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### EECS+320+06+carrier+modeling+-+carrier+density

Course: EECS 320, Spring 2012
School: Michigan
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Word Count: 377

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320 06 EECS Carrier Modeling Carrier Density (chapter 2.3.3 2.3.5) Carriers Carriers are electrons or holes that can conduct (carry) current conduct (carry) current Notation: n = number of (conducting) electrons/cm3 p = number of (conducting) holes/cm3 room temperature Intrinsic (i.e. pure) silicon has 4N valence electrons which fill the entire valence band at 0 K. But at room temperature, some electrons can...

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320 06 EECS Carrier Modeling Carrier Density (chapter 2.3.3 2.3.5) Carriers Carriers are electrons or holes that can conduct (carry) current conduct (carry) current Notation: n = number of (conducting) electrons/cm3 p = number of (conducting) holes/cm3 room temperature Intrinsic (i.e. pure) silicon has 4N valence electrons which fill the entire valence band at 0 K. But at room temperature, some electrons can acquire thermal energy to generate n and p carriers. n = p = ni ~ 11010 / cm3 Ku/EECS 320 How conducting are those intrinsic carriers? In silicon, there are 5 x 1022 atoms/cm3 (how to get this?) There are 4 valence electrons per silicon atom. 2 x 1023 valence electrons/cm3 At room temperature, only 1 out of 1013 electrons becomes carriers. 1 m2 silicon For every mm, the resistance is 108 ! Ku/EECS 320 Diode Again Positive voltage: current flows Negative voltage: current stops P-silicon I V N-silicon Ku/EECS 320 Doping toy model review Silicon is a semiconductor and has 4 valence electrons/atom. Phosphor has 5 valence electrons/atom. bandgap 4 3 2 1 Si--Si--Si--Si--Si--Si--Si--Si B P Terminology: We call phosphor-doped silicon N-type silicon & Boron-doped silicon P-type silicon. P is donor B is acceptor Ku/EECS more 320 Doping realistic picture When phosphor atom replaces one of silicon atoms in the crystal, the fifth valence electron is still bound to the phosphor atom. To set free this extra electron and make it become a carrier, it must absorb enough thermal energy. Silicon lattice lattice P+ How much is enough? thermal energy Ku/EECS 320 Donor binding energy Silicon lattice P+ Like a hydrogen atom except that both the nucleus and the electron are now in the silicon lattice. * mn q 4 ~ 0.1eV From quantum mechanics (eq 2.1 & 2.5): EB ~ 2 2(4 K S 0 ) = h / 2 Ku/EECS 320 Energy band diagram with donors EC EC EV EV EB x x One donor added Intrinsic silicon How long should I draw this line? Silicon lattice R P+ Eq (A.4): 4 K S 0 R~ * mn q 2 2 o ~ 5.3 Electron stays within 2R ~ 1 nm There are ~ 4 x 4 x 4 silicon atoms within that space. Ku/EECS 320 Carrier concentration with doping Typical donor or acceptor concentration ~ 1018 /cm3. 1 donor or acceptor every 50000 silicon atoms. EC EB Dashed line used. EV 1018 /cm3 x donor added added At 0 K, extra electrons from the donors in silicon do not hop from one donor site to the other. Exercise: How about donors in GaAs? Ku/EECS 320
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