High speed (dynamic) issues within VCSELs

Pertinent to the integration of VCSELs into OEICs is the issue of how fast, and with what characteristics, the laser might respond to some applied modulation. Ideally the device output characteristics, under high applied modulation rates, should remain highly stable.

Injection current modulation of VCSELs results, as with in-plane lasers (IPLs), in a time dependent shift of the emission wavelength. This effect, commonly referred to as chirp, is due to changes in the refractive indices of the laser active layers caused by the rapidly varying carrier

concentrations. These index changes are, for frequencies greater then IMHz, predominantly caused by band-filling and plasma effects.

The large carrier densities attained within the active layers of lasers (~10^*cm‘^ around threshold) give rise to band filling effects [Faist et al. ‘89] which change the active material bandgaps [Chen et al. ‘93]. This alters (reduces) the real refractive indices of the active layers (~nGaAs~3.52) by as much as 1%, near threshold. In this way nacdve => nactivc - -0.03, when the injection level is changed by ~lxlO*®cm‘^. Of course the gain above threshold is clamped. The current contributing to gain therefore saturates and additional injected current, in the ideal case, contributes to increasing the lasers power output. Any refractive index changes due to carrier injection effects upon the QW band structure are thus greatly reduced above threshold. Importantly, this effect is dependent upon the structure of the active layers, it is marginally greater for QW active layers.

Under these high carrier injection regimes the plasma effect also becomes important [Hunsperger ‘91]. It is attributed to the interaction of free carriers with the optical field and may alter the refractive index by -5x10'^. Magnitudes of the refractive index change (Anpiasma) may be calculated, at a wavelength X, from equation 5.3.1a. Here % is the refractive index of the unpumped active material (no injected carriers), N is the injection level, q is the electron charge, Eo is the free space permitivity and nv represents the reduced electron-hole (m^-mh) effective mass (equation 5.3.1b). The plasma effect is relatively independent of the active layer structure.

An,,»™ = “ 2 n„etm , ....

m , = (5.3.1b)

Together, during current modulation above threshold, the band-filling and plasma effects result in changes to the active layer refractive indices of order 10'^. This corresponds to shifting the lasing wavelength by a few angstroms (more below threshold, ~nm).

One advantage of VCSELs over (simple) in-plane lasers is that the carrier injection induced changes in refractive index are not large enough to cause the laser to hop between longitudinal modes. This is because of the extremely short optical cavity, which results in a large longitudinal mode separation (see chapter 2). The inability of VCSELs to hop between modes limits the wavelength shift, due to chirp (or injection tuning for that matter), to that due to changes in the optical length of the cavity. Mode stability is maintained, as would be desirable in most communications applications. Maximum dynamic shifts in wavelength of 0.7Â have been recorded for InGaAs/GaAs based VCSELs (980nm emission) operating at frequencies between

500MHz-! GHz [Mukaihara et al. ‘94], at injection levels of 1/1* =1.1. These values suggest that the mechanisms quoted above are indeed the main contributors to the wavelength shift.

The small dimensions of VCSELs result in a number of other improvements when high speed modulation, primarily of the laser output amplitude, is considered. Firstly, and perhaps most obviously, the device dimensions (which are generally of order 1 0x l0x l0|jm) may be chosen to minimise capacitance. This lowers the resistance/capacitance (RC) time constant of the laser. The capacitance, C, for such a device may be approximated (assuming A » d) by equation 5.3.2. Here A is the device area, Eq is the free space permitivity (8.85xlO'*^Fm *), £r and d are the relative permitivity and thickness of the intrinsic (cavity) region respectively. We may approximate the relative permitivity of the cavity, Er, as the square of the (real) refractive index of GaAs (nGaAs~3.6) which forms the major contribution to the cavity. Assuming a device diameter of 1 0pm and an active layer of thickness 1pm the capacitance is then found to be of order 1x10*'* Farads.

C = (5.3.2)

The corresponding series resistance R, which is due primarily to the DBRs, may be reduced through the use of graded heterointerfaces, as discussed in chapter 3, or intracavity contacts. Resistances of order 100 Ohms are obtainable for air post devices of diameter 10pm, however the DBRs are still regarded as the major parasitic contribution to the laser CW and high frequency characteristics.

Choosing R to be 100 Ohms then gives an RC value of IxlO ’^ s. This value falls below the parasitics introduced by the device contacts and drive circuitry which will limit the device modulation to frequencies of order 100 GHz. In practise these modulation rates are further limited by physical processes relating to carrier and photon transport and interaction mechanisms. These effects, which impose the ultimate limit upon the device modulation, are highly dependent upon the laser structure and upon the method chosen to achieve modulation.

In order to gain further insight into the high frequency response of a current modulated VCSEL we may study (theoretically) the small signal response of the device. We will use data derived from the models developed within chapter 2. This analysis should highlight the main mechanisms contributing to the high speed response of the laser, neglecting the RC parasitics discussed above.

A laser’s dynamical response is governed by two rate equations, these dictate the interdependence of the carrier and photon densities within the laser cavity. The basic set of rate equations are given below as equations 5.3.3 and 5.3.4 [Lau, chapter 5, in Zory ‘93].

dN

J

N