The RF power output can be calculated from the following expression:
PRF = (½)(VRF)2|Gp|Aj,
(14)
where V RF is the amplitude of fundamental component of the RF voltage. The L-S DC to RF conversion efficiency of IMPATT diode is given by
(15)
where P DC = J 0 V B A j is the input DC power and J 0 is the DC bias current density.
The widths of the n- and p-epitaxial layers (W n, W p), corresponding doping concentrations (N D, N A), and bias current density parameter (J 0) of DDR IMPATTs based on 〈111〉, 〈100〉, and 〈110〉 oriented GaAs are chosen appropriately subject to the optimum performance of the device at different mm-wave frequencies (f d) by using the transit time formula by Sze and Ryder [25] and NSVE L-S simulation method [15–20]. The doping concentrations of n +- and p +-layers (N n+ and N p+) are taken to be much higher (~1025 m−3) as compared to those of n- and p-layers (N D and N A). Structural and doping parameters of the devices are given in Table 1. Effective junction diameter (D j) is scaled down from 55 μm to 20 μm as the frequency of operation increases from 35 GHz to 220 GHz through a thorough steady-state thermal analysis for continuous-wave (CW) mode of operation, considering proper heat sinking aspects which is sufficient to avoid the thermal runway and burn out of the device [19] and corresponding D j values are given in Table 1.
Structural, doping, and other parameters.
| Design parameters | Design frequency, fd (GHz) | |||
|---|---|---|---|---|
| 35 | 94 | 140 | 220 | |
| W n (μm) | 0.780 | 0.350 | 0.225 | 0.145 |
| W p (μm) | 0.800 | 0.350 | 0.225 | 0.145 |
| N D (×1023 m−3) | 0.420 | 1.500 | 3.500 | 7.500 |
| N A (×1023 m−3) | 0.400 | 1.500 | 3.400 | 7.500 |
| N n+, N p+ (×1025 m−3) | 1.000 | 1.000 | 1.000 | 1.000 |
| Dj (μm) | 55.000 | 35.000 | 25.000 | 20.000 |
The electron (a n, b n) and hole (a p, b p) ionization coefficients in GaAs for different crystal orientations measured by Pearsall et al. [13] for the electric field range of 3.0 × 107 to 6.6 × 107 V m−1 are given in Table 2. The electric field dependence of α n and α p can be represented by the empirical relation [26] given by
(16)
The values of the constants m n and m p in the above equations are also given in Table 2.
Electron and hole ionization rate constants for 〈111〉, 〈100〉, and 〈110〉 oriented GaAs [13].
| Carrier | a n,p (×107 m−1), b n,p (×107 V m−1) and m n,p | Crystal orientation | ||
| 〈111〉 | 〈100〉 | 〈110〉 | ||
| Electrons | a n | 0.776 | 0.912 | 219.000 |
| b n | 4.450 | 4.770 | 29.500 | |
| m n | 6.910 | 3.480 | 1.000 | |
| Holes | a p | 63.100 | 34.700 | 34.700 |
| b p | 23.100 | 21.800 | 22.700 | |
| m p | 1.000 | 1.000 | 1.000 |
The realistic electric field dependence of drift velocities (v n,p) of charge carriers and other material parameters such as bandgap (E g), intrinsic carrier concentration (n i), effective density of states of conduction and valance bands (N c,v), effective mass of electrons in conduction band (m n *) and that of holes in valance band (m p *), density of state effective mass of charge carriers (m d *), electron and hole mobilities (μ n,p), and diffusion lengths (L n,p) of 〈111〉, 〈100〉, and 〈110〉 oriented GaAs (at realistic junction temperature of 500 K) are taken from the published experimental reports [27].
The static or DC characteristics of the devices under consideration are obtained from the simulation by keeping the voltage modulation factor m x = 0. The important DC parameters such as peak electric field (ξP), breakdown voltage (V B), avalanche zone voltage drop (V A), ratio of drift region voltage drop to break down voltage (V D/V B; where V D = V B − V A), avalanche zone width (x A), and ratio of avalanche zone width to total depletion layer width (x A/W; where W = W n + W p) of DDR IMPATTs based on 〈111〉, 〈100〉, and 〈110〉 oriented GaAs designed to operate at different mm-wave frequencies are obtained from the DC simulation and given in Table 3.
Static parameters of 35, 94, 140, and 220 GHz DDR IMPATTs based on 〈111〉, 〈100〉, and 〈110〉 oriented GaAs.
| fd (GHz) | Crystal orientation | J0 (×108 A m−2) | ξP (×107 V m−1) | VB (V) | VA (V) | VD/VB (%) | xA (μm) | xA/W (%) |
|---|---|---|---|---|---|---|---|---|
| 35 | 〈111〉 | 0.85 | 4.6622 | 45.69 | 21.14 | 53.73 | 0.536 | 33.92 |
| 〈100〉 | 0.85 | 4.7048 | 46.51 | 25.35 | 45.49 | 0.648 | 41.01 | |
| 〈110〉 | 0.85 | 4.7423 | 47.37 | 26.41 | 44.25 | 0.670 | 42.41 | |
| 94 | 〈111〉 | 5.60 | 5.4736 | 22.26 | 11.48 | 48.45 | 0.254 | 36.29 |
| 〈100〉 | 5.60 | 5.7099 | 23.45 | 14.20 | 39.43 | 0.312 | 44.57 | |
| 〈110〉 | 5.60 | 5.5628 | 22.82 | 13.16 | 42.35 | 0.292 | 41.71 | |
| 140 | 〈111〉 | 10.20 | 6.4306 | 12.71 | 7.57 | 40.44 | 0.146 | 32.44 |
| 〈100〉 | 10.20 | 6.8431 | 14.24 | 9.22 | 35.27 | 0.172 | 38.22 | |
| 〈110〉 | 10.20 | 6.3306 | 12.28 | 7.26 | 43.32 | 0.140 | 31.11 | |
| 220 | 〈111〉 | 22.45 | 7.5306 | 8.38 | 5.61 | 33.03 | 0.094 | 32.41 |
| 〈100〉 | 22.45 | 8.1556 | 9.63 | 6.89 | 28.45 | 0.110 | 37.93 | |
| 〈110〉 | 22.45 | 7.0806 | 8.16 | 4.76 | 39.43 | 0.082 | 28.27 |
The static electric field profiles of the above-mentioned devices are shown in Figures 4(a)–4(d). It is observed from Figures 4(a)–4(d) and Table 3 that peak electric field (ξ P) of the 35 GHz DDR diodes based on 〈110〉 oriented GaAs is highest among other diodes under consideration. However the same parameter of DDR diodes based on 〈100〉 oriented GaAs exceeds its other counterparts for higher mm-wave frequencies. The same nature is observed in breakdown voltage (V B); that is, the breakdown voltage is highest for the DDR diodes based of 〈100〉 oriented GaAs operating at 94, 140, and 220 GHz while at 35 GHz, the same is highest in 〈110〉 oriented GaAs based DDR diode. It is interesting to observe from Table 3 that the DDR diodes based on 〈111〉 oriented GaAs have the narrowest avalanche zone width (x A) and consequently minimum avalanche zone voltage drop (V A) up to 94 GHz, whereas, for the higher mm-wave frequencies, 〈110〉 oriented GaAs based DDR diodes possess the narrowest x A and consequently minimum V A.