Integrated optics and new wave phenomena in optical waveguides

This paper proposes and examines three different plots for the determination of the saturation current, the ideality factor, and the series resistance of Schottky diodes and solar cells from the measurement of a single current (I)/voltage(V) curve. All three plots utilize the small signal conductance and avoid the traditional Norde plot completely. A test reveals that the series resistance and the barrier height of a test diode can be determined with an accuracy of better than 1%. Finally it is shown that a numerical agreement between measured and fittedI/V curves is generally insufficient to prove the physical validity of current transport models.

Schottky barrier and pn-junction I/V plots — Small signal evaluation

An important function in semiconductor‐device analysis and transport theory is the widely tabulated Fermi‐Dirac integral, F (η) =2π−1/2F∞0[exp(x−η)+1]−1f dx, f=x1/2, which relates, for example, the Fermi energy ηkT to the carrier density N=FN0 in a parabolic semiconductor band (N0=effective density of states). We show that the classical or Boltzmann approximation to this integral (η=lnF, η≲−2) is extended to cover the Fermi‐energy range of semiconductor lasers (η≲+2) by the expression η=lnF+2−3/2F and by other simple differentiable approximations applicable to higher degeneracy (η≲7) or to nonparabolic bands (f≠x1/2).

Analytic approximations for the Fermi energy of an ideal Fermi gas

We show that the 2kT current in double‐heterostructure AlxGa1−xAs p‐n junctions is primarily due to surface recombination at the junction perimeter. The rate of surface recombination is evaluated by means of two luminescence experiments. Both experiments provide evidence that the rate of surface recombination increases with bias as exp(eV/2kT) and has the correct magnitude to account for the measured I‐V curves. It is shown theoretically that recombination at a depleted surface is proportional to exp(eV/2kT) at high bias. The 2kT behavior is a consequence of the nearly constant ratio of electron and hole densities at the surface. The nearly constant ratio is needed to maintain equality of surface and surface depletion layer charge. p‐n junction perimeters of cleaved, etched, and proton‐bombarded interfaces are evaluated and found to have similar rates of nonradiative recombination with the rate of surface recombination given by R=s0(np)1/2, where s0 is approximately 4×105 cm/sec.

The effect of surface recombination on current in AlxGa1−xAs heterojunctions

Growth of III–V semiconductors by molecular beam epitaxy and their properties

Measurements of the electrical characteristics of double-heterostructure (DH) stripe-geometry AlGaAs junction lasers are reported. We show that the electrical characteristics of these lasers are adequately represented by a resistor in series with a p-n junction characterized by a classical diode equation, I = I_{s} [\exp (q V_{j}/\etakT) - 1] . Devices have been measured with almost ideal junction characteristics with both the saturation current, I s , and the exponential parameter, η, constant, while in other diodes both η and I s exhibit a strong current dependence. Measurement of the first derivative dV/dI and the product IdV/dI is shown to be an especially useful technique for electrical characterization, yielding accurate and direct determination of the series resistance, the exponential junction parameter, and the laser threshold current. The observation of lasing threshold from an electrical measurement, instead of from the more usual optical measurement, is discussed in terms of the saturation behavior of the junction voltage at and above threshold.

Derivative measurements of the current-voltage characteristics of double-heterostructure injection lasers

GaAs-Al x Ga 1-x As double-heterostructure (DH) lasers with Si-doped n-type active layers have been prepared by molecular-beam epitaxy (MBE) and the laser properties evaluated. With 0.2-μm-thick active layers and 300-μm cavity lengths, typical room-temperature threshold current densities J th of 5.0 \times 10^{3} A/cm2and best values of 2.5 \times 10^{3} A/cm2have been obtained. Stripe-geometry devices were run CW up to 9°C. Photoluminescence (PL) studies of single layers grown with the donors Si, Ge, and Sn show that the luminescent intensity for MBE n-type layers depends on the substrate temperature during growth. The PL intensity for Sn-doped MBE layers was greater than for high-quality Sn-doped liquid-phase-epitaxial layers.

P. Barnes

Papers

Derivative measurements of the current-voltage characteristics of double-heterostructure injection lasers

Application of molecular-beam epitaxial layers to heterostructure lasers