**5. Conclusions**

230 Numerical Simulation – From Theory to Industry

waves.

GHz. When a small microwave signal is applied to the input antenna, the excitation of space charge waves in the 2D electron gas takes place. The space charge waves are subject to amplification, due to the negative differential conductivity. The stable implicit difference scheme is used. The following parameters have been chosen: 2D electron concentration in the film is *n*0 = 5x1014 cm-2, the initial uniform drift velocity of electrons is *v0 ≈ 2*x107 cm/s (*E0 =1*5 – 20 kV/cm), the length of the film is *Lz =* 0.1 mm, the thickness of the film is *2h* = 0.1 - 1 μm. The typical output spectrum of the electromagnetic signal is given in Fig. 4. The input carrier frequency is *f =* 12 GHz. The amplitude of the input electric microwave signal is *Em =* 25V/cm. Although the growth rate decreases as the *rf* frequency increases, for our case an amplification of 25 dB is obtained. The maximum of the input pulse occurs at *t1 =* 2.5 ns. One can see both the amplified signal at the first harmonic of the input signal and the harmonics generations of the input signal, which is generated due to the non-linearity of space charge

**Figure 5.** The spatial distributions of the alternative part of the electric field component *E*~z of space charge wave (a); the component of electric field *E*~y (b); alternative part of the electron concentration *n*~ (c); and the component of the electron drift velocity *v*z (d). The length of the film is 0.1 mm. The

transverse width of the film along Y axis is 1 mm.

A theoretical study of two-dimensional amplification and propagation of space charge waves in n-InP films is presented. A microwave frequency conversion using the negative differential conductivity phenomenon is carried out when the harmonics of the input signal are generated. A comparison of the calculated spatial increment of instability of space charge waves in n-GaAs and n-InP films is performed. An increment in the amplification is observed in InP films at essentially higher frequencies *f* > 44 GHz than in GaAs films, which is due to its larger dynamic range. The maxi mum amplification (gain of 25 dB) is obtained at *f* = 35 GHz, using a distance between the input and output antennas of about 0.09 mm.
