Institut für Integrierte Systeme Integrated Systems Laboratory Bipolar Transistor WS 2011 1 Introduction In this exercise we want to simulate the IV characteristics of a bipolar transistor and draw the Gummel plot and current gain. Additionally, the device shall be optimized with the help of simulation by changing the base doping. The bipolar transistor is one of the key devices in discrete and integrated circuits. Modifications are being used in power electronics IGBTs). In integrated circuits fast switching times are realized by bipolar transistors; here CMOS and bipolar technologies are integrated on chip BiCMOS). A bipolar transistor is a pnp- or a npn-structure, where each region has an electrical contact. The middle region is very thin which enables the interaction of the two pn-junctions that s why a bipolar transistor is more than the series connection of two diodes). In Fig. 1 the structure of a pnp-transistor is shown schematically. V I p + W n p I K VK IB V B Figure 1: Principle structure of a pnp-transistor. The heavily doped p-region p + ) is called emitter, the moderately doped n-layer is called base, and the lowly doped p-region is the collector. We denote by I K the current which flows into the collector and by V K the potential at the collector contact. Base and emitter quantities are labeled likewise. Currents can be split Ted in electron and hole contributions, e.g. I K = I K,n + I K,p. Kirchhoff s law connects all currents, I + I B + I K = 0 For voltages between two contacts we use the notation V B = V V B. The emitter injection efficiency factor is the hole contribution of the emitter current majority carriers), γ = I,p /I. As the emitter is heavily p-doped, the current is made up of holes almost exclusively, i.e. γ 1. The base transport factor is the part of the emitter hole current that reaches the collector, α T = I K,p /I,p,
it is also approximately 1. The common-base current gain is the product of both, α 0 = γα T. Hence the collector current can be written as I K = α 0 I + I K,n, 1) where I K,n is the leakage current of the reversed-biased base-collector junction. For the computation of the IV characteristics we make the following simplifications: We assume abrupt transitions between space charge regions and neutral regions. p- and n-regions are homogeneously doped. Generation and recombination in the space charge region are neglected. The concentration of majority carriers is assumed to be constant in each neutral region. The series resistance of the neutral regions is neglected. In particular, we use the boundary values of the minority carrier densities at the edges of the space charge regions, n 0) = n 0 qv B/) p B 0) = p 0 B qv B /) p B W) = p 0 B qv KB /) n K W) = n 0 K qv KB /) Here we have defined coordinates in such a way that the width of the space charge layers has been neglected, i.e. we consider them small compared to W. With this boundary conditions and with the general solution of the drift-diffusion equation in the neutral regions n n 0 p = C x/ ) + C + x/ ) with the diffusion length = D n τ n ) one obtains n x) n 0 = n 0 p 0 B p B x) p 0 B = sinh W/L p ) n K x) n 0 K = n0 K ) ] x { ) From this we obtain the emitter currents 2I,n = I,p = qd n A dn dx 0) = qd nan 0 qd p A dp B dx 0) = ) ) ] ] ) W x qd p Ap 0 B L p sinh W/L p ) { x sinh ) ] L p ) + ) ] sinh ) ] ) W cosh + 1 L p 2) )} W x L p 3) )} 4) and the collector currents by simply interchanging with K in above ressions. A is the active cross-sectional area of the transistor in the yz-plane. 2
Starting with these formulas, we now may compute characteristic parameters of the transistor, e.g. the base transport factor 1 α T coshw/l p ) 1 W 2 2L 2 p where we have assumed qv B /) 1 qv KB /) which means nothing more than qv B and qv KB shall be large compared to, and V KB shall be negative). We see that a thin base is necessary for a large α T. In the same limit we obtain for the emitter efficiency γ 1 + D n n 0 L p D p p 0 tanh W ) 1 B L p In circuit applications the common emitter configuration is most often used, where the emitter contact is grounded and the base and collector potentials are related to the emitter. With such a topology one can achieve a gain > 1. With 1) we can write the collector current in the common emitter configuration as I K = α 0 I B + I K ) + I K,n. 5) The common emitter current gain is defined as follows: β 0 I K I B. If we resolve 2) for I K, divide by I B and set α T 1 which is well fulfilled for todays transistors), the gain will only depend on the emitter efficiency. β 0 = α 0 = γ 1 α 0 1 γ = D p p 0 ) ) B W D n n 0 coth p0 B 1 L p L p n 0 N W N B W The current gain increases with rising ratio between emitter and base doping. After this rather accumulated theory you just need to copy the necessary input files into your home directory, >> mkdir biptrans >> mkdir tecplot_macro >> cp ~hlbe/biptrans/* biptrans/ >> cp ~hlbe/tecplot_macro/cut.mcr tecplot_macro/ >> cp ~hlbe/.alias. >> source.alias >> cd biptrans Let s start with the practical part. 2 Task 1: Gummel Plot We want to simulate the stationary IV curve. First, the emitter-collector voltage is ramped from 0 to 2.5 V, i.e. the transistor is driven into its working point. Then the base voltage is ramped from 3
0 to 1 V. Have a look at the Solve Section in the input file biptrans_des.cmd. Start the Sentaurus Structure ditor with the following command: sde biptrans_mdr Return The name of the device to be edited is handed to sde as an parameter. The program will automatically load the boundary file biptrans_mdr.bnd and the command file biptrans_mdr.cmd. To build the mesh you have to click mesh build mesh in the drop down menu bar. A new dialog box will open and ask for a file name where to save the grid data. nter bip as file name and choose Mesh as meshing engine, leave everything else as it is and confirm by pressing Build Mesh. The program will take care of file extensions. Now you can see the structure of the device. At the bottom there is the collector with the collector contact, top right you find the heavily-doped emitter and in-between the base which is contacted top left. The critical region of a bipolar transistor is the base, therefore the base region must be refined more than the other regions to obtain correct electron and hole currents. You can check that this was already accounted for in the command file. Leavesde and do not save changes to the model. Now we can start the simulation with sdevice biptrans_des.cmd Return. When the simulation is finished, you should plot the collector current and the base current as a function of the base voltage. For that, start the inspection tool inspect with inspect gummel_bip_des.plt & Return These two IV-curves are called Gummel plot. Now we want to plot the current gain. Select New... in inspect under Curves and try to plot the ratio I K /I B. Select the Y right axis as y-axis for the gain with linear scale. Answer the following questions: i) What is the value of the maximum of the gain? ii) At which base voltage has the gain its maximum? iii) Compare the maximum gain with the ratio of the doping concentrations between emitter and base. Which value is larger and why? iv) Do not close inspect, since you can just update this plot by pressing simulations. ) after the next 3 Task 2: Device Optimization by Simulation As we have seen in the Introduction, the common emitter current gain depends on the ratio of doping concentrations between emitter and base β 0 N N B see the last formula in the Introduction). On one hand one wants do increase the doping density in the base to minimize its resistance. On the other hand the doping level in the base must not be too high, in order to avoid a degradation of the current gain. We let the emitter doping unchanged and will try to optimize the gain by changing the base doping. Vary the base doping in the limits 2e17 cm 3 to 1e18 cm 3. Do the following: 1. Open the command-file biptrans_mdr.cmd with an editor e.g. emacs or gedit) 4
2. You will find in this file on line 77 the following statements: Function = GaussPeakPos = 0.1, PeakVal = 2e+17, StdDev = 0.06) 3. The base doping is set with PeakVal = 2e+17. 4. Set the PeakVal to a value in the range from 2e17 to 1e18. 5. Save the changes and generate the new SDVIC input files with sde -e -l sde_batch.scm Return 6. Run the simulation with sdevice biptrans_des.cmd Return 7. Plot the gain as in task 1. Find the base doping in the range from 2e17 cm 3 to 1e18 cm 3, where the gain becomes maximum. Answer the following questions: i) What is the value of this base doping? ii) How large is the maximum current gain for this doping level? iii) What happens when you further decrease the base doping concentration and why? What happens when you increase the base doping beyond 1e18 cm 3 and why? 5