Current-voltage characteristics

Figure4.4 shows the current density j = I/Aas a function of V_int measured ac-cording to the geometry of Fig.4.3(a)for samples A1, B, and C. All contacts exhibit a rectifying behavior as expected for metal/semiconductor Schottky contacts. No-tably, only sample A1 shows an appreciable current density in the reverse direc-tion. It is shown later that the resistance of the barrier with respect to reverse current flow is of crucial importance for the spin injection properties of the con-tact.

To gain further insight, the current-voltage characteristics can be analyzed using standard theory. Figure4.5 shows a schematic diagram of the energy bands at a forward-biased metal/n-type semiconductor Schottky contact. Here,φ_B denotes the Schottky barrier height, V_int again describes the voltage applied to the inter-face,ξ₂is the Fermi energy of the semiconductor with respect to the bottom of the conduction band,φis the potential energy of the barrier, andE_mis the energy of the tunneling electrons.

Depending on the particular barrier shape and temperature of operation, differ-ent mechanisms are responsible for the electronic transport. At elevated tempera-tures, the main contribution to the current is the thermionic emission (TE) of

elec-Chapter 4 Electrical spin generation in ferromagnet/n-GaAs hybrid structures

Figure 4.4:Current densityjas a function ofV_intfor samples A1, B, and C at 20 K.

trons over the top of the barrier. However, for low temperatures and high doping levels, tunneling through the barrier dominates the transport. Thermionic-field emission (TFE) refers to the tunneling of electrons which upon thermal excitation reach an energy level where the barrier is sufficiently narrow. In degenerate semi-conductors, field emission (FE) of electrons near the Fermi energy is a substantial contribution.

A rough criterion^88,92 to determine the relevant transport mechanism involves a comparison of the thermal energyk_BTto the tunneling parameterE₀₀, which is given by⁹¹

whereedenotes the elementary charge, ¯hthe reduced Planck constant,m^∗the elec-tron effective mass of the semiconductor,ε_sits permittivity,Nthe doping density close to the interface, k_B the Boltzmann constant andT the absolute temperature.

The regimes are then defined as: E₀₀ ≤ _0.5k_BTfor TE, 0.5k_BT < E₀₀ < ₅k_BTfor TFE, andE₀₀≥5k_BTfor FE.

The investigated spin transport structures are designed such that tunneling con-tributions are dominant in the temperature range of interest. The evaluation of

4.3 Ferromagnetic metal/n-GaAs contacts

V_int φ_B

φ

ξ₂ E_m

Figure 4.5:Potential energy diagram of a forward-biased Schottky contact with the metal on the left and the degenerately dopedn-type semiconduc-tor on the right side (from Ref. 91). T emission describes the thermionic emission of electrons over the barrier. F and TF indicate the tunneling con-tributions to the electronic transport, i.e., field emission and thermionic-field emission, respectively. The other labels are explained in the main text.

equation 4.4 using parameters of GaAs and a density of donors in the highly-doped interface region of 5×10¹⁸cm⁻³yields

E₀₀∼=44 meV ,

which is larger than k_BT even at room temperature. As a consequence, in the investigated samples FE is expected to constitute the dominant transport process below about 100 K complemented by TFE for higher temperatures.

Padovani and Stratton⁹¹ derive expressions for the tunneling current contri-butions, which can be used to fit the current-voltage characteristics as shown in Fig.4.6. For the forward-biased contact – that is for electron flow from the semi-conductor into the metal, which is the relevant configuration for electrical spin

Chapter 4 Electrical spin generation in ferromagnet/n-GaAs hybrid structures

Figure 4.6:(a)Forward and(b)reverse current characteristics for samples A1, B, and C at 20 K. The solid lines are fits according to equations4.5and 4.6.

extraction – the current can be written as⁹³

j= j_sexp[eV_int/(nk_BT)]^FE= j_sexp(eV_int/E₀₀)_{. (4.5)} j_sdenotes the saturation current density andnthe ideality factor. While the ideal-ity factor generally accounts for all transport mechanisms and deviates from unideal-ity in the case of tunneling contributions, the term on the right-hand side constitutes the expression for the limit of pure field emission.⁹¹As explained above, one can assume pure field emission for the investigated contacts at low temperatures, and the tunneling parameters E₀₀ of 54 meV (sample A1), 47 meV (B), and 60 meV (C) obtained from the fitting of the forward-current characteristics at 20 K are all in reasonable agreement with the estimate from equation4.4. However, a slight enhancement of the tunneling parameters is observed in the experiment as com-pared to the theoretical estimate, which possibly indicates additional tunneling paths through the barrier due to defect-assisted tunneling.⁹³

Electrical spin injection requires a reverse current, and the corresponding ex-pression from Ref. 91for low temperatures andeV_int >φ_Breads

j= A^∗

4.3 Ferromagnetic metal/n-GaAs contacts

Figure 4.7:Temperature dependence of(a)the current-voltage character-istics and(b)the tunneling parameterE₀₀ and ideality factornextracted from the forward current according to equation 4.5 for sample A2. RT denotes room temperature.

By taking the value ofE₀₀deduced above and treating the effective Schottky bar-rier heightφ_Band the effective Richardson constant of the metal A^∗as fit param-eters, one obtains a satisfactory agreement with the experimental reverse-current density as shown in Fig.4.6(b). From the fitting procedure,φ_Bis determined to be 0.26 eV (sample A1), 0.61 eV (B), and 0.56 eV (C). The high leakage current in the reverse direction for sample A1 in comparison with samples B and C is directly reflected in the smaller effective Schottky barrier height, which will be shown to be advantageous for the spin injection properties of the contact. The origin of a re-duction inφ_Bcan lie in an increased density of defects at the metal/semiconductor interface.⁹⁴

The temperature dependent current-voltage characteristics of sample A2 pre-sented in Fig.4.7(a)further support that field emission is the dominant transport mechanism in the devices. As seen from Fig.4.7(b), the tunneling parameter de-duced from the forward current according to equation4.5is essentially indepen-dent of temperature up to room temperature, which indicates that transport pro-cesses other than field emission are not relevant in this regime.^91,93

Chapter 4 Electrical spin generation in ferromagnet/n-GaAs hybrid structures

4.4 Non-local spin valve

In this section, the electrical spin generation and subsequent non-local detection of a spin accumulation in the semiconductor is discussed. The spin-induced volt-ages are investigated as a function of transport length, current, and perpendicular magnetic field. From this analysis, important sample properties such as the spin diffusion length and the spin lifetime of the channel are deduced. Furthermore, it is shown that the spin generation efficiency decreases with increasing interface bias, and possible physical origins of this decay are discussed. A consequence of this bias dependence is the fact that a larger area of the injector contact can lead to an enhanced range of operational currents for spin injection.