Basics
Measurements of contact potential differences and external voltage drop profiles.
As it was already noted, there are some deviations in measured surface voltage drops from actual voltage drop. The whole voltage drop between n- and p- sides of the structures is more than two times lower, than the actual drop. At higher biases (curve 1200 mV) the voltage appears to drop also on the well conductive emitters. As the bias grows, the SKM detects an increasing positive potential on the grounded n-substrate. All these effects can be explained taking into account the contribution of the capacitance of the probe sides into the SKM signal. To illustrate, let's we have absolutely flat probe (e.g. cantilever without a pyramidal tip). Then, the potentials measured on n- and p- sides of the structure would be almost equal to each other. The ideal situation (the measured by SKM CPD profile coincides with the actual surface potential profile) can be only realized when the contribution of the very end of the tip to the whole probe - sample capacitance is overwhelming. In reality the contribution of the different parts of the probe into the whole capacitance are comparable, and one needs to account for all those additional capacitance using a convolution procedure. However, the convolution procedure will hardly reveal reliably some additional features in the surface voltage drop profiles, since it will just improve spatial resolution and increase the amplitude of the features in the measured signal. Therefore we consider the approach to analyze the measured surface voltage drop as completely substantiated.
In the scan description, it was also assumed, that the bulk potential variations in semiconductor are traced by the surface potentials. Indeed, the local values of surface and bulk potentials of the semiconductor are rigidly bound with each other through the magnitude of the subsurface barrier. Our assumption means that the profile of the subsurface barrier across the semiconductor structure is independent on the applied bias distribution. It can be considered as a first approximation, whose effectiveness is confirmed not only by the presented above results, but also by the following arguments.
The magnitude of the subsurface barrier measured in air for GaAs-based materials is ФB ~ 1V. This barrier is determined by the charge trapped on the surface states, which must be equilibrated (screened) by the opposite charge of impurities in the depletion region of the semiconductor. For impurity concentrations in the range of 1-5x1018 cm-3 typical for highly doped conductive layers of a laser diode, the depth of the depletion region or the length in which the surface charges are screened is l~10-6 cm. The electric field in the subsurface region of a highly doped semiconductor is ESФB/l~108 Vm-1=106 Vcm-1, and the corresponding density of the surface charge is
sSS~e0x ES~10-2 Cm-2=10-6 Ccm-2. At the same time, between two conductive (n- and p-doped layers) parts of the laser diode, separated by the isolating (undoped) waveguide region of width L~ 10-4 cm, there exists a similar potential difference Ф ~ 1V. Due to the electric field in this region, the additional density of charge may be induced on the surfaces of the conductive layers of the diode, sA~e0xФ/l~10-8Cxcm-2. According to the estimation sA<< sSS we can conclude that, at least in the highly doped layers the subsurface barrier remains constant in the range of biases of a few volts. A more precise approach, extending beyond this approximation, is the object of further work. The proximity of the AFM tip to the semiconductor surface may influence the value of the subsurface barrier, although in air this effect seems not to be dominant for GaAs-based semiconductors having an extremely high density of the surface states. The subsurface barrier may also be changed in the light emitting structure due to the surface photo-voltage effect, or by a sizable variation of the screening length of the semi-insulating waveguide layer under injection of non-equilibrium carriers.
References
1. H.O. Jacobs, H. F. Knapp, A. Stemmer, Review of Scientific Instruments, March 1999, Volume 70, Number 3, 1756-1760, "Practical aspects of Kelvin probe force microscopy".
2. F. Robin, H. Jacobs, O. Homan, A. Stemmer, and W. Bachtold, Applied Physics Letters, May 15, 2000,Volume 76, Issue 20, pp. 2907-2909, "Investigation of the cleaved surface of a p-i-n laser using Kelvin probe force microscopy and two-dimensional physical simulations".
3. С.М. Зи, Физика полупроводниковых приборов, Москва, "Энергия", 654 стр. (1973)
