Diamond — the host material

Diamond is a very exceptional material with widespread applications. First of all it is certainly the most famous gemstone due to its special optical properties. Apart from that its unsurpassed hardness and thermal conductivity pave the way for various applications such as for grinding and polishing tools as well as for heat sinks. Other upcoming applications are in the field of conventional semiconductors like Si or GaAs. Although diamond is perfectly stable under ambient conditions it is not the stable allotrope of carbon. All of its special properties originate from its lattice properties.

2.1.1. Characteristics

The diamond lattice consists of covalently bond carbon atoms. Each of the four valence electrons of the sp³-hybridized carbon participates in bonds to neighboring atoms (dis-tance 1.44 Å). This leads to a face-centered cubic (fcc) lattice structure with two-atomic basis where one fcc sub-lattice is shifted against the other one fourth along the space diagonal of the unit cell (lattice constant 3.57 Å, see figure 2.1). The covalent bonds make the diamond very stiff and the completely saturated valence electrons lead to a huge bandgap (5.48 eV). Hence, diamond is a formidable insulator and is optically trans-parent deep into the UV. It also possesses a large refractive index of 2.42.

In addition, its hardness makes it unlikely for other impurity atoms to enter the lat-tice, except for boron and nitrogen which are the major lattice impurities. Actually, a small amount of impurities can give diamond specific colors. Boron, for instance, leads to blue diamonds whereas nitrogen colors them yellow and irradiation damaged crystals appear green or brown. An increasing content of NV centers leads first to pink, later to purple and finally to almost black diamonds.

Naturally, diamonds are formed under high pressure and high temperature conditions in the earth crust. This is the stable region of diamond in the phase diagram of carbon.

2. Single NV centers in diamond

Figure 2.1.: Diamond lattice structure and NV defect center. left, Two unit cells of the diamond lattice where the one contains an NV color center. The unit cell boundaries are h001i directions. Carbon atoms (“C”) are dark gray, the substitutional nitrogen atom is marked with “N”

and the vacancy with “V”. Lattice relaxation due to the NV center is neglected. right, NV center and two shells of nearest neighbor carbon atoms around the vacancy. The c_3v symmetry axis or NV axis is pointing upwards (dark arrow) and coincides with the h111i direction of the diamond lattice.

Most of the artificially created diamonds are also generated by applying high temper-atures and pressures but with the addition of catalysts. These diamonds are therefore called high pressure high temperature (hpht) diamonds. A second way is chemical vapor deposition (CVD) (more specifically microwave plasma assisted CVD). As most of the diamonds used in this work are CVD diamonds we explain this technique is explained in more detail below.

The CVD diamond growth is a homoepitaxial technique (i.e. one needs a diamond surface as a seed layer) and the process is described according to [98, 99]. Often, a [001] surface orientation is chosen as a seed layer because less defects are created dur-ing growth [100, 101, 102]. The seed crystal is put into a plasma growth chamber on a heater which holds the diamond at around 800^◦C at a pressure of∼30 mbar. Above the diamond a plasma of hydrogen mixed with methane (0.5−5 %) is created by microwave radiation of several hundred Watts at∼2 GHz. The plasma is fed by a constant stream of new gas at a rate of several hundred standard cubic centimeters per minute. The gas for the plasma can also contain argon [98] or the hydrogen part can be replaced by deuterium which drastically increases sample quality [99]. The hydrogen or deuterium in the plasma is converted to highly reactive atomic H or D which etches particularly non-diamond bonded material and graphite and can also etch diamond layer by layer.

Most importantly it creates dangling bonds of the carbon atoms by breaking the bonds of the reconstructed surface. When methane is added to the plasma it can be converted to CH₃ or CD₃which is also reactive and its carbon atom can bind to the dangling bonds of the carbon atoms of the diamond surface. This way the diamond grows layer by layer due to addition of carbon atoms from the methane. The quality of the gas mixture can

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2.1. Diamond — the host material

Figure 2.2.: Colored diamonds with different defects. Micrometer sized diamonds with dif-ferent defects after difdif-ferent preparation steps. The yellow diamond contains large amounts of substitutional nitrogen ( 1ppm). The green diamond is an electron irradiated version of the yellow one (i.e. it contains many vacancies). After annealing the green diamonds the violet ones appear due to the creation of NV centers.

be controlled to a very high degree such that the purity of the diamond crystal is also very high. Particularly, the nitrogen content of the final CVD diamond can be lowered below 1 ppb (i.e. 176 nitrogen atoms per µm³ or an average nitrogen-nitrogen distance of 178 nm, compare appendix A). With the control of the growth speed it is possible to reduce structural defects in the diamond lattice. In addition to the reduction of the nitrogen content during growth also the isotropic composition of the used carbon can be controlled such that diamonds with ¹²C concentrations down to 99.99 % were produced for this work. On the other end of this scale hpht diamonds with 100 % ¹³C have been produced. In this work natural as well as artificial hpht and CVD diamonds with various

12C contents are used.

2.1.2. Lattice defects

Although diamond has a very stiff lattice there are many known defects existing and it is out of the scope of this work to name all of them. First of all we only concentrate on point defects. Of these only the very prominent ones and those related to the present work are shortly introduced. Since we are interested in the optical and spin properties of the NV center we are concerned about optical and spin properties of other defects as well.

The most trivial intrinsic defect is the vacancy where a single carbon atom in the lattice is missing. It can act as electron donor as well as acceptor and can thus be

2. Single NV centers in diamond

type N content sub-type feature [N] in ppm

I high Ia aggregates of N <3000

Ib single substitutional N <500

II low IIa very low N content <∼1

IIb significant boron content

→p-type semiconductor

<∼1

Table 2.1.: Types of diamond regarding their most abundant impurities (N, B). Additional sub-types exist for type Ia [105].

paramagnetic (S=¹/2 andS =³/2for positively and negatively charged vacancy [103]).

In addition it is weakly optically active [19, 103] and colors diamond green (see figure 2.2). Vacancies in the diamond lattice become mobile above≈600^◦C [19]. On their way through the lattice they can form multi-vacancy complexes that are immobile or they can be trapped by other lattice defects (e.g. by nitrogen [19]). Multi-vacancies can be paramagnetic and give the diamond a brown color in high concentrations. One possible way of producing vacancies is the irradiation with particles such as high energy ions or electrons [103]. This is also true for carbon interstitial related defects where one or more carbon atoms are displaced from their lattice position (e.g. due to more than one atom per lattice site). These are also optically active and paramagnetic.

Apart from these intrinsic defects diamond can contain other atoms such as nitrogen or boron. Both have roughly the same size as carbon and thus fit well into the lattice.

However, they have either one electron more or less than carbon (i.e. they act as donor or acceptor respectively). Usually nitrogen is much more abundant in diamond than boron. This holds for natural as well as artificially created diamonds. Nitrogen is a paramagnetic defect and due to its high abundance well studied. Especially in natural diamond samples defects comprised of aggregates of nitrogen atoms can be found because over the ages nitrogen migrated through the lattice until less mobile nitrogen clusters were formed. These can be paramagnetic as well. In fact, diamonds can be categorized mainly according to their impurity contents of nitrogen and boron [104, 105] (see table 2.1).

Apart from the above mentioned lattice defects some kind of inhomogeneity arises from the isotropic composition. Mostly carbon is present as ¹²C (98.9%) and seldom as

13C. In contrast to the first the latter contains a nuclear spin ofI =¹/2which influences the electron spin of the NV center.

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