Electron traps emerging in β-Ga2

reverse bias annealing

Torbjørn Østmoe

Thesis submitted for the degree of

Master in Physics: Materials, nanophysics and quantum technology 60 credits

Department of Physics

Faculty of mathematics and natural sciences

UNIVERSITY OF OSLO

after reverse bias annealing

Torbjørn Østmoe

Electron traps emerging in β-Ga₂O₃ after reverse bias annealing http://www.duo.uio.no/

Printed: Reprosentralen, University of Oslo

This thesis addresses deep level defects emerging in β-Ga₂O₃ after reverse bias an- nealing (RBA). Electric field induced point defects are reported in HVPE grownβ-Ga₂O₃ films for the first time. Collected deep level transient spectroscopy (DLTS) data show both temperature and field dependency. We observe an intriguing link between low dose proton irradiation and the RBA phenomenon. Defect states are induced by irradiation only when a diode has been subjected to RBA beforehand. A consecutive RBA process on the same irradiated diode further affects the defects induced by irradiation and RBA.

Cathodoluminescence (CL) excitation remarkably showed a difference in luminescence below RBA exposed proton irradiated Schottky contacts, in comparison to virgin (irradi- ated) areas never exposed to electric fields. This agrees with the generated defects being spatially defined to the volume of the depletion region during DLTS. A larger difference in CL intensity was found for more shallow electron implantation depths, further indicating that the generation of RBA defects scales with the electric field.

Three models for how RBA defects form are discussed in detail. Applying the prime model, we suggest candidates for the point defects being measured after RBA. We con- clude that the deepest traps, E5 and E6, generated with pure RBA conditions (no irradia- tion) likely have an intrinsic origin, more specifically, possibly being the Ga-vacancy (V_Ga) and O-vacancy (V_O). Literature values on certainV_Gaand V_O configurations suggest that they form defect states suitably positioned in the bandgap with respect to the experi- ments. As for the connection to defects being measured after irradiation in combination with RBA, complexes related to V_Ga and V_O are thought to be measured.

Tusen, tusen takk til hovedveilederen min Prof. Andrej Kuznetsov for all tiden han har brukt p˚a ˚a diskutere med meg. At du har vist stor interesse for problemstillingen og resultatene har vært motiverende, og inspirerende. Dessuten, jeg setter pris p˚a din evne til ˚a forklare konsepter med fargerike analogier - dette har styrket fysikkforst˚aelsen min.

Videre ønsker jeg ˚a takke medveilederen min Marianne E. Bathen for ˚a alltid være tilstede. Takk for alle møtene hvor du har latt meg sette ord p˚a ting. Takk for ˚a stille vanskelige spørsm˚al som har tvunget meg til ˚a sjekke detaljene. Til syvende og sist har dette vært helt kritisk!

En spesiell takk til to PhD-studenter som jeg har plaget med spørsm˚al. Nærmere bestemt - Ymir, takk for t˚almodigheten og alt du har lært meg om vakanser i Ga₂O₃, og hvordan jeg kan sammenligne eksperimentell data med DFT beregninger. En ekstra takk for ˚a dele dataen til dannelsesenergidiagrammene som brukes i kap 5. Og den eksperimentelle utgaven - Chris, takk for ˚a dele dine tanker om dataen jeg samlet. Ikke minst for kjappe, men detaljerte tilbakemeldinger p˚a alle spørsm˚alene jeg har stilt. Dere har begge vært veldig nyttige for prosjektet mitt!

Mads, selve oppdageren av RBA fenomenet i β-Ga₂O₃. Takk for ˚a gi meg tips n˚ar jeg trengte det, i tillegg for ˚a ha skrevet en hyppig lest doktorgradsavhandling.

For ˚a nevne noen flere fra LENS som har hjulpet meg, tusen takk til: Lasse for hans oversikt over alt p˚a forskningsgruppen. Cristian og Jon for hjelpen med CL m˚alingene.

Robert og Ilia for innsatsen de har gjort for ˚a holde E-labben g˚aende. Viktor for ˚a ha gjennomført bestr˚alingene.

En vennlig takk til alle masterstudenter p˚a LENS som har vært med p˚a ˚a lage gode minner, f.eks Norgekampene vi har vært p˚a sammen. En ekstra takk til Yannik - for diskusjonene og v˚ar interne humor, Espen og Erlend - for motiverende ord under ko- ronatiden (hard tid ˚a skrive masteroppgaven).

Sist men ikke minst, takk til alle medstudentene mine de siste fem ˚arene. Da tenker jeg særlig p˚a: Cecilie som viste meg at fysikk ikke behøver ˚a være s˚a vanskelig. Jeg er vanvittig stolt av hva du f˚ar til. Takk for gode innspill og alt du har lært meg. I tillegg, takk til Ivarfor inspirerende samtaler (oftest over en Bunnpris-kaffe) og Metin for alt vi deler med hverandre.

Torbjørn Østmoe, 12. mai 2020, Oslo.

BFOM Baliga figure of merit BZ Brillouin zone

CL Cathodoluminescence

CLS Cathodoluminescence spectroscopy CV Capacitance-Voltage

DFT Density functional theory

DLTS Deep level transient spectroscopy E-beam Electron beam

EFG Edge-defined film-fed growth FD Fermi-Dirac

HVPE Halide vapor phase epitaxy IV Current-Voltage

MBE Molecular beam epitaxy NEB Nudged elastic band PVD Physical vapor deposition RBA Reverse bias annealing RT Room temperature

SEM Scanning electron microscopy

SRIM The Stopping and Range of Ions in Matter

A Area

C Capacitance

C_rb Reverse bias capacitance

e_n Emission rate for electrons from trap to conduction band E^† Transition state energy

E_b Dielectric breakdown field

E_t Energy difference between trap level and nearest band edge E_F Fermi level energy

ε₀ Vacuum permittivity ε_r Relative permittivity

γ Temperature independent, material specific constant G Gibbs free energy

h Planck’s constant H Helmholz free energy I Intensity

k Wavenumber k Wavevector

k_B The Boltzmann constant λ Wavelength

m^∗ Effective mass

µ Mobility of charge carriers

n Electron carriers in the conduction band N_D Donor concentration

n_t Actual number of electrons at a deep level N_t Deep level trap concentration

p Hole carriers in the valence band ψ Wavefunction

R_p Projected range

σ_na Apparent capture cross section for electrons S_w DLTS signal for rate window w

t Time

T Temperature W Weighting function

x_d Depletion region in Schottky diode

Chapter 1 Introduction 1

Chapter 2 Semiconductor physics 3

2.1 Crystal lattices . . . 3

2.2 Ga₂O₃: growth and properties . . . 5

2.2.1 Thermal and electrical properties of the β-Ga₂O₃ polymorph . . . 5

2.2.2 Growth and epitaxy . . . 6

2.3 Defects in semiconductors . . . 7

2.3.1 Classification and fundamental description . . . 7

2.3.2 Carrier statistics and the Fermi Level . . . 8

2.3.3 Electrical properties of deep level defects . . . 10

2.3.4 Literature data on the deep level defects in Ga₂O₃ . . . 11

2.4 Schottky diodes . . . 12

2.4.1 Introduction . . . 12

2.4.2 IV characteristics of the SD . . . 12

2.4.3 CV characteristics of the SD . . . 13

Chapter 3 Techniques 14 3.1 Fabrication steps . . . 14

3.1.1 Sample preparation . . . 14

3.1.2 Physical vapor deposition with e-beam heating . . . 14

3.2 Current measurements . . . 15

3.3 Capacitance measurements . . . 16

3.4 Deep-Level Transient Spectroscopy . . . 17

3.4.1 Introduction . . . 17

3.4.2 Schottky diodes with voltage pulses . . . 17

3.4.3 The DLTS spectrum . . . 17

3.4.4 Extracting parameters from Arrhenius plots . . . 19

3.4.5 Depth profiling . . . 20

3.5 Ion implantation and irradiation experiments . . . 20

3.6 Scanning electron microscopy . . . 21

3.7 Cathodoluminescence spectroscopy . . . 21

Chapter 4 Results and discussion 24

4.1 Diode layout and sample labelling . . . 24

4.2 Bulk samples are not affected by RBA . . . 25

4.3 Observing RBA defects in HVPE samples . . . 25

4.3.1 Gradually increasing the temperature . . . 25

4.3.2 Higher voltages . . . 27

4.3.3 Pulse capacitance during DLTS . . . 29

4.4 Distribution of RBA traps . . . 30

4.4.1 Subsequent measurements with reduced reverse bias . . . 30

4.4.2 Depth profiling measurements for the deep levels at high temperature 31 4.5 Effect of proton irradiation . . . 32

4.5.1 Sample selection for the irradiation . . . 32

4.5.2 Irradiation induced defect generation in diode B1, i.e. diode sub- jected to RBA . . . 33

4.5.3 Irradiation induced defect generation in diode B4, i.e. diode with- out RBA . . . 35

4.5.4 Extended discussion on irradiation data . . . 37

4.6 Cathodoluminescence . . . 38

4.6.1 Sample selection . . . 38

4.6.2 Cathodoluminescence of RBA defects . . . 38

4.6.3 Preliminary evidence for RBA defects being vacancy related . . . 40

Chapter 5 Models and point defects 41 5.1 Models for RBA defect generation . . . 41

5.1.1 Diffusion barriers and direct effects of an electric field . . . 41

5.1.2 Linear field model . . . 42

5.1.3 A model that describes both temperature and field requirement . 44 5.2 Possible point defects measured as RBA defects . . . 46

5.2.1 Overview . . . 46

5.2.2 The gallium vacancy . . . 46

5.2.3 The oxygen vacancy . . . 48

5.2.4 Role of impurities, orientation, and fabrication methods . . . 49

Chapter 6 Conclusions and outlook 51 6.1 Conclusions . . . 51

6.2 Outlook . . . 52

A.2 Transition state theory and the nudged elastic band method . . . 59 A.3 Formation energy diagrams . . . 60

Introduction

Everyone is affected by semiconductors because of their presence in almost all electronic devices. The physics of semiconductors has demonstrated much progress in understanding material properties, growth, and defect analysis to production and characterization of devices, e.g. sensors and transistors. However, despite of the progress, new materials are introduced to reach even further.

This thesis deals with an example of such materials, specifically β-Ga₂O₃, which has garnered much interest the past years, as illustrated by an exponential increase in the number of publications on the material. Indeed, β-Ga₂O₃ shows a tremendous potential in power electronics devices. Devices created with wide bandgap semiconductors, as Ga₂O₃, are expected to perform significantly better than silicon based devices under extreme conditions, e.g. exposure to large applied reverse bias. Effectively, the use of wide bandgap semiconductor components results in energy saving, in particular, by efficiently converting the electrical power [1], obviously demanded in years ahead. Combined with its promises, Ga₂O₃ is advantageous since it can be grown from inexpensive techniques, surpassing its more mature material competitors such as GaN and SiC [2].

By today, researchers have reached several milestones with Ga₂O₃, even though the exploration of this promising material has just begun. Among the fabricated devices are Schottky photodetectors with good characteristics, that are blind to wavelengths above 260 nm [3], and modulation-doped double heterostructure field effect transistors promis- ing for high power / high frequency applications [4]. Using a vertical heterostructure, breakdown fields as large as 5.2 MV/cm have been achieved experimentally [5].

However, in order to tailor semiconductors for the applications, it is crucial to identify and understand defects, including so-called point defects. Indeed, point defects are zero- dimensional structural imperfections in an otherwise periodic lattice. Due to the breaks in translation symmetry, point defects result in discrete energy levels appearing inside the energy bandgap, which impacts several electrical properties. Understanding of point defects allows to design materials for specific use, while lack of knowledge could be a reason for the devices’ failure. Isamu Akasaki, Hiroshi Amano and Shuji Nakamura received a Nobel prize in 2014 for their work on defects in GaN that have manifested in

energy efficient LEDs [6]. This underlines how important it is to characterize defects in semiconductors.

Recently, a remarkable defect phenomenon was discovered in β-Ga₂O₃. The material was simultaneously subjected to high temperatures and electric fields, conditions col- lectively called reverse bias annealing (RBA). Using deep level transient spectroscopy (DLTS), it was observed that three distinct defect states appeared inside the energy bandgap as a result of RBA, labelled E3*, E5 and E6 [7]. In short, it can be seen in Fig.

1.1 that defect states appear as peaks in the DLTS spectrum (details are discussed in Sec.

3.4). In Ref. [7], RBA was reported to affect samples grown with molecular beam epi- taxy (MBE) only, which also exhibit a specific surface orientation. Ingebrigtsen et al. [7]

discussed three possible mechanisms that could be responsible for the RBA generated de- fects:

Figure 1.1: E3*, E5, and E6 generation caused from reverse bias annealing of β-Ga₂O₃, after Ref. [7]. The figure is reprinted with permis- sion from the publisher.

(1.) Generation of new intrinsic point defects; (2.) In-diffusion of the mo- bile defects from the bulk of the sam- ple; (3.) Changing the configuration of already existing defects. As a result, more measurements were envisaged in or- der to draw unambiguous conclusions on the microscopic mechanisms responsible for the RBA point defect formation inβ- Ga₂O₃.

This thesis addresses the challenge of looking deeper into the origin of the point defects produced during RBA in β-Ga₂O₃. If the defect generation is not controlled, devices can degrade under the RBA conditions. A thorough investiga- tion and understanding of RBA gener-

ated defects is thus required for Ga₂O₃to take the next leap as a leading power electronics material.

Semiconductor physics

Starting by the basics of solid state physics, this chapter introduces crystals, with and without defects, as well as properties emerging from periodic potentials. In some parts, the text refers to specific examples in Ga₂O₃. Finally, the physics of Schottky diodes is discussed in detail since these devices are used in the investigation of defects in this thesis.

2.1 Crystal lattices

Crystalline materials seek to minimize their free energy, and they do so by arranging the atoms in a periodic manner. The Pauli principle and Coulomb forces oppose each other, resulting in an equilibrium separation length between the nuclei that make up the lattice.

Accordingly, energy bands form because of lattice periodicity. Every lattice point, R, in crystalline structures, is described through a linear combination of the crystals’ lattice vectors, a_i. We associate the lattice points with a certain repeating “basis” that could consist of one or several atoms. In total, Fig. 2.1(a) exemplifies a lattice with a diatomic basis.

a₁ a₂

Γ X

M

b₁ b₂

a) Real space b) 1st BZ in k-space

Figure 2.1: a) 2D square lattice in real space. The diatomic basis is encircled with a dashed line. b) The linked Brillouin zone (BZ). All material properties can be described within the 1st BZ.

Importantly, since phonons and electrons can be described as waves, their properties are best described in the reciprocal space, often referred to as k-space. The reciprocal lattice vectors,b_i, can be constructed by cross products between real lattice vectors [8]. If we squeeze the real lattice in Fig. 2.1(a) along the horizontal axis, it will correspondingly extend horizontally in k-space. It does not exist any ruler small enough to measure the nanoworld, consequently we rather use waves as probes. For all wave phenomena in periodic structures, such as electrons in semiconductors or light in photonic crystals, it is easier to work with wavevectors, k. Furthermore, the smallest repetitive reciprocal volume (spanned out by all b_i) has special interest. This confinement, called the 1st Brillouin zone (1st BZ) is important in solid state physics because practically all material properties can be described within it. By making use of all symmetry properties that leaves the crystal invariant, it is possible to describe all material properties with an even smaller confined reciprocal volume, colored in Fig. 2.1(b) [9].

Felix Bloch was interested in understanding why metals have electrons propagating much longer than the atomic spacing before being scattered [10]. By Fourier analysis, he found that electrons behave as plane waves, except from being modulated by a function with equal periodicity as the crystalline lattice. He understood that electron wavefunc- tions in such materials could be described with

ψ_nk(r) = u_nk(r) exp{ik·r}, (2.1) also known as Bloch’s theorem. Here,u_nk(r) is the function that has the same repetency as the crystal lattice. We also assign two indices for u_nk that represents the band index, n, and wavevector, k. Eq. (2.1) applies to semiconductors and explains appearance of the energy bands. Bloch’s theorem guarantees wavevectors to be conserved in periodic lattices and thus allows electrons to traverse unscattered within a band [11].

Thek-space, Bloch’s theory and Schr¨odinger equation are neatly connected and crucial in order to understand the concept of bandstructures. In a simplified case, if we solve the Schr¨odinger equation for free electrons, energy eigenvalues depend quadratically upon the wavenumber (E ∝ k²). By imagining several evenly spaced parabolas in k-space, as illustrated in Fig. 2.2, bandgaps appear where the parabolas cross. These crossing points corresponds to the BZ edges where solutions are in form of the standing waves. Fig. 2.2 shows two bandgaps appearing, that is, two gaps on the energy axis where there are no legal electron states. The shape of the energy band structure allows us to classify solids as metals, semiconductors or insulators. The latter two have completely filled valence bands (with electrons) and are only differentiated by the magnitude of the bandgap. We refer to the completely filled band as the valence band while the unfilled band above as the conduction band.

In terms of the bandstructure formalism, fundamental concepts of semiconductors may be readily described. For instance, electrons in the valence band can be thermally or optically excited into the conduction band. Such a process creates the two different

ka E =

π 2π 3π

−π 0

−2π

−3π

Figure 2.2: The origin of the bandgap.

charge carriers that exist in semiconductors, namely electrons in the conduction band and holes in the valence band. Electrons move freely in the conduction band because only a few states are occupied there. When an electron is excited, it leaves behind an empty orbital, allowing the holes to move in the valence band too. Notably, it is the effective that is enrolled in transport phenomenon. Indeed, all energy extrema in Fig. 2.2, colored red, can be approximated with a parabolic energy dispersion, E ≈ E₀ +k(∂E/∂k) + k²(∂²E/∂k²)/2. Equating this with the energy for free electrons,E = ¯h²k²/2m^∗, it yields an effective mass

m^∗ = h¯²

∂²E/∂k², (2.2)

if we consider an isotropic material. Consequently, it has been proven that electrons and holes move with a mass related to the curvature of the energy dispersion.

2.2 Ga

O

: growth and properties

2.2.1 Thermal and electrical properties of the β-Ga

O

polymorph

Ga₂O₃ exhibits four different polymorphs labelled α, β, γ and ε. Literature frequently lists five polymorphs, however recently it was discovered that the former δ-phase indeed is a nanocrystalline version of theε-polymorph [12]. Out of the structures, the monoclinic β-phase stands out as most stable and all other polymorphs transform into it at elevated temperatures [13]. Aβ-Ga₂O₃ supercell with 160 atoms is depicted in Fig. 2.3 along the materials’ three lattice vectors. Gallium atoms are colored green and oxygen atoms are colored red. Moreover, there exists two inequivalent gallium sites, coordinated tetrahe- drally or octaheadrally [14], respectively. Likewise, β-Ga₂O₃ exhibits three inequivilent oxygen sites. Fig. 2.3 shows that the structure is highly anisotrophic, in other words, the crystal looks drastically different depending on the orientation you consider from.

Figure 2.3: 160 atom β-Ga₂O₃ supercell (1×4×2 conventional cells [15]) constructed with VESTA [16]. From left to right, the crystal is depicted along the a,b and c axes.

From the introduction we know thatβ-Ga₂O₃is an ultra-wide bandgap semiconductor.

The material has a reported bandgap of approximately 4.7 eV [17]. Strictly speaking, the bandgap is indirect, however, its valence band is remarkably flat, as predicted with first principle calculations [18]. A measure for how promising a material is for power electronics purposes is the Baliga figure of merits (BFOM) defined [19]: BFOM =ε_rµE_b³, whereε_r is the relative permittivity andµis the mobility of the charge carrier. Materials with a bandgap become conductive when the applied electric field surpasses the dielectric breakdown field,E_b. Ga₂O₃ is expected to have E_b ∼8 MV/cm [20]. This is significantly larger than its competitors GaN (3.3 MV/cm) and SiC (2.6 MV/cm) [2], and since the Baliga figure of merit is strongly dependent on the critical dielectric field, Ga2O3 has a better BFOM than its competitors, even though the material only exhibits a decent µ.

A high Eb relates to a low device resistance in the “on”-state, meaning that little power is lost. And hence, Ga2O3 is suitable for energy saving. Experimentally, devices with Eb = 5.2 MV/cm already been fabricated [5].

The two main challenges for β-Ga2O3 are the lack of p-type doping and its poor ther- mal conductivity. Without p-doping, the type of devices that can be made are vastly limited. Because of the heat removal issues, heat spreader technologies that were devel- oped for GaN will come in handy for Ga2O3 too. Both these challenges are currently being addressed [21, 22, 23].

2.2.2 Growth and epitaxy

One of the reasons why Ga₂O₃ has such great potential is because of easy production with melt-based techniques such as Czochralski (CZ) [24] and edge-defined film-fed growth (EFG) [25]. Homoepitaxial extensions of the crystal bulk can be achieved with halide vapor phase epitaxy (HVPE) [26] or molecular beam epitaxy (MBE) [27]. The two latter are epitaxial techniques for thin-film growth, where the epitaxial layer follows the lattice pattern of the bulk substrate. HVPE grown films are mostly used in this work.

Epitaxially grown films achieve defect concentrations much lower compared to within the bulk, and are hence suited for defect investigation. The RBA generated defects were first detected in MBE grown samples [7], precise growth technique for thin-films that allows deposition with monolayer control [28]. For β-Ga₂O₃, MBE samples are oriented along the (010)-crystal plane, while HVPE samples are similarly grown in the (001) orientation.

2.3 Defects in semiconductors

2.3.1 Classification and fundamental description

Vacancy Interstitial Substitutional

Figure 2.4: Typical elementary point defects that exist in real solids, which may yield states in the bandgap.

The concept of a perfectly periodic crystal presented in Fig. 2.1 is too optimistic in the real world. Perfect crystals do not exist, and the deviation from the symmetry occurs in the form of defects.

The simplest defect imaginable is a vacancy, i.e. simply the lack of an atom in a regular matrix site. Notably, every crystal contains an equilibrium number of vacancies, n, that minimize the change in Gibbs free energy, ∆G, for a specific temperature. We focus on ∆G because we want to see whether or not adding (or removing) vacancies results in a cost or gain in energy. By examining the enthalpy, H, and entropy,S, terms separately as

∂n∆G=∂n(∆H−T∆S) = 0, (2.3)

it becomes clear that ∂_n∆H increases with n because it costs energy to break electron bonds between the atoms. However, the ∂_nT∆S term increases too since the crystal gets progressively more disordered with the addition of vacancies. Together, this leads to an optimal vacancy concentration. Typical point defects (vacancy, interstitial and substitutional) are illustrated in Fig. 2.4. We can further categorize defects into being either intrinsic or extrinsic, where the latter incorporates impurity atoms into the crystal.

The vacancy is an intrinsic point defect that always is present, however extrinsic defects are introduced during the material growth process. Thereby the number of unwanted extrinsic defects decrease when the growth processes gets better. Other extrinsic point

defects include interstitials and foreign substitutionals. Since point defects disturbs the lattice, additional local stress is always present related to the defect. Complexes are de- fects composed of a few clustered defects, e.g. a coupled impurity-vacancy pair. Notably, complexes and extrinsic defects are not necessary harmful for devices. As an example, so- called NV-centers (Nitrogen-Vacancy) in diamond can be utilized for quantum computing purposes [29]. The understanding of extrinsic defects in semiconductors has enabled the making of the technological devices all around us today. In addition to point defects and complexes, materials may also contain defects with higher dimensionality such as dislocations, stacking faults and precipitation.

Bloch functions (Eq. (2.1)) are wavefunction solutions for periodic lattices. This however changes when point defects are introduced as perturbations, breaking the trans- lational symmetry of the lattice. New states may emerge inside the bandgap. By con- sidering that the perturbed potential, V_p, varies slowly over a unit cell, and by taking into account the effective mass approximation, it is possible to derive the envelope wave equation [30]

− ¯h²

2m^∗∇²+V_p(r)

ψ(r) = [E−E_C]ψ(r), (2.4) which states that a defects energy level can be related to the conduction band minimum, E_C. In addition, Eq. (2.4) also reveals that the crystals lattice potential is completely eliminated, meaning that only the perturbed potential determines the eigenvalue of the state. With the envelope equation, it is straightforward to calculate the energy eigenvalues for hydrogen-like¹ defects introduced under doping. Borrowing theory from the hydrogen atom, the defect state energy can be found with

Et =EC −13.6 eV× 1 j²

1 ε²_r

m^∗

m , (2.5)

with j as integer, and m being the electron rest mass. The electrons behaves as if they were in a homogeneous medium with the crystals dielectric constant, ε_r, and an effective mass of the corresponding electronic band [30]. Typically, defect levels are classified as shallow or deep, depending on their position in the bandgap. When materials are doped, shallow levels form in the vicinity of one of the bands. So-called donor states are positioned close to the conduction band, and therefore electrons on these states are easily donated to the crystal. Acceptors have energy levels close to the valence band, making them able to accept electrons from the valence band. Deep levels will be described in Subsec. 2.3.3.

2.3.2 Carrier statistics and the Fermi Level

Electrons are described by a total antisymmetric wavefunction because they are fermions.

They follow the Pauli principle, which says that only one identical electron can occupy

1e.g. P-atom in Si-crystal, one electron is donated to the conduction band.

a quantum state. Because of the spin property of electrons, m_s = ±1/2, it is possible to put two electrons with opposite spins in the same state. Fermions are distributed with energies according to Fermi-Dirac (FD) statistics. In a simplified case, valid for conditions in the rest of this thesis, the chemical potential is taken to be equal to the Fermi Level energy [8],µ=E_F. Thus, we have

f(E, T) = 1 1 + exp_E−EF

kT

. (2.6)

Eq. (2.6) clearly states at the Fermi level, i.e. withE =E_F, have a 50% chance of being occupied. At zero Kelvin, all states below E_F are filled with electrons, and likewise, no states above are filled with electrons. The FD distribution is symmetric around E_F, making the Fermi level a natural reference energy when counting carriers [31].

The density of state (DOS) quantifies the number of states that have the same energy inside a solid. If a semiconductor consists of N number of electrons, N can be found by integrating the product between DOS and the FD distribution over all energy states

N = Z ∞

0

DOS(E)f(E, T)dE. (2.7)

The integral interval in Eq. (2.7) can be changed into counting hole and electron car- riers. We exemplify the theory with n-type conductivity hereafter. All electrons in the conduction band are counted by performing the integral in (2.7) from EC −ε to infinite energy. Furthermore, since electrons in the conduction band typically have energies close to EC, we can justify an approximation that rewrites the DOS into an effective density of states, NC, exactly with energy E = EC. Furthermore, by assuming that the defect state is several kT belowEC, the integral in Eq. (2.7) is easily solved. We calculate

n= Z ∞

EC−ε

N_Cf(E)δ(E−E_C)dE =N_Cf(E_C)≈N_Cexp

−E_C−E_F kT

, (2.8)

where the value of NC is derived (see Ref. [31]) to only be dependent on temperature and the effective mass for electrons in the conduction band,

N_C = 2

2πm^∗kT h²

3/2

. (2.9)

Moreover, using Eq. (2.8) it can be proven [31] that the carrier concentrations can be found with

n=n_iexp

E_F −E_i kT

and p=n_iexp

E_i−E_F kT

, (2.10)

wheren_i is the intrinsic carrier concentration in a crystal without defects. Only the direct valence to conduction band transitions are allowed for electrons in intrinsic crystals. By using Eq. (2.10), it is straightforward to understand the temperature dependence of the carrier concentration in a doped semiconductor. If we imagine a donor state atT →0 K, all electrons are localized at the respective donor atoms. With increasing temperature,

the electrons are emitted to the conduction band. Since the energy required to excite an electron from the valence band to the conduction band is much larger than that from a defect state near the conduction band minimum, the carrier concentration is maintained equal to the defect concentration, n ≈ N_d, over a broad temperature range. At higher temperatures, however, electron excitations from the valence band to the conduction band determine the carrier concentration, making the semiconductor perform as intrinsic [31].

2.3.3 Electrical properties of deep level defects

Deep-level defects are also present in crystal structures besides the shallow dopants dis- cussed in the previous subsection. Deep-level defects are important for the electrical properties of a semiconductor since they can act as electron traps or recombination cen- ters.

Four specific processes can take place related to deep level traps [32]. Electrons can be emitted from a trap to the conduction band, or inversely, a trap can capture electrons from the conduction band. These processes have emission and capture rates denoted e_n and c_n. Similarly, we can imagine holes being captured and emitted, in this case related to the valence band, equivalently, with emission and capture rates are denotede_p andc_p. This text will argue for trap-conduction band exchange, but all concepts surely applies identically for holes. The capture rate for electron traps are proportionally related to the capture cross section, σ_n and electron flux, i.e.

c_n=σ_nhv_nin, (2.11)

where the capture cross section represents an area in which the defect captures electrons and hv_ni is the average thermal velocity for the electrons.

Suppose we have n_t electrons at a number of traps that could hold N_t electrons, the net change in n_t can be described using

dn_t

dt = (cn+ep)(Nt−nt)−(cp+en)nt, (2.12) where Nt − nt describes the non-occupied trap states. Eq. (2.12) makes use of the rates defined above. In thermal equilibrium, occupied and non-occupied states emit and capture electrons at the same rate. The fraction of filled trap states,nt/Nt, can be found using the FD distribution with E =Et. Collectively this results in [32]

n_t

N_t = c_n c_n+e_n =

1 + exp

E_t−E_F kT

−1

. (2.13)

Non-degenerate semiconductors have electron carrier concentrations given by Eq. (2.8).

By combining all quantities and equations in this subsection, it is possible to examine the temperature dependence of the emission rate for electrons [32]. Both the thermal

velocity and effective density of states are temperature dependent. Henceforth, it is straightforward to derive the emission rate in thermal equilibrium to be given by

e_n(T) =σ_nhv_niN_cexp

−E_c−E_t kT

=γT²σ_naexp

−E_na kT

, (2.14)

where all temperature independent values are contracted into γ = 2√

3(2π)^3/2k²m^∗h⁻³, calculated to γ ≈ 8.13× 10²⁰ cm⁻² for β-Ga₂O₃. Eq. (2.14) says that the emission rate depends on the apparent cross section, σ_na and apparent capture trap energy, E_na. Usually, we want to extract the real capture cross section and energy position of the trap. For temperature independent capture cross sections, we can interpret the activation energy E_na = ∆H [32].

2.3.4 Literature data on the deep level defects in Ga

O

The literature data documenting deep level properties in β-Ga₂O₃ is still limited. To be specific, Tab. 2.1 summarizes the results from Ref. [33]. Notably, the data indicate rather large uncertainties for the RBA generated defects, i.e. E3*, E5, and E6. Obviously, the data is incomplete, which motivates for further work.

Table 2.1: Energy position, capture cross sections and features of known electron traps inβ-Ga₂O₃. The table is reprinted from Ref. [33].

Energy E_t [eV] Capture cross section [cm²] Cause E1 0.56±0.03 0.3−5×10⁻¹³

E2* 0.75±0.04 3−7×10⁻¹⁴ Irradiation E2 0.78±0.04 0.2−1.2×10⁻¹⁵

E3 1.01±0.05 2×10⁻¹⁴−1×10⁻¹²

E3* 0.92−1.05 0.2−6×10⁻¹³ RBA

E4 1.4±0.15 3×10⁻¹⁵−2×10⁻¹²

E4* 1.4±0.15 3×10⁻¹⁵−2×10⁻¹² Irradiation

E5 1.5±0.15 10⁻¹⁴−10⁻¹¹ RBA

E6 1.8±0.2 10⁻¹²−10⁻⁹ RBA

2.4 Schottky diodes

2.4.1 Introduction

Diodes are electrical components that only allows current going in one direction. In this study, metal-semiconductor junctions, also called Schottky diodes (SD), are used in the DLTS technique (see Sec. 3.4) to characterize defect states. An advantage of SD, compared to PN-junctions, is that they do not rely on p-type doping, which is not yet achieved in Ga₂O₃. Both rectifying and ohmic contacts can be made by depositing a suitable metal directly on the sample.

Figure 2.5: Band bending in metal- semiconductor junctions.

The Fermi levels of a metal and a semicon- ductor align when the materials are brought together. Charge exchange causes the en- ergy bands of the semiconductor to bend, giv- ing rise to an energy barrier, Φ_B, as illus- trated in Fig. 2.5. More specifically, Fig. 2.5 presents the Schottky-Mott rule which uses the metals workfunction, φ_M, and the semi- conductors electron affinity, χ_SC, to estimate the barrier height², Φ_B = φ_M −χ_SC. The bending forms a depletion region close to the metal-semiconductor interface, free of mobil- ity carriers. The fixed charges associated with donors in the depletion region result in an electric field which stops the exchange of elec- trons. The potential barrier is a sum of the applied voltage, V_a, and the built in voltage,

V_b. Since the depletion region is positively charged, a positive potential applied on the semiconductor with respect to the metal will enhance the band bending. These are the reverse bias conditions. The depletion region also has an associated capacitance that is dependent on the applied voltage. Several junction spectroscopic techniques are based on the fact that the capacitance is dependent on the applied voltage [35].

2.4.2 IV characteristics of the SD

By applying a voltage equivalent to the built in voltage, V_a =V_b, the electrons will start to diffuse from the semiconductor into the metal. This is because we break down the barrier shown in Fig. 2.5. Electrons that have enough energy to surpass the energy barrier are said to be thermionic [36]. For highly doped substrates, a tunnelling current

2In reality, the barrier is much less dependent upon the metals work function. See Ref. [34] for full description.

is possible in addition to the thermionic case [36], but this is beyond the scope of this text. In the thermionic regime, the current can be expressed with a saturation current, I₀, and an exponential function

I =I0

exp qVa

ηkT −1

, where I0 =RT²Aexp h

− ΦB

kT i

. (2.15)

Here A is the area of the diode, and R is the material dependent Richardson’s factor.

Moreover, η represents the diodes ideality factor, with η equal unity being perfect. Eq.

(2.15) corresponds to rectification.

2.4.3 CV characteristics of the SD

The depletion width,x_d, can be found by solving Gauss’ law [32]. This allows us to relate the electrostatic potential, V, and charge density, ρ(x). By assuming a homogeneously doped semiconductor, ρ(x) = eN_D, the depletion width increases with applied reverse bias voltage and decreases with substrate doping, following the expression

x_d= s

2ε₀ε_r(V_a+V_b) qND

. (2.16)

Blood and Orton [32] gives a thorough derivation that leads to the differential capacitance for a SD being similar to a parallel plate capacitor. In the low temperature limit, the capacitance can therefore described with

C =ε₀ε_rA x_d =

s

A²qε₀ε_rN_D

2(V_a+V_b). (2.17)

Here it becomes clear how capacitance and applied voltage are related. The scenario is similar to a parallel plate capacitor because there are no free charges within the depletion region. Consequently, only the charge fluctuations at x_dgive rise to the capacitance [32].

However, there is a crucial difference separating a SD from regular parallel plate capacitor, being that the CV relation is not linear. Similar derivations can be used to determine the carrier concentrations for in-homogeneously doped semiconductors (see Ref. [32] for details). By using

n(x)≈ND(x) = C³

ε₀ε_rqA^2dC_dV , x=ε0εr

A

C(V), (2.18)

it is possible to depth profile the carrier concentration. When the voltage is varied, the depletion depth varies allowing us to probe deeper into the material, or likewise, closer to the vicinity of the Schottky junction.

The derivation of Eq. (2.17) works by utilizing the depletion approximation, which states thatx_d is sharply defined. The Debye screening length, L_D, questions the validity of the depletion approximation, only being valid when x_d >> L_D. This thesis concerns diodes operating at high temperatures, i.e. at which the Debye length increases, however quick calculations estimates that L_D <60 nm and x_d∼1 µm in the experiments, which validates the depletion approximation.

Techniques

Fabrication steps required for creating a Ga₂O₃ Schottky diode are outlined. These steps include laser cutting, cleaning and physical vapor deposition (PVD). Current-voltage (IV) and capacitance-voltage (CV) measurements are used to investigate the diodes character- istics. Deep level transient spectroscopy (DLTS) and cathodoluminescence spectroscopy (CLS) are introduced as techniques to identify and study deep-level defects in semicon- ductors.

3.1 Fabrication steps

3.1.1 Sample preparation

All samples were cut to ∼5 x 5 mm² pieces with a laser cutter, ensuring multiple diodes on each sample. The cleaning routine removes organic contaminants. The three listed rinsing steps below were carried out before deposition, each occurring in an ultrasonic bath for five minutes:

1. Aceton 2. Isopropanol 3. Distilled water

Afterwards, the samples were blown dry with a nitrogen gun.

3.1.2 Physical vapor deposition with e-beam heating

Physical vapor deposition was used to deposit a thin film on top of a semiconductor substrate. Within the PVD chamber, the pressure is pumped down to a p ∼ 10⁻⁶ torr vacuum. The crucible containing the metal to be deposited is placed below the sample.

The three main crucible heating systems are resistive, inductive and e-beam [36]. The advantage with the latter is that only the charge can be heated, while the crucible itself is cooled. This guarantees lower contamination [36]. E-beam heating works by colliding accelerated electrons with the material to be deposited. The electrons propagate in a trajectory following a 270^◦ turn, caused by a bending magnet, resulting in a perpendicular

collision with the charge surface. When the charge has high enough temperature it leaves the crucible as vapor. The deposition rate is determined by the properties of the charge, its temperature and the chamber geometry [36]. The machine performs in-situ measurements on the thickness of the grown film. A quartz crystal resonates with a frequency according to its mass. During deposition, the resonance frequency gets shifted, and by knowing the material that is deposited it is possible to calculate the thickness of the film [28].

Ga₂O₃ Bulk/HVPE/MBE

Ni 150 nm

Ti 10 nm

Al 150 nm

Figure 3.1: Schottky diode design. The unpolished backside of the substrate is marked with a thicker line. The figure shows three schottky diodes on one sample.

The Schottky barriers are formed at the interfaces between the Ga₂O₃-substrate and Ni contacts. Circular Ni contacts were deposited through a shadow mask with 480 µm diameter holes. A thin 10 ˚A layer of Ti was deposited on the unpolished backside and further extended with 100−150 nm Al. A visual of the final SD is shown in Fig. 3.1.

The design is in accordance with the initial study [7].

3.2 Current measurements

6 4 2 0

Voltage (V) 10 ¹⁰

10 ⁷ 10 ⁴

Current (A)

15 10 5 0

Voltage (V) 1

2 3 4 5 6

Conductance (S)

1e 7

Figure 3.2: IV and conductance measurements. The two measurements are not linked.

Rectification is a fundamental property of a SD. Recalling Eq. (2.15) we know that the current increases exponentially with forward bias, while it should maintain little current in reverse bias. The current saturates for large forward bias because of series resistance. IV-curves are plotted logaritmically as in Fig. 3.2, because it efficiently shows how rectifying a diode is (at least 8 orders of magnitude in the example). Furthermore,

Fig. 3.2 also plots the conductance of a diode. When it comes to DLTS-measurements (soon presented), it is important that the conductance is low (usually ∼ 10⁻⁷ S in this study) and decreasing with increasing reverse bias, as the measurement in Fig. 3.2. A low conductance means a high resistance in reverse bias.

3.3 Capacitance measurements

10 8 6 4 2 0

Voltage (V) 15

20 25 30 35 40

Capacitance (pF)

10 8 6 4 2 0

Voltage (V) 1

2 3 4 5

1/C2(1/F2) 1e21

Figure 3.3: CV-curves plotted in two different ways. The plot to the right is most convenient when extracting parameters.

CV measurements are crucial when verifying the quality of a diode. Measurements on a particular diode, with design according to Fig. 3.1, is shown in Fig. 3.3. With CV measurements it is possible to extract important parameters such as carrier concentration and the built in voltage barrier. It is convenient to rewrite Eq. (2.17) when extracting relevant information from CV measurements

1

C² = 2(V_bi+V)

A²qε_rε₀N_D ⇒ N_D = 2

A²qε_rε₀^d(1/C_dV ²⁾. (3.1) The mask area, A, is chosen under fabrication. Extrapolation through the V-axis in Fig. 3.3 yields the built in voltage, and the carrier concentration can be found from the slope as derived in Eq. (3.1). The example calculates to N_d ≈ 9.07×10¹⁵ cm⁻³ and V_bi ≈1.38 V.

From the discussion of current and capacitance of SDs, it is apparent that its circuit equivalent is a resistor and capacitor in parallel. In reality, the equipment measures the complex impedance of the junction and thereafter determines parameters such as conductance and capacitance [32, 35].

3.4 Deep-Level Transient Spectroscopy

3.4.1 Introduction

D. V. Lang invented Deep-Level Transient Spectroscopy (DLTS) [37] which has become a widespread technique for experimentally measuring electron traps within the bandgap.

During conventional DLTS, a temperature scan is carried out while a reverse biased diode is perturbed by voltage pulses that are “positive” with respect to the reverse bias. Using DLTS, it is possible to determine properties of deep levels such as concentration, trap level and capture cross section. Defect concentrations as low as 10¹⁰cm⁻³ can be characterized for semiconductors doped withN_D ≈10¹⁵ cm⁻³, indicating a remarkable sensitivity [35].

A major advantage with the technique is that the defects appear as peaks in the resulting spectrum. However, it can be challenging to establish from where a defect originates, as the technique yields no information about its chemical identity. Another drawback of the technique is that it can be, in some cases, difficult to separate peaks due to a overlap.

3.4.2 Schottky diodes with voltage pulses

The underlying physics behind DLTS measurements can be divided into three steps.

Starting from equilibrium state with a diode subjected to a specific reverse bias voltage (e.g. −10 V), the diode is perturbed with a 50 ms voltage pulse (e.g. up to 0 V). The voltage pulse shrinks the depletion zone, concurrently filling traps with electrons. After the falling edge of the voltage pulse, capacitance is measured while the electrons thermally emit from the traps back into the conduction band, once again reaching equilibrium. The capacitance at equilibrium, further denoted C_rb¹ and presented in Eq. (2.17), is modified with the perturbation pulse, correcting the equation into

C(t) = s

(N_D−n_t(t)) A²qε₀ε_r

2(V_a+V_b), (3.2)

using n_t as defined in Subsec. 2.3.3. To repeat, there are n_t electrons placed at N_t trap sites. Eq. (3.2) shows that the capacitance is time dependent when the electrons ther- mally emit after the filling pulse. By assumingn_t=N_texp{−e_nt} N_D, we approximate the capacitance transient as [32]

C(t) = C_rb

1− N_t

2N_D exp{−e_nt}

. (3.3)

3.4.3 The DLTS spectrum

The most intuitive way to construct a DLTS spectrum is by imagining the boxcar weight- ing function. How boxcar works is plotted in Fig. 3.4. Here, the DLTS signal is created

1C_rbis used in the text. DLTS-figures with ∆C/C on they-axis means ∆C/C_rb.

0.0 0.2 0.4 0.6 0.8 1.0 Time [arb.unit]

39.6 39.7 39.8 39.9 40.0

Capacitance [pF]

(a) Transients.

150 160 170 180 190 200

Temperature [K]

0.00 0.01 0.02 0.03

DLTS signal [pF]

(b) DTLS signal.

Figure 3.4: The DLTS signal can be constructed by measuring capacitance transients.

by taking the difference in capacitance between two different times, ∆C=C(t₂)−C(t₁) when the transient is measured. The transients, shown in Fig. 3.4(a), are plotted using Eq. (3.3) with typical numbers. A linear array of emission rates, {e_n}, is used in the illustration. Three different time windows (reciprocally called rate windows) colored blue, red and green, are used to measure the transient. The difference in capacitance, between the dark vertical line at t = 0.1 [a.u] and the edges of the colored regions, is used to extract ∆C. Be aware that the time windows are overlapping in Fig. 3.4. A temperature array is further computed by solving Eq. (2.14) numerically. In general, the DLTS signal is formalised to

S_w = Z

dt∆C(T, t)W(t) = 1 w

t_d+tw

X

tj=td

∆C(T, t_j)W(t_j), (3.4) where W is the weighting function, and t_d is a delay time before the transient starts being measured. The delay time is required because the falling edge of the filling pulse is not infinitely steep. Moreover, t_j is a running time variable that ends at t_w +t_d (the w-subscript denotes the window number). The generalization in Eq. (3.4) expresses the boxcar weighting function with delta functions asW =δ(t−t₂) +δ(t−t₁). By combining Eqs. (3.3) and (3.4), the DLTS signal can be used to extract trap concentrations using

S_w =C_rb N_t 2N_D

1 w

td+tw

X

tj=td

exp{(−e_nt)}W(t_j)≡C_rb N_t

2N_DF_w, (3.5) where the latter parameter, F_w, also is a numerical parameter that must be determined for each rate window. Many constants were set equal to one when Fig. 3.4 was created, scaling the axis to reasonable numbers in the end.

This study uses t_w = 10×(2ⁿ) ms on then = 1,2,· · · ,6 time windows. The transient is thus measured with 2⁶ = 64 points. A more complex weighting function called lock-in is applied in this study, because it achieves better signal-to-noise ratio and more narrow peaks. The appearance of the DLTS spectrum depends on the weighting function that is

used. How lock-in filters out emission rates, compared to the outlined boxcar weighting function, is mathematics and beyond the scope of this text. For completeness, we express the lock-in weighting function as [38]

W_lock−in =







−1, 0< t < tw/2 1, t_w/2< t < t_w.

(3.6)

3.4.4 Extracting parameters from Arrhenius plots

300 400 500 600

Temperature [K]

0.002 0.000 0.002 0.004 0.006 0.008

NT/ND=2C/C

28 30 32 34

1/(kBT) 12

10 8

log(emax/T2)

Fit: Et = 0.79 ± 0.04eV = (1.3E-15 - 1E-14 )cm²

Figure 3.5: How the emission rate and temperature of each peak maximum are extracted, and plotted in terms of an Arrhenius plot that gives information about capture cross section and trap energy.

All the produced peaks are associated with a corresponding emission rate and temper- ature, (e_n,max, T). Per definition, we want the temperature derivative of the DLTS-signal to equal zero at the peaks, ^dS_dT^w|_peak = 0. Applying the chain rule, the statement can be rearranged into: ^dS_dT^w = _d(e^dSw

nt) d(ent)

T . We understand that the latter fraction never equals zero, and hence only the former fraction needs to equal zero at a peak. From the various rate windows, an array {(e_n,max, T)} must be determined numerically for all peaks. Fur- ther, Eq. (2.14) can be used to extract both the capture cross sections and trap energy levels with a linear regression of an Arrhenius plot

ln

e_n(T) T²

= ln(γσ_na)− E_t

k_BT. (3.7)

A practical example with real data is shown in Fig. 3.5. We can see that a large peak, corresponding to a defect, appears between T = 350−400 K. The details are left to the results chapter, but indeed, Fig. 3.5 demonstrates how emission rates and temperatures are plotted, and thereby how Eq. (3.7) works. The corresponding energy to the defect is E_t = 0.79±0.04 eV. The apparent capture cross section is calculated to σ_na = (e^14.9±1.1)/(8.13×10²⁰) cm². Standard deviations are calculated by taking the square root of the diagonal elements in the covariance matrix. This study sometimes

multiplies the DLTS-spectrum in Fig. 3.5 with the carrier concentration determined from a beforehand CV-measurement, and in such a case, the trap concentration is directly plotted on the axis. Furthermore, this study usually only shows the smoothest rate window (leftmost curve in Fig. 3.5(a)), with t_w = 640 ms. Reverse bias annealed defects are studied by comparing the change in the DLTS signal for this rate window during the course of heating and cooling. This is in line with the initial investigation of RBA defects [7] (see Fig. 1.1).

3.4.5 Depth profiling

A conventional DLTS-spectrum incorporates no details on the electron trap distribution throughout the depletion zone. It is however possible to determine the distribution with depth profiling measurements. The technique is used in conjunction with DLTS, therefore presented here. A derivation of the depth profiled trap concentration can be found in Blood and Orton [32]. By neglecting the λ-correction factor, the trap concentration can be found with

N_t=−qx²_r

N_d⁺(x_r)N_d⁺(x_p)δ(∆C/C)

δV_p , (3.8)

whereN_d⁺ is the ionized donor concentration atx_r and x_p, determined with a beforehand CV-measurement. Here,r andpdenote reverse and pulsing bias conditions, respectively.

0 t V_p

Vrb

Figure 3.6: Voltage pulses used during depth profiling.

Opposed to the operation of DLTS, depth profiling measurements are isothermal. The depletion zone, and thus the probing depth, is varied by scanning over different applied voltages. The diode is kept at a constant re- verse bias while voltage pulses fill traps closer and closer to the SD junction, as illustrated in Fig. 3.6. The voltage pulse derivative of the DLTS signal, in Eq. (3.8), indeed has the same shape as the trap distribution for ho- mogeneously doped samples. This study av- eraged the transient 10 times for each voltage pulse to ensure smooth ∆C/C.

3.5 Ion implantation and irradiation experiments

Ion implantation can be used to dope semiconductors and is thus important for device fabrication. Foreign introduced atoms can act as donors, acceptors or deep-levels in semiconductors. An ion implanter is used to introduce such atoms by bombarding the sample with a dose of ions that carry a specific energy. In addition, the implanter can be used to generate intrinsic defect states by high energy irradiation.

Coulomb scattering from the nuclei and a viscous-like electron drag force causes the ions to slow down inside the material, reaching a mean depth, R_p, called the projected range [36]. Numerous factors such as R_p and vacancy generation can be estimated with Monte Carlo simulations. The Stopping and Range of Ions in Matter (SRIM) code [39]

has been used in this study.

3.6 Scanning electron microscopy

By using electron beams to image sample surfaces, in contrast to electromagnetic waves as in optical microscopes, it is possible to achieve far better resolutions. From a LaB₆ filament, electrons accelerate towards the sample surface. The electrons traverse through an optical system consisting of electromagnetic lenses and apertures. Once the elec- trons reach the sample, a variety of different interactions are possible. For instance, the incoming electrons can back-scatter, or secondary electrons from the specimen can be emitted back. A detector measures what is radiated from the sample and converts the information into a micrograph. Brightness contrasts in the micrograph results from the secondary electron yield being different for tilted planes [40]. The resolution of the SEM micrograph is limited by aberrations. For maximized resolution, it is required to find the optimum aperture angle. Both spherical and diffractive aberrations causes the objective lens to blur the electron beam focus [40].

Clearly, when charged electrons are bombarding the surface, the charge accumulates within the specimen. Charging effects should be avoided because they affect the electron beam and consequently the micrograph. The solution is to apply a conductive metal between the specimen and the stage. Silver paste is applied to the backside of the sample in this study. Similarly to ion implantation, electron ranges can be found with Monte Carlo simulations. In the case of electrons, the projected range increases with electron gun voltage and decreases with material density and atomic numbers [40].

3.7 Cathodoluminescence spectroscopy

3.7.1 Principles

Light emission by spontaneous emission in solids is collectively called luminescence. Ei- ther photons or electric currents are used as the excitation mechanism for achieving luminescence. Thereby, luminescence is separated into photo- and electroluminescence.

It is possible to study material defects utilizing the inverse photoelectric effect, called cathodoluminescence (CL), which can be thought of as a type of electroluminescence [41].

In the experiments, electrons with energies above 1 keV bombard the crystal surface, leading to light emission from the sample. The technique resembles SEM and can there-

Stage

E-beam source

O.S

Grating

Detector

Figure 3.7: A typical cathodoluminescence spectroscopy setup.

fore be performed within the same experimental setup. The practical difference between CL spectroscopy (CLS) and SEM is that a parabolic mirror must be inserted between the electron beam source and sample. Fig. 3.7 illustrates the main components of the experimental setup. The electron beam needs to be focused through a hole in the mir- ror. Once luminescent light is emitted from the sample, the parabolic mirror collects the light, further sending it collimated towards an optical system (O.S). Afterwards, the light is focused through a slit and onto a diffraction grating that separates the various wavelengths. Lastly, the various wavelengths are detected and analysed.

CL spectra contain intensities of emitted light as a function of wavelength. However, in this study, CL is used to support experimental findings together with DLTS. The wavelength axis of the spectrum is thus converted into an energy scale. Wavelengths and energies are related through

E = hc

λ ≈ 1240 nm eV

λ . (3.9)

In addition, the intensity scale must be corrected because of the inverse proportionality of energy and wavelength, with the so-called Jacobian transformation [42]. By applying the identityI(λ)dλ=I(E)dE, it follows that the corresponding intensity scale in energy units is expressed as

I(E) = I(λ)

1240 nm eVλ². (3.10)

Lastly, it should be mentioned that thermodynamic (DLTS) and optical transitions (CL) are not the same, are not expected to yield the same defect eigenvalues [43]. In short, the difference lie in whether or not the process is slow or fast. It leads to absorption having greater eigenvalues compared to the thermodynamic that is measured with DLTS [43], moreover, emission energies that are measured with CLS should be lower compared to the thermodynamic transitions.

300 400 500 600 700 Wavelength [nm]

10

10

Int en sit y ( ) [a .u]

No filter LP filter

Figure 3.8: Artifacts are present in CL-spectra when measuring Ga₂O₃.

3.7.2 CL in β -Ga

O

Ga₂O₃ exhibits a broad band luminescence spectrum with many contributions [44]. When performing CL spectroscopy on Ga₂O₃, the peak maximum in the CL spectrum shifts between measurements, both intensity and wavelength-wise, depending on the region being probed. When averaging the CL signal over a larger area, consistent data is achieved when comparing two seemingly identically looking regions.

Secondly, Ga₂O₃ produces artifacts in the CL data. A higher order harmonic artifact of the broad luminescence peak can be seen by plotting the CL signal against wavelength, i.e. what is presented in Fig. 3.8. Two peaks appear when scanning β-Ga₂O₃ without a filter. The peak at longer wavelengths is the artifact, only reflecting the presence of the peak at shorter wavelengths.

Since the defects that are measured with DLTS have energies E_t ≥ 1 eV, only the intensities at corresponding wavelengths are of special interest. Using Eq. (3.9), light emission withλ = 690 nm is calculated to an energyE_t≈1.8 eV from a band-edge. The artifact hence affect the reliability to explore RBA defects using CL spectroscopy.

A long pass (LP) filter that only allows 400 nm and longer wavelengths to pass was applied in order to detect the larger wavelengths. Fig. 3.8 clearly verifies that the peak at the longer wavelengths indeed is an artifact, since it gets removed by utilizing the LP filter. Furthermore, since the LP filter is physical, it is expected that the CL signal gets lowered when it is inserted. This is the case in Fig. 3.8.