Lecture #3 OUTLINE Band gap energy Density of states Doping Read: Chapter 2 (Section 2.3)

Spring 2007EE130 Lecture 3, Slide 2 Band Gap and Material Classification E c E v E G = 1.12 eV E c E G = ~9 eV Si SiO 2 metal E c E v Filled bands and empty bands do not allow current flow Insulators have large E G Semiconductors have small E G Metals have no band gap –conduction band is partially filled

Spring 2007EE130 Lecture 3, Slide 3 Measuring Band Gap Energy  EGEG can be determined from the minimum energy (h of photons that are absorbed by the semiconductor.  photon photon energy: hv  E  E G E c E v electron hole Band gap energies of selected semiconductors

Spring 2007EE130 Lecture 3, Slide 4 Density of States E E c E v E c E v  gc(E)gc(E) gv(E)gv(E) E  E c E  EvE  Ev g(E)dE = number of states per cm 3 in the energy range between E and E+dE Near the band edges:

Spring 2007EE130 Lecture 3, Slide 5 Donors: P, As, SbAcceptors: B, Al, Ga, In Doping By substituting a Si atom with a special impurity atom (Column V or Column III element), a conduction electron or hole is created.

Spring 2007EE130 Lecture 3, Slide 6 Doping Silicon with Donors Example: Add arsenic (As) atom to the Si crystal The loosely bound 5th valence electron of the As atom “breaks free” and becomes a mobile electron for current conduction.

Spring 2007EE130 Lecture 3, Slide 7 Example: Add boron (B) atom to the Si crystal Doping Silicon with Acceptors The B atom accepts an electron from a neighboring Si atom, resulting in a missing bonding electron, or “hole”. The hole is free to roam around the Si lattice, carrying current as a positive charge.

Spring 2007EE130 Lecture 3, Slide 8 Donor / Acceptor Levels (Band Model) E c E v Donor Level Acceptor Level EDED E A Donor ionization energy Acceptor ionization energy Ionization energy of selected donors and acceptors in silicon

Spring 2007EE130 Lecture 3, Slide 9 Charge-Carrier Concentrations N D : ionized donor concentration (cm -3 ) N A : ionized acceptor concentration (cm -3 ) Charge neutrality condition:N D + p = N A + n At thermal equilibrium, np = n i 2 (“Law of Mass Action”) Note: Carrier concentrations depend on net dopant concentration ( N D - N A ) !

Spring 2007EE130 Lecture 3, Slide 10 N-type Material N D >> N A (N D – N A >> n i ):

Spring 2007EE130 Lecture 3, Slide 11 P-type Material N A >> N D (N A – N D >> n i ):

Spring 2007EE130 Lecture 3, Slide 12 Terminology donor: impurity atom that increases n acceptor: impurity atom that increases p n-type material: contains more electrons than holes p-type material: contains more holes than electrons majority carrier: the most abundant carrier minority carrier: the least abundant carrier intrinsic semiconductor: n = p = n i extrinsic semiconductor: doped semiconductor

Spring 2007EE130 Lecture 3, Slide 13 Summary The band gap energy is the energy required to free an electron from a covalent bond. –E G for Si at 300K = 1.12eV –Insulators have large E G ; semiconductors have small E G Dopants in Si: –Reside on lattice sites (substituting for Si) –Group-V elements contribute conduction electrons, and are called donors –Group-III elements contribute holes, and are called acceptors –Very low ionization energies (<50 meV)  ionized at room temperature Dopant concentrations typically range from cm -3 to cm -3