Outline

1. Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics Chap. 3 P-N Junctions Chap. 4 Metal-Semiconductor Junctions Chap. 5 Semiconductor Heterojunctions Chap. 6 Semiconductor Solar Cells & Photodiodes Chap. 7 Light Emitting Diodes & Semiconductor Lasers Chap. 8 Quantum Dots for Biological Fluorescent Probes

2. Chapter 5 Semiconductor Heterojunctions 5.1 Heterojunctions and Band Diagram 5.2 I-V Characteristics of Abrupt PN Heterojuncitons 5.3 Injection Properties of PN Heterojunctions

3. 5.1 Heterojunctions and Band Diagram • AHeterojunctionis formed when two semiconductors with different bandgaps and lattice constants are brought together, usually by epitaxy. (1960) • Heterojunctions usually have higher injection efficiencies compared to homojunctions. • Anisotype heterojunctions：p-nGe-GaAs（p-type Ge and n-type GaAs） • Isotype heterjunctions：n-nGe-GaAs（n-type Geand n-type GaAs） • Abrupt heterojuncitons：the transition between two semiconductors occurs in a distance of several atoms.

4. 5.1 Heterojunctions and Band Diagram • Graded heterojuncitons ： the transition between two semiconductors occurs in a distance of several diffusion length. • The band diagrams of abrupt heterojunctions are well understood. • The band diagrams of heterojunctions are much more complicate than those of homojunctions, due to the differences in the electron affinities, bandgaps, work functions, and dielectric constants of the two semiconductors, as well as the presence of interface states due to the lattice mismatch.

5. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt pn heterojunctions（before junction formation） Vacuum level ：electron affinity W：work function Eg：bandgap After contact, electrons (holes) will flow from n-(p-) region to p- (n-) region, until the Fermi levels are equal. p-type n-type

6. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt pn heterojunctions（after junction formation） Vacuum level • Space-charge region: x1~x2, built-in E field. • Discontinuous E field at x0due to the different dielectric constants. • In the space-charge region: 1) band bending due to the built-in potential. 2) band offsets at x0 (Ec and Ev) due to different affinities. p-type n-type E

7. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states Example: Abrupt p-nGe-GaAsheterojunctions Vacuum level (due to small difference in ) (due to large difference in Eg and small difference in ) The built-in potentials VD1,VD2 are determined by doping density, depletion region width, and dielectric constants. =1.43 p-Ge n-GaAs

8. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Built-in potentials and barrier region width Assume uniform distribution of impurities with densities of NA1and ND2. The width of space charge region: d1=x0-x1, d2=x2-x0 Vacuum level By resolving the Poisson’s equation near the interface (x0), the built-in potentials are: 1,2are the dielectric constants of the p- and n-type semiconductors. p-type n-type XD

9. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Built-in potentials and barrier region width In the space charge region, positive charge = negative charge , Vacuum level Barrier region width: p-type n-type XD

10. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt pn heterojunctions（after junction formation） • Built-in potential VD Vacuum level • Conduction band offset: • Valence band offset: Applicable to all of the abrupt heterojunctions. p-type n-type E

11. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt np heterojunctions Vacuum level Vacuum level n-type n-type p-type p-type after junction formation before junction formation

12. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt nn heterojunctions Vacuum level n-type n-type n-type n-type after junction formation before junction formation In isotype heterojunctions, one side is depletion region, and the other is accumulation region.

13. 5.1 Heterojunctions and Band Diagram （1）NO interfacial states • Abrupt pp heterojunctions Vacuum level p-type p-type p-type p-type before junction formation after junction formation

14. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states • Fabrication methods: epitaxial growth or vacuum evaporation. • Lattice mismatch：2(a2-a1)/(a1+a2)，a1,a2are lattice constants of the two semiconductors making the junction. • The lattice mismatch results in dangling bonds in the interface, leading to interfacial states. Dangling bonds Before contact After contact

15. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states • If the bond density at the interface are Ns1,Ns2, after junction forms, unsaturated bonds are present on the surface of semiconductor with smaller lattice constants. The dangling bond density in an abrupt heterojunction is: • Nsis determined by the lattice constants and the lattice plane.

16. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states - + • For an n-type semiconductor, the dangling bonds are acceptors. Negatively charged surface. Upward bending of the bands. n-type - + • For a p-type semiconductor, the dangling bonds are donors. Positively charged surface. Downward bending of the bands. p-type High density of interfacial states

17. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states If the density of dangling bonds (interfacial states) is very high, the E field due to the interfacial charges is usually larger than that due to the contacts of two semiconductors.  The band diagram of heterojunctions are usually determined by the band bending owning to the interfacial states. p-type p-type

18. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states （high density of interfacial states） Dangling bonds as donors pp pn np Dangling bonds as acceptors nn pn np p-type n-type

19. 5.1 Heterojunctions and Band Diagram （2） Considering interfacial states • If the lattice constants of the two semiconductors are similar, the interfacial states due to lattice mismatch could be ignored. • In reality, at high temperatures, due to the difference in the coefficients of thermal expansion, lattice mismatch also occurs, results in interfacial states. • In heterojunctions made from compounds, the diffusion of elements could also introduce interfacial states.

20. 5.2 I-V Characteristics of Abrupt PN Heterojuncitons • Two different models are used to get the I-V characteristics, based on the different height of spikes in the band diagram. • Low barrier spike: the spike is lower than the bottom of conduction band of the p-region, Ec < qVD1Diffusion model. • High barrier spike: the spike is much higher than the bottom of conduction band of the p-region, Ec > qVD1 Emission model. P N P N High barrier spike (高势垒尖峰) Low barrier spike (低势垒尖峰)

21. 5.2 I-V Characteristics of Abrupt PN Heterojuncitons （1）Low barrier spike ----- diffusion model • Under forward bias V, (V1,V2 are applied voltage on the p- and n-region) Total current density: Forward bias No bias P N P N

22. 5.2 I-V Characteristics of Abrupt PN Heterojuncitons （1）Low barrier spike ----- diffusion model • Under forward bias V, Ec>0, Ev>0, and much larger than k0Tat room temperature. The electron current dominates and the hole current is very small. Due to the existence of the conduction band offset Ec , the barrier height for electrons in the n-region lowers from qVD to qVD-Ec , and increases by Evfor the holes in the p-region. electron current much larger than hole current. P N

23. 5.2 I-V Characteristics of Abrupt PN Heterojuncitons （2）High barrier spike ----- thermionic emission model For electrons diffusing to the barrier region from the n-region, only those with energy higher than the spike could enter the p-region by thermionic emission. • Under forward bias V, Forward current is dominated by the electron current from n to p. EFn EFp According to the emission model, the forward current also exponentially increases with applied voltage. P N

24. 5.3 Injection Properties of PN Heterojuncitons （1） High injection The injection ratio of electrons to holes for low barrier spikes: （saturated impurity ionization） Diffusion coefficient D diffusion length L are of the same order, ND2 <NA1 High injection ratio, even when

25. 5.3 Injection Properties of PN Heterojuncitons （1） High injection E.g.: p-nGaAs-Al0.3Ga0.7As Impurity density in p-region: Impurity density in n-region: Although the impurity density in n-region is two orders of magnitude lower than that in p-region, the injection ratio is as high as . The high injection ratio of heterojunctions differentiate them from the p-n homojuntions.

26. 5.3 Injection Properties of PN Heterojuncitons （2） Superinjection • Superinjection: the injected minority carrier density in the narrow-bandgap semiconductor exceeds the majority carrier density in the wide-bandgap semiconductor.Firstly observed in p-nGaAs-Al0.3Ga0.7As. • Under forward bias, if the voltage is high enough, the bottom of conduction band in the n-region could even be higher than that in the p-region. • Since the bottom of conduction band in the p-region is closer to EFn , compared to the n-region, the electron density in the p-region is higher.

27. 5.3 Injection Properties of PN Heterojuncitons （2） Superinjection • Ratio of electron density in the p-region to that in the n-region： If the bottom of conduction band in the n-region exceeds that in the p-region by 2k0T, n1 will be nearly one order of magnitude higher than n2. Superinjection is another important property of heterojunctions, which is desirable in semiconductor heterojunction lasers.

28. Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics Chap. 3 P-N Junctions Chap. 4 Metal-Semiconductor Junctions Chap. 5 Semiconductor Heterojunctions Chap. 6 Semiconductor Solar Cells & Photodiodes Chap. 7 Light Emitting Diodes & Semiconductor Lasers Chap. 8 Quantum Dots for Biological Fluorescent Probes

29. Chapter 6 Semiconductor Solar Cells and Photodiodes

30. Introduction • Solar cells are devices that convert solar radiation to electrical energy. • Photodiodes: one of the photodetectors, that detect radiation signals. • Solar cells and photodiodes have the same basic principles ---- photovoltaic effect.

31. 6.1 Light Absorption Visible Infrared Ultraviolet near extreme far near mid far extreme Wavelength  Photon energy h

32. 6.1 Light Absorption • Intrinsic absorption: light absorbed for electron transfer from the valence to the conduction band, eg. (a) and (b). Intrinsic transition or band-to-band transition. • Condition for intrinsic absorption: hvEg • Wavelength of intrinsic absorption edge: • If hv>Eg, besides the generation of e-h pairs, excess energy hv-Eg will be dissipated as heat. The process of light absorption • Non-intrinsic transition: if hv<Eg, light absorbed for electron transitions to the defect or impurity states, eg., (c).

33. 6.1 Light Absorption • Absorption coefficient Under the light irradiation, in the direction of light propagation, the flux (the number of photons perpendicularly passing through unit area at unit time) at a distance of x from the surface of semiconductor: c Number of photons absorbed in a distance of x, (x)x Absorption coefficient is a function of the photon energyh, so called absorption curve. abruptly drops at c,.

34. 6.1 Light Absorption • Direct transition Under light illumination, the electron transitions by absorbing photons, should obey conservation of energy and momentum. hk’ – hk = momentum of photon Since the momentum of photon is much smaller than that of electrons in the bands, the momentum of photons can be ignored.k’  k(direct transition, unchanged wave vector in transitions). Eg., AB, OO’. Belongs to intrinsic transitions.

35. 6.1 Light Absorption • Direct transition • Electrons with energies not smaller than Eg, and with any wave vection k, could be absorbed. • Direct bandgap semiconductors: the top of valence band and the bottom of the conduction band occur at the same value of k. The intrinsic absorption is dominated by the direct transition. E.g., GaAs

36. 6.1 Light Absorption • Measurements of Eg of direct bandgap semiconductors. Based on theoretical calculations, the absorption coefficient  for direct transitions, A: a constant UV-Vis Absorption spectrum  Eg Eg

37. 6.1 Light Absorption • Indirect transition • Indirect bandgap semiconductors: the top of valence band and the bottom of the conduction band occur at different value of k. E.g., Ge, Si. • Indirect transition: one phonon is released or absorbed, besides absorption of photons. • The phonon energy could be ignored. • The probability of indirect transition (absorption coefficient) is much smaller than that of direct transition. kp: wave vector of the phonon. hk’ – hk = hkp Direct transition Indirect transition

38. 6.1 Light Absorption • Measurements of Eg of indirect bandgap semiconductors. The absorption coefficient  for indirect transitions, Direct transition A’: a constant In the plot, the intercept on x axis of the linear fit gives Eg。 Indirect transition

39. 6.1 Light Absorption • Excitons：bound electron-hole pairs. • Exciton absorption：photon energy hv<Eg, the valence electron is excited, but does not yet enter the conduction band (free electron) and still attracted by the hole in the valence band. Ec Eex Eex Ev A series of sharp absorption peaks at the low energy side of the band edge of direct bandgap semiconductors. Eex : the binding energy of the exciton.

40. 6.1 Light Absorption • Free carrier absorption： photon energy hv<Eg, intraband transition of free carriers.

41. 6.1 Light Absorption • Impurity absorption：absorption by the electrons and holes bound to the impurity levels. Electrons transfer to the conduction band and holes transfer to the valence band. • Phonon absorption：in the far infrared region. Photon energy converts to the phonon (lattice vibration) energy.

42. 6.2 Solar Cells • Solar cells constitute a critical technology for overcoming global environmental and energy problems. • Abundant: radiation for 40 min＝energy needs of the whole world for one year. • Clean: no “greenhouse effect”, no pollution. • Convenient: no geographical restrictions and low costs, compared to hydro energy, wind energy, etc.

43. 6.2 Solar Cells • Solar cells converts solar radiation directly into electrical energy. • Also called photovoltaiccells, utilizing photovoltaic effect of all kinds of potential barriers. • In 1883, Fritts firstly made a photovoltaic cell using Se. • In 1941, Ohl fabricated single crystalline Si photovoltaic cell. • In 1954, Pearson at Bell lab made the first practical Si solar cell.

44. 6.2 Solar Cells • Advantages of solar cells: long life time, high efficiency, reliable performance, low costs, and pollution free. • Solar cells are used on almost all of the space equipments and devices. • At AM1.5, the efficiency of single crystalline Si solar cells has reached 24%, and amorphous Si solar cells ~13.2% . • The market share of Si solar cells is about 85%, and 15% for thin-film solar cells.

45. 6.2 Solar Cells • Photovoltaic effect of p-n junctions: the absorption of solar energy generates electromotive force across the p-n junctions. • The basic structure of a Si solar cell: Electrode on the front side Anti-reflection film (or P+) (or N) Counter electrode (evaporated metal film with a large-area )

46. 6.2 Solar Cells • Three primary physical processes of the photovoltaic effect: （1）Absorption of solar energy and generation of non-equilibrium electron-hole pairs; （2）Drift or diffusion of non-equilibrium carriers towards the potential barriers (barriers in p-n junctions or Schottky barriers in M-S junctions or barriers in heterojunctions); （3）Separation of electron and holes in the barrier region, accumulating electrons on the n-side and holes on the p-side  Potential difference forms.

47. 6.2 Solar Cells • Open circuit voltageＶoc: the maximum voltage obtained at the load under open-circuit conditions of the diode. • Photocurrent: the current through the p-n junction with load. • Short circuit current Isc: the maximum current through the load under short-circuit conditions. Isc • Under illumination, the e-h pairs generated in the diffusion region will be separated in the space charge region. Electrons (holes) will accumulate at the boundary region of n- (p-) side.  Light induced E field opposite to the built-in E field. ImP VmP Voc

48. 6.2 Solar Cells • For the open-circuited diode, under illumination (hv>Eg), the presence of non-equilibrium carriers means an increase (decease) of the Fermi level of electrons (holes) in the n-(p-) side. The difference between them is qVoc.The barrier height is lowered by qVoc, compared to the case in the dark. • For the short-circuited diode, the direction of short-circuit current is from n to p, inside the diode. No accumulation of non-equilibrium carriers Voc=0. Under illumination Open-circuit Under illumination Short-circuit Dark

49. 6.2 Solar Cells • In reality, even no loads, effective series resistance Rsalways exists. • Only parts of the photocarriers accumulate on the p-n junction  barrier lowered by qV (V<Voc). The Fermi level difference between p- and n-side is qV. Under illumination With series resistance The photogenerated current is in the direction of the reverse current in case of electrical injection.

50. 6.2 Solar Cells • Dark current: the barrier lowering due to light illumination is equivalent to the case under forward bias  injection of electrons (holes) to the p- (n-) side  dark current ID (namely, the forward current under forward bias, in the opposite direction of photogenerated current). Dark current is bad for solar cells and should be minimized. Under illumination With series resistance