MIT OpenCourseWare http://ocw.mit.edu 3.23 Electrical, Optical, and Magnetic Properties of MaterialsFall 2007For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.3.23 Fall 2007 – Lecture 14 INHOMOGENEOUS SEMICONDCUTORS Images removed due to copyright restrictions. Russell Ohl Shockley, Bardeen, and Brattain 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) William Shockley Electronic Bands in Sodium Chloride (advisor John C. Slater, MIT, 1936) http://dspace.mit.edu/handle/1721.1/10879 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 13.23 Electronic, Optical and Magnetic Properties of Materials Nicola Marzari (MIT, Fall 2007)3.23 Electronic, Optical and Magnetic Properties of Materials Nicola Marzari (MIT, Fall 2007) --2•Last time 1. Band structure of direct- and indirect-gap semiconductors, in excruciating detailin excruciating detail 2. Carriers in thermal equilibrium, density of available states 3. Law of mass action 4. Consequences for intrinsic semiconductors, extrinsic semiconductors 5. Impurity levels, hydrogen model of donors, acceptor states 6. Temperature dependence of majority carriers: intrinsic range, extrinsic/saturation range, freeze out. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Study • Early part of Chap 29 (InhomogeneousEarly part of Chap 29 (Inhomogeneous semiconductors) ,Ashcroft-Mermin (to be posted, together with Chap 28, really to be posted, s'il vous plaît) 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 3Density of available states ⎛2 m= c⎞3/⎛ T ⎞3/2 2.5⎜ ⎟⎜ ⎟10 19 / cm 3 ⎝ m⎠⎝ 300 K⎠ 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Law of Mass Action npcv = NcPe−Ek g/ BT v 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 4Intrinsic case gBnn==ppNPe −Ek/2 T icicvv ccvv nT T−− kT() ()= N e()εµcB/ Image removed due to copyright restrictions. cc Please see: Fig. 11 in Sze, S. M. "Physics of Semiconductor Devices." pT() ()= P T e()µεvB Chapter 1 in Physics and Properties of Semiconductors - A Resume.−− / kT New York, NY: John Wiley & Sons, 1981.vv ⎛⎞ vµε 13m=+Ek+ Tlniv g B ⎜⎟24 mc⎝⎠ 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Extrinsic case −=(()p ((Tn∆nT) p) cv )cv3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 5Extrinsic case 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Temperature dependence of majority carriers 6 Image removed due to copyright restrictions. Please see Fig. 13.3 in Kittel, Charles, and Herbert Kroemer. Thermal Physics. San Francisco, CA: W. H. Freeman, 1980.Image removed due to copyright restrictions. Please see Fig. 2.22 in Pierret, Robert F. Semiconductor Device Fundamentals. Reading, MA: Addison-Wesley, 1996.Impurity types, levels Image removed due to copyright restrictions. Please see: Fig. 13 in Sze, S. M. "Physics of Semiconductor Devices." Chapter 1 in Physics and Properties of Semiconductors - A Resume. New York, NY: John Wiley & Sons, 1981. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Population of impurity levels (donor) 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 7Population of impurity levels (acceptor) 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Conductivity in semiconductors eτeeτ hσ= ne + ne e hme mh eeττ µe = e me eτhµh = me Text removed due to copyright restrictions. Please see: Table 3 in Kittel, Charles. "Introduction to Solid State Physics." Chapter 8 in Semiconductor Crystals. New York, NY: John Wiley & Sons, 2004. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 8Impurity band conduction 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Equilibrium carrier densities of impure semiconductors 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 9–Equilibrium carrier densities of impure semiconductors 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Semiconductor carrier engineering • Adding impurities to determine carrier type 2 10203 n 2 for Si: ~1020cm-3 ni for Si: cm – Add 1016cm-3 (~1ppm) phosphorous (donors) to Si: nc~Nd –nc~1016cm-3, pv~104 (ni2/Nd) • Adding impurities to change carrier density –1 part in 106 impurity in a crystal (~1022cm-3 atom density) –1022/ 106 =1016 dopant atoms per cm-3 – conductivity is proportional to the # of carriers leading to 6 orders of magnitude change in conductivity! of magnitude change in conductivity! Impurities at the ppm level drastically change the conductivity (5-6 orders of magnitude) 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 10Simplified expressions 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Abrupt junction Image removed due to copyright restrictions. Please see: Fig. 29.1 in Ashcroft, Neil W., and Mermin, N. David. Solid State Physics. Belmont, CA: Brooks/Cole, 1976. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 11The p-n junction (diode) p-type material at equilibrium n-type material at equilibrium p~NA n~ND n~ni2/N p~ni2/N µ =µA − kTln ⎛ NA ⎞ µ =µD+ kTln ⎛ ND ⎞ p i b ⎜ ⎟ n i b ⎜ ⎟ ⎝ ni ⎠⎝ ni ⎠ E Ec Ec µ µ Ev Ev What happens when you join these together? Joining p and n p n Ecc µ Ev Carriers flow under driving force of diffusion until µ is horizontal --+ + --++ + Holes diffuse Electrons diffuse 12----++ + + Holes diffuse Electrons diffuse ++ + +----Electrons diffuse ----++ + + ----++ + + E An electric field forms due to the deviation from charge neutralityg y Therefore, a steady-state balance is achieved where diffusive flux of the carriers is balanced by the drift flux Chemical potential Image removed due to copyright restrictions. Please see: Fig. 29.2 in