Alkaline Earth Metal Dihalides as possible Dielectrics for Wide Band Gap Applications

Lu Wang and Marcelo A. Kuroda

Department of Physics - Auburn University

Support :

High k dielectrics in WBG Semiconductors

2SiC MOS Workshop 2018 - UMD

Si

1.1 eV4H-SiC

3.2 eV

SiO2

~9 eV

Al2O3

8.8 eV

3.05 eV

2.7 eV

3.2 eV

4.7 eV

0.7 eV

0.5 eV

-Ga2O3

4.7-4.9 eV

3.1-3.6 eV

~1.0 eV

Search for candidate materials suitable for WBG dielectrics in power and RF applications:

high-k (larger than SiO2)

Adequate band alignment

Advantages: Lower electric field in the oxide in the

“blocking” or off-state improves reliability

Higher conductivities (for same dielectric thickness and voltages) reduce power consumption

Band gap vs k trend

3SiC MOS Workshop 2018 - UMD

Robertson & Wallace, MSE R 88, 1 (2015)

*BeO

AX2

*

We will focus on studying a class of insulating materials: Alkaline earth metal dihalides (AX2)

Beryllium oxide (BeO).

Acceptable performance demonstrated on Si/CaF2

Smith et al., Appl. Phys. Lett. 45, 907 (1984).

Previous experimental results

4SiC MOS Workshop 2018 - UMD

AX2 Eg (eV) k

MgF2 12.41 4.9, 5.9 [4-5]

CaF2 12.02 6.8 - 7.4[4-5]

SrF2 11.12 6.5 – 7.7[4-5]

BaF2 10.52 7.32 [5]

MgCl2 7.53 -

CaCl2 6.93 -

SrCl2 7.53 9.19 [5]

BaCl2 7.03 9.81 [5]

BeO 7.0 - 10.74 7.35 [5]

[1] Thomas et al., PSS B 56, 163 (1973)[2] Pong et al., Phys.Rev. B 18, 4422 (1978).[3] Sugiura, Phys. Rev. B 9, 2679 (1974).[4] Schulz et al., Springer Materials.[5] Lide, CRC Handbook of Chemistry and Physics, CRC Press, 84th edn. (2003)

Question: Which material is suitable/best?

Outline

Comprehensive Study of AX2 materials dielectric

Phase analysis

Band gap

Dielectric constant

Electronic properties

Beryllium oxide

5SiC MOS Workshop 2018 - UMD

Crystal structures

AX2 crystal structures obtained from aflow database with: A = Mg, Ca, Sr, and Ba

X = F, Cl, Br, and I

Search not limited to most stable or experimentally observed phases

“Hundreds” of outputs

6SiC MOS Workshop 2018 - UMD

aflow.org

Calculation Details

Density functional theory (DFT)

Norm conserving pseudo-potentials

Cutoff energies: Ewfc > 700 eV

Monkhorst-Pack k-point grid

PBE parameterization of the xc-functional

Hybrid method (HSE), x = 0.25

7SiC MOS Workshop 2018 - UMD

Example MgF2

8SiC MOS Workshop 2018 - UMD

CUB FCC HEX ORCC TET TRI

Lattice constant(Å)

a = 5.01 a = 4.99a = 3.38c = 6.50

a = 2.83, b = 6.99,c = 3.23,

a = 4.69,c = 3.09,

a = 5.87,b = 5.85,c = 3.91,

Formation energy(Ry/AX2)

-204.630 -204.610 -204.556 -204.587 -204.645 -204.623

Formation Energy

9SiC MOS Workshop 2018 - UMD

Systematic Analysis

• DFT band structure

• Indirect band gap from D-sol method [Chan et al., PRL 105, 196403 (2010)]

• Band gap from hybrid HSE method, computationally more expensive [Heyd et

al., JCP 118, 8207 (2003)]

• Dielectric constant

• Bader charge and Interatomic distance analysis

10SiC MOS Workshop 2018 - UMD

Band Structure MgF2

11SiC MOS Workshop 2018 - UMD

Halogenp-bands

Alkaline earth metal s-bands

G G

(DFT) Band gap Eg for different phases

12SiC MOS Workshop 2018 - UMD

DE (eV)

DFT Band gap vs Average Bond Length

13SiC MOS Workshop 2018 - UMD

HSE Band Gap We compute band structure using hybrid functionals.

14SiC MOS Workshop 2018 - UMD

HSE

DFT

DFT vs HSE Band gap comparison

15SiC MOS Workshop 2018 - UMD

DFT band gaps are approximately 1.5 eV

smaller than those of HSE

Static Dielectric Constant

Computed dielectric response using DFPT

16SiC MOS Workshop 2018 - UMD

Electronic contributionIonic contribution

where

Gonze et al., Phys. Rev. B 55, 10355 (1997)

Band gap vs Dielectric Constant

17SiC MOS Workshop 2018 - UMD

Indirect Band Gap vs Bader Charge

18SiC MOS Workshop 2018 - UMD

We analyze the Bader charge

DqA

DqX

DqA = -DqX

BeO Band structure and DOS

19SiC MOS Workshop 2018 - UMD

Phase HEX TET FCC

Lattice constant(Å)

a = 2.71c = 4.40

a = 4.64c = 2.70

a = 3.64

Formationenergy

(Ry/AX2)-48.746 -48.745 -48.674

EgDFT (eV) 7.5 7.2 8.2

EgHSE(eV) 9.6 10.0 11.6

e 7.4 7.2 9.4

Summary

Compared properties of AX2 phases

Computed band gap using different methodologies

Most stable phases have largest band gap

Band gap decreases as halogen atomic weight increases (i.e. flouridesare best candidates for high k dielectrics)

HSE band gap approximately 1.5 eV larger than DFT results

Results are consistent with experimental reports

Different trends found linking composition to electronic properties

Beryllium oxide also good high k dielectric candidate

20SiC MOS Workshop 2018 - UMD