FEKT VUT v BrněESO / L1 / J.Boušek1 Intrinsic semiconductor

FEKT VUT v BrněESO / L1 / J.Boušek2 Doped semiconductor N-type

FEKT VUT v BrněESO / L1 / J.Boušek3 Doped semiconductor P-type

ESO / L2 / J.Boušek4 Electric current in semiconductors Drift of charged carriers

ESO / L2 / J.Boušek5 I p,drift = qpv d AJ p,drift = qpv d v d = μ p E J p,drift = qμ p pE J n,drift = qμ n nE Electric current in semiconductors

ESO / L2 / J.Boušek6

7 Dependence on dopant concentration

ESO / L2 / J.Boušek8 Diffusion

ESO / L2 / J.Boušek9 Diffusion 1. Fick-Law:

ESO / L2 / J.Boušek10 Einstein equation Diffusion + Drift

ESO / L2 / J.Boušek11 Generation = need energy = generation in pairs: (electron + hole) - photo-generation - thermal excitation of the crystal lattice - high energy electron Recombination = loss of energy = recombination in pairs: (el. + hole) : - large number of complicated processes - direct (interband) - undirect (recombination centres, traps) - surface generation lifetime recombination electrones…  n holes….  p Generation and recombination

ESO / L2 / J.Boušek12 Doped semiconductor: Type N  n >>  p ; Type P  p >>  n Usually :  n,  p ≈ 1  s High quality silicon :  n,  p ≥ 1 ms High density of traps / of recombination centres :  n,  p ≈ 1  s ÷1 ns - High speed devices: Intentionally... Au (Al) - Low quality production: Crystal distortions, Impurities Lifetime of the carriers

ESO / L2 / J.Boušek13 p 0 n 0 = n i 2 equilibrium state (index "0") Distortion of thermal equilibrium: n = n 0 +  n ; p = p 0 +  p (  n a  p concentration of non-equilibrium carriers) Injection : np > n i 2 low (  n > n 0 ) Extraction : np < n i 2. Thermal equilibrium

ESO / L2 / J.Boušek 14 Depletion region PN-Junction in equilibrium state

ESO / L2 / J.Boušek15 Electrons in N: n n = N D = m -3 Electrons in P: n p = ni 2 / N A = m -6 / m -3 = m -3 Difference in concentration 10 7 electron diffusion to P !!!!! In N only ionized donors (N D +) standing firmly in the lattice Holes in P: p p = N A = m -3 Holes in N: p p = ni 2 / N D = m -6 / m -3 = m -3 Difference in concentration 10 7 diffusion of holes to N !!!!! In N only ionized donors (N D +) standing firmly in the lattice PN-Junction in equilibrium state Concentration of dopants: N D = m -3 N A = m -3 Ionized dopants create space charge !!!!!!!!!

ESO / L2 / J.Boušek16 Space charge in depletion area Electrical field Potential

ESO / L2 / J.Boušek17 Density of the space charge given by dopants concentration Junction area with lower dopants concentration ís wider Consequence : Electrical field in depletion area Emax- in metalurgical junction !!!! Actual potential value given by the shape of electrical field Potential difference between P and N : Diffusion voltage. PN-Junction in equilibrium state

ESO / L2 / J.Boušek18 Band-diagram of PN-Junction

ESO / L2 / J.Boušek19 Band-diagram of PN-Junction 1) The position of E F in both areas P and N must correspond to the type of semiconductor / type of conductivity. (shift E F to E V in case of “P-type“ or to E C in case of “N-type“) 2) In Thermal equilibrium the value of Fermi level E F is constant. To fulfuill both 1) + 2) : a) mutual shift of Conductive and Valence bands (band-bending) b) The shift corresponds to qU D. qU D : energetic treshold - prevents diffusion of majority carriers.

ESO / L2 / J.Boušek20 PN junction in FORWARD polarisation Diffusion voltage - barrier against diffusion of majority carriers Equilibrium state : Only small diffusion current which is compensated with the drift casused by potential difference in space charge area. majority carriers - diffusion minoritní carriers - drift In forward polarisation : external voltage acts against the potential in depletion area - the barrier / treshold is lower !!! Forward current is made by DIFFUSSION of majority carriers !!

ESO / L2 / J.Boušek21 Polarity of external voltage is the same as the polarity of electrical field in the space charge region: !! Electrical field in the space charge region grows !! Electrical field in space charge region enhance the drift of minority carriers from quasineutral parts of the junction: -The concentration of minority carriers in quasineutral parts of the junction drops. - When increasing the reverse voltage the reverse current does not increase !!!! Reverse current : DRIFT current of minority carriers !!!! PN junction in REVERSE polarisation