Photoreflectance (PR) & Contactless Electroreflectance (CER) Lab

Photoreflectance (PR) is an optical modulation spectroscopy technique where an above-bandgap chopped laser pump beam periodically injects electron-hole pairs, which drift to screen and modulate the sample's built-in surface or interface electric field. Simultaneously, a monochromatic probe beam reflects off the wafer. By detecting the normalized differential reflectance \(\Delta R / R\) with a phase-sensitive lock-in amplifier referenced to the chopper frequency, PR suppresses uninteresting broad background reflection by four orders of magnitude. According to Aspnes' low-field theory, the resulting differential signal is proportional to the third derivative of the unperturbed complex dielectric function with respect to photon energy, yielding exceptionally sharp, localized critical-point resonances.

In intermediate-to-high electric fields (such as space-charge depletion layers or polar heterojunctions), carriers can quantum mechanically tunnel into the forbidden bandgap via the Franz-Keldysh effect. When photon energy \(E\) exceeds the fundamental bandgap \(E_g\), constructive and destructive quantum interference of the electron and hole wavefunctions produces periodic ripples in the differential reflectance known as Franz-Keldysh Oscillations (FKOs). The energy positions \(E_m\) of the oscillation extrema scale as \((4/3\pi)(E_m - E_g)^{3/2} = (m - 1/2)\hbar\Theta\), where \(\hbar\Theta = (e^2\hbar^2F^2 / (2\mu))^{1/3}\) is the electro-optic energy parameter. By plotting \((4/3\pi)(E_m - E_g)^{3/2}\) against the extremum index \(m\), the slope directly yields \(\hbar\Theta\), enabling direct, non-destructive extraction of the internal built-in electric field \(F_{\text{int}}\).

In GaN/AlGaN RF power high-electron-mobility transistors (HEMTs), huge spontaneous and piezoelectric polarization gradients create an intense built-in electric field (typically 200 to 500 kV/cm) across the AlGaN barrier layer. By Gauss's interface boundary condition, the discontinuity in electric displacement \(D\) is directly terminated by the two-dimensional electron gas (2DEG) sheet charge: \(D = \epsilon_0 \epsilon_r F_{\text{int}} = e N_s\). Because PR extracts \(F_{\text{int}}\) with sub-1% precision from the FKO period without requiring fabricated metal gates, ohmic contacts, or Hall bars, it provides an instantaneous, wafer-scale, 100% non-contact determination of the 2DEG channel density \(N_s\).

Photoreflectance (PR) modulates the sample's built-in electric field optically using photo-injected free carriers from a chopped laser beam, making it completely contactless and requiring only an optical window. However, in certain low-lifetime or highly luminescent materials, the pump laser can induce intense photoluminescence (PL) that enters the detector. Contactless Electroreflectance (CER) overcomes this limitation by placing the sample between two transparent capacitor electrodes separated by a thin air/vacuum gap (typically 0.1 to 0.5 mm) and applying an AC voltage (0.5 to 2 kV at 1 kHz). Both PR and CER generate identical third-derivative modulation lineshapes and FKOs, offering complementary non-destructive metrology for both luminescent and non-luminescent wafers.