Direct determination of the piezoelectric field using the quantum-confined Stark effect in a strained [111]-oriented zinc-blende MQW-SOA

Abstract

Here, we present a method, based on Stark shifts induced by the quantum-confined Stark effect, to directly determine the piezoelectric field in strained zinc-blende quantum wells (QWs) grown along the 111 direction and embedded in the p–i–n diode structure ( p-iMQW-n) of a semiconductor optical amplifier. Under short-circuit and open-circuit conditions and resonant optical excitation, we experimentally determine the energy of the 1s e-hh excitonic resonance and the potential difference across the p-iMQW-n junction. Using these parameters in an analytical expression derived in this work, we directly determined a piezoelectric field of −108.71 ± 8.51 kV/cm acting on each of the eight 12-Å-wide strained [111]-oriented In0.687Ga0.313As /In0.807Ga0.193As0.304P0.696 QWs of a semiconductor optical amplifier (SOA). The theoretical prediction of −112.24 kV/cm was in very good agreement, within the experimental error, with the value of the piezoelectric field extracted through the proposed procedure, which was also indirectly validated by comparing the experimental value of the 1s e-hh excitonic resonance Stark shift with the extracted one. Even though the implemented technique was specially designed to experimentally determine the piezoelectric field acting on each of the QWs of a multiple quantum well SOA, it can be applied to any p–i–n structure with electrodes and strained [111]-oriented zinc-blende QWs embedded in its intrinsic region. Remarkably, the method proposed here allows direct experimental determination of the piezoelectric field through an analytical expression, with which it is also possible to estimate, with high reliability, the precision of the result and how it is affected by the accuracy of each measuring instrument intervening in the procedure.

Piezoelectric constant temperature dependence in strained [111]-oriented zinc-blende MQW-SOAs

“…4 with error bars and were obtained in a manner similar to that described in Ref. [11]. Due to the high absorption of the 1S e-hh ER, the OSA noise floor generates inaccuracies in the determination of E x sc,oc 1,2 , which is the main cause of the dispersion of the e 14 e , Āehh , and ΔE s sc values represented with open crosses in Fig.…”

“…Considering that F w n causes a negligible change in E b , from Eq. ( 1), the energy difference (ΔE x os n = E x oc n − E x sc ) existing between the 1S e-hh ER energies under open-and short-circuit conditions (OCC and SCC) becomes practically equal to the total Stark shift difference (ΔE s oc n − ΔE s sc ) experiencing 1S e-hh ER under OCC and SCC [11] . Indeed, since the energies E x ocn and E x sc are defined by Eq.…”

“…( 1), their difference, for the same temperature, causes the cancellation of E g , E q , and E b , and therefore of the effects of temperature and segregation phenomenon on E g . Consequently, ΔE x os n is given in eV by [11,12]…”