Suppression of Surface-Related Loss in a Gated Semiconductor Microcavity

We present a surface-passivation method that reduces surface-related losses by almost 2 orders of magnitude in a highly miniaturized $\mathrm{Ga}\mathrm{As}$ open microcavity. The microcavity consists of a curved dielectric distributed Bragg reflector with radius of approximately $10\mu \mathrm{m}$ paired with a $\mathrm{Ga}\mathrm{As}$-based heterostructure. The heterostructure consists of a semiconductor distributed Bragg reflector followed by an $n$-$i$-$p$ diode with a layer of quantum dots in the intrinsic region. Free-carrier absorption in the highly-$n$-doped and highly-$p$-doped layers is minimized by our positioning them close to a node of the vacuum electromagnetic field. The surface, however, resides at an antinode of the vacuum field and results in significant loss. These losses are much reduced by surface passivation. The strong dependence on wavelength implies that the main effect of the surface passivation is to eliminate the surface electric field, thereby quenching below-band-gap absorption via a Franz-Keldysh-like effect. An additional benefit is that the surface passivation reduces scattering at the $\mathrm{Ga}\mathrm{As}$ surface. These results are important in other nanophotonic devices that rely on a $\mathrm{Ga}\mathrm{As}$-vacuum interface to confine the electromagnetic field.

Figure 1

Ultrahigh-$Q$-factor optical microcavity as a sensitive probe of surface-related losses. (a) Schematic of the microcavity involving a curved dielectric DBR and an $n$-$i$-$p$ heterostructure with self-assembled $\mathrm{In}\mathrm{As}$ QDs on top of a semiconductor DBR (“nip-DBR”). (b) Simulated reflectance of the nip-DBR with SB center ${\lambda }_C=920\mathrm{nm}$. (c) Calculated vacuum field amplitude across the heterostructure for three different wavelengths, $-30$, $0$, and $+30$ nm with respect to the SB center. As the antinodes of the vacuum field shift in position with wavelength, thereby changing the MCF in the $\mathrm{Ga}\mathrm{As}$ capping layer, surface-related absorption in the capping layer (${10}^{-10}$–${10}^{-8}{\mathrm{cm}}^{-1}$) can be probed via the microcavity by our measuring its $Q$ factor across the SB. At ${\lambda }_C$, where the coupling to the QDs is maximized, free-carrier absorption in the highly-$p$-doped and highly-$n$-doped gates is minimized by our placing them close to a vacuum field node. Note also that the highly reduced vacuum field at $\lambda -{\lambda }_C=-30\mathrm{nm}$ arises because at this wavelength the largest vacuum electric field is located in the vacuum gap.

Figure 2

Mirror characterization via reflection measurements. Each mirror is investigated by our recording the spectrum of white light reflected off the sample using a dark-field confocal microscope [28]. Via 1D transfer-matrix methods (essential macleod), the designed layer thicknesses can be refined to fit the experimentally observed oscillations. (a) Dielectric DBR I. The reflected signal is recorded on a flat surface away from the curved part of the mirror and normalized by the white-light spectrum. (b) Unpassivated nip-DBR. Here the reflectance spectrum is obtained by our normalizing the signal reflected from the mirror by the signal reflected from a $\mathrm{Au}$ contact pad (by our moving the piezoelectric nanopositioner laterally by a few microns).

Figure 3

Microcavity characterization via $Q$-factor measurements using DBR I paired with passivated nip-DBR with contacts (black dots), two unpassivated nip-DBRs without contacts (blue triangles), and DBR I (DBR II) paired with five (one) unpassivated DBRs with contacts (red squares). (a) Measured transmission signal as a function of laser detuning at $\lambda -{\lambda }_C\sim 10\mathrm{nm}$ at fixed mirror separation. The $Q$ factor is determined by a double-Lorentzian fit (solid lines). (b) Evaluated $Q$ factors for several wavelengths. Mean values and standard deviations originate from data from two cavity modes and up to six measurements. Two surface-loss mechanisms are modeled: absorption and scattering. The solid lines are calculated $Q$ factors with our taking into account free-carrier absorption (absorption coefficients from Ref. [13]) and Franz-Keldysh (FK) absorption [17, 18] for electric fields in the capping layer $F_{\mathrm{cap}}=(200,320,470)$ kV/cm. The dotted lines are calculated by our taking into account surface scattering only [31]. For the passivated case, the dotted black line is modeled with roughness at both the $\mathrm{Ga}\mathrm{As}$-alumina interface and the alumina-vacuum interface $\sigma =({\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3},{\sigma }_{{\mathrm{Al}}_2{\mathrm{O}}_3\text{−}\mathrm{vac}})$, and is found to be $\sigma =(0.14,0.14)\mathrm{nm}$; alternatively $\sigma =(0.0,0.55)\mathrm{nm}$ yields similar results. In the unpassivated cases, the dotted blue and red lines are modeled with ${\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}\mathrm{vac}}=0.5\mathrm{nm}$ and ${\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}\mathrm{vac}}=1.0\mathrm{nm}$ at the $\mathrm{Ga}\mathrm{As}$-vacuum interface, respectively. The solid gray line is the model without any surface losses. (c) By comparing measured and simulated $Q$ factors, and assuming that the scattering losses are negligible, one can deduce the absorption coefficient $\alpha$ as a function of photoenergy. $\alpha$ is fitted to the Franz-Keldysh result with $F_{\mathrm{cap}}$ as a fitting parameter.

Figure 4

Determination of surface-related losses via $Q$-factor measurements using DBR II with a nip-DBR. We probe the double role of surface passivation. Four positions in the contacted sample are probed: three passivated areas, A, B, and C (circles), and an unpassivated region (red squares). Mean values and standard deviation result from the measurements on the two cavity modes. We implement a mixed model to fit the data: Franz-Keldysh-like absorption and reasonable values of surface roughness are probed together. For the passivated regions, surface roughness alone explains the observed data. We estimate a roughness $\sigma =({\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3},{\sigma }_{{\mathrm{Al}}_2{\mathrm{O}}_3\text{−}\mathrm{vac}})$ for each region: at region A $\sigma =(0.5,0.5)\mathrm{nm}$, alternatively $\sigma =(0.0,1.0)\mathrm{nm}$; at region B $\sigma =(0.25,0.8)\mathrm{nm}$, alternatively $\sigma =(0.0,1.4)\mathrm{nm}$; at region C $\sigma =(0.5,3.0)\mathrm{nm}$, alternatively $\sigma =(0.0,3.75)\mathrm{nm}$. For the unpassivated region, surface roughness alone cannot account for the $Q$-factor dependence on wavelength alone: with a surface roughness of ${\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}\mathrm{vac}}=0.3\mathrm{nm}$, an electric field $F_{\mathrm{cap}}=400$ kV/cm is still needed to fit the data.

Figure 5

Undoped semiconductor heterostructure: reflectance and $Q$-factor measurements. (a) Reflectance measurement of a semiconductor heterostructure without doping (${\lambda }_C=956\mathrm{nm}$) at $4.2$ K. The heterostructure contains a $\lambda$ layer of $\mathrm{Ga}\mathrm{As}$ on top of 33 pairs of $\mathrm{Al}\mathrm{As}$($\lambda /4$)/$\mathrm{Ga}\mathrm{As}$($\lambda /4$). A layer of QDs is included at the center of the $\mathrm{Ga}\mathrm{As}$ layer. To record a reference spectrum, parts of the sample are covered by a $\mathrm{Au}$ film by means of electron-beam evaporation. (b) $Q$ factor of a microcavity at $4.2$ K consisting of this heterostructure without doping paired with dielectric top mirror DBR I: experimental results (circles) and simulation with surface roughness ${\sigma }_{\mathrm{Ga}\mathrm{As}\text{−}\mathrm{vac}}=0.5\mathrm{nm}$ (solid red line). The dotted red line is the expected $Q$ factor upon passivation of the surface with a 8.0-nm-thick ${\mathrm{Al}}_2{\mathrm{O}}_3$ layer. The solid gray line corresponds to expected $Q$ factor without any surface losses.

Figure 6

AFM images of different semiconductor samples. Each image depicts the same scan area of $0.8\times 0.8\mu {\mathrm{m}}^2$ (obtained in tapping mode) and from a height of $-4$ to $+4\mathrm{nm}$. (a) Piece of passivated wafer. The root-mean-square surface roughness measured at several similar sample locations lies in the range $0.3\mathrm{nm}\le \sigma \le 1.9\mathrm{nm}$. (b) Piece of unpassivated bare wafer. The range of surface roughness for similar sample locations is $0.3\mathrm{nm}\le \sigma \le 0.7\mathrm{nm}$. (c) Unpassivated sample with contacts. Similar samples exhibit $0.4\mathrm{nm}\le \sigma \le 7.3\mathrm{nm}$. (d) Piece of unpassivated bare wafer from a semiconductor DBR without $n$-type and $p$-type layers. Different sample locations exhibited surface roughness in the range $0.2\mathrm{nm}\le \sigma \le 0.9\mathrm{nm}$.

Figure 7

Band structure and Franz-Keldysh effect. (a) Simulation of the conduction and valence bands in the $n$-$i$-$p$ diode (nextnanomat) at $4.2$ K. The surface is modeled via a Schottky barrier of $E_g/2=0.76$ eV reflecting the midgap Fermi-level pinning at the $\mathrm{Ga}\mathrm{As}$ surface [24]. The effect of surface passivation is to eliminate the electric field at the capping layer. (b) Schematic of the Franz-Keldysh effect [14, 15]. An electric field applied to a semiconductor allows both electrons and holes to tunnel into the forbidden energy, leading to below-gap absorption processes. (c) Room-temperature Franz-Keldysh absorption coefficients for different electric fields within a $p$-$i$-$n$ double heterostructure (IMG 2020 IEEE. Reprinted, with permission, from Ref. [18]). The solid lines correspond to the calculated absorption coefficients according to Refs. [16, 17] [Eqs. (2)–(6)].

Figure 8

Measured $Q$ factors and cavity transmittance of a purely dielectric microcavity. A dielectric top mirror (${\lambda }_C=973\mathrm{nm}$) paired with a dielectric bottom mirror (shifted to ${\lambda }_C=976\mathrm{nm}$, nominally the same coating) at $300$ K. The cavity transmittance is measured by our relating the transmitted power at the cavity resonance to the laser power before the objective lens multiplied by a fitted in-coupling efficiency of 59%. The solid black line (dashed red line) corresponds to the calculated $Q$ factor (cavity transmittance) with our taking into account material extinction coefficients $k_{{\mathrm{Si}\mathrm{O}}_2}=4\times {10}^{-7}$ and $k_{{\mathrm{Ta}}_2{\mathrm{O}}_5}=4.5\times {10}^{-7}$ [39]. Additionally, an interface roughness of $\sigma =0.25\mathrm{nm}$ above each of the five-last-grown ${\mathrm{Ta}}_2{\mathrm{O}}_5$ layers and $k=4k_{{\mathrm{Ta}}_2{\mathrm{O}}_5}$ in the last-grown ${\mathrm{Ta}}_2{\mathrm{O}}_5$ layer are introduced heuristically to fit the experimental data.