Semiconductor Physics - 1Copyright © by John Wiley & Sons 2003 Review of Basic Semiconductor Physics

Semiconductor Physics - 2Copyright © by John Wiley & Sons 2003 Current Flow and Conductivity Charge in volume A  x =  Q = q n A  x = q n A v  t Current density J = (  Q/  t)A -1 = q n v Metals - gold, platinum, silver, copper, etc. n = cm -3 ;  = 10 7 mhos-cm Insulators - silicon dioxide, silicon nitride, aluminum oxide n < 10 3 cm -3 ;  < mhos-cm Semiconductors - silicon, gallium arsenide, diamond, etc < n <10 19 cm -3 ; <  < 10 4 mhos-cm

Semiconductor Physics - 3Copyright © by John Wiley & Sons 2003 Thermal Ionization Si atoms have thermal vibrations about equilibrium point. Small percentage of Si atoms have large enough vibrational energy to break covalent bond and liberate an electron.

Semiconductor Physics - 4Copyright © by John Wiley & Sons 2003 Electrons and Holes T 3 > T 2 > T 1 Density of free electrons = n : Density of free holes = p p = n = n i (T) = intrinsic carrier density. n i 2 (T) = C exp(-qE g /(kT )) = cm -6 at 300  K T = temp in  K k = 1.4x joules/  K E g = energy gap = 1.1 eV in silicon q = 1.6x coulombs

Semiconductor Physics - 5Copyright © by John Wiley & Sons 2003 Doped Semiconductors Extrinsic (doped) semiconductors:p = p o ≠ n = n o ≠ n i Carrier density estimates: Law of mass action n o p o = n i 2 (T) Charge neutrality N a + n o = N d + p o P-type silicon with N a >> n i : p o ≈ N a, n o ≈ n i 2 / N a N-type silicon with N d >> n i : n o ≈ N d, p o ≈ n i 2 / N d

Semiconductor Physics - 6Copyright © by John Wiley & Sons 2003 Nonequilibrium and Recombination Thermal Equilibrium - Carrier generation = Carrier recombination n = n o and p = p o Nonequilibrium - n > n o and p > p o n = n o +  n and p = n o +  n ;  n = excess carrier density Excess holes and excess electrons created in equal numbers by breaking of covalent bonds Generation mechanisms -light (photoelectric effect), injection, impact ionization Recombination - removal of excess holes and electrons Mechanisms - free electron captured by empty covalent bond (hole) or trapped by impurity or crystal imperfection Rate equation: d(  n)/dt = -  n  Solution  n =  n (0) e -t 

Semiconductor Physics - 7Copyright © by John Wiley & Sons 2003 Carrier Lifetimes  = excess carrier lifetime Usually assumed to be constant. Changes in two important situations.  increases with temperature T  decreases at large excess carrier densities ;  =  o /[1 + (  n/n b ) 2 ] Control of carrier lifetime values. Switching time-on state loss tradeoff mandates good lifetime control. Control via use of impurities such as gold - lifetime killers. Control via electron irradiation - more uniform and better control.

Semiconductor Physics - 8Copyright © by John Wiley & Sons 2003 Current Flow J drift = q µ n n E + q p µ p E µ n = 1500 cm 2 /V-sec for silicon at room temp. and N d < cm -3 µ p = 500 cm 2 /V-sec for silicon at room temp. and N a < cm -3 Drift Diffusion J diff = J n + J p = q D n dn/dx - q D p dp/dx D n /  n = D p /  p = kT/q ; Einstein relation D = diffusion constant,  = carrier mobility Total current density J = J drift + J diff

Semiconductor Physics - 9Copyright © by John Wiley & Sons 2003 PN Junction

Semiconductor Physics - 10Copyright © by John Wiley & Sons 2003 Formation of Space Charge Layer Diffusing electrons and holes leave the region near metallurgical junction depleted of free carriers (depletion region). Exposed ionized impurities form space charge layer. Electric field due to space charge opposes diffusion.

Semiconductor Physics - 11Copyright © by John Wiley & Sons 2003 Quantitative Description of Space Charge Region Assume step junction.

Semiconductor Physics - 12Copyright © by John Wiley & Sons 2003 Contact (Built-in, Junction) Potential

Semiconductor Physics - 13Copyright © by John Wiley & Sons 2003 Reverse-Biased Step Junction

Semiconductor Physics - 14Copyright © by John Wiley & Sons 2003 Forward-Biased PN Junction Forward bias favors diffusion over drift. Excess minority carrier injection into both p and n drift regions. Minority carrier diffusion lengths. L n = [D n  n ] 0.5 L p = [D p  p ] 0.5

Semiconductor Physics - 15Copyright © by John Wiley & Sons 2003 Ideal PN Junction I-V Characteristics Excess carriers in drift regions recombined and thus more must be constantly injected if the distributions np(x) and pn(x) are to be maintained. Constant injection of electrons and holes results in a current density J given by v J v J v - J s i forward bias reverse bias combined characteristic

Semiconductor Physics - 16Copyright © by John Wiley & Sons 2003 Reverse Saturation Current Carrier density gradient immediately adjacent to depletion region causes reverse saturation current to flow via diffusion. J s independent of reverse voltage V because carrier density gradient unaffected by applied voltage. J s extremely temperature sensitivity because of dependence on n i 2 (T.)

Semiconductor Physics - 17Copyright © by John Wiley & Sons 2003 Impact Ionization E ≥ E BD ; free electron can acquire sufficient from the field between lattice collisions (t c ≈ sec) to break covalent bond. Energy = 0.5mv 2 = q E g ; v = q E BD t c