Model of High-Energy-Density Battery Based on SiC 

Schottky Diodes 

by Yves Ngu, Marc Litz, and Bruce Geil 

ARL-TR-3981 Ocotber 2006 

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ARL-TR-3981 October 2006 

Model of High-Energy-Density Battery Based on SiC 

Schottky Diodes 

Yves Ngu, Marc Litz, and Bruce Geil 

Sensors and Electron Devices Directorate, ARL 

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Model of High-Energy-Density Battery Based on SiC Schottky Diodes 

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Yves Ngu, Marc Litz, and Bruce Geil 

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U.S. Army Research Laboratory 

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14. ABSTRACT 

Silicon carbide (SiC) diodes are being investigated as direct energy converters (DECs) for use in small, long-lived nuclear 

power sources for unattended sensors. Voltage and current measurements on Schottky diodes fabricated from both Si and SiC 

result in typical efficiencies of 5 to 15%. A drift-diffusion model has been developed to predict the output and to help us 

better understand the radiation-induced current that results. This report describes the initial conditions, the drift-diffusion 

algorithm, and the material parameters used in the model. The results of the model compare well to experimental data. 

15. SUBJECT TERMS

Silicon carbide, schottky model, DEC 

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Yves Ngu 

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iii 

Contents 

List of Figures iv

List of Tables iv

1. Background 1

2. Approach 2

3. Circuit Model 4

4. Results 5

5. Conclusions 9

6. References 12

Distribution List 13
iv 

List of Figures 

Figure 1. SiC Schottky diode......................................................................................................... 2 

Figure 2. Current flow under a) open circuit and b) load condition. ............................................. 3 

Figure 3. Equivalent circuit of diode and load............................................................................... 3

Figure 4. Vout versus load resistance simulated results. ............................................................... 6 

Figure 5. Iout versus load resistance simulated results.................................................................. 7 

Figure 6. Iout versus Vout simulated results. (The Voc is 150 mV and the Isc is 950 nA.) ....... 7 

Figure 7. Vout versus load resistance simulated results with Gen(x)............................................ 8 

Figure 8. Iout versus load resistance simulated results with Gen(x). ............................................ 9 

Figure 9. Iout versus Vout simulated results. (The Voc is 120 mV and the Isc is 40 nA.) ......... 9 

List of Tables 

Table 1. Material properties of SiC................................................................................................ 4 
1 

1. Background 

Nuclear batteries can have a small but significant impact as a power source for long-lived 

sensors (1-3). Consider embedded sensors for bridges and foundations of large buildings. These 

sensors can provide information about the structural integrity (4-6). Unattended sensors for 

temperature measurement in the oceans would need no maintenance during an increased 

operational lifetime. Unique opportunities are waiting for sensors that benefit from “keep-alive” 

power lasting decades. 

Chemical power sources can store the total energy required, but electrical leakage and 

deterioration of the batteries keep them from delivering the power over a decade. Nuclear 

batteries offer a unique power source to fill the niche. Even though the energy-density of nuclear 

isotopes is six orders of magnitude greater than that possible in chemical bonds, the stigma 

associated with nuclear materials will require careful design and thoughtful application. Sensors 

embedded in structures, which provide information useful to monitor structural integrity (i.e., 

bridges, helicopter blades), may be just the application to overcome these difficulties. 

Semiconductor based radioisotope power converters use the energy generated by the decay of 

radioisotopes to create a power source. A battery of this type is composed of three main parts: 

1) a radioisotope source of high energy density, 2) an energy converter (diode) that changes the 

radiation output of the radioisotope energy source into some form of usable electrical energy, 

and 3) a load that can consume or store the electrical energy. A simple nuclear battery design 

consists of alternating layers of isotope, sandwiched in between layers of silicon carbide (SiC) 

diodes. A sample battery in AA format is currently being constructed. The isotope consists of 

11 each, 50-μm-thick, 2-mm-diameter foils of nickel (63Ni). The 63Ni is surrounded by layers 

of SiC diodes. The diodes are 5-mm-square, 400-μm-thick devices. 

The goal of this report is to establish a model for the direct energy converter (DEC), as well as to 

characterize the impact of the load on the output power generated. The model will enable us to 

predict device efficiency and improve the efficiency in future design iterations. One way to 

improve battery efficiency is to match the penetration of beta (or gamma) decaying from the 

isotope, to the range of penetration (stopping power) of the DECs. The DEC undergoing 

consideration is a SiC based Schottky diode, as seen in figure 1. 
2 

Figure 1. SiC Schottky diode. 

Section 1 identifies the motivation for our efforts and discusses some of the applications that will 

benefit from the investigations. Section 2 discusses the overall approach taken in the model. 

Section 3 describes details of the model and values of material parameters applied. Section 4 

details the significant results, and section 5 provides conclusions and impacts of these results on 

the larger goal of developing efficient nuclear batteries for long-lived sensors. 

2. Approach

The energetic particles emitted during the decay of the radioisotopes create a multitude of 

electron-hole pairs within a semiconductor. The distribution of generated carriers is modeled via 

a Monte Carlo radiation transport code (MCNPX) and has been examined previously (7). Once 

the carriers are generated, we have positive charges flowing into the semiconductor, leading to a 

generated current Ig which is equivalent to a short circuit current (Isc). The displaced carriers 

effectively forward biases the p-layer, as seen in figure 2(a). The forward bias junction yields a 

current (Id) through the junction, opposing the generated current. In the presence of very small 

load (short), Isc = Id while the output voltage with very high load (open) is Voc, the open circuit 

voltage. When a load is connected to the diode’s output terminals as in figure 2(b), the current 

attributable to the forward bias junction is split between the current into the load (Iout) and Id so 

that Ig = Id + Iout. 
3 

Figure 2. Current flow under a) open circuit and b) load condition. 

The objective is to estimate how the diode’s structure and the connected load affect the output 

voltage of the battery. The structure of the diode defines the generated current (Ig). 

Furthermore, the “leakage current” (Id, forward current) in the diode determines the amount of 

lost current. Omitting the radioisotope layer (which would be in direct contact with the Schottky 

contact of the diode—Ni/Ti/Al/Pt/Au metal layer), the diode and the load are modeled by the 

equivalent circuit displayed in figure 3. 

Figure 3. Equivalent circuit of diode and load. 

The values of components of figure 3 are derived from material properties of the semiconductor. 

The devices presently being evaluated are SiC Schottky diodes using nickel as metal contact. 

Most of the material properties of SiC were obtained from literature (8) and are tabulated in 

table 1. In figure 3, RL represents the load resistance, and the components for which values and 

expressions need to be determined are Rsh, Rs, Ig, and Id in which 

• Rsh is the shunt resistance that arises from leakage of current around the cell, via the edges 

of the device. It is estimated as the resistance present across the diode at 10 mV forward 

bias. 

• Rs is the series resistance attributable to contacts and internal resistance of the diode. 

• Ig is the generated electron current (dependent on carriers within the depletion region as 

well as those outside, with collection efficiency higher when closer to depletion region). 

• Id is the current flowing in the diode attributable to the forward biased junction (“leakage 

current”). 
4 

Table 1. Material properties of SiC. 

Parameter Symbol Value (unit) 

Intrinsic Conc.* ni 1.6E-6 (cm–3) 

Electron Affinity* X 3.5 (eV) 

Band Gap* Eg 3.23 (eV) 

Dielectric Constant* Ks 9.66 (cm2/V-s) 

Recombination Coef.* Rc 1.5E-12 

Hole Mobility* up 120 (cm2/V-S) 

Electron Mobility* ue 900 (cm2/V-S) 

Diffusion Length* L 1.5E-4 (cm) 

Doping Level Na 1E15 (cm–3) 

Build in Voltage** Vbi 0.86 (eV) 

Schottky Barrier** Vbar 0.95 (eV) 

Device Area Area 0.25 (cm2) 

Ni Work Function work_Ni 5.15 (eV) 

*Extracted from (2) 

**Assumes Fermi level is pinned (4)

3. Circuit Model 

The various components values are determined by basic semiconductor equations that use the 

doping level and size described in figure 1, with the top SiC layer referred to as active layer and 

the bottom layer as the substrate. The concentration of carriers generated within the depletion 

region is identified as Conc(in), whereas the concentration of carriers generated outside the 

depletion region is identified as Conc(out). The model for the shunt resistance, Rsh, is given in 

equation 1. It is derived from the diode current expression for a diode at 10 mV forward bias. 

Equation 2 is the model of series resistance, Rs, where the contact resistance was neglected. 

Equation 3 gives an expression for the generated current, Ig. This current is attributable to 

electron carriers. It is assumed that electrons located within the depletion region, which have 

acceptable energy values (discussed in the next section), will have a collection efficiency of a 

100% (fully contribute to drift current). Alternately, carriers generated outside the depletion 

region will have an exponential collection efficiency, where X is the distance between the carrier 

and the edge of the depletion region, and L is the diffusion length. Equation 4 refers to diode 

“leakage current”, which is controlled by the output current and load resistance. 

exp -1) k * T

10e - 3

Area * Jsat * (

10e3

Rsh = (1) 

⎟

⎠

⎞ ⎜

⎝

⎛ = +

Nsub

Wsubstrate

Na

Wactive

Rs * q * up * Area

1 (2) 
5 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

= * ( ) + ( ) *exp 2*Ks* eo

* * * * 2

L

X

Conc in Conc out q up Na W AreaIg (3) 

exp 1 *

* ( )

* −

+

= k T

Iout Rs RL

Id Isat (4) 

In the equations above, Ks is the coefficient describing the relative dielectric constant eo, up is 

electron mobility, Wactive is the thickness of upper SiC layer, and W is the thickness of the 

depletion region. 

All these equations were modeled with MATLAB1. Equation 5 allows us to solve for the 

internal diode voltage, V1. V1 is then used to determine the output voltage and current with 

equations 6 and 7, respectively. Finally, Vout versus RL, Iout versus RL, and Vout versus Iout

are all plotted as our results. 

RL Rs

V V

Ig Id

+ = + +

1

Rsh

1 (5) 

RL Rs

V

Vout RL

+ = 1 * (6) 

RL Rs

V

Iout

+ = 1 (7) 

4. Results 

As mentioned in the previous section, carriers contributing to the generated current require an 

acceptable energy level. The idea of acceptable energy level results from the fact that carriers 

generated by beta sources have a large range of kinetic energy. Once these carriers are 

introduced in our device, not all of them can contribute to current. Most of the contribution is 

supported by the lower energy (<50 keV) electrons (7). Generally, in such a system, many 

physical phenomena such as secondary electron production, hole-electron pair generation, 

cathod-luminescence, x-ray generation, and other processes contribute to energy losses (9). 

The lower energy electrons contribute more to electrical power output because their energy is 

more easily collected by the diode. From the electron energy spectrum (7), we can estimate that 

about 5 of every 1000 generated carriers have energy comparable to that exerted by the device’s 

internal electric field. Consequently, to a first order approximation, the concentration of carriers 

obtained from MCNPX simulation can be scaled by 0.2e–3 to represent the carriers relevant to 

current generation. 

 1

MATLAB is a registered trademark of the MathWorks. 
6 

0 2 4 6 8 10 12

x 107

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Load Resistance (ohms)

Vout (V)

Output Voltage vs. Load Resistance

The results of the numerical simulation, based on the equations described in section 3, produce 

reasonable values for the unknown parameters of the current into the load, Iout, and voltage 

across the load, Vout. The current Iout and the voltage Vout are measured values in the 

experimental verification of this model. These values are measured as a function of RL, the load 

resistance. The load resistance is varied from 1 Ω to 1 MΩ. The numerical results for these 

simulations are shown in figures 4, 5, and 6. 

Figure 4 is a plot of Vout versus RL, figure 5 is a plot of Iout versus RL, and figure 6 is a plot of 

Iout versus Vout. In figure 4, the curve deviates from the straight line curve that would be 

expected from a resistive circuit. This behavior is attributable to the increased “leakage current” 

(Id) via the diode (see figure 3) as Vout increases. With increased load, Vout increases as well 

as Id; thus, the slope of Vout versus RL decreases and curvature can be observed. This curvature 

is also present in figure 5 where it can be seen that less and less of the generated current (Ig) 

flows through RL. Figure 6 is in a sense a combination of figures 4 and 5. The shape of this 

curve mimics the typical response of photovoltaic cell. The output current is maximum (Iout = 

Isc = 95 nA) when the Vout = 0 (output shorted yielding short circuit current). The maximum 

output (Vout = Voc = 0.15V) occurs at near zero output current (the load is extremely large 

yielding open circuit voltage). 

Figure 4. Vout versus load resistance simulated results. 
7 

0 2 4 6 8 10 12

x 107

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x 10-7

Load Resistance (ohms)

Iout (A)

Output Current vs. Load Resistance

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x 10-7

Vout (V)

Iout (A)

Output Current vs. Output Voltage

Figure 5. Iout versus load resistance simulated results. 

Figure 6. Iout versus Vout simulated results. (The Voc is 

150 mV and the Isc is 950 nA.) 

Throughout this analysis, the generated current was described by equation 3. In this equation, 

the concentration distribution is obtained from MCNPX and described in discrete form. 

Furthermore, equation 3 is based on the electric field inside the depletion region (described by 

equation 8). The “1⁄2” in the equation is used to obtain an average field within the depletion 

region. This average field multiplied by the concentration of generated charge, their mobility, 

and the device area (as described in equation 3) should yield the overall generated current. 

However, it was noted that equation 8 is a poor description of average electric field, assuming 

that the presence of an average field within the depletion region is somewhat incorrect. 

2 *Ks*eo

q * Na*W

Efield = (8) 
8 

In a photodiode with a given photgeneration rate (Gen) and assuming this rate to be uniform 

throughout the diode, the generated current should be described by equation 9. In this equation, 

all the minority carriers (electrons) created within the depletion region (W) and one diffusion 

length (L) await from the junction are swept by an electric field to the opposite side of the 

junction derby yielding a current. This approach also holds in the case of carriers generated by 

radioisotope particles except that the generation rate is no longer uniform. However, the 

generated charge distribution obtained from MCNPX was curve fitted to yield generation 

function (Gen(x)) that is position dependent (see equation 10). In equation 10, “events”

describes the particle emission rate of the radioisotope (number of events per second). The 

generated current can be represented by equation 11, which is a modified version of equation 9 

for non-uniform distribution rate and the derivative is taken from 0 (schottky junction) to W+L 

(distance of the farthest electron that can be collected). 

Ig = q * Area*(W + L) *Gen (9) 

exp

0.014* ( ) * 2.9 4* x Gen x events e − = (10) 

∫

+

=

W L

Ig q Area Gen x dx

0

* * ( ) (11) 

The generated current obtained with equation 11 was introduced in our original equivalent circuit 

and the output curves obtained are plotted in figures 7, 8, and 9. 

Figure 7. Vout versus load resistance simulated results with Gen(x). 

0 2 4 6 8 10 12

x 106

0

0.02

0.04

0.06

0.08

0.1

0.12

Load Resistance (ohms)

Vout (V)

Output Voltage vs. Load Resistance
9 

Figure 8. Iout versus load resistance simulated results with Gen(x). 

Figure 9. Iout versus Vout simulated results. (The Voc is 

120 mV and the Isc is 40 nA.) 

5. Conclusions 

The model showed some dependency on load resistance value. To further understand what 

might be happening, an analysis of the effects of Schottky contact metal (work function) and 

generated carrier concentration was undertaken. 

0 0.02 0.04 0.06 0.08 0.1 0.12 1

1.5

2

2.5

3

3.5

4

4.5

x 10-8

Vout (V)

Iout (A)

Output Current vs. Output Voltage

0 2 4 6 8 10 12

x 106

1

1.5

2

2.5

3

3.5

4

4.5

x 10-8

Load Resistance (ohms)

Iout (A)

Output Current vs. Load Resistance
10 

It is noted that an increase in generated carrier concentration led to “similar increase in generated 

carriers (one order magnitude increase in generated carrier led to approximately one order of 

magnitude increase in current). Also, as the carrier concentration was increased, the I-V curve of 

the device displayed an increase bending (knee), as would be expected in the case of a 

photovoltaic. As the carrier concentration is decreased, the bending of the I-V curve is lost. This 

is probably because at low current, the output voltage is low, making the diode component (Id) 

of the model negligible, rendering the behavior of the circuit similar to that of a resistive circuit. 

In this way, the model behavior resembles that of a simple resistive circuit. 

Simulations were also run to determine the effect of the metal used for the Schottky contact. The 

parameter changed to indicate that change in metal was the metal work function value. This is 

the minimum energy that must be given to an electron to liberate it from the surface of a 

particular metal. Changes of the metal (work function) used for the Schottky contact indicated 

that as a metal with small work function is used, the generated current is increased via greater 

built-in voltage, barrier voltage, depletion region, and maximum electric field in the depletion 

region. 

The model established in this document has two distinct modes of operation. On the one hand, 

all the semiconductor voltages (built-in and barrier) are obtained from basic semiconductor 

equation. On the other hand, the assumption was made that the electronic behavior of our SiC 

devices displays a Fermi level pinning effect. According to (4), the lattice imperfection existing 

near the surface of the SiC (defect level with activation energy=0.96eV) leads to the pinning of 

the Fermi level in p-type SiC. This behavior yields a fixed barrier voltage of about 0.95eV with 

nickel, independent of the SiC doping concentration. This pinning also makes negligible any 

effects attributed to the Schottky metal work function since the built-in voltage and barrier 

voltage are about constant. 

When we compared the simulation made with and without Fermi level pinning, it was observed 

that the absence of pinning yielded currents one order of magnitude greater. Not only was the 

current level greater, but so was the open circuit voltage. The values obtained were much more 

removed from the experimental results (numerically and curve shape) than was the case when 

Fermi level pinning was assumed. In both cases, it was noted that generated carrier 

concentration was directly linked to the value of generated current (increasing charge 

concentration increases generated current) although the current levels assuming Fermi level 

pinning were much lower. The lower current is because the pinned Fermi level generates a 

lower built-in voltage, barrier voltage, depletion region, and electric field inside the depletion 

region. 

It was noticed that the electric field within our Schottky diode could not be assumed as constant, 

as described in equation 8. Drawing some parallelism between our DEC and typical photodiode, 

the generated current can be determined independently of the internal field. The assumption in 

this case is that the depletion region volume times the generation rate would yield generated 
11 

current (charge/sec). This current is derived by equation 11. This approach gives way to a 

generated current that is closer to experimental results compared to the other technique. 

However, the trends described in the previous paragraphs still hold. 

The model has been established for our battery system. The behavior of the battery can be 

predicted, given the load. However, we still need to determine accurately what values to use for 

our collection efficiency and to more precisely describe the carrier generation rate. This will 

enable output currents to be in the same range as our experimental values. 
12 

6. References 

1. Blanchard, James P. Stretching the Boundaries of Nuclear Technology. The Bridge 32.4, 

2002, 29-34. 

2. Ahearne, John F. The Future of Nuclear Energy. Editorial. The Bridge 31.3, 2001, 3. 

3. Bugliarello, George. Our Energy Future. Editorial. The Bridge 32.2, 3-4. 

4. Lal, Amit; Blanchard, James. The Daintiest Dynamos. IEEE Spectrum Sept. 2004, 36-41. 

5. Lal, A.; Blanchard, James. By Harvesting Energy From Radioactive Specks, Nuclear 

Micrbatteries Could Power Tomorrow’s Microelectromechanical Marvels-And May Be Your 

Cellphone Too. IEEE Spectrum September 2004, 36-41. 

6. Litz, M.; et al. On-Demand High Energy Density Materials. Amer. Inst. of Aero. and Astro. 

7. Litz, M.; Blaine, K. Isotope Generated Electron Density in Silicon Carbide Direct Energy 

Converters; ARL-TR-3964; U.S. Army Research Laboratory: Adelphi, MD, August 2006 

8. Levinstein, M.; et al. Properties of Advanced Semiconductor Materials: GaN, AlN, InN, 

BN, SiC, SiGe. John Wiley & Sons (2001). 

9. Everhart, T. E.; Hoff, P. H. Determination of Kilovolt Electron Energy Dissipation vs 

Penetration Distance in Solid Material. Journal Appl. Phys. December 1971, 42 (13). 
13 

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