Enhanced Photoyield with Decreasing Film Thickness on Metal-Semiconductor Structures
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y ý _I• .(hv-
E13)2(1)
8EFhv
(hv is the photon energy and E1 is the barrier energy) if (hv-EB)/kBT>3 which is obtained from the photoemission of electrons from a metal into the vacuum. Some attempts have been made during the last decades to overcome the assumed simplifications, e.g. the neglect of carrier scattering processes inside the photoemitter [4],[5] and the quantum-mechanical reflection at the Schottky barrier [6]. But the lack of reliable absolute values of Yi(hv) prevented refined theoretical models from being accepted. Therefore, the interpretation of IP measurements is still based on the Fowler relation [1], [2]. The present paper is focused on the experimental determination of the internal quantum yield on thin film metal-semiconductor heterojunctions thereby discussing the effects of carrier scattering in the emitter layer (process 2) . This is based on the measurement of the optical absorptance in the photoemitting layer (1) and an estimation of the processes (3,4).
413 Mat. Res. Soc. Symp. Proc. Vol. 448 ©1997 Materials Research Society
THEORETICAL MODEL The theoretical model of IP in metal- semiconductor structures, including carrier scattering in the emitter and in the image force region, is only outlined in the present work. The detailed description is given in a previous publication [7]. emitting layer
ky
x.
o
e-e
==> injection
e-p
Fig. la: Momentum (k) space of photoexcited charge carriers with the escape cone for being injected (hatched region)
Fig. ib: Elastic isotropic hot carrier scattering e - p at phonons and impurities, reflection at the metal layer boundaries and inelastic collisions e - e with cold carriers
The optical excitation of charge carriers in thin metal films is assumed to be homogeneous with isotropic carrier momentum distribution (free electron gas). The escape cone for IP determines that part of the excited carriers which have sufficient momentum normal to the barrier to cross EB and it is given by the Fowler equation [8]
f E YF(EF,EB,hv,T)
= kB ' T
1In(•
e(EF-E)/kBT)dE (2)
EF+EB-hv
4f E 1/2. (I + e(E-EF)/kB'T)-1dE EF-hv
T is the temperature, EF the Fermi energy of the metal and kB the Boltzmann's constant. Extending the theory of Fowler the scattering theory includes analytically the elastic scattering of photoexcited (hot) carriers at the layer boundaries and phonons, neglecting the energy transfer to the latter (Fig. 1) and inelastic collisions with thermalized (cold) carriers, as it was calculated by Kane[4] and Dalal[5]. The reflection at the layer boundaries is assumed to be diffuse and the scattering due to phonons to be isotropic. The attenuation lengths for inelastic carrier- carrier scattering le (E) depend on the energy of the hot carriers [9] and for elastic carrier-phonon scattering lp. (T) on temperature. The elastic scattering at grain boundaries in polycrystalline films is not included in this analytical theory. Scattering in the image force region of the semiconductor (between interface and Schottky barrier maximum x0 ) is considered b
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