Heavily-doped strained germanium (Ge) can emit light efficiently thanks to its pseudo direct band gap characteristic. This makes Ge a good candidate for on-chip monolithic light sources in silicon (Si) photonics systems. We propose fin-shaped Ge-Si heterojunction light-emitting diode (LED) with metal gates, which can enhance light emission by coupling with surface plasmon resonant modes and modulate light emission from the LED. We verify these two aspects through numerical analysis and device simulations. We develop the method to find the optimal device structure and specific device dimensions to maximize the spontaneous emission rate enhancement. Also we find that the LED can be modulated by a gate voltage bias.
© 2014 Optical Society of America
As integrated circuits (ICs) are scaled down following Moore’s law, challenges in data communication through electric interconnects are arising due to bandwidth limit [1–4]. Even in short distance level communications such as chip-to-chip and intra-chip communication, optical interconnects become increasingly necessary to overcome this bottleneck. This is why Si photonics, which is the discipline of integrating optical components on a complementary metal-oxide-semiconductor (CMOS) chip, is considered as a solution of the bandwidth problem in future ICs. In state-of-the-art Si photonics technology, nearly all optical components such as modulators [5, 6], detectors , waveguides and nonlinear elements  have been well implemented monolithically except an efficient light source. Currently, III-V semiconductor based external light sources are used mainly in Si photonics systems. Another solution is to construct a hybrid device like III-V semiconductor based vertical-cavity surface-emitting lasers on a silicon-on-insulator substrate [9, 10]. This is because group IV materials like Si and Ge have indirect band gaps while other semiconducting materials like GaAs have direct band gaps, showing superior light emitting property compared to indirect band gap semiconductors. However, if we can make use of group IV semiconductors as light-emitting materials, the manufacturing process can be cheaper and easier because it is more compatible with the well-established Si-based process than hybrid devices manufacturing processes.
Recently, it has been proved that Ge can be used as an efficient light emitting material for on-chip monolithic light sources [11, 12]. Ge lasers  and LEDs [14, 15] were already demonstrated and actively studied. To make Ge a good light emitting material, band structure engineering of Ge is needed by means of controlling the lattice constant. Ge has a pseudo direct band gap behavior because the energy difference between the indirect conduction valley (the L-valley) and the direct conduction valley (the Γ-valley) is relatively small (only 0.136 eV, Fig. 1(a)). For this reason, Ge has been used in some photonic devices like Ge photodetectors. J. Liu et al. showed tensile-strained and heavily doped n-type Ge is more likely to have direct-band-gap-like property thanks to the Γ-valley lowering . Strained Ge can be obtained by epitaxial growth on a Si substrate. Due to the lattice mismatch, tensile stress is applied to the Ge epilayer on the Si substrate and gives tensile strain to make the lattice constant of Ge large, resulting into lowering of the energy level of the Γ-valley. Also, heavy n + doping on Ge can increase electron population on the Γ-valley, which can further enhance the direct recombination. Strain larger than 2% can eventually make Ge a true direct band gap material, but dramatic energy band gap narrowing occurs (Fig. 1(b)) . Weak and moderate straining on Ge does not alter the energy band gap significantly (0.664 eV, light emission of 1550 nm wavelength) and it still takes advantage of the Γ-valley lowering to become more direct-band-gap-like. About 0.2% strain on Ge is widely used for this reason [13–15]. By counting the electron population in each valley with the Fermi-Dirac statistics, the possible maximum internal quantum efficiency (q, Fig. 1(c)) of 0.2% strained and heavily n + doped (~1019/cm3) Ge is calculated to be approximately 10% . But this is an ideal value. The actual value of q is smaller than the calculated value and depends on a defect condition in the Ge epilayer .
If we could increase q by enlarging radiative recombination rate γr which corresponds to the spontaneous emission rate, Ge can emit light with improved efficiency. In this paper, we propose a fin type device structure with metal gates and show that we can obtain an enhanced γr and the q, thereby more light emission, by surface plasmon mode coupling in the cavity of the metal gates. We conduct a rigorous numerical analysis to obtain a device structure for maximizing the light emission. For various values of quantum efficiency without the enhancement effect, and for various types of gate metal, the optimal device structure and specific device dimensions can be obtained. In addition, device simulations show that light modulation is possible by simply modulating the gate voltage on the metal gate. The modulating speed of the device can reach 5 GHz order.
2. Surface plasmon-enhanced fin Ge-Si LED
We propose a new LED design (Fig. 2(a)) which has fin Ge-Si heterojunction p-n diode structure . This device inherently has a small footprint by adopting a fin structure. The fin Ge-Si LED is sandwiched by two metal film gates to form a plasmonic nano-cavity consisting of a metal-dielectric-metal waveguide structure. The heavily doped n + Ge region is the light emitting part. As forward bias Vd is applied, holes injected from the p-Si region recombine with electrons in the n + Ge region by both the radiative and nonradiative processes (Fig. 2(b)). The metallic film is the most crucial part for the working of the device. It can enhance light emission of the LED by coupling with the surface plasmonic resonant modes [19–21]. This is due to an optical cavity effect called the Purcell effect, which explains the phenomena that the spontaneous emission can be changed by surrounding environment . Nanophotonic environments such as photonic crystal constructing photonic band structures  and metal interface causing surface plasmon resonance [19–21] can alter the spontaneous emission rate of a light emitter in those environments. Also, the metal gates can be used to modulate the injection of the carriers in the LED. Thus it can be used as a switch and a modulator. When the gate bias Vg on both metal gates is applied, the potential barrier for holes in the Ge region will obstruct hole transport through the p-n diode (Fig. 2(c)). Furthermore, this device can be used as a photodetector. It means that this device can be used for both the transmitter (LED) and the receiver (photodetector) in one form.
For the respective dimensions of the device, the height of the fin (600 nm) is properly chosen to reduce defects in Ge. The most area of the fin is composed of Ge (500 nm) because it is the light emitting region. The oxide thickness tox is also determined for proper passivation from the metal gates and for moderate plasmon effect. If tox is too thin, light emission near the metal gates is absorbed by the metal and does not radiate out to the free space due to dissipation by Joule heating. This phenomenon is called the quenching which is a loss . The quenching effect is not significant if we set tox = 5 nm, which also gives good gate controllability. Other dimensions of the structures such as the thickness of Ge tGe and the thickness of the metal gate tm are variables.
This device can be built on a standard CMOS wafer with well-established manufacturing processes as follows: first, Ge is grown epitaxially on a p-doped Si substrate using ultra high vacuum chemical vapor deposition (UHV-CVD), for example, in . Ge is in situ doped by the n-type impurities such as PH3 during the growth process. The fin type device structure with ‘microbridge’ form may be adopted in our fin type LED for further enhancement in the light emission . After the fin array is patterned by etching process, deposition of oxide follows. Metal gate is deposited on both side of the fin. According to the analysis result in section 4, very thin metal layer under 5 nm may be needed. Implications on the thin metal film in the process difficulty and electrical characteristics will be commented in the discussion section. Transparent contact like indium tin oxide (ITO) for Ge electrode may be deposited above the device after filling the empty space between the fin arrays.
3. Analysis method
To determine tGe and tm, we performed a numerical analysis for the emission property of an emitter in the Ge region to maximize the surface plasmon coupling and enhance the spontaneous emission rate. The Purcell effect only affects γr by a factor of the Purcell enhancement factor E, and decreases τr, not altering the γnr (Fig. 1(c)). γr becomes Eγr, enhancing the internal quantum efficiency accordingly . If the quantum efficiency without the Purcell effect is q0 = γr / (γr + γnr) (hereafter called the intrinsic internal quantum efficiency), then the enhanced q can be expressed as a function of E and q0 asFig. 3(a). As examples with the points marked with ‘x’ in Fig. 3(a) (x-points), if q0 of strained Ge is 1%, (this means the ratio of γr to γnr is 1:99) and γr is enhanced by a factor of 100 (E = 100), γr: γnr becomes 100:99 and q becomes about 50%. If q0 is 10% and E is 100, then the q becomes about 91%.
For the calculation of the E, we assume our structure as a one-dimensional (1D) multilayer system (Fig. 3(b)). This can be justified because the aspect ratio of our device is relatively large and the wavelength of surface plasmonic mode is short compared to the fin height . γr of an emitter is given by Fermi’s golden rule as28–30]. The LPDOS can be expressed as28–30]. is the unit tensor. The delta function source represents an oscillating dipole in the multilayer system. To obtain the dyadic Green’s function in the 1D multilayer system analytically, each term in Eq. (4) is transformed by the spatial Fourier transform, from functions of position r = (x, y, z) to functions of wave vector k = (kx, ky, kz). It means that the dyadic Green’s function can be represented as the superposition of plane waves propagating in all directions. k is decomposed into the in-plane component k|| = (kx, ky, 0) and the normal component k⊥ = (0, 0, kz). The integral through the normal component kz can be removed if we obtain the reflectivities of both the upper and the lower layers of the multilayer system (R↑ and R↓ in Fig. 3(b)). Hence the final form of the dyadic Green’s function, and hence the LPDOS, are represented as integrals over the magnitude of in-plane wave vector |k||| = k||. From the calculated dyadic Green’s function of the 1D multilayer system, the LPDOS can be written as [31, 32]Fig. 3(b)). They are represented as31, 32]. These reflectivities account for the emission enhancement through constructive interference by the phase coincidence between the emitter and reflected lights.
Since γr is proportional to the LPDOS (by Fermi’s golden rule, Eq. (2)), E near the metal gate can be calculated by obtaining the ratio of the LPDOS for a certain device dimensions (tm and tGe) to the LPDOS without enhancement in the bulk Ge. Equation (5) means the LPDOS for certain wavelength can be considered as a density spectrum of the in-plane wave vector. In this spectrum, the region where the magnitude of the in-plane wave vector k|| is smaller than the magnitude of the wave vector |k| = k can be interpreted as directional emission (going to θ = sin−1(k||/k)) of free space waves. If k|| is larger than k, then this gives imaginary k⊥ which corresponds to plane-bounded surface plasmonic modes.
For the electrical simulation to see the controllability of metal gate potential to the carrier injection, the Sentaurus device simulation tool with standard device simulation models has been used .
4. Results and discussion
We consider the light with the wavelength of 1550 nm, which is the emission peak of strained Ge . First, we calculate E with varying tm and tGe for an emitter located at the center of the multilayer (Fig. 4(a), for gold (Au) gate). The value of E is typically 0~100, and sometimes exceeds 100 for certain geometric conditions. With the calculated E, we can obtain the enhanced quantum efficiency from q = q(E, q0) in Eq. (1) for a certain value of q0. The q values with q0 = 5% enhanced by E from Fig. 4(a) is plotted in Fig. 4(b). Comparing Fig. 4(a) with Fig. 4(b), the region of coordinate space (tm, tGe) having large value of q becomes broader.
And then, we suppose the total emission is given by q(E, q0)tGe. This holds if the current density is same for various tGe, and if q(E, q0) for the whole fin area is same. It includes the propagation loss of surface plasmonic guided modes. The total emission for a device with the Au gate is depicted in Fig. 4(c) for several q0, i.e. 1%, 5%, and 10% which is the theoretical maximum. As q0 increases, the maximum emission point occurs at thicker tGe. This is because tGe becomes more dominant than q for devices with higher q0. From this data we can choose the optimal device dimension maximizing the total emission (x-points in Fig. 4(c)). The graph in Fig. 4(d) justifies the assumption that E is invariant under the emitter position; as the dipole location deviates from the center of the fin, E does not vary significantly. Figure 4(e) shows the total emission with various gate metals (silver (Ag), aluminum (Al), and tungsten (W)) when q0 is 5%. It shows similar patterns with Fig. 4(c). To design the optimal device, we should properly choose the device dimension (tm, tGe) for a given q0 and material for the metal gate. Practically, formation of such a thin layer of metal in the conventional CMOS process may be a challenging task, due to a difficulty in depositing good quality film with reasonable metal characteristics. In this case, of course, our calculations may be considered to be too optimistic. However, the researches in this area are actively performed. For example, Uniform ruthenium (Ru) thin films (<5nm) can be successfully obtained with atomic layer deposition (ALD) under certain conditions [34, 35].
We can see interesting points when we carefully investigate and compare the LPDOS density spectrum of the in-plane wave vector (the integrand in Eq. (5)) for metal-less and metal-gated structures. The gate metal is Au and tGe is fixed to 30 nm in the following analysis. Before the metal gate is deposited, there is no LPDOS portion in the surface plasmon region where the in-plane wave vector magnitude is larger than the magnitude of the wave vector. As tm is increased from 0 to 1.5 nm, the surface plasmonic portion in the LPDOS density spectrum dramatically emerges while free-space wave component is not changed significantly (the top graph of Fig. 5(a)). E versus tm is depicted in Fig. 5(b) with the points denoting the data in Fig. 5(a). Figure 5(b) is also the cross section of the graph in Fig. 4(a) cut by the dotted line. The total area bounded by curves in the top graph of Fig. 5(a) corresponds to the points marked with ‘o’ (o-points) in Fig. 5(b) (normalized to the LPDOS for bulk Ge). E is maximized at tm = 1.5 nm. As tm increases further, the area bounded by LPDOS density shrinks, resulting into decreased LPDOS and E. The peaks of the LPDOS spectrum in the surface plasmon region are coincident with the surface plasmonic guided modes (the bottom graph of Fig. 5(a)) which are calculated by finding the minimum of the reflectivity of the whole multilayer system . Two peaks correspond to even and odd plasmonic modes, respectively. It indicates that the energy from the emitter near metal is efficiently transferred to those modes by near-field coupling. Also it means that enhancement of γr by constructing another radiative reaction path which is caused by the surface plasmon polariton coupling. Electric field profile of the even surface plasmonic mode (Fig. 5(a), bottom) is depicted in Fig. 5(c). The wavelength of this plasmonic mode is 170 nm and typically short compared with free space wavelength (1550 nm) as already mentioned. Several wavelengths can come inside to seemingly short fin height (600 nm). This fact justifies the 1D multilayer approximation.
Device simulation results to see the gate modulation of the carrier injection, thereby the light modulation are shown in Fig. 6. When Vd is applied on the Ge-Si p-n diode (Fig. 2(a)), positive Vg raises the potential barrier of holes in the diode (Fig. 2(c)), inhibiting the p-n diode current accordingly. This gate modulation effect is much more dominant in the p-i-n diode (100 nm of intrinsic Ge is inserted between p-Si and n + Ge in the fin LED) than p-n diode (Fig. 6(a)). This is because the energy barrier is modulated more easily in the undoped region. All previous optical optimization analysis is still applicable for the p-i-n structure because doping on Ge does not change the optical property significantly. We cannot completely turn off the diode because gate bias just raises the energy barrier without blocking all the carrier transfer. Gate modulation works well for thinner tox (Fig. 6(b)) and tGe (Fig. 6(c)) due to easier electric field penetration. Figure 6(d) shows the transient response of the total recombination amount in Ge region when an on-off pulse signal is applied. For diode on-off mode, the off-state is Vd = 0 V and the on-state Vd = 0.7 V while Vg is fixed to 0 V. For gate on-off mode, the off-sate is Vg = 1 V and the on-state is Vg = 0 V while Vd is fixed to 0.7 V this time. Both modulations by the gate voltage and the diode voltage are possible and show similar responses. Considering the rising time and the falling time of the transient response, the maximum modulation speed is calculated to be about 5 GHz. It should be noticed that the device simulation used in this work considers only the electrical carrier transport, so the optical response time may not be properly predicted. However, we may claim that the optical response time is always shorter than the response time predicted by the device simulation. Electrical response time is determined by total recombination rate which is sum of the radiative and nonradiative recombination rates. Due to the Purcell effect, the radiative part will be enhanced so total response time will be reduced. In order to estimate enhancement of the response time quantitatively, more comprehensive numerical analysis coupling the electrical transport and the Purcell effect is needed, which is out of scope of this work.
We have proposed a fin Ge-Si LED with metal gates by which the spontaneous emission and quantum efficiency are enhanced due to coupling with surface plasmon resonant modes. In addition, the emitted light can be modulated directly by the gate voltage by controlling the injection of the carriers in the diode. Through the analysis based on numerical simulations, it has been shown that the enhancement of the light and gate modulation is dependent on the device dimensions such as the fin semiconductor thickness, gate oxide and the metal thickness. Our device can be an efficient on-chip monolithic Ge light source for Si photonics systems. Furthermore, the analysis methods proposed in this paper can be extended to designing not only the fin Ge-Si LED but also any surface plasmon-enhanced LEDs and nano-cavity lasers . As future works, calculations based on the three-dimensional finite element method are needed to obtain the exact dyadic Green’s function and the LPDOS of the emitter for estimation of the spontaneous emission enhancement in arbitrary device structures such as a pillar structure providing more localized light emission.
This work was supported by the Center for Integrated Smart Sensors funded by the Ministry of Science, ICT & Future Planning as Global Frontier Project (CISS-2013072206). This work was supported by the Brain Korea 21 Plus Project in 2014.
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