4.3 Electrical simulations
4.3.2 RF simulations
The frequency and bias dependent behavior of the real and imaginary part of the Y parameters are determined. This is done by ramping the anode from -2.5V to 1.5V and imposing a RF signal with a frequency sweep from 1GHz-50GHz.
Figure 4.3 shows the Real and Imaginary part of the Y21 parameter in reverse bias at -2.5V with the fit of the equivalent circuit of Figure 3.7 without the induction element. The Real part in-creases with ω2and the Imaginary part divided by ω is constant for low frequencies but decreases at higher frequencies. These two phenomena are due to the combination of the Capacitance Cof f
and series resistance Rs in this frequency range. Equation (31) describes the admittance Y for a combination of a capacitance C and resistance Rs.
Figure 4.4 shows the Real and Imaginary part of the Y21parameter in forward bias at 0.85V with the fit of the equivalent circuit of Figure 3.7 without the induction element. It can be seen that in forward bias the injection resistance R is more dominant; the Real part is constant at low fre-quencies. However, at high frequencies the Real part increases again according to equation (31) because the depletion capacitance becomes dominant again. It can also be seen in forward bias that the fit mismatches with the simulation data at low frequencies. This is most likely due to the presence of diffusion capacitance in forward bias, therefore the Real and Imaginary part are higher than expected at low frequencies. The diffusion capacitance vanishes when the frequency is much higher than the lifetime (ωτ >> 1). Figure 4.5 shows the lifetime of the electrons over the PiN diode, in the intrinsic region the lifetime is approximately between 10−8− 10−9 s.
With this understanding of the PiN diode behavior in the simulation it can be concluded that Ron is determined with 1/Real(Y21) in forward bias around a fixed current or voltage point and Cof f is determined with Imag(Y21)/ω in reverse bias at -2.5V at low frequencies were the series resistance is not important.
Y = ω2RsC2
1 + ω2Rs2C2 + j ωC
1 + ω2R2sC2 (31)
Figure 4.3: The simulated Real (left) and Imaginary part (right) of the Y21 parameter with fre-quency at -2.5V. Including the fit of the equivalent circuit of Figure 3.7 without the induction element
Figure 4.4: The simulated Real (left) and Imaginary part (right) of the Y21 parameter with fre-quency at 0.85V. Including the fit of the equivalent circuit of Figure 3.7 without the induction element
Figure 4.5: The lifetime of the electrons in the PiN diode (left) and the eLifeTime is plotted with X at Y=5 (right).
5 Results and discussion
In this section the results of the DC and RF measurements will be shown and discussed. The results are divided in six sections. First, the general observed behavior of the PiN diode is discussed; the I-V curves in DC and the frequency and bias dependent behavior of the Real and Imaginary part of the Y parameters in RF. Secondly, the area scaling is shown. Thirdly, the effect of using parallel structures is discussed. Here the parallel structures designed by NXP are discussed and complemented with simulations of variations on these structures. Consequently, the scaling of the EPI thickness is evaluated for measurements and simulations. After this, the PPLUS and PSB diodes are compared for the DC measurements and a prediction is made for the RF measurements.
At last, the temperature scaling in DC is discussed.
5.1 Behavior of the PiN diode
Before one can investigate the most optimal diode structure, first the general behavior of the diode has to be checked. In this section, the 10x10 diode will be taken to show the I-V curves, the frequency behavior at fixed bias and the bias behavior at fixed frequency.
Figure 5.1 and 5.2 shows the I-V curves of the 10x10 diodes with anode and cathode biasing respectively. In both curves the ideal diode behavior (until 0.9V) and the influence of the series resistance can be recognized; the I-V curve deviates from the ideal exponential behavior after 0.9V.
Additionally, the most important difference between anode and cathode biasing can be observed with the substrate current. The substrate current is the difference between the anode and cathode current (Is= −[Ia+ Ic]). There is a difference between these currents because the connection to the substrate of the PiN diode represents a parasitic PN structure (Figure 3.8). The low p-doped substrate layer is grounded and the n-layer is also grounded or at a negative voltage with anode and cathode biasing respectively. The substrate current is higher with cathode biasing because the n-layer is not grounded, thus the parasitic PN structure is forward biased and more current with leak through the substrate.
As explained in section 3.2, the I-V curves can be fitted with equation (21) to obtain I0, the ideality factor n and the series resistance Rs. Figure 5.3 shows the fit through the I-V curve of the 10x10 diode with anode biasing with I0= 1.09 · 10−17A, n = 1 and Rs= 3.38Ω.
Figure 5.1: The IV curves of the 10x10 diode when anode biasing is applied with the anode current (Ia), the cathode current (Ic) and the substrate current (Is) in linear (left) and semi-logarithmic scale (right). The compliance of the set-up is 100mA, therefore the current saturates after 1.1V.
Figure 5.2: The IV curves of the 10x10 diode when cathode biasing is applied with the anode current (Ia), the cathode current (Ic) and the substrate current (Is) in linear (left) and semi-logarithmic scale (right). The compliance of the set-up is 100mA, therefore the current saturates after 1.1V.
Figure 5.3: The IV curves of the 10x10 diode fitted with the ideal diode equation and the lambertw equation, with I0= 1.09 · 10−17A, n = 1 and Rs= 3.38Ω
Figure 5.4 and 5.5 shows the real and imaginary part of the four Y parameters at 2 GHz with anode biasing. In these figures, two phenomena are notable. Firstly, it can be seen that the Y parameters are not equal. This is again due to the parasitic PN structure with the substrate.
Therefore, the Y parameter of interest in this research is the Y21parameter because this represents the PiN diode that is located between anode (port 2) and cathode (port 1). Secondly, both the Real and Imaginary part increase with the bias, as expected. However, after approximately 0.9V the Real and Imaginary part decrease again. This is due to the induction that is present and be-comes important in this region, because the depletion capacitance vanishes here when the built-in voltage is overcome. This can be confirmed with checking the frequency dependent behavior are various bias voltages, and comparing this with the proposed equivalent circuit.
Figure 5.6 and 5.7 shows the real and imaginary part of the Y21parameter with frequency in for-ward and reverse bias respectively. It can be seen that the frequency dependent behavior matches with the behavior of the equivalent circuit of Figure 3.7. However, at low frequencies in forward bias the imaginary part of the measurement is increasing, most likely this is due to the diffusion capacitance that is present at low frequencies in forward bias.
In conclusion, Roncan be determined with 1/Re(Y21) at a certain frequency and voltage or current, Cof f is determined with Imag(Y21)/ω at -2.5V at low frequencies were the induction is not dom-inant. With this approach and the understanding of the behavior of the diode, the most optimal diode can be studied upon area scaling, parallel structure, EPI thickness in the upcoming sections.
Figure 5.4: The Real part of the four Y parameters @ 2GHz in linear (left) and semi-logarithmic scale (right)
Figure 5.5: The Imaginary part of the four Y parameters @ 2GHz in linear (left) and semi-logarithmic scale (right)
Figure 5.6: The Real (left) and Imaginary part (right) of the Y21 parameter with frequency at 0.85V. Also including the fit of the equivalent circuit of Figure 3.7, this fit shows that the PiN diode in reality indeed behaves as expected from the proposed equivalent circuit
Figure 5.7: The Real (left) and Imaginary part (right) of the Y21parameter with frequency at -2.5V.
Also including the fit of the equivalent circuit of Figure 3.7, this fit shows that the PiN diode in reality indeed behaves as expected from the proposed equivalent circuit