A model for the calculation of the absorption and emission spectra for GaAs at carrier concentrations in excess of 1×1018 cm−3 is described. This model utilizes a Gaussian fit to Halperin‐Lax band tails for the concentration‐dependent density of states and also includes an energy‐dependent matrix element. The calculated absorption and emission spectra are compared to previous experimental results. All results are for 297 K. For p‐type GaAs, the agreement is very good. The concentration dependence of the effective energy gap is obtained and can be expressed as Eg (eV) =1.424−1.6×10−8 [p (cm−3)]1/3. The concentration‐dependent thermal equilibrium electron‐hole density product n0p0 and the radiative lifetime τr are calculated for p‐type GaAs. The value of n0p0 increases from the low‐concentration value of 3.2×1012 cm−6 to 1.2×1013 cm−6 at p=1.6×1019 cm−3. This value of n0p0, together with the thermal generation rate obtained from the experimental absorption coefficient, gives τr as 0.37 nsec at p=1.6×1019 cm−3.

Concentration‐dependent absorption and spontaneous emission of heavily doped GaAs

Theoretical and experimental studies of the electron mobility and the free‐carrier absorption of n‐type InP were carried out in the temperature range 77–300 °K. All major scattering processes and screening effects were taken into consideration. It was found that the experimental dependence of electron mobility and free‐carrier absorption on temperature and/or on carrier concentration can be consistently explained only when the effect of compensation is quantitatively taken into account. Convenient procedures are presented for the determination of the compensation ratio from the values of electron mobility and from the free‐carrier absorption coefficient. The high contribution of optical‐phonon scattering in InP limits the applicability of the free‐carrier absorption approach to electron concentration n≳1017 cm−3. Electron mobility, however, can be reliably employed for the determination of the compensation ratio for n≳1017 cm−3 at 300 °K and n≳1015 cm−3 at 77 °K.

Electron mobility and free‐carrier absorption in InP; determination of the compensation ratio

Nano-scale properties of defects in compound semiconductor surfaces

n‐type silicon‐doped epitaxial layers of gallium arsenide grown by molecular‐beam epitaxy (MBE) or metal‐organo chemical vapor deposition (MOCVD) have been investigated by measurements of the Hall effect and the strengths of the localized vibrational modes (LVM) of silicon impurities using both Fourier transform absorption spectroscopy and Raman scattering at an excitation energy of 3 eV close to the E1 band gap. Lines from Si(Ga) donors, Si(As) acceptors, Si(Ga)‐Si(As) pairs, and Si‐X, a complex of silicon with a native defect, were detected and correlated for the two techniques. The maximum carrier concentration [n] found for samples grown under standard conditions was 5.5×1018 cm−3. At higher doping levels Si‐X becomes dominant and acts as an acceptor, so reducing [n]. An integrated absorption of 1 cm−2 in the Si(Ga) LVM line corresponds to 5.0±4×1016 atoms cm−3: a similar calibration applies to the Si(As) line, but for Si‐X, an absorption of 1 cm−2 corresponds to only 2.7±1.0×1016 defects cm−3. Possib...

The calibration of the strength of the localized vibrational modes of silicon impurities in epitaxial GaAs revealed by infrared absorption and Raman scattering

A detailed analysis of the role of charged native point defects in controlling the solubility of electrically active dopants in gallium arsenide is presented. The key roles of (a) positively charged arsenic vacancies (VAs+) in determining the doping range over which the solubility curve is linear and (b) multiply negative charged gallium vacancies (VGam−) determining annealing and diffusion behavior in n+ material are demonstrated. An equilibrium thermodynamic model based on these concepts is shown to accurately describe the doping behavior of Te, Zn, Sn, Ge, Si, and C and the formation and annealing of the deep level denoted EL2 (assumed to be the arsenic antisite defect AsGa) in melt- and solution-grown crystals. The model provides a much more comprehensive and accurate description of dopant solubility than the widely cited Schottky barrier model of bulk nonequilibrium dopant incorporation. It is unambiguously shown that partial autocompensation of donor dopants by the donor–gallium vacancy acceptor com...

A comprehensive thermodynamic analysis of native point defect and dopant solubilities in gallium arsenide

Previously reported annealing effects on the carrier density and free‐carrier absorption are correlated with photoluminescence and localized vibrational mode infrared absorption measurements of annealed samples of heavily doped GaAs: Si. Annealing in the range 400≤TA≤750 °C produces the following qualitative changes: (i) a major reduction in the free‐carrier concentration ne, (ii) an increase in the carrier absorption cross section, (iii) a reduction of the SiGa localized mode absorption band, and (iv) the introduction of a new photoluminescence band at 0.98 eV. A defect model is proposed which is consistent with the observed changes. There is a major reduction in [SiGa], the Si donor concentration, which is a function of the anneal temperature between 400 and 750 °C. The reduction is probably through the formation of (SiGa − VGa) pairs. There is little change if any in [SiAs] the Si acceptor concentration. When TA = 400°C the ne = [SiGa] −[SiAs]. When TA = 600 and 750°C, a new acceptor is formed having c...

Si‐defect concentrations in heavily Si‐doped GaAs: Changes induced by annealing

Silicon‐site distribution in GaAs under the influence of a second dopant was studied by measuring the Si localized vibrational modes and the carrier concentrations of a series of samples. Each sample had the same total Si concentration, [Si], but with different concentrations of a second dopant. Semiquantitative results give a relationship between [SiGa]/ [SiAs] and the concentration of the second dopant which is compared with a calculation based on the thermodynamically predicted Fermi‐level effect as formulated by Longini and Greene.

Determination of Fermi‐level effect on Si‐site distribution in GaAs : Si

Isothermal and isochronal annealing measurements were performed on heavily Si‐doped GaAs. Infrared reflectivity measurements were used to determine the free‐carrier concentration after each annealing stage. A factor of [inverted lazy s]5 decrease in free‐carrier concentration was observed as a result of annealing at temperatures as low as 400°C. This annealing effect can be important when fabricating devices using GaAs: Si. Possible explanations of this effect are discussed.

Effects of annealing on the carrier concentration of heavily Si-doped GaAs

Backscattering and channeling‐effect measurements with 2.5‐MeV helium ions and measurements of the position of the infrared reflectivity plasma edge were used to investigate the absolute concentration of Te, the percentage of Te on lattice sites, and the free‐carrier concentration in GaAs doped with [Te] ≈ 1019 cm−3 as a function of anneal. A 700°C anneal produced a reduction in carrier concentration [ne] by 20±2% (from the preanneal value of 5×1018 cm−3), and in the fraction of Te atoms on lattice sites. After an anneal at 1100°C, followed by quenching, [ne] rose to 7×1018 cm−3 while the Te distribution reverted to the original highly substitutional form. Throughout the experiment no measurable change from [Te]=9×1018 cm−3 was found. The correlations are discussed and related to existing models for anneal‐dependent complexes.

Investigation of Te-Doped GaAs Annealing Effects by Optical- and Channeling-Effect Measurements

The infrared plasma reflectivity and free carrier absorption of heavily Si‐doped n‐type are examined and the results show that shallow reflectivity minima and increased free carrier absorption cross sections are a consequence of high levels of compensation in the samples. The frequency dependence of the extinction coefficient in compensated as well as uncompensated samples is found to be different from that described by the Drude‐Zener theory in the frequency region near or higher than the plasma‐edge frequency. Based on the experimentally observed frequency dependence of , correction factors are evaluated in determining carrier concentration from the frequency of the infrared plasma reflectivity minimum when the reflectivity minimum is shallow. The correction factors are applied to the measured results of a series of samples and the resulting carrier concentrations are compared with those obtained from Hall effect measurements.

W. G. Spitzer

Papers

Si‐defect concentrations in heavily Si‐doped GaAs: Changes induced by annealing

Determination of Fermi‐level effect on Si‐site distribution in GaAs : Si

Effects of annealing on the carrier concentration of heavily Si-doped GaAs

Investigation of Te-Doped GaAs Annealing Effects by Optical- and Channeling-Effect Measurements

Infrared Reflectivity and Free Carrier Absorption of Si‐Doped, N‐Type GaAs