The above work shows that microwave emission can occur at
various electric fields. The first results were for fields which | were able to cause breakdown. The results by Musha et.al. and
Bekefi et.al. occur at fields where breakdown is not present. This section deals with the theory and experimentation involved with emission below the breakdown region.
In 1972 Gornik78 reported emission from InSb at 2 & 4.2 K j for electric fields above lOOVcm-i and magnetic fields of up to
0.8 T. (Crystal characteristics : uncompensated donor concentration of 7x1Q!® cm-®, electron mobility of 7x10®
76Musha,Lindvall & Hagglund, Appl.Phys.Letts. 2 » 157 (1966)
77Bekefi,Bers & Bmek, Phys.Rev.Letts. 19 , 24 (1967)
78Gomik, Phys.Rev.Letts. 29,9 , 595 (1972)
cm 2V -!s'! and impurity concentration of 4.5x1 Q!4 cm-®.) This
was identified as emission from electrons relaxing from low conduction band landau levels to impurity levels. Maximum power levels measured were 10-® W with an external power efficiency found to be 10-®.
In 1973 Kobayashi et.al.7® repeated and furthered the work done by Gornik, though with a pulsed electric field (400 ps,15 Hz, 0-20 V), and a perpendicular magnetic field (up to 2 T). They noted that the current-voltage characteristic did not change for any value of applied electric field (though they did not specify what it would have changed from). However, for the fields applied, it was expected that the current-voltage characteristics would be
effectively linear. In connection with their experimental findings Kobayashi et.al.®® went on to measure and calculate quantities like the electron concentration in Landau levels as a function of
electric field; the electron temperature as a function of electric field; the dependence of transverse resistivity with electric field & lattice temperature; and the energies of the Landau levels as a function of magnetic field.
By 1975 Gornik®! had progressed to the development of the CR emission into tuneable far-infrared sources. Three
semiconducting materials were considered : InSb, GaAs & HgOdTe. The sources were used to measure Zeeman splitting of shallow donors in InP & GaAs to demonstrate their usefulness. The power output and wavelength dependences on magnetic field were
calculated for InSb & GaAs for samples with geometries : 5x5x0.2 mm® and uncompensated donor concentrations of 1x10!4 cm ®. The electric field required was between 3 and 10 Vcm-!, which
corresponded to an effective electron temperature of 25 K. Tyssen et.al.®® analysed the Landau emissions in InSb by Fourier spectroscopy for frequencies below and above the optical phonon frequency and deduced that LO phonon-electron coupling was causing the cyclotron frequencies to increase for a given magnetic field and also induced an increase in the line width.
79Kobayashi et.al., Phys.Rev.Letts. 30.15 , 702 (1973) 8®Kobayashi & Otsuka, J.Phys.Chem.Sol. 35. , 839 (1974) 8lGomik, Optics&Laser Tech. % , 121 (1975)
26
83Gomik et.al., IR.Phys. 12 , 109 (1976) 84McCombe et.al., Phys.Rev. M l , 253 (1976) 83Bauer et.al., Phys.Stat.Sol. 21 , 543 (1976) 86Müller et.al., Phys.Stat.Sol. 22 , 205 (1978) 87Gornik et.al., Phys.Rev.Letts. 42 , 1151 (1978) 88Müller et.al., IR.Phys. 18. , 691 (1978)
89Gornik, Proc.Conf.ed.Ryan, 329 (1978)
Gornik et.al.®®, in order to sharpen the linewidth, introduced a helium temperature Fabry-Perot interferometer. The emission from InSb was compared with that from a HCN laser. Due to the rapid decay in intensity in higher order harmonics for the CR
emission it was concluded that the emission was too divergent. An improved optical system was suggested.
McCombe et.al.®4 undertook a systematic study of quantum limit cyclotron resonance linewidths in several InSb samples and concluded that, for fields where ionised impurity scattering is the dominant relaxation mechanism, the linewidths are proportional to the square root of the ionised impurity concentration; the
linewidth exhibits a minimum in its relation with magnetic field and the linewidths and the position of their minimum value are independent of the free carrier concentration.
In 1976 the effect of background radiation on the electron population of Landau levels and the consequent effect on emission was investigated by Bauer et.al.®®. This was followed up later on in more detail by Müller et.al.®® who concluded that the effects of background radiation could account for the differences in the results obtained on emission so far.
In 1977 measurements leading to the evaluation of
electronic lifetimes for electrons in the first Landau level and impurity levels were made by Gornik et.al.®7 They concluded that the electronic lifetimes were determined by inter-electron
scattering in the first Landau level and by acoustic phonons in the impurity levels.
More work on the rise time and resolution of CR emission from InSb & GaAs was carried out by Müller et.al.®®. This
demonstrated that InSb has superior power dissipation, but GaAs has a narrower linewidth.
A summary of the work done in connection with OR emission was made by Gornik®® in 1978. Included is the relation between
electric field and effective electron temperature and the
concentration of electrons in the Landau levels for several electric field values. The latter demonstrates the effect of optical phonon scattering in preventing emission by relaxation from levels above the optical phonon energy.
®®Kadushkin, Sov.Phys.Semicon. 1 , 1549 (1972) ^Ifilaut-Blachev, Sov.Phys.Semicon. 9 , 247 (1975) ®®Fossum et.al., Phys.Rev.B 2 , 2850 (1973)
93Grisheckina & Luchina, Sov.Phys.Semlcon. 9 , 153 (1975)
94Gulyaev, Sov.Phys.Semlcon. 9 , 599 (1975)
93Vladimirov, Sov.Phys.Semlcon. 14 , 247 (1980)
96Malyutenko et.al., Sov.Phys.Semlcon. 14 , 457 (1980) 97Müller et.al, Phys.Stat.Sol(b) M , 205 (1978)
2.4.2 Experimental and Theoretical Work on CR and Microwave I Emission at Fields Above Breakdown.
After the discovery of microwave emission associated with breakdown, this property was studied in order to probe the
processes involved with breakdown. Initially work was done on determining the radiative recombination lifetime at
breakdow n90,9i,92 Experimentation on the recombination radiation led to the conclusion that the orientation of an applied magnetic field had no effect on the emitted radiation, though it was
observed to affect the threshold field for breakdown (E^h « 40 - 250 Vcm-! for B « 0.8 - 1.0 T). It was noted that the electric field at the onset of radiation was always less than the threshold
field®®. The effect of optical phonon scattering on the non- linearity involved with breakdown was considered®^. The
possibilities of instabilities in the electron-hole plasma causing or being associated with the non-linearities was also
investigated®3. The diffusion length for the recombination
radiation in this regime was found to be about 50 to 80 pm®®. The effect of reabsorption is significant and was also dealt with by Müller et.al®7.
Spontaneous emissions at frequencies up to the sub-mm wavelength region were predicted for electric fields great enough to induce intense impact ionisation of the valence band (330 GHz
28
at E « 600 Vcm"!)®8. Further work done on the breakdown region provided a calculated l-V characteristic for n-lnSb at 77 K and more evidence of the magnetic dependence of the breakdown electric field®®. The carrier concentration of the breakdown plasma has been measured. For a crystal with an uncompensated donor concentration of « 1 x 10^4 cm ® the carrier concentration after breakdown was « 7 x 10“*® cm ® (dependent on the threshold field and hence the magnetic field)!®®.
2.5 Experimental and Theoretical Work on The Electrical