Slide # 1 Hydrogenic model of doping impurities The simple model for a hydrogen atom can be used to describe the behavior of an impurity in a semiconductor. Thus, the formula for the ionization energy of a hydrogen atom, and the radius of the lowest orbit of the electron around the hydrogen nucleus can be applied in modified form to calculate how an electron or hole will interact with its parent impurity atom. m o and o are replaced by m* (effective mass) and s respectively, since we are now concern with charge embedded in a semiconductor and not in vacuum (or free space). Source:
Slide # 2 Radiative transitions in semiconductors Process 1: Intraband transition Process 2: Band-to-band transition Process 3: Excitonic transition Process 4: Valence band to donor transition Process 5: Conduction band to acceptor transition Process 6: Shallow donor to shallow acceptor transition excitons shallow donors Deep donors shallow acceptors Deep acceptors Others: Donor to conduction band, acceptor to valence band
Slide # 3 Intraband and interband transitions Process 1: Intraband transitions Hot electrons relax their energy mainly by emitting phonons, but sometimes under phonon’s or/and other electron’s assistance can also emit photons. This mechanism is truly rare as many particles are involved K Process 2: Band-to-band transitions Direct Indirect 1/2 g0 )()(EEAE Direct bandgap: Indirect bandgap: +ve and –ve signs are for absorption and emission Peak of the emission spectrum hc/E g = absorption coefficient, E p is the phonon energy. Intensity proportional to
Slide # 4 Other radiative transitions Process 3: Excitonic transitions For free excitons: hv = E g - E ex bind For bound excitons: hv = E g - E ex bind – E b Process 4 and 5: Free-bound transitions For D o h: hv = E g - E D For A o e: hv = E g - E A excitons shallow donors Deep donors shallow acceptors Deep acceptors Process 6: Donor-acceptor pair transitions where r is the distance between the donor and acceptor E b is the energy binding the exciton to the donor or acceptor