# Radiation Action on IV Characteristics of Power Semiconductor Devices Based on Silicon

## Results of theoretical research of influence of cumulative dose on I-V characteristics (IVC) of power semiconductor devices based on silicon are presented.

*Results of theoretical research of influence of cumulative dose on I-V characteristics (IVC) of power semiconductor devices based on silicon are presented. It is shown that unlike low-power devices at which the radiation leads to falling of threshold voltage and building up of differential resistance, the threshold voltage of power devices under the radiation influence, as a rule, grows, and differential resistance practically doesn’t change.*

Nowadays power electronics applications based on powerful semiconductor devices are used in various areas of human activity: household (vacuum cleaners, refrigerators, air conditioners, washing machines, etc.), electric-power industry (frequency and voltage converters in power stations, technical process capacity regulators residential sector (elevators and lighting), automotive industry (robotic assembly lines, welders, conventional and hybrid engine management systems), aerospace industry (power-supply systems and electric drives). Major part of power semiconductor devices (PSD) is used in metal manufacture and communications (induction furnaces, high-performance power supplies, converters and control devices). Computer and power electronics responsible for the work of “mind” and “muscle” of modern technics accordingly, become the primary technology of the 21-st century. And at the same time, large-scale usage of PSDs leads to constant expansion of the range of conditions in which these devices have to operate.

Part of these conditions is connected with the effect penetrating radiation produces on PSD. This, in particular, happens due to the implementation of the latest electronic developments in atomic energetics, altitude aircrafts, and also by the increasing usage of power electronics in space research including interplanetary flights. All this, together with the current safety and failure-free operation requirements makes research in radiation effects on various PSD characteristics extremely relevant.

One of the most important characteristics of PSD is the I-VC, since their output capacity and performance factor greatly depend on it. The reviews of the research works on the radiation effects on I-VC and other PSD characteristics are presented fairly wide in today’s literature [1-12]. However in these works the main attention is usually given to the area of comparatively low current density (up to 50 А/cm2) where the major physical effect determining I-VC is the interaction of injected carriers with deep impurity levels that act as recombination and trapping centers. In this research we present the theoretical study of the influence of the cumulative dose on powerful high-voltage devices which, unlike low-power devices, generally operate at high current density (over 50 А/cm2) and high injection levels and in which the following effects of the carriers interaction become significant: loss of emitter junction injection rates, electron-hole recombination (EHR) and Auger recombination.

## I-VC of power electronic devices

As it is known [13; 14], at high injection levels, p-n-p-n-structures I-VC correspond to p-i-n-diodes I-VC which, in case of on-state, can be presented as follows [14-20]

$$VF \approx \frac{\eta kT}{e} ln \left ( \frac{I_F}{I_{Si}} \right ) + \frac{1,5kT}{e} exp \left ( \frac{W_n}{2L_p} \right ) +$$

$$+\frac{W_{n}I_{F}}{GS\left ( \frac{T}{300} \right )^{\beta }}+\frac{\left ( C_{n}+C_{p}\tau _{2}^{p} \right )}{e^{2}\left ( \mu _{n}+ \mu _{p} \right )} \left ( \frac{I_{F}}{S} \right )^{2} , \ \ \ \ (1)$$

where IF - direct current; VF - forward voltage drop in the device; η - ideality factor which in this research equates η ≈ 1,6; e – electron charge; k - the Boltzmann constant; G ≈ 16 (Ohm∙cm)–1; T – absolute temperature of the element; S – it’s surface; Wn - low-doped n-base thickness; μn and μp- electron and hole mobility accordingly; τp - lifetime of minority carriers (holes) in the base; Cn и Cp – Auger recombination constants; β – exponent of power: ß ≈ 1 .

Ambipolar length of hole diffusion in the base Lp, which is included in the formula, is determined by the expression [14-18]

$$L_p = \sqrt{\frac{2b}{b+1} D_p \tau _p} , \ \ \ \ (2)$$

where Dp=kTμp/e - hole diffusion rate and b=μn/μp - electron and hole mobility ratio, which is b ≈ 2,7 for silicon.

Value ISi is presented as follows [14-18]

$$I_{Si} \approx \frac{2eD_pn_iS}{L_p} \frac{bsh(W_n / L_p)}{bch(W_n / L_p) +1} , \ \ \ \ (3)$$

where ni - concentration of intrinsic carriers in the base.

Comparison of calculations, performed by formula (1) with the results of experimental measurements is presented in figure 1.

*Figure 1: I-VC of the high-power diode D053-7100-4-N (Proton-Electrotex): markers – measurement results; block curves – the results of the theorectical calculations by Formula (1)*

As the figure shows, Formula (1) is in the satisfactory fit with the experimental data. The first item in the formula is direct voltage drop in p-n-junction, the second item is voltage drop with allowance for base conductance modulation by injected carriers, the third one registers voltage drop, conditioned by EHD, and the decrease of emitter injection coefficient, and finally, the forth – voltage drop, conditioned by the Auger-recombination.

As it is shown in figure 1, under high current the curve of PSD I-VC becomes practically linear and can be approximated by the following expression

$$V_F \approx V_{T0} + rI_F., \ \ \ \ (4)$$

where VT0- threshold voltage; r – differential resistance of the device.

Reverse current of silicon PSD is mostly generated and is determined by the expression [17]

$$I_R \approx \frac{en_id_nS}{2 \sqrt{\tau _p \tau _n}} , \ \ \ \ (5)$$

where τn- lifetime of the electrons in the p-emitter and dn- thickness of layer of space charge in the n-base.

Being represented in micrometers, this thickness (in μm) can be expressed [17]

$$d_n \approx 0, 52 \sqrt{\rho _n V_R} , \ \ \ \ (6)$$

where ρn- specific resistivity of silicon in the n-base (Ohm∙cm); VR- reverse voltage (V).

## Changes in silicon properties under the action of radiation

Radiation action leads to [1-12] the atomic ionization of the semiconductor and produces radiation defects and new atomic energy level defects in the band gap of the semiconductor, and as a consequence, leads to:

- decreasing of lifetime of the charge carriers:

$$\frac{1}{\tau (\Phi)} = \frac{1}{\tau _0} + K_{\tau} \Phi; \ \ \ \ (7)$$

- decreasing of charge carrier concentration:

$$n \Phi = n_0exp(-K_n \Phi) ; \ \ \ \ (8)$$

- change in mobility:

$$\frac{1}{\mu \Phi} = \frac{1}{\mu _0} + K_{\mu} \Phi . \ \ \ \ (9)$$

In turn, the change in concentration and mobility leads to the change in specific resistance of silicon:

In the proportions (7)-(10), values with Index 0 refer to silicon characteristics before irradiation and the letter Ф denotes the cumulative radiation flux (fluence). Constants Kτ, Kn, Kμ and Kρ are radiation constants which depend on the manufacturing technique and the specific resistance of the basic material, nature of the radiation, and the type of radiation defects. In the further calculations we used values of these constants which are given in Research [21] for CZ-silicon, irradiated with fast neutrons (with energy of about 1-1,5 MeV). In particular, we considered that WKτ is specified by the following empirical relations:

For n-silicon:

For p-silicon:

Where p- and n- - hole and electron concentration in silicon accordingly

Results of mathematical simulation of radiation action on I-VC of PSDs and discussion Formulas (1)-(10) allow to perform mathematical simulation of radiation action on I-VC of PSDs. In particular, figure 2 shows the results of the simulation of neutron radiation action on I-VC of PSDs. As the results show, uniform irradiation of PSD leads to the change in the threshold voltage of the devices but almost does not alter their differential resistance. Thereat, as our calculations show, change in PSD characteristics is mostly connected with the decreasing lifetime of the charge carriers (7), and the decrease of carrier concentration (8) and mobility (9) has almost no effect on I-VC of PSD. Inconsiderable dependency of PSD differential resistance on radiation can be explained by the fact that under major current density it is mostly defined, as it is seen from the comparison of (1) and (4), by electron-hole recombination processes [the third item in (1)], and consequently does not directly depend on the lifetime of the charge carriers. Under the radiation action, PSD resistance can change considerably only due to the change of the Auger-recombination speed [the fourth item in (1)].

Total change in threshold voltage of PSD is conditioned by the voltage drop in p-n-junction [the first item in Formula (1)] and the increase of voltage in the base [the second item in (1)]. Speed of the threshold voltage change equals

Figure 2: Theoretical I-VC of power diode D053-7100-4-N, irradiated by neutrons (block curves): 1 - Φ = 3∙1012 cm–2; 2 – Φ = 1013 cm–2; 3 – Φ = 3∙1013 cm–2. Thin curves – T = 298 K; thick curves – T = 443 K; dotted line – I-VC of the unirradiated diode.

where

Dependency τp(Φ) in Formula (11) is defined by the Expression (7) and Lp(Φ) - by Formula (2), where τp=τp(Φ)

High dependence of voltage change speed (11) on relation Wn/Lp is quite noticeable. This dependence causes threshold voltage in the devices with thin base Wn<2Lp to reduce at small values of cumulative radiation flux. However with the increase of the cumulative dose and in case of Wn≥2Lp threshold voltage of PSD increases rather quickly due to the leading voltage rise in the base as compared to the voltage drop in p-n-junction. At that, charge carrier lifetime degradation (7) leads to the increase of the reverse current (5) at any values of cumulative radiation flux:

Conclusion

The results we have got show that the emerging effects, connected with the interaction of charge carriers with each other - decreasing constants of emitter junction injection, electron-hole recombination, additional Auger-recombination channel – cause sufficient difference in I-VC of powerful high-voltage devices and low-voltage devices, which lack the mentioned effects. Particularly, unlike low-voltage devices that show threshold voltage drop and rise of differential resistance, resistance of high-voltage devices conditioned by EHD processes remains almost unchanged, and threshold voltage generally rises.

The latter circumstance is connected with the fact that at high current density the change in threshold voltage under irradiation is conditioned mostly by the voltage change in the low-doped n-base, which greatly depends on the relation between the base thickness and the length of the minority carrier free path Wn/Lp and increases due to the reduction of minority carrier lifetime under the action of irradiation. At the same time, power devices with thin base Wn<2Lp, as it is shown in Formula (11), can show threshold voltage drop at values of cumulative radiation flux (i.e. as long as the inequation Wn<2Lp is fulfilled), which can be used (and is being used) for purposeful modification of device characteristics by means of irradiation methods

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This article originally appeared in the Bodo’s Power Systems magazine.

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