Cross-Plane Seebeck Coefficient Anomaly in a High Barrier Superlattice

We have measured the cross-plane Seebeck coefficient of short period InGaAs/InAlAs superlattices with 5nm wells and 3nm barriers with different doping concentrations. Contrary to the behavior of conventional bulk III-V materials, the Seebeck coefficient did not decrease monotonically with increasing doping concentration. A detailed numerical calculation based on semi-classical Boltzmann transport equation was developed that takes into account miniband formation. This model can explain the thermopower anomaly that was measured for superlattices with doping concentrations varying from 2x10 to 3x10 cm. Based on this model, we proposed a structure for an n-type material with a positive Seebeck coefficient. N-type semiconductors normally have a negative Seebeck coefficient. It is shown that in a suitable superlattice structure it is possible to selectively emit “low” energy electrons from the anode to the cathode. Thus, the heat transferred from the anode to the cathode is equivalent to a material with a positive Seebeck coefficient. This will be useful in cascading thermoelements because changing the doping material during the growth is not necessary. INTRODUCTION Thermionic emission cooling in heterostructures has been proposed by Shakouri et al. to overcome the limitations of vacuum thermionics at lower temperatures. In the linear transport regime, thick barrier InGaAs/InAlAs superlattices have been predicted to provide close to an order of magnitude improvement in the overall ZT over the bulk InGaAs value. In this paper we will examine the experimental and theoretical thermoelectric properties of short period InGaAs/InAlAs superlattices. Contrary to the structures studied in reference [3], miniband transport is essential in the calculation of the thermoelectric properties of the superlattice structures introduced in this paper. EXPERIMENTS N-type InGaAs/InAlAs multilayers lattice-matched to InP substrate were grown using molecular beam epitaxy (MBE). Each device consists of a superlattice and 0.5μm-thick highly doped (1x10cm) InGaAs layers used as the top and bottom contact regions. The superlattice contained 25 periods of 5nm thick n-doped InGaAs with varying silicon doping concentrations, 2x10, 4x10, 8x10 to 3x10 cm, and 3nm thick undoped InAlAs. Devices with various sizes (70-100 microns in diameter) were fabricated using conventional lithography, dry etching, and metallization techniques. Ni/AuGe/Ni/Au was used to make ohmic contacts to both electrodes. A thin film heater was deposited on top of the microcooler and used as both a heat source and temperature sensor. At last, the sample was attached to a package, wire bonded, and loaded into the cryostat for measurements. There were total of four samples under test with different doping concentrations. We used two device sizes, 100x100μm and 70x70μm for measurements. First, we calibrated the heater resistance with the stage temperature. To reduce the influence of the contact wires and pads, we used a four-wire measurement for gauging the resistance. At a given heater power, the top of the superlattice device was heated up by the thin film heater to a fixed temperature (Th). The substrate was attached to the heatsink inside the cryostat, where the temperature was controlled by the flow of liquid Helium (Ts). The temperature difference across the device (∆T=Th-Ts) generates a voltage difference (∆V), which can be measured by probing the microcooler and ground contacts. Thus, the effective Seebeck coefficient of the device could be calculated easily from T V S ∆ ∆ = . The ∆V and ∆T are the voltage and temperature differences across the device. As long as we could measure the voltage and temperature differences accurately, the Seebeck coefficient could be calculated. The difficulty of characterizing the Seebeck coefficient of a superlattice thin film lies in simultaneously measuring the voltage and temperature drops to within a few microns on both sides of a thin film. The Seebeck coefficients were measured at cryostat temperature changes from 50K to 300K. Figure 1 illustrates the measured Seebeck coefficients for samples A, B, C, D with doping concentrations ranging from 2x10 up to 3x10 cm. From the graph, we can see the Seebeck coefficient increases with temperature from 10K to 300K for all samples. The Seebeck coefficients measured using 100x100μm (squares) and 70x70μm (circles) devices match very well, except for one case (sample D). We found that the discrepancy was due to a heater fabrication error for the 100x100μm sample D. THEORETICAL ANALYSIS For the calculation of the transport coefficients of these samples, we use the model presented in reference [3] with some changes in the key equations for our purpose here. In brief, a linear Boltzmann transport equation was used to calculate the thermoelectric characteristics of the InGaAs bulk device. As for the superlattice properties, since the barrier layer thickness is short and the miniband transport is dominant, the transmission probability is calculated using the Transfer Matrix Method (TMM). The resulting minibands’ widths are either on the order of, or larger than the thermal energy (~20meV and 100meV for the first two minibands). Thus, a bulk-type Boltzmann transport with a correction due to the quantum mechanical transmission above and below the barrier is assumed. This is shown in equation 1 for the number of electrons participating in the superlattice transport: ] , ) ) , , , ( ( , ) ) , , , ( ( [ 4 1 (V) n