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Bonding Forces in Solids
Na (Z=11) [Ne]3s1
Cl (Z=17) [Ne]3s1
3p5
Na+ Cl
_](https://image.slidesharecdn.com/lecture5energybandsandchargecarriers-140701034233-phpapp01/75/Lecture-5-energy-bands-and-charge-carriers-3-2048.jpg)
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Lecture 5 energy bands and charge carriers
- 1. Energy bands andcharge carriers in semiconductors
- 2. 2 Bonding Forces &Energy Bands in Solids In Isolated Atoms In Solid Materials 3rd Band 2nd Band 1st Band Core
- 3. 3 Bonding Forces inSolids Na (Z=11) [Ne]3s1 Cl (Z=17) [Ne]3s1 3p5 Na+ Cl _
- 4. 4 Bonding Forces inSolids e _ Na+
- 5. 5 Bonding Forces inSolids
- 6. 6 Bonding Forces inSolids Si<100>
- 7. 7 Energy Bands PauliExclusion Principle C (Z=6) 1s2 2s2 2p2 2 states for 1s level 2 states for 2s level 6 states for 2p level For N atoms, there will be 2N, 2N, and 6N states of type 1s, 2s, and 2p, respectively.
- 8. 8 3-1-2. Energy Bands Atomicseparation Diamond lattice spacing Energy 1s 2s 2p Valence band Conduction band 2p 2s 2s-2p 4N States 4N States Eg 1s
- 9. 9 Metals, Semiconductors & Insulators For electrons to experience acceleration in an applied electric field, they must be able to move into new energy states. This implies there must be empty states (allowed energy states which are not already occupied by electrons) available to the electrons. The diamond structure is such that the valence band is completely filled with electrons at 0ºK and the conduction band is empty. There can be no charge transport within the valence band, since no empty states are available into which electrons can move.
- 10. 10 Metals, Semiconductors & Insulators The difference bet- ween insulators and semiconductor mat- erials lies in the size of the band gap Eg, which is much small- er in semiconductors than in insulators. Insulator Semiconductor Filled Filled Empty Empty Eg Eg
- 11. 11 Metals, Semiconductors & Insulators Metal Filled Partially Filled Overlap In metals the bands either overlap or are only partially filled. Thus electrons and empty energy states Metal are intermixed with- in the bands so that electrons can move freely under the infl- uence of an electric field.
- 12. 12 3-2-3. Intrinsic Material A perfect semiconductor crystal with no impurities or lattice defects is called an Intrinsic semiconductor. In such material there are no charge carriers at 0ºK , since the valence band is filled with electrons and the conduction band is empty.
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- 14. 14 3-2-3. Intrinsic Material If we denote the generation rate of EHPs as and the recombination rate as equilibrium requires that: )(Tgi )( 3 scm EHPri ii gr = Each of these rates is temperature depe- ndent. For example, increases when the temperature is raised. )( 3 scm EHPgi iirri gnpnr === 2 00 αα
- 15. 15 3-2-4. Extrinsic Material In addition to the intrinsic carriers generated thermally, it is possible to create carriers in semiconductors by purposely introducing impurities into the crystal. This process, called doping, is the most common technique for varying the conductivity of semiconductors. When a crystal is doped such that the equilibrium carrier concentrations n0 and p0 are different from the intrinsic carrier concentration ni , the material is said to be extrinsic.
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- 19. 19 3-2-4. Extrinsic Material We can calculate the binding energy by using the Bohr model results, consider-ing the loosely bound electron as ranging about the tightly bound “core” electrons in a hydrogen-like orbit. rKn hK mq E εεπ 022 4 4,1; 2 ===
- 20. 20 3-2-4. Extrinsic Material Example 3-3: Calculate the approximate donor binding energy for Ge(εr=16, mn * =0.12m0).
- 21. 21 3-2-4. Extrinsic Material eVJ h qm E r n 0064.01002.1 )1063.6()161085.8(8 )106.1)(1011.9(12.0 )(8 21 234212 41931 22 0 4* =×= ××× ×× = = − −− −− εε Answer: Thus the energy to excite the donor electron from n=1 state to the free state (n=∞) is ≈6meV.
- 22. 22 3-2-4. Extrinsic Material Whena ш-V material is doped with Si or Ge, from column IV, these impurities are called amphoteric. In Si, the intrinsic carrier concentration ni is about 1010 cm-3 at room tempera-ture. If we dope Si with 1015 Sb Atoms/cm3 , the conduction electron concentration changes by five order of magnitude.