levels in the region of the junction as described following p n 0e eoI hoI
- 6. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The total potential difference required to produce a uniform chemical potential (often called built-in potential, which is necessary to maintain equilibrium at the junction) AD NNn Tk V TkE C B BG eNp eNn / /)( Consider n type, for some range of T, all donors and acceptors are ionized AD C BGn NN N TkE lna D C BG N N TkE ln~ Consider p type, for some range of T, all donors and acceptors are ionized DA NNp A V B DA V Bp N N Tk NN N Tk ln~lna
- 7. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias A V B D C BGpn N N Tk N N TkEe lnln The total potential difference required to produce a uniform chemical potential (often called built-in potential, which is necessary to maintain equilibrium at the junction) VC AD BG NN NN TkE ln TkE VCi BG eNNnpn /2 Law of mass actiona 2 ln i ADB n NN e Tk 322 m10 DA NN at T = 300 K for Si and Ge ? 316 m102 in 319 m102 in (take , and intrinsic carrier concentrations at RT for Si and Ge are (Si) (Ge) a eV7.0~ eV3.0~(Si) (Ge)
- 8. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The width of depletion layer and the variation of the electrostatic potential )(x Start on two assumption 1) The boundary between the n and p regions is sharp 2) The majority carrier concentrations decrease very rapidly from their ‘bulk’ value at the edges of the depletion layer 0x p=type n=type DN AN AeN DeN x x pn, )(x Then the charge density near the junction )(x DeN AeN 0 0 xwp nwx 0 elsewhere pw nw
- 9. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The width of depletion layer and the variation of the electrostatic potential )(x )(x DeN AeN 0 0 xwp nwx 0 elsewhere 0 2 2 )( x dx d From Poisson’s equation a dx d E )( 0 p A wx eN )( 0 D D wx eN 0 xwp nwx 0 E should be continuous at x=0 a nDpA weNweN (charge neutrality)
- 10. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The width of depletion layer and the variation of the electrostatic potential )(x Integrating the electric field a )(x 2 0 )( p A wx eN 2 0 0 )( n D wx eN 0 xwp nwx 0 The depletion layer is wider in more lightly doped junctions should be continuous at x=0)(x 2 0 0 )( 2 nDpA wNwN e nDpA weNweN a 2 00 )( 2 DAD A n NNeN N w 2 00 )( 2 DAA D p NNeN N w 321 m10~~ DA NN 323 m10~~ DA NN a μm1~np ww μm1.0~np ww
- 11. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias DN AN AeN DeN x x pn, )(x pw nw )(xE 0 )(x 0
- 12. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias The values of n, and p at any point being determined by the position of the chemical potential relative to the conduction and valence band edges respectively Tk V TkE C B BG eNp eNn / /)( a ]/)(exp[)( ]/)(exp[)( 0 0 Tkxepxp Tkxenxn B B Where and are the concentrations of electrons and holes at points where is zero. 0n 0p )(x The rapid fall-off in majority carrier concentrations at the edges of the depletion layer occurs because is small compared to the total energy difference across the junction TkB 0e
- 13. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with Zero Bias In equilibrium, the current density due to diffusion and due to the electric field must cancel each other. a 0 Ene x n eD ee 0)drift()diffusion( JJ ]/)(exp[)( ]/)(exp[)( 0 0 Tkxepxp Tkxenxn B B Differentiating n )(xn xTk e x n B And x E a e TkD B e e e TkD B h h Einstein relation
- 14. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias p n - - - + + + Forward bias p n - - - + + + reverse bias Applied voltage appears across t he depletion layer The total potential difference across the depletion layer is Vpn 0 Forward bias reduces the total potential difference whereas reverse bias increase p otential difference
- 15. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias p n - - - + + + Forward bias p n - - - + + + reverse bias Applied voltage appears across t he depletion layer The width of depletion layer is decreased by forward bias and increased by reverse bias The width of depletion layer can be obtained by replacing 2/1 00 )( )(2 DAD A n NNeN VN w 2/1 00 )( )(2 DAA D p NNeN VN w
- 16. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias p n )( 0 Ve eoI hoI Ve p n )( 0 Ve eoI hoI eV Forward bias Reverse bias
- 17. Solid State Physics UNIST, Jungwoo Yoo
- 18. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias The electric current through a p-n junction produced by the applied bias. Current in equilibrium, 0eI Let’s consider for p to n0eI If the lifetime of the electrons per unit volume on the p side of the junction is then the recombination and generation rates for electrons on this side of the junction are both equal to per unit volume. pn p ppn / is electrons generated within one diffusion length of the depletion layer edge are likely to diffuse to this edge and cross to the n region before recombination. 0eI On average a newly generated electron moves a distance of one diffusion lengt h before recombination. eL eIe 0 X(generation rate/volume)X(volume within Le of depletion layer) AL n e e p p Where A is the area of the junction.
- 19. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias If all the acceptors on the p side are ionized, Aipip Nnpnn // 22 2/1 pee DL a A NL neD I Ae ie e 2 0 Forward bias reduces the barrier by an amount of eV, whereas the reverse bia s increase the barrier by an amount of leVl And the occupancy of electron states within the conduction band is given by a Boltzmann distribution, which leads to an increase by a factor in the number of electrons on the n side with sufficient energy to overcome t he barrier )/exp( TkeV B The electron current from n to p increases to )/exp(0 TkeVI Be The electron current from p to n does not change Therefore, the net electron current through the junction is given by 1)/exp(0 TkeVII Bee
- 20. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias The net electron current through the junction 1)/exp(0 TkeVII Bee A NL neD I Ae ie e 2 0 The hole electron current through the junction 1)/exp(0 TkeVII Bhh A NL neD I Ah ih h 2 0 The total current is obtained by summing the electron and hole contributions 1)/exp(0 TkeVIIII Bhe Dh h Ae e ihe NL D NL D AenIII 2 000 TkE VCi BG eNNn /2
- 21. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias 1)/exp(0 TkeVII B
- 22. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias Some deviations i) High voltage effect ),2/exp('1)/exp(' 00 TkeVITkeVIIII BBtot 2 0 inI inI '0 ii) The recombination and generation within the depletion layer itself a Important for low voltage and low current iii) Reverse breakdown: a sudden increase of current that occurs when the reverse bias increases through some critical value, ~ 3eV. The top of valence band on the p side of the junction lies above the bottom of the conduction band on the n side a Tunneling through the potential barrier consisting of the central region of the depletion layer Mechanism for breakdown in more heavily doped p-n junctions where the depletion layer and hence the potential barrier is narrower. a Zener breakdown a Zener diodes
- 23. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias Depending on the level of doping, the threshold voltage changes a Zener diodes
- 24. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias As breakdown voltage increases, the electric field within the depletion layer leads to excitation of an electron from the valence band to the conduction band a Avalanche breakdown
- 25. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias For a very heavily deped p-n junctions, the Fermi level can lie in the valence band on the p-side and in the conduction band on the n side a The bottome of the conduction band on the n side is then below the top of the valence band on the p side even with zero bias a The depletion layer is very narrow and a large tunneling current can be observed at small forward bias a With increasing forward bias further, the overlap in energy between the conduction on the n side and the valence band on the p side eventually disappears a Can introduce negative differential resistance, dV/dI<0 a Tunnel diodes
- 26. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias
- 27. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias p n - - - + + + Forward bias p n - - - + + + reverse bias Applied voltage appears across t he depletion layer A change in the width of the depletion layer via applied bias a nDpA dweNdweNd 2/1 0 00 ))((2 VNN NN dV dw eN dV d V Q C DA DAn D a A voltage variable capacitance ! a Varactor diodes or varicaps
- 28. Solid State Physics UNIST, Jungwoo Yoo The p-n Junction with an applied bias Recombination of electron and hole in the depletion layer a Emission of photon a Light emitting diodes (LEDs) For a heavily doped junctions, a Forward bias can induces population inversion a Stimulated emission Absorption of photon in the depletion layer a Create electron and hole a Built-in potential leads current (Solar cells)
- 29. Solid State Physics UNIST, Jungwoo Yoo )(0 SMee mFE The metal-semiconductor junctions metal n vE cE n Consider for n-type and M mFE SM S Particle flow Electron diffusion Electron drift metal n E - - - - - - - - - + + + w M S Electrostatic potential )( MB ee Schottky barrier The equilibrium potential differnece can be decresed or increased by the application of either forward- or reverse- bias voltage e
- 30. Solid State Physics UNIST, Jungwoo Yoo The metal-semiconductor junctions metal p vE cE p Consider for p-type and M mFE SM S Particle flow hole diffusion hole drift metal p E + + + + + + + + + - - - w M S Electrostatic potential Schottky barrier The equilibrium potential differnece can be decresed or increased by the application of either forward- or reverse- bias voltage e mFE )(0 SMee
- 31. Solid State Physics UNIST, Jungwoo Yoo p n - - - + + + Forward bias p n - - - + + + reverse bias Applied voltage appears across t he depletion layer The total potential difference across the depletion layer is V 0 Forward bias reduces the total potential difference whereas reverse bias increase p otential difference - - - - - - - - - - - - - - - - - - The metal-semiconductor junctions
- 32. Solid State Physics UNIST, Jungwoo Yoo Forward bias reverse bias The metal-semiconductor junctions )( 0 Ve mFE )( Me eV V V )( 0 Ve mFE )( Me vE cE n V I Current-voltage characteristic 1/ 0 TkeV B eII Schottky barrier diode - Typically minority carrier injection is negligible
- 33. Solid State Physics UNIST, Jungwoo Yoo mFE The metal-semiconductor junctions metal n vE cE n Consider for n-type and M mFE SM S Particle flow Electron diffusion Electron drift metal n E + + + + + + + + + - - - w Barrier for electron to flow is negligible No depletion layer M S Electrostatic potential )(0 MSee )( Me
- 34. Solid State Physics UNIST, Jungwoo Yoo The metal-semiconductor junctions metal p Consider for p-type and SM Particle flow Hole diffusion Hole drift metal p E - - - - - - - - - + + + w M S Electrostatic potential vE cE p M mFE S )(0 SMee M mFE Barrier for hole to flow is negligible No depletion layer
- 35. Solid State Physics UNIST, Jungwoo Yoo The metal-semiconductor junctions Typical schottky barriers: surface state lead to charges at the metal-semiconductor interface. These surface states often lies in semiconductor band gap and pin the Fermi level at a fixed position, regardless of the metal used.
- 36. Solid State Physics UNIST, Jungwoo Yoo The metal-Insulator-semiconductor junctions metal nI metal nI 0 x eNlog 0 x eNlog mFE vE cE n eV mFE vE cE n eV vE cE n M-I-S
- 37. Solid State Physics UNIST, Jungwoo Yoo The metal-Insulator-semiconductor junctions
- 38. Solid State Physics UNIST, Jungwoo Yoo n n Transistors Field effect transistors Junction gate field effect transistor (JFET) p P Gate Source Drain Source Drain Gate
- 39. Solid State Physics UNIST, Jungwoo Yoo Transistors Field effect transistors Junction gate field effect transistor (JFET) Gate Source Drain n n p PSI GI DI
- 40. Solid State Physics UNIST, Jungwoo Yoo n n Transistors Field effect transistors Junction gate field effect transistor (JFET) Gate Source Drain p PSI GI DI
- 41. Solid State Physics UNIST, Jungwoo Yoo n n Transistors Field effect transistors Junction gate field effect transistor (JFET) Gate Source Drain p PSI GI DI
- 42. Solid State Physics UNIST, Jungwoo Yoo n n Transistors Field effect transistors Junction gate field effect transistor (JFET) Gate Source Drain p PSI GI DI At pinch-off voltage, maintains a saturation level defined as since a very small channel still exists with a current of very high density DI DSSI The absence of a drain current would remove the posssibility of different potential levels through the n-channel material to establish the varying levels of reverse bias along the p-n junction. The result would be a loss of the depletion region
- 43. Solid State Physics UNIST, Jungwoo Yoo Transistors Field effect transistors Junction gate field effect transistor (JFET)
- 44. Solid State Physics UNIST, Jungwoo Yoo p Transistors Field effect transistors MOSFET Depletion type n nn DI DSV GSV
- 45. Solid State Physics UNIST, Jungwoo Yoo Transistors Field effect transistors MOSFET Depletion type p n nn DI DSV GSV
- 46. Solid State Physics UNIST, Jungwoo Yoo Transistors Field effect transistors MOSFET Enhancement type p n n DI DSV GSV
- 47. Solid State Physics UNIST, Jungwoo Yoo Transistors Field effect transistors MOSFET Enhancement type p n nn DI DSV GSV
- 48. Solid State Physics UNIST, Jungwoo Yoo p Transistors Field effect transistors MOSFET Enhancement type n n DI DSV GSV
- 49. Solid State Physics UNIST, Jungwoo Yoo Heterojunctions GaAs : 1.42 eV AlAs : 2.16 eV Ga1-xAlxAs Band gap engineering vE cE p Ga1-xAlxAs Ga1-xAlxAsGaAs
- 50. Solid State Physics UNIST, Jungwoo Yoo Heterojunctions GaAs : 1.42 eV AlAs : 2.16 eV Ga1-xAlxAs Band gap engineering vE cE Ga1-xAlxAs Ga1-xAlxAsGaAs p-type P+-type n-type recombination
- 51. Solid State Physics UNIST, Jungwoo Yoo Heterojunctions High-electron-mobility transistor (HEMT)

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