1. Introduction

Linear voltage regulators are key devices in many spacecraft and widely used in space systems because of their cost, low power consumption and high reliability. For the device, radiation exposure in space is unavoidable. This leads to the parameter degradation of the device. So the effects of ionizing radiation on the linear voltage regulators have received a great deal of attention. Many studies regarding performance degradation with total dose have been reported for linear voltage regulators^{[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, and the mechanisms of degradation of bipolar linear voltage regulators are comprehensively analyzed^[5]. However, most of the radiation studies on the linear voltage regulator reported so far have mainly focused on experimental results on radiation-induced changes in the electrical characteristics. To the best of the authors' knowledge, very little data regarding 1/$f$ noise performance degradation have been reported for the bipolar linear voltage regulator. In this paper, the total dose l/$f$ noise performance of the adjustable 3-terminal positive voltage regulator LM117 radiated at a dose rate of 0.1 Gy(Si)/s is presented. It is suggested that the band-gap reference subcircuit is the critical component which leads to the 1$/f$ noise degradation of the LM117, which can explain well the experimental results.

2. Theory

2.1 Output voltage

The LM117 is an adjustable 3-terminal positive voltage regulator. Figure 1 shows a circuit diagram of the LM117. The basic operation of the LM117 is described in Reference ^[11]. Reference ^[5] has identified that the degradation of the output voltage of the LM117 is decided by the degradation of the band-gap reference. The band-gap reference, shown in Figure 2, is composed of two vertical NPN bipolar junction transistors (Q17 and Q19), two lateral PNP bipolar junction transistors (Q16 and Q18), and two resistors ($R_{1}$ and $R_{2})$^[5].

The reference voltage, $V_{\rm REF}$, is set by:

$$\begin{equation} \label{eq1} V_{\rm REF} =V_{\rm BE17} +V_{\rm A}, \end{equation}$$

(1)

where $V_{\rm BE17}$ is the voltage drop across the base-emitter junction of transistor Q17, and $V_{\rm A}$ is the voltage drop across $R_{2}$. The voltage, $V_{\rm A}$, is set by the emitter currents $I_{\rm o}$ of Q19 and the emitter currents $I_{\rm o}+\Delta I_{\rm o}$ of Q17,

$$\begin{equation} \label{eq2} V_{\rm A} =R_2 (2I_{\rm o} +\Delta I_{\rm o}). \end{equation}$$

(2)

The current $\Delta I_{\rm o}$ is zero when the base currents in all four band-gap reference transistors are neglected ^[5].

Combining Equations (1) and (2) gives:

$$\begin{equation} \label{eq3} R_2 (2L_{\rm o} +\Delta I_{\rm o})=V_{\rm REF} -V_{\rm BE17}, \end{equation}$$

(3)

$$\begin{equation} \label{eq4} I_{\rm o} =\frac{V_{\rm REF} -V_{\rm BE17} }{2R_2 }-\frac{\Delta I_{\rm o} }{2}. \end{equation}$$

(4)

The two NPN bipolar junction transistors of the band-gap circuit operate at different current densities, hence different base-emitter voltages^[5]. For the LM117, the current density of Q19 is 10 times the density of Q17^[5],

$$\begin{equation} \label{eq5} I_{\rm s19} =10I_{\rm s17}, \end{equation}$$

(5)

where $I_{\rm s}$ is the reverse-bias base-emitter junction current. When the relationship between collector current and base-emitter voltage is reduced to the equation:

$$\begin{equation} \label{eq6} I_{\rm c} =I_{\rm s} \exp \left( {{V_{\rm BE} }/{V_{\rm T} }} \right), \end{equation}$$

(6)

the difference of the base-emitter voltage of Q17 minus the base-emitter voltage of Q19 can be expressed as$^{ ^[5]:

$$\begin{equation} \label{eq7} \Delta V_{\rm BE} =V_{\rm BE17} -V_{\rm BE19} =V_{\rm T} \left[{\ln \left( {{10I_{\rm c17} }/{I_{\rm c19} }} \right)} \right]. \end{equation}$$

(7)

By observing the reference circuit, one can determine that:

$$\begin{equation} \label{eq8} \Delta V_{\rm BE} =R_1 I_{\rm o}. \end{equation}$$

(8)

Combining Equations (4) and (7) gives:

$$\begin{equation} \label{eq9} V_{\rm REF} =V_{\rm BE17} +{2R_2 \Delta V_{\rm BE} }/{R_1 }+R_2 \Delta I_0. \end{equation}$$

(9)

Equation (9) is critical to the regulator's operation and is useful in understanding radiation-induced degradation of the output voltage.

The three-terminal voltage regulator circuit shown in Figure 3 is often applied, which is also used for electrical parameter and noise parameter measurements. From Figure 3, we can obtain

$$\begin{equation} \label{eq10} V_{\rm out} =V_{\rm REF} \frac{R_x +R_y }{R_x}, \end{equation}$$

(10)

where $R_{x}$ and $R_{y}$ are the external resistance.

2.2 Output 1/$f$ noise voltage

Since the degradation of the LM117 is mainly caused by the degradation of the band-gap reference, and the band-gap reference is the dominant source of noise in the voltage regulators ^[12], the 1/$f$ noise degradation of the band-gap reference is only considered. As shown in Figure 2, the band-gap reference is composed of two NPN transistors and PNP transistors. The radiation induces the degradation of the base surface current of the bipolar junction transistor, which leads to a degradation of base current. The changes of base current will cause the changes of the base 1/$f$ noise of the bipolar junction transistor.

The base current $I_{\rm B}$ is decomposed into a volume, $I_{\rm V}$, and surface, $I_{\rm S}$, recombination components $I_{\rm B} =I_{\rm V} +I_{\rm S}$. And the base current fluctuations are decomposed into surface and volume originated noise sources$^{ ^[13]. The surface noise is ascribed to the low frequency fluctuations in the surface recombination current component due to the dynamic trapping-detrapping of carriers into oxide-trapped charges. The volume noise component results from the intrinsic fluctuations of the diffusion current due to the carrier number fluctuations in the volume of the space charge region. If one assumes uncorrelated fluctuation sources both in the volume and in the surface current components, the base current 1/$f$ noise $S_{\rm IB}$ can be expressed in the form^[13],

$$\begin{equation} \label{eq11} S_{\rm IB} =K_{\rm S} \frac{I_{\rm S}^2 }{f}+K_{\rm V} \frac{I_{\rm V}^2 }{f}, \end{equation}$$

(11)

where the constants $K_{\rm s}$ and $K_{\rm v}$ are characteristics of each mechanism, and $f$ is the frequency. Since $\gamma$ radiation effects in bulk silicon are negligible, radiation-induced change in the volume noise components is also negligible.

Now we only consider the bipolar transistor Q19, and assume that Q19 is a bipolar transistor without other circuits. As shown in Figure 4, the 1/$f$ noise voltage across the B-E terminal can be given by

$$\begin{equation} \label{eq12} S_{\rm VBE} =r_{\rm b19}^2 S_{\rm IB19} +r_{\pi 19}^2 S_{\rm IB19} +R_1^2 S_{\rm IB19}, \end{equation}$$

(12)

where $S_{\rm IB19}$ is the base 1/$f$ noise current of the bipolar transistor Q19, $r_{\rm b}$ is the base internal series resistances, and $r_{\pi}$ is the input base emitter resistance .

If the base 1/$f$ noise currents of transistors Q16 and Q18 are considered, the base 1/$f$ noise current of Q16, $S_{\rm IB16}$, the base 1/$f$ noise currents of Q18, $S_{\rm IB18}$, and the 1/$f$ noise current through the collector $\beta _{18}^2 S_{\rm IB18}$ which is an amplified $S_{\rm IB18}$ would flow through the emitter of Q19. So the 1/$f$ noise voltage across $R_{1}$ would become $R_1^2 \left[{\left( {\beta _{18}^2 +1} \right)S_{\rm IB18} +S_{\rm IB16} } \right]$. The 1/$f$ noise voltage across the B-E terminal can be rewritten as

$$\begin{equation} \begin{split} \label{eq13} S_{\rm V1} ={}& r_{\rm b}^2 S_{\rm IB19} +r_\pi ^2 S_{\rm IB19} +R_1^2 S_{\rm IB19} \\[2mm]& +R_1^2 \left[{\left( {\beta _{18}^2 +1} \right)S_{\rm IB18} +S_{\rm IB16} } \right]. \end{split} \end{equation}$$

(13)

Similarly, we can obtain 1/$f$ noise voltage across $R_{2}$

$$\begin{equation} \begin{split} \label{eq14} S_{\rm V2} {}& =R_2^2 \beta _{16}^2 S_{\rm IB16} +R_2^2 \left( {\beta _{17} +1} \right)^2S_{\rm IB17} \\[2mm]& +R_2^2 \left( {\beta _{19} +1} \right)^2S_{\rm IB19} +R_2^2 \left[{\left( {\beta _{18} +1} \right)^2S_{\rm IB18} +S_{\rm IB16} } \right]. \end{split} \end{equation}$$

(14)

From Figure 2, we can obtain

$$\begin{equation} \label{eq15} S_{\rm VREF} =S_{\rm V1} +S_{\rm V2} . \end{equation}$$

(15)

According to Figure 3, we can obtain 1/$f$ noise voltage at the output terminal

$$\begin{equation} \label{eq16} S_{\rm V} =S_{\rm VREF} \left( {\frac{R_x +R_y }{R_x }} \right)^2. \end{equation}$$

(16)

If we assume that the 1/$f$ noise voltage in the other noise source is $S_{\rm Vother}$, we can obtain the total output 1/$f$ noise voltage

$$\begin{equation} \label{eq17} S_{\rm Vout} =S_{\rm VREF} \left( {\frac{R_x +R_y }{R_x }} \right)^2+S_{\rm Vother} . \end{equation}$$

(17)

3. Experiment and discussion

3.1 Experiment

The LM117 adjustable 3-terminal positive voltage regulators were used in this work. All regulators were irradiated with ionizing gamma-radiation from a Co$^{60}$ source at room temperature. The dose rate was 0.1 Gy(Si)/s. The accumulated total dose at each test step was 100, 300, 500, 700 Gy(Si). The devices were periodically removed from the source in order to track the changes in the device parameters at each total dose level. The output voltage was set 10 V by configuring the proper resistance ($R_{x}$ and $R_{y})$. The output current was set to 20 mA by configuring the proper resistance $R_{\rm L}$. The bias conditions were held constant during the radiation and the measurement. The measured electrical parameter was the output voltage, which was measured using a multimeter. The measured noise parameter was the output noise voltage $S_{\rm Vout}$, which was measured with the XD3020 noise measurement system that was described in Reference ^[14]. The circuit was used for parameter measurements, as shown in Figure 3.

3.2 Result and discussion

The variance in the output voltage, $\Delta V_{\rm out}$, is plotted versus the total dose in Figure 5, where $\Delta V_{\rm out}=V_{\rm out}-V_{\rm out0}$, $V_{\rm out0}$ are the pre-irradiation parameters, and $V_{\rm out0}$ is post-irradiation parameter. The output voltage decreased with the increase in the total dose. According to Equation (10), the variation of output voltage was caused by the reference voltage. Many studies show that radiation-induced current gain degradations in NPN and PNP bipolar junction transistors are due to the accumulation of oxide-trapped charges and interface states at the surface of the device^{[15, 16, 17, 18]}. The band-gap reference is composed of two NPN transistors and two PNP transistors. First, we consider the change in the PNP transistor, and assume no change in the NPN transistor. When the radiation leads to an increase in the base current of the PNP transistor, this causes the collector current of Q17 to drop relative to the collector current in Q19. According to Equation (7), $\Delta V_{\rm BE}$ drops , and $\Delta I_{\rm o}$ becomes negative. According to Equation (9), this causes the reference voltage to drop. Then, we consider the change in the NPN transistor and assume no change in the PNP transistor. When the radiation leads to an increase in the base current of the NPN transistor, since the collector currents of Q19 and Q17 remain unchanged, $\Delta V_{\rm BE}$ will not change. Prior to the radiation, the base currents of both transistors are matched. However, as the part was exposed to more total dose, the base current of Q19 will change significantly more than the base current of Q17. This is because Ql9 operates at a base to emitter voltage which is 60 mV less than that of Q17^[5]. This makes $\Delta I_{\rm o}$ become negative. According to Equation (9), this causes the reference voltage to drop. So, radiation-induced current degradations in the NPN and PNP transistors would reduce the reference voltage. According to Equation (10), the output voltage would drop.

The noise performance with the accumulated total dose is shown in Figure 6. Figure 6 shows that low frequency 1/$f$ noise increases with the total dose.

The power spectral density of the voltage can be commonly expressed as follows:

$$\begin{equation} S_{\rm V} =A+B/f^\gamma, \end{equation}$$

(18)

where $A$ is the amplitude of white noise (V$^{2}$/Hz), and $B$ is the amplitude of 1/$f$ noise (V$^{2}$/Hz). $\gamma$ is the exponential factor of 1/$f$ noise, and $f$ is the frequency.

At the frequency range of 10-100 Hz, the graph of $\Delta B$ as a function of the doses is shown in Figure 7, where $\Delta B=B-B$, $B_{0}$ and $B$ are the pre-irradiation and post-irradiation amplitude of 1/$f$ noise, respectively. As shown in Figure 7, $\Delta B$ increase with the dose.

Since the band-gap reference is the dominant noise source, and its degradation causes the variation of the output voltage, we only consider the variation of the 1/$f$ noise voltage of the band-gap reference, and assume that it leads to the variation of the output 1/$f$ noise voltage. According to Equation (17), we can obtain the following relationship

$$\begin{equation} \label{eq18} \Delta S_{\rm Vout} =\Delta S_{\rm VREF} \left( {\frac{R_x +R_y }{R_x }} \right)^2. \end{equation}$$

(19)

According to Equation (11), the base surface 1/$f$ noise current increases with the base surface current, which leads to an increase in the base 1/$f$ noise current. When the transistor is in the forward active region, $\beta \gg 1$. From Equations (13), (14), and (15), we can obtain the following relationship:

$$\eqalign{ & {S_{{\rm{VREF}}}} = r_{\rm{b}}^2{S_{{\rm{IB19}}}} + r_\pi ^2{S_{{\rm{IB19}}}} + R_1^2{S_{{\rm{IB19}}}} \cr & + R_1^2\left( {\beta _{18}^2{S_{{\rm{IB18}}}} + {S_{{\rm{IB16}}}}} \right) + R_2^2\beta _{16}^2{S_{{\rm{IB16}}}} \cr & + R_2^2\beta _{17}^2{S_{{\rm{IB17}}}} + R_2^2\beta _{19}^2{S_{{\rm{IB19}}}} \cr & + R_2^2\left( {\beta _{18}^2{S_{{\rm{IB18}}}} + {S_{{\rm{IB16}}}}} \right). \cr}$$

(20)

Similarly, first, we consider the change in the PNP transistor, and assume no change in the NPN transistor. The radiation leads to an increase in the base current of the PNP transistor, which leads to a reduction in the current gain. For 1/$f$ noise voltage, we need to determine the change of $R_2^2 \beta _{16}^2 S_{\rm IB16}$. $R_2^2 \beta _{16}^2 S_{\rm IB16}$ can be written as

$$\begin{equation} \label{eq20} \beta _{16}^2 S_{\rm IB16}= K_{\rm S} \left( {\frac{I_{\rm C} }{I_{\rm V} +I_{\rm S} }} \right)^2\frac{I_{\rm S}^2 }{f} =\left( {\frac{I_{\rm C} }{{I_{\rm V} }/{I_{\rm S} }+1}} \right)^2\frac{K_{\rm S} }{f}. \end{equation}$$

(21)

From Equation (21), we can see that the current gain $\beta =I_{\rm C}/(I_{\rm V}/I_{\rm S}+1)$ increases with the base surface current $I_{\rm S}$, which makes $\beta _{16}^2 S_{\rm IB16}$ increase. So $R_1^2 \left[{\beta _{18}^2 S_{\rm IB18} +S_{\rm IB16} } \right]+R_2^2 \beta _{16}^2 S_{\rm IB16} +R_2^2 \left( {\beta _{18}^2 S_{\rm IB18} +S_{\rm IB16} } \right)$ increases. According to Equations (19) and (20), the output 1/$f$ noise voltage increases. Similarly, the radiation leads to an increase in the base current of NPN transistors, which will lead to an increase in the output 1/$f$ noise voltage. So we can draw a conclusion that the output 1/$f$ noise voltage increases with the total dose.

The output voltage and the output 1/$f$ noise voltage degradation of LM117 can be attributed to the same physical origin, and these two kinds of degradations are the results of the degradation of the band-gap reference. So the output 1/$f$ noise voltage may be used as a means to evaluate the radiation resistance capability of LM117. In order to make a comparison, $\Delta B/B_{0}$ and $\vert \Delta V_{\rm out}/V_{\rm out0} \vert$ are plotted versus the total dose in Figure 8. Notice that this is a semi-log graph. Figure 8 shows that their degradations have a similar trend, and the increase in the output 1/$f$ noise voltage is more significant than in the output voltage on the same total dose. After a radiation dose up to 700 Gy(Si), $\vert \Delta V_{\rm out}/V_{\rm out0} \vert$ is 1%, and $\Delta B/B_{0}$ is 1305%. It is clear that the $\Delta B/B_{0}$ is more sensitive than $\vert \Delta V_{\rm out}/V_{\rm out0} \vert$.

4. Conclusion

The radiations cause the variance of the output voltage and 1/$f$ noise voltage. These two kinds of degradations are caused by the degradation in the band-gap reference. The radiations cause an increase in the base surface current of NPN and PNP bipolar junction transistors of the band-gap reference, which leads to the degradation in the output voltage. At the same time, the 1/$f$ noise of the band-gap reference increases with the increase in the base surface current of bipolar junction transistors, which brings about an increase in the output 1/$f$ noise voltage. Compared to the electrical parameter, the 1$/f$ noise parameter is more sensitive. In this work, 30 devices were radiated. Although the number of samples is small, on the basis of the research, 1$/f$ noise measurement may be used as a means to evaluate the radiation resistance capability of LM117. Also, 1$/f$ noise has been already used to evaluate the radiation resistance capability of many devices, for example, the MOS transistor^{[19, 20]} and optoelectronic coupled devices^[21]. In theory, 1$/f$ noise may be used as a means to evaluate the radiation resistance capability of other devices. Continuing to study the 1/$f$ noise of other devices will be the future works.