Silicon Resonant Cavity Enhanced Schottky Photodetector at 1 . 55 μ m

In this paper we propose the design of a Silicon resonant cavity enhanced Schottky photodetector based on the internal photoemission effect, working at 1.55μm, and entirely compatible with ULSI Silicon technology.


I. INTRODUCTION
Traditionally, the operation of conventional and resonant cavity enhanced (RCE) photodetectors are based on the semiconductor interband transition effect.Such devices give an electrical signal when the photon energy is greater than the semiconductor band-gap.In silicon (Si), this corresponds to a cutoff wavelength of about 1.1 µm, which is not in the 1.3-1.55µm fiber optic communication wavelength range.A possible alternative is the use of silicon-germanium, but the growth of this compound on silicon is still a challenge in terms of cost and complexity [1,2].The exploitation of the internal emission effect over the metal-semiconductor Schottky barrier may offer a solution.In fact, depending on the height of the metalsemiconductor barrier, the cut-off wavelength can be shifted at wavelength well beyond 1.6 µm [3,4].
Si photodetectors have already found wide acceptance for visible light (0.400-0.700 µm) applications, because of their near perfect efficiency at these wavelengths.Regarding near IR wavelengths for data communications applications, Si could offer the potential of low fabrication cost and direct integration with complementary metal-oxide-semiconductor (CMOS) circuits.In this paper, the design of a RCE Si Schottky photodiode operating at 1.55 µm, and based on the internal photoemission effect, is proposed.The advantage is that the design is completely compatible with ULSI silicon technology.

II. INTERNAL PHOTOEMISSION
Internal photoemission is the optical excitation of electrons in the metal to an energy above the Sckotty barrier and then transport of these electrons to the conduction band of the semiconductor [5].The standard theory of photoemission from a metal into the vacuum is due to Fowler [6].
In a gas of electrons obeying the Fermi-Dirac statistic, if energy photon is close to potential barrier (hν≈Ф B ), the fraction (F e ) of the absorbed photons, which produce photoelectrons with the appropriate energy and momenta before scattering to contribute to the photocurrent, is given by: where hν is photons energy, Ф B is the potential barrier and E F is metal fermi level.
The previous equations were obtained without taking into account the thickness of the Schottky metal layer.In order to study the quantum efficiency for thin metal films, the theory must be further extended, taking into account multiple reflections of the excited electrons from the surfaces of the metals film, in addition to collisions with phonons, imperfections and cold electrons.
Assuming a thin metal film, a phenomenological, semiclassical, ballistic transport model for the effects of the scattering mechanisms resulting in a multiplicative factor for quantum efficiency has been developed by Vickers [7].According to this model the accumulated probability P e that the electrons will have sufficient normal kinetic energy to overcome potential barrier is given by: where d is the metal thickness and a L e the mean free path.

III. OPTICAL DESIGN
The proposed device is a RCE metal Schottky photodetector illuminated from the metal side, based on internal photoemission effect, and operating at 1.55 micron.The resonant cavity has a Fabry-Perot vertical-to-the-surface structure.It is formed using a buried reflector and a mirror top interface.The buried reflector is formed by alternating layers of different refractive indices.The semiconductor part of the Schottky junction is a λ/2-silicon-layer.A protection coating layer deposited on the semitransparent Schottky metal functions as the top reflector of the resonant cavity (Fig. 1).
The exploitation of the internal emission effect over the metal-semiconductor Schottky barrier allows the realization device operation at infrared wavelengths, therefore, in the spectral region of Si transparency.The low quantum efficiencies characterizing the internal photoemission effect are enhanced by the fabry-Perot micro-cavity operating at the ( ) ( ) resonance wavelengths (corresponding to a roundtrip phase of 2π in the Fabry-Perot cavity).In fact, the effective optical path length is enhanced greatly by the multiple reflections occurring at the top and bottom cavity mirrors.
The quantum efficiency of a RCE metal Schottky photodetector, based on internal photoemission effect, can be obtained by the formulas [7]: where F e and P e are given by formulas 1 and 2, respectively.In order to calculate A T we use an approach based on the Transfer Matrix Method (TMM) [8].We consider the restriction to variations of n(z), i. e. the unidimensional refractive index profile along the propagation direction (z).
According to TMM approach the absorptance A T in the schottky metal layer is given by: , , , are the elements of the matrix calculated from interface between metal and λ/2 layer to the final plane (Fig. 2).Let E inc and E R be the amplitudes of the incident and reflected plane waves at interface between air and Si 3 N 4 coating and E 4,F and E 4,B the amplitudes of the transmitted and incident plane waves at interface between metal and λ/2-silicon layer.These amplitudes are related by the 2x2 tranfer matrix M R1 : The reflection coefficient is defined as: where the reflectivity of the top mirror is given by: ( ) According to the same approach, being M R2 the transfer matrix of bottom mirror, the reflection coefficient is defined as: where the riflectivity of the bottom mirror is given by: ( ) The large index contrast provided by Si and SiO 2 allows the realization of high-reflectivity, wide spectral stopband Si-SiO 2 Distributed Bragg Reflector (DBR) made of few periods.
The technique, based on a double silicon-on-insulator (SOI) process, has been already exploited for the realization of buried distributed Bragg reflector on silicon wafers [9].
Anyway, limitations in fabrication process do not allow for layer thickness as thin as (1/4n) λ, for this reason (3/4n) λ layers for Si were used.Starting from this results, in our design we propose a DBR centered at 1.55µm.The DBR could be formed by alternate layers of Si and SiO 2 having refractive index 3.45 and 1.45, and thickness of 340nm and 270nm, respectively.A DBR with 1 period of Si/SiO 2 has a reflectivity of 0.49, with 2 periods the reflectivity is 0.88, with 3 and 4 the reflectivity is 0.975 and 0.993, respectively, over a broad range of wavelengths.
The top reflector of the resonant cavity can be formed by a protection coating layer deposited on semitransparent Schottky contact.In our design, in order to satisfy the relation B hν φ ≅ at the wavelength of 1.55 µm, we choose gold as the Schottky metal (real part of the complex refractive index 0.174, extinction coefficients 9.96 [10] and fermi level 5.53eV).Finally, a Si 3 N 4 layer, having refractive index 2.0, can be deposited on top of the gold layer, the optimum value of reflectivity is mainteined for a special Si 3 N 4 thikness.
In Fig. 3 is reported the absorptance as function of the reflectivity of the first mirror for different values of bottom mirrors reflectivity.In Fig. 4, we report the quantum efficiency calculated for resonance case with bottom mirror reflectivity of 0.88 and 0.993.
In the first case maximum efficiency is obtained for top mirror reflectivity of 0.78, this value is linked at a metal thickness of 13nm and Si 3 N 4 thikness of 350nm, the thickness of the n-Si-layer between the two mirrors, calculated in order to fulfill constructive interference condition, is 410 nm.The microcavity Q-value calculated is about 150.In the last case maximum efficiency is obtained for top mirror reflectivity of 0.94, this value is linked at a metal thickness of 30nm and Si 3 N 4 thikness of 320nm.The thickness of the n-Si- layer between the two mirrors, calculated in order to fulfill constructive interference condition, is 425 nm.The microcavity Q-value calculated is about 485.
In order to prove the enhancement due to the cavity effect, the efficiency as function of wavelength has been calculated and is reported in Fig. 4 for antiresonance case.It is evident that the microcavity, operating in resonance condition, produces an enhancement of the efficiency of about one order of magnitude.

V. CONCLUSION
In this paper, the design of a Si resonant cavity enhanced Schottky photodetector, based on the internal photoemission effect, and operating at 1.55 micron is reported.Using Au-Si as Schottky barrier a 0.1% quantum efficiency has been obtained.Moreover we prove that the enhancement due to the presence of cavity has a significant effect.This preliminary theoretical results are encouraging for future investigations.
n 4 ] is the real part of the refractive index of the 2the matrix calculated from interface between protection coating and metal to the final plane,

Fig. 3 .
Fig. 3. Absorbance as function of the metal thickness in resonance case for different values of bottom mirrors reflectivity IV.NUMERICAL RESULT